WEBVTT

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music

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welcome to the 2019

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Mario and Alma Pastega Awards Event 

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so pleased to see all of you

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here together to celebrate

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our colleagues accomplishments

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and recognition as you all

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probably know this is the

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highest award that we offer

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faculty at Western Oregon

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University I was looking back

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through how many how many

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award recipients do you think

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we've had for research? Any guesses?

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you quickly look in the

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brochure in cal this is the

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fortieth I think this is the

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fortieth one we used to call

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the faculty honors award 

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six years later -- we develop

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the the award for teaching I

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believe the year after that

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we develop the staff award 

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the Mario and Alma Patega 

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Staff Award. so today we're

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going to honor both doctor

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Scott Beaver and doctor Rachel

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Harrington. They are going to have 

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some presentations -- to share

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with us so I'm very excited

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to be able to introduce the

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Rachel Harrington my friend 

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and colleague and I brought

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some notes because I could

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talk about Rachel for hours

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and also because I promised

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Rachel that I wouldn't cry

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and they wouldn't be could

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cry because we really have a long history of

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crying together actually

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think of academics as being

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people who are maybe specialize

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only in one thing or maybe not

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well rounded but Rachel Harrington is

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a very well rounded person I

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think is the renaissance women

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if you don't know Rachel 

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very well we chose not only an

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amazing teacher and researcher

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bat she loves the Pittsburgh

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Steelers she will give you

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great canning recipes over the

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summer for how to make 

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Zucchini relish and I think

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of her whenever I eat zucchini

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relish now she grew up in

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a tiny town in Southeastern

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Alaska and she comes from a

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big family and she worked in

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the cannery and has worked shift

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work and then all sorts of

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interesting things and I think

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because of that many of our

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students here at Western really

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you can relate to that meant

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they relate to you and you

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know you just bring a practical

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common sense no nonsense

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notion to so many things

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you do and frankly academia

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really needs that.

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I love that about you but

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at the same time Rachel is

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one of the most talented

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teachers I've ever known

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And I know a lot of teachers.

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She can take advanced concepts and make them accessible to students 

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in really amazing ways. She leads graduate students through

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advanced research projects and thesis work.

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She builds their identities as writers and researchers.

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Many of her students have published in professional journalism 

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and newsletters and just the other day she was running down the hall

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Showing us a published article from one of her 

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former students, in Teaching Children Mathematics which is 

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the journal in mathematics education 

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And when I suggested to Rachel that that was part of the 

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seeds she had planted with this student she refused 

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to take any acceptance for that, but I know that teachers are inspired by Rachel.

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To not only be math teacher but also mathematicians and teacher researchers. 

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Rachel is an amazing colleague and many

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her colleagues here in the

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division and outside of the

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division are here today.

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she's the type of friend and colleague  

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Who  pays attention when

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people are having a bad day

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and she suggests that you go

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get a coffee treat to make

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it better she's always the

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first one to use fractions

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to make everything just a

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little bit better. Don't worry Marie were one fourth

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Of the way through EDTPA

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We have almost graded two thirds of the lit reviews.

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 but she's also the first

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person to arrange meals for a

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colleague in need or to go to

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bat with leadership for someone

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who deserves a fair shake -- I

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just simply listen when people

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need good advice she's also

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an excellent adviser entry

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leader for students she'll sit and

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counselor teacher candidating

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crisis and listen to them so

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carefully and carrying but she will 

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also give students a straight

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talk when they need to hear it

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a few years ago Rachel and I

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right before we were going on

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sabbatical and had a little bit

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of senioritis ourselves 

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We lead a group of lively

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MATers here you were finishing

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their action research project

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each week Rachel and I would joke

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about to be good cop or bad

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cop to motivate the students to

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finish their projects the end

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result can wear both hats well

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she knows how to give that pep

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talk when students need it but

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she also knows how to gently

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and firmly direct students back

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on the path she's an amazing

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teacher I know because I could

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Co taught with her probably a dozen

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times now -- every time I learn

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something new and I become a

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better teacher for working with

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her she's creative, she's

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organized, she's well prepared

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she student centered, she is

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beloved by her students I see

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a couple of her students here

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today and for good reason and it's not jus the "mathies"

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these as I like to call them

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who love Rachel. Rachel

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teachers are future elementary

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students many of whom will

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come in and say well I don't

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think I'm very good at math

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I can't do math and she will not allow that.

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she helps them to love and

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have a rich tool box and then

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Amazing  ways to make math

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meaningful and transformational

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to children and she does

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this because she has a huge

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passion for math education

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in mathematical thinking and

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she builds advocacy in future

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teachers she's just a can do person

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And students leave her 

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class with the how and why of

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math education so like I said

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she's about growth mindset

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you are not allowed to tell

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Rachel that you're not good

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at math she will not listen

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to that it's not allowed and

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she will humbly but I also think a little b

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bit probably share her own

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AP math test score with her

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future students to show that it's not where

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you start it's where you

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end up and then standardized

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assessments are not indicative

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of potential even as a mathie she 

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knows why children should

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never be accessed only through

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quantitative measures and are

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you strongly for why qualitative

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details matter her teaching

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and research illustrate  this 

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learners are so much more

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than numbers in her classroom

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And in her research she makes

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math fun and meaningful and

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important to everyone who

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knows her and certainly to our

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students she wears fun math pun t-shirts

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has geometry themed Toms

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and she owns several "pi" P-I

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inspired pie plates. PI day March 14

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for those non mathies out there 

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national holiday and Rachel's

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life and now in the

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college of education students

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Sing pi themed carols, create pi themed art

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and of course devour pi treats 

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In her classes. Back to that Renaissance woman 

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She makes all of her pie crust.

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from scratch it's like a family pride.

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Thank you Maria.

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I just wanted to start off today

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by a first acknowledging my

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colleague Scott Beaver it's

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an honor to be speaking with

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him today Scott and I actually

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have a lot in common we were

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both from Alaska we both lived

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in Pennsylvania for awhile we

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both studied math and we both

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think Cheryl Beaver is awesome

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I've noticed that about us 

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I also want to acknowledge the

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Pastega family I don't

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know if they're any one of

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them was able to make it today

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but once a month I 

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go to a support group at the

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Pastega Cancer Research Center

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in Corvallis my mother in

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law hooked up her RV

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into the Pastega house for

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three weeks while her husband

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was in the hospital my children

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go through the Pastega 

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Christmas lights every year

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for five times and I just we

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We have a Pastega room in our building I just I've considered

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a great honor to be associated

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with this family and I'm very

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very proud of this award today

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I also want to think -- Marie

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Marie is probably my closest

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friend here at Western over the

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years and we've been through

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a lot together a lot of tears

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I was nervous about today's

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preparation -- presentation so

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I made the mistake of watching

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Marie's talk from last year

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and -- when it got done they

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told my husband I do not want

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to do this now I just watched

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I just watched Marie's and I feel way worse and he

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said well what was her research

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on and I said it's about

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how children interact with

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storybooks and picture books

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and my husband the librarian

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said your research can't

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compete with that argument just

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just just do what you need to

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do it'll be fine just don't try

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to compete so Marie I'm not

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going to try to compete today

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I'm gonna try to keep up a

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little bit and I can finally I

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want to mention my husband Ryan

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I I have a lot of presentations

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and publications on my CV and

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everyone of those presentations

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is a weekend where he was

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left home alone with kids I'm

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gonna get emotional -- and I

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appreciate all of his support

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in this process they didn't

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identify him as the love of my

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life so -- they'll biography

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like Scott did. That was my mistake

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and finally I want to thank

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the audience thank you for

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being here today signing up

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for it to listen to two talks

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about mathematics on a sunny

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Thursday afternoon is a big

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snacks that we have but I I

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appreciate you being here when

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people ask me -- what I do for

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a living I often just say that

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I work in teacher preparation

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I don't typically say that I'm

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a math educator because I find

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that when I say I'm in math

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education people want to tell

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me about all of the horrible

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experiences they've had over

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he hears and sometimes I just

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want to stand in the line it

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WinCo and buy my groceries

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so I I fully acknowledge that

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there are some great mathies

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in the audience today but

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they're also a lot of people

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who have some really bad

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experiences and frankly some

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trauma in their past related

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to mathematics so when I was

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thinking about things to talk

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about today I I realized I

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have a little bit of imposter

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syndrome when it comes to my

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scholarship and I struggled

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with what to talk about but I

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also knew that this audience

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didn't really want your thirty

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minutes of me talking about how

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teachers engage with web based

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curriculum in the classroom

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and so I started thinking to

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myself I'm going to have this

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room full of really interesting

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people and they have to listen

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to me for twenty five minutes

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this is my chance to advance

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my agenda that and then I

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realize no that's kind of a

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negative perspective I think

00:10:28.000 --> 00:10:30.000
you could ask my students

00:10:30.000 --> 00:10:31.000
some of whom are here today

00:10:31.000 --> 00:10:32.000
and if you ever want to kill

00:10:32.000 --> 00:10:33.000
an hour in Rachel's class

00:10:33.000 --> 00:10:35.000
Ask her about one of those four

00:10:35.000 --> 00:10:37.000
topics and she'll just go off

00:10:37.000 --> 00:10:39.000
but I decided instead to try

00:10:39.000 --> 00:10:40.000
to have a more positive focus

00:10:40.000 --> 00:10:42.000
today and I asked myself okay

00:10:42.000 --> 00:10:43.000
what's that my court what do

00:10:43.000 --> 00:10:45.000
I fundamentally believe about

00:10:45.000 --> 00:10:47.000
math education and what can

00:10:47.000 --> 00:10:49.000
I share with people today and

00:10:49.000 --> 00:10:51.000
I believe fundamentally that

00:10:51.000 --> 00:10:52.000
children should be thinking

00:10:52.000 --> 00:10:54.000
and math class and that

00:10:54.000 --> 00:10:55.000
thinking happens when they

00:10:55.000 --> 00:10:57.000
solve problems and I'm sure

00:10:57.000 --> 00:10:59.000
think well that's not very

00:10:59.000 --> 00:10:61.000
groundbreaking isn't that what

00:11:01.000 --> 00:11:02.000
we do in math class we spend

00:11:02.000 --> 00:11:03.000
a lot of time thinking and

00:11:03.000 --> 00:11:05.000
solving problems but I would

00:11:05.000 --> 00:11:06.000
argue against that I think

00:11:06.000 --> 00:11:08.000
a lot of us are experiences

00:11:08.000 --> 00:11:09.000
we didn't get to do a lot of

00:11:09.000 --> 00:11:11.000
thinking in math class we were

00:11:11.000 --> 00:11:13.000
asked to remember and repeat

00:11:13.000 --> 00:11:14.000
what our teachers had done

00:11:14.000 --> 00:11:16.000
and we weren't actually push

00:11:16.000 --> 00:11:17.000
to do a lot of thinking on

00:11:17.000 --> 00:11:19.000
our own and I would say that

00:11:19.000 --> 00:11:20.000
we didn't spend enough time

00:11:20.000 --> 00:11:22.000
solving problems and instead we

00:11:22.000 --> 00:11:23.000
spent too much time working on

00:11:23.000 --> 00:11:26.000
exercises and doing tasks that

00:11:26.000 --> 00:11:28.000
did not involve complex problem

00:11:28.000 --> 00:11:30.000
solving I want children to be

00:11:30.000 --> 00:11:32.000
thinking in math class and so

00:11:32.000 --> 00:11:33.000
today that's what I'm going

00:11:33.000 --> 00:11:35.000
to try to share with you is a

00:11:35.000 --> 00:11:37.000
little bit about my philosophy

00:11:37.000 --> 00:11:38.000
on what thinking looks like

00:11:38.000 --> 00:11:41.000
and also -- what I feel problem

00:11:41.000 --> 00:11:42.000
solving looks like so this is

00:11:42.000 --> 00:11:44.000
my feeble attempt to make my

00:11:44.000 --> 00:11:45.000
presentation as interesting as

00:11:45.000 --> 00:11:47.000
Marie's I'm gonna sprinkle

00:11:47.000 --> 00:11:49.000
in some of my favorite quotes

00:11:51.000 --> 00:11:53.000
these are some quotes that have carried me through as a

00:11:53.000 --> 00:11:56.000
as a math educator and I also

00:11:56.000 --> 00:11:57.000
thought that you know if I was

00:11:57.000 --> 00:11:58.000
going to make my presentation

00:11:58.000 --> 00:11:60.000
more engaging I should just you

00:12:00.000 --> 00:12:01.000
know what better way to do that

00:12:01.000 --> 00:12:02.000
include some cute pictures of

00:12:02.000 --> 00:12:05.000
my kids -- but I will tell you

00:12:05.000 --> 00:12:07.000
it's not just cute pictures of

00:12:07.000 --> 00:12:08.000
my kids so each one of these

00:12:08.000 --> 00:12:10.000
pictures is somehow related

00:12:10.000 --> 00:12:12.000
to something that I'm about

00:12:12.000 --> 00:12:14.000
to tell you afterwards and so

00:12:14.000 --> 00:12:16.000
that's my little -- puzzle with

00:12:16.000 --> 00:12:18.000
in the presentation see if you

00:12:18.000 --> 00:12:21.000
can figure it out. Alright, so

00:12:21.000 --> 00:12:23.000
let's talk first about what it

00:12:23.000 --> 00:12:25.000
means to have do a math problem

00:12:25.000 --> 00:12:26.000
or what a math problem really

00:12:26.000 --> 00:12:29.000
is Stein and Smith talk about

00:12:29.000 --> 00:12:30.000
the things that we do in math

00:12:30.000 --> 00:12:32.000
class and as falling into four

00:12:32.000 --> 00:12:34.000
different levels and they talk

00:12:34.000 --> 00:12:36.000
about how we asked children to

00:12:36.000 --> 00:12:37.000
do things that are just purely

00:12:37.000 --> 00:12:38.000
memorization and those would

00:12:38.000 --> 00:12:40.000
be things like do you know

00:12:40.000 --> 00:12:41.000
the definition of a trying all

00:12:41.000 --> 00:12:42.000
can you do your multiplication

00:12:42.000 --> 00:12:44.000
facts what are some things

00:12:44.000 --> 00:12:45.000
that you have memorized that

00:12:45.000 --> 00:12:47.000
you can just repeat without

00:12:47.000 --> 00:12:49.000
without thinking they also talk

00:12:49.000 --> 00:12:51.000
about us asking children to

00:12:51.000 --> 00:12:52.000
do a lot of procedures without

00:12:52.000 --> 00:12:54.000
connections and so those are

00:12:54.000 --> 00:12:55.000
tasks that we give kids that

00:12:55.000 --> 00:12:57.000
are not connected in any way to

00:12:57.000 --> 00:12:59.000
a picture or two a contacts or

00:12:59.000 --> 00:12:62.000
to language they're just math

00:13:02.000 --> 00:13:04.000
exercises or procedures that

00:13:04.000 --> 00:13:06.000
we carry out we start looking

00:13:06.000 --> 00:13:08.000
When we cross the dotted line

00:13:08.000 --> 00:13:10.000
into more high cognitive demand

00:13:10.000 --> 00:13:11.000
tasks when we asked children

00:13:11.000 --> 00:13:12.000
to carry out procedures that

00:13:12.000 --> 00:13:14.000
are connected to something

00:13:14.000 --> 00:13:15.000
so we asked them to carry

00:13:15.000 --> 00:13:16.000
out a procedure that somehow

00:13:16.000 --> 00:13:19.000
connected to let's say a graph

00:13:19.000 --> 00:13:20.000
so maybe I I give children two

00:13:20.000 --> 00:13:22.000
equations and I say okay I want

00:13:22.000 --> 00:13:24.000
to find the solution to the

00:13:24.000 --> 00:13:25.000
system of the two equations

00:13:25.000 --> 00:13:26.000
show me how it appears on the

00:13:26.000 --> 00:13:27.000
graph what is that look like

00:13:27.000 --> 00:13:29.000
when I graph it and connecting

00:13:29.000 --> 00:13:30.000
those two representations

00:13:30.000 --> 00:13:32.000
together would be an example

00:13:32.000 --> 00:13:34.000
of a procedure with connection

00:13:34.000 --> 00:13:35.000
what we really want children

00:13:35.000 --> 00:13:38.000
going though -- what our goal

00:13:38.000 --> 00:13:39.000
should be in math class is

00:13:39.000 --> 00:13:40.000
to have them do what Stein 

00:13:40.000 --> 00:13:42.000
and Smith call doing mathematics

00:13:42.000 --> 00:13:44.000
we want them to actually do

00:13:44.000 --> 00:13:46.000
mathematics and the way they

00:13:46.000 --> 00:13:48.000
define mathematics and doing

00:13:48.000 --> 00:13:49.000
mathematics are ill structured 

00:13:49.000 --> 00:13:51.000
tasks tasks that don't have

00:13:51.000 --> 00:13:53.000
a clearly defined path on how

00:13:53.000 --> 00:13:55.000
to solve them or tasks that

00:13:55.000 --> 00:13:57.000
we engage in in our everyday

00:13:57.000 --> 00:13:59.000
lives what is math that we see

00:13:59.000 --> 00:13:62.000
every day as human beings I I

00:14:02.000 --> 00:14:04.000
sometimes talk about math real

00:14:04.000 --> 00:14:07.000
world and real world math and

00:14:07.000 --> 00:14:08.000
math real world would be those

00:14:08.000 --> 00:14:09.000
kind of word problems that

00:14:09.000 --> 00:14:11.000
you always found at the end

00:14:11.000 --> 00:14:12.000
of the exercises in your math

00:14:12.000 --> 00:14:14.000
textbook they're sort of poorly

00:14:14.000 --> 00:14:16.000
constructed contacts that we

00:14:16.000 --> 00:14:17.000
try to do is match people to

00:14:17.000 --> 00:14:19.000
make ourselves feel better like

00:14:19.000 --> 00:14:21.000
it somehow applies but doing

00:14:21.000 --> 00:14:22.000
mathematics is more than that

00:14:22.000 --> 00:14:23.000
that is the math you do is you

00:14:23.000 --> 00:14:25.000
engage in in just everyday life

00:14:25.000 --> 00:14:27.000
in an example of that might

00:14:27.000 --> 00:14:28.000
be I you know my family and

00:14:28.000 --> 00:14:29.000
I are going to take a trip to

00:14:29.000 --> 00:14:30.000
the enchanted forest and we

00:14:30.000 --> 00:14:32.000
have a hundred fifty dollars

00:14:32.000 --> 00:14:35.000
to spend is that enough that's

00:14:35.000 --> 00:14:37.000
a poorly constructed task I is

00:14:39.000 --> 00:14:40.000
solution to that you haven't

00:14:40.000 --> 00:14:42.000
given me enough information how

00:14:42.000 --> 00:14:43.000
much does it cost to get in am

00:14:43.000 --> 00:14:45.000
I gonna buy a bracelet am I

00:14:45.000 --> 00:14:46.000
Going to buy tickets and I get a pack a

00:14:46.000 --> 00:14:48.000
lunch am I going to buy a lunch?

00:14:48.000 --> 00:14:50.000
There is lots of more information I need

00:14:50.000 --> 00:14:52.000
to know the solution and there

00:14:52.000 --> 00:14:53.000
really is no right answer maybe

00:14:53.000 --> 00:14:54.000
a hundred fifty dollars is

00:14:54.000 --> 00:14:55.000
enough for one family but not

00:14:55.000 --> 00:14:57.000
for another and so that would

00:14:57.000 --> 00:14:58.000
be an example of something

00:14:58.000 --> 00:14:61.000
that is doing mathematics the

00:15:01.000 --> 00:15:02.000
National Council of teachers

00:15:02.000 --> 00:15:04.000
of mathematics have helped

00:15:04.000 --> 00:15:05.000
us to understand that what's

00:15:05.000 --> 00:15:06.000
happening on the right side

00:15:06.000 --> 00:15:07.000
of the line is what we call

00:15:07.000 --> 00:15:09.000
conceptual understanding what's

00:15:09.000 --> 00:15:11.000
happening on the left side of

00:15:11.000 --> 00:15:13.000
the line is procedural fluency

00:15:13.000 --> 00:15:15.000
and it's not that left is bad

00:15:15.000 --> 00:15:17.000
right is good it's that we need

00:15:17.000 --> 00:15:19.000
balance in our classrooms and

00:15:19.000 --> 00:15:20.000
so much of our experiences in

00:15:20.000 --> 00:15:22.000
math class has been on the left

00:15:22.000 --> 00:15:23.000
side of the line and we need

00:15:23.000 --> 00:15:24.000
to give kids more experiences

00:15:24.000 --> 00:15:26.000
on the right the analogy I give

00:15:26.000 --> 00:15:28.000
my students and methods as I

00:15:28.000 --> 00:15:30.000
say to them when you sign up

00:15:30.000 --> 00:15:32.000
to be on the basketball team

00:15:32.000 --> 00:15:33.000
you usually have obligations

00:15:33.000 --> 00:15:35.000
were you have to attend practice

00:15:35.000 --> 00:15:37.000
and you also get to go to games

00:15:37.000 --> 00:15:38.000
and playing games and what

00:15:38.000 --> 00:15:40.000
I see is what's happening on

00:15:40.000 --> 00:15:41.000
the right side of the line is

00:15:41.000 --> 00:15:43.000
playing the game of mathematics

00:15:43.000 --> 00:15:44.000
what's happening on the left

00:15:44.000 --> 00:15:46.000
side of the line or the drills

00:15:46.000 --> 00:15:47.000
in the activities that happen

00:15:47.000 --> 00:15:49.000
in practice that help me get

00:15:49.000 --> 00:15:51.000
better at playing the game but

00:15:51.000 --> 00:15:52.000
the reality is we often tell

00:15:52.000 --> 00:15:54.000
children you're not ready to

00:15:54.000 --> 00:15:56.000
play the game you're just need

00:15:56.000 --> 00:15:58.000
to keep practicing you need to

00:15:58.000 --> 00:15:59.000
keep going to practices and I

00:15:59.000 --> 00:15:61.000
say to them if you signed up

00:16:01.000 --> 00:16:02.000
for basketball your coach said

00:16:02.000 --> 00:16:03.000
you will never get to play in

00:16:03.000 --> 00:16:05.000
a game you you can you need

00:16:05.000 --> 00:16:06.000
to come to practice every day

00:16:06.000 --> 00:16:07.000
and you need to do all the

00:16:07.000 --> 00:16:09.000
drills but you will never get

00:16:09.000 --> 00:16:10.000
to play in the game you would

00:16:10.000 --> 00:16:12.000
quit basketball all the fun

00:16:12.000 --> 00:16:14.000
is is when you play the game

00:16:14.000 --> 00:16:15.000
and I argue that we are not  giving

00:16:15.000 --> 00:16:17.000
children enough time they're

00:16:17.000 --> 00:16:20.000
on the right plane the game

00:16:20.000 --> 00:16:21.000
so in this next part I really

00:16:21.000 --> 00:16:23.000
want to dig into what I think

00:16:23.000 --> 00:16:25.000
mathematics problems really are

00:16:25.000 --> 00:16:27.000
so some examples of what those

00:16:27.000 --> 00:16:28.000
look like and share with you

00:16:28.000 --> 00:16:31.000
some of my favorites so back

00:16:31.000 --> 00:16:33.000
in nineteen ninety eight my

00:16:33.000 --> 00:16:35.000
college methods professor at

00:16:35.000 --> 00:16:36.000
Western Washington University

00:16:36.000 --> 00:16:37.000
came to me and a handful of

00:16:37.000 --> 00:16:39.000
colleagues and said I want

00:16:39.000 --> 00:16:41.000
you to work on a project and I

00:16:41.000 --> 00:16:42.000
didn't know it at the time but

00:16:42.000 --> 00:16:44.000
that was my first example of

00:16:44.000 --> 00:16:45.000
scholarship that was my first

00:16:45.000 --> 00:16:47.000
dive into scholarship basically

00:16:47.000 --> 00:16:49.000
what we did is we went to his

00:16:49.000 --> 00:16:50.000
house and we opened up a file

00:16:50.000 --> 00:16:52.000
cabinet that was jammed tight

00:16:52.000 --> 00:16:54.000
with problems he had collected

00:16:54.000 --> 00:16:55.000
over the years and he said

00:16:55.000 --> 00:16:57.000
organize these so teachers can

00:16:57.000 --> 00:16:59.000
use them and that's what we did

00:16:59.000 --> 00:16:60.000
and don't you love my fabulous

00:17:00.000 --> 00:17:03.000
Microsoft Word clip art that

00:17:03.000 --> 00:17:04.000
was on the cover circa nineteen

00:17:04.000 --> 00:17:07.000
ninety eight it's called you

00:17:07.000 --> 00:17:09.000
thought you had problems and

00:17:09.000 --> 00:17:11.000
what we basically do it is is

00:17:11.000 --> 00:17:12.000
collected all of these really

00:17:12.000 --> 00:17:14.000
unique and interesting problems

00:17:14.000 --> 00:17:15.000
and organize them for teachers

00:17:15.000 --> 00:17:17.000
and I still use these problems

00:17:17.000 --> 00:17:18.000
today I have it fortunately

00:17:18.000 --> 00:17:19.000
it's not a three ring binder

00:17:19.000 --> 00:17:21.000
anymore and I have lost the two

00:17:21.000 --> 00:17:22.000
floppy disks that came with it

00:17:22.000 --> 00:17:25.000
but it is is safely scanned and

00:17:25.000 --> 00:17:28.000
now stored on the Google drive

00:17:28.000 --> 00:17:29.000
all right so this is the first

00:17:29.000 --> 00:17:31.000
task that sometimes share with

00:17:31.000 --> 00:17:33.000
my students in my elementary

00:17:33.000 --> 00:17:35.000
middle and middle high methods

00:17:35.000 --> 00:17:37.000
classes call adding the square

00:17:37.000 --> 00:17:39.000
in the context of the task is

00:17:39.000 --> 00:17:41.000
that it A + B is 17.

00:17:41.000 --> 00:17:43.000
C + D is eighteen, so all

00:17:43.000 --> 00:17:44.000
of the sums of those

00:17:44.000 --> 00:17:46.000
letters that the arrow

00:17:46.000 --> 00:17:47.000
goes through it tells you

00:17:47.000 --> 00:17:48.000
what the sum is and what

00:17:48.000 --> 00:17:49.000
I ask students to do in

00:17:49.000 --> 00:17:50.000
my classes tell me what's

00:17:50.000 --> 00:17:52.000
the value of A B C D?

00:17:52.000 --> 00:17:55.000
and -- they set to work on

00:17:55.000 --> 00:17:57.000
it what I love about this

00:17:57.000 --> 00:17:58.000
task is that my middle

00:17:58.000 --> 00:17:59.000
high method students will

00:17:59.000 --> 00:17:61.000
immediately set up a system

00:18:01.000 --> 00:18:02.000
of equations and they'll say

00:18:02.000 --> 00:18:03.000
okay I know A + B is 17

00:18:04.000 --> 00:18:05.000
C + D is eighteen. 

00:18:05.000 --> 00:18:08.000
A+ C is 12 and they'll do some

00:18:08.000 --> 00:18:09.000
substitution and elimination

00:18:09.000 --> 00:18:12.000
and I'll get the answer my

00:18:12.000 --> 00:18:13.000
elementary middle students

00:18:13.000 --> 00:18:14.000
will look at that and say

00:18:14.000 --> 00:18:15.000
well if A + B is 17

00:18:15.000 --> 00:18:18.000
And C + D is 18 then I know all four 

00:18:18.000 --> 00:18:20.000
of them together are probably

00:18:22.000 --> 00:18:23.000
that the answer of any of

00:18:23.000 --> 00:18:25.000
those negative so we'll just

00:18:25.000 --> 00:18:26.000
go with that and they pull out

00:18:26.000 --> 00:18:29.000
thirty five box unifix cube

00:18:29.000 --> 00:18:31.000
Or unit cubes and they

00:18:31.000 --> 00:18:32.000
start moving around until they

00:18:32.000 --> 00:18:35.000
fall into four piles and this

00:18:35.000 --> 00:18:36.000
problem I love this problem

00:18:36.000 --> 00:18:37.000
because it's an excellent

00:18:37.000 --> 00:18:39.000
opportunity for us to look at

00:18:39.000 --> 00:18:40.000
different solution strategies

00:18:40.000 --> 00:18:42.000
and talk about their benefits

00:18:42.000 --> 00:18:44.000
and drawbacks and compare how

00:18:44.000 --> 00:18:45.000
their similar and different

00:18:45.000 --> 00:18:46.000
and the other thing that I like

00:18:46.000 --> 00:18:48.000
about it is is what's called

00:18:48.000 --> 00:18:51.000
a low floor high ceiling task

00:18:51.000 --> 00:18:53.000
so it's low floor for example

00:18:53.000 --> 00:18:55.000
I can give this problem to

00:18:55.000 --> 00:18:56.000
Seamus I could tell him 

00:18:56.000 --> 00:18:57.000
Seamus here's thirty five blocks

00:18:57.000 --> 00:18:58.000
and I want you to put them

00:18:58.000 --> 00:18:60.000
into four containers so that

00:19:00.000 --> 00:19:02.000
this is true and he could do

00:19:02.000 --> 00:19:04.000
Do it or I could opened it up

00:19:04.000 --> 00:19:06.000
to the class who maybe has had

00:19:06.000 --> 00:19:08.000
some algebra and they could

00:19:08.000 --> 00:19:10.000
solve it in a different way

00:19:10.000 --> 00:19:11.000
the exciting thing is it's not

00:19:11.000 --> 00:19:13.000
just low floor it's not just a

00:19:13.000 --> 00:19:15.000
task that anyone can enter it's

00:19:15.000 --> 00:19:16.000
got some really interesting

00:19:16.000 --> 00:19:18.000
things that we can talk about

00:19:18.000 --> 00:19:19.000
it's got a high ceiling we

00:19:19.000 --> 00:19:21.000
can go really far with it for

00:19:21.000 --> 00:19:23.000
example do I really need to

00:19:23.000 --> 00:19:25.000
know all six of those sums? 

00:19:25.000 --> 00:19:27.000
how many do I need to know is

00:19:27.000 --> 00:19:29.000
would two be enough would four

00:19:29.000 --> 00:19:32.000
be enough what would happen if

00:19:32.000 --> 00:19:33.000
something was negative we made

00:19:33.000 --> 00:19:34.000
this assumption that all the

00:19:34.000 --> 00:19:36.000
values were positive with any

00:19:36.000 --> 00:19:37.000
of these solutions strategies

00:19:37.000 --> 00:19:38.000
that we figured out work if the

00:19:38.000 --> 00:19:40.000
values were negative how would

00:19:40.000 --> 00:19:41.000
that look different in our

00:19:41.000 --> 00:19:43.000
representations there's lots

00:19:43.000 --> 00:19:44.000
of interesting conversations

00:19:44.000 --> 00:19:45.000
we can have about this task

00:19:45.000 --> 00:19:47.000
and has a high ceiling another

00:19:47.000 --> 00:19:49.000
example of a low floor high

00:19:49.000 --> 00:19:51.000
ceiling task that I enjoy

00:19:51.000 --> 00:19:52.000
doing with students is called

00:19:52.000 --> 00:19:54.000
cutting the cube it says all

00:19:54.000 --> 00:19:55.000
the faces of the cube painted

00:19:55.000 --> 00:19:57.000
its then cut into twenty seven

00:19:57.000 --> 00:19:59.000
equal sized cubes how many

00:19:59.000 --> 00:19:61.000
painted faces does each small

00:20:01.000 --> 00:20:02.000
cube have what if you cut it

00:20:02.000 --> 00:20:04.000
into sixty four so four by

00:20:04.000 --> 00:20:06.000
four by four or what if you

00:20:06.000 --> 00:20:07.000
cut it into a N by N by N

00:20:07.000 --> 00:20:09.000
how many faces would there 

00:20:09.000 --> 00:20:11.000
each have and again low floor

00:20:11.000 --> 00:20:13.000
I bought my Rubik's cube in

00:20:13.000 --> 00:20:14.000
here for Seamus today because

00:20:14.000 --> 00:20:16.000
I imagine that Chrissy and Eva

00:20:16.000 --> 00:20:18.000
could give you a Rubik's cube

00:20:18.000 --> 00:20:19.000
and you could make a table and

00:20:19.000 --> 00:20:21.000
you could plot the different

00:20:21.000 --> 00:20:23.000
values and you can investigate

00:20:23.000 --> 00:20:24.000
the patterns that are happening

00:20:24.000 --> 00:20:25.000
with the different faces and

00:20:25.000 --> 00:20:27.000
these are first graders third

00:20:27.000 --> 00:20:29.000
graders fourth graders they

00:20:29.000 --> 00:20:30.000
can engage in an interesting

00:20:30.000 --> 00:20:32.000
way with this problem however

00:20:32.000 --> 00:20:33.000
I imagine some of you in this

00:20:33.000 --> 00:20:35.000
room if I give you a pill

00:20:35.000 --> 00:20:36.000
of blocks could build a four by

00:20:36.000 --> 00:20:38.000
four by four model and start

00:20:38.000 --> 00:20:39.000
to look at some things and

00:20:39.000 --> 00:20:40.000
maybe some of you could even

00:20:40.000 --> 00:20:41.000
predict what a five by five by

00:20:41.000 --> 00:20:43.000
five would and some of you might

00:20:43.000 --> 00:20:44.000
even be able to generalize to

00:20:44.000 --> 00:20:46.000
the N by N by N. and so this

00:20:46.000 --> 00:20:47.000
is an exciting problem because

00:20:47.000 --> 00:20:49.000
of the low floor these folks

00:20:49.000 --> 00:20:50.000
everyone up here in the front

00:20:50.000 --> 00:20:52.000
few tables can engage with

00:20:52.000 --> 00:20:53.000
this task in a different way

00:20:53.000 --> 00:20:55.000
we can have some really in

00:20:55.000 --> 00:20:56.000
interesting conversations

00:20:56.000 --> 00:20:57.000
about the algebra that's

00:20:57.000 --> 00:20:60.000
underneath it the final one

00:21:00.000 --> 00:21:01.000
is I throw in here because I I

00:21:01.000 --> 00:21:03.000
a joke sometimes that my true

00:21:03.000 --> 00:21:05.000
dream, career  profession was

00:21:05.000 --> 00:21:07.000
always to be a mathematician

00:21:07.000 --> 00:21:09.000
for professional baseball team

00:21:09.000 --> 00:21:10.000
and I love this problem it

00:21:10.000 --> 00:21:11.000
says the Major League Baseball

00:21:11.000 --> 00:21:13.000
strike so to raise a rectangle

00:21:13.000 --> 00:21:15.000
approximately fifteen inches

00:21:15.000 --> 00:21:16.000
by forty inches. What effect is there

00:21:16.000 --> 00:21:17.000
there on the size of the strike

00:21:17.000 --> 00:21:19.000
zone if the umpire adds just two

00:21:19.000 --> 00:21:22.000
inches to all sides again this

00:21:22.000 --> 00:21:24.000
is a really interesting problem

00:21:24.000 --> 00:21:26.000
because it's poorly worded

00:21:26.000 --> 00:21:28.000
what is the effect so what I'm

00:21:28.000 --> 00:21:29.000
what I'm a trying to figure out

00:21:29.000 --> 00:21:31.000
here is this an area problem

00:21:31.000 --> 00:21:34.000
is is a percent problem what a

00:21:34.000 --> 00:21:37.000
quadratic equation help me here

00:21:37.000 --> 00:21:39.000
would a graph like what is this

00:21:39.000 --> 00:21:41.000
I don't know what this is and

00:21:41.000 --> 00:21:42.000
that's what I love about this

00:21:42.000 --> 00:21:43.000
problem is it doesn't matter

00:21:43.000 --> 00:21:44.000
it's got a low floor their

00:21:44.000 --> 00:21:46.000
students you even just have a

00:21:46.000 --> 00:21:47.000
basic understanding of the area

00:21:47.000 --> 00:21:49.000
of a rectangle can engage with

00:21:49.000 --> 00:21:51.000
this task but I was talking

00:21:51.000 --> 00:21:53.000
with Scott about this task and he

00:21:53.000 --> 00:21:54.000
was telling me how I'm now we

00:21:54.000 --> 00:21:55.000
have this new video technology

00:21:55.000 --> 00:21:57.000
that allows us to make strike

00:21:57.000 --> 00:21:59.000
zone three dimensional and

00:21:59.000 --> 00:21:61.000
so I could even take this in

00:22:01.000 --> 00:22:02.000
those kinds of conversations

00:22:02.000 --> 00:22:04.000
once kids get an answer they're

00:22:04.000 --> 00:22:05.000
comfortable with here the

00:22:05.000 --> 00:22:06.000
other thing I'll tell you you

00:22:06.000 --> 00:22:08.000
want to go down a rabbit hole

00:22:08.000 --> 00:22:10.000
do a Google image search for

00:22:10.000 --> 00:22:12.000
strikes zone I'm trying to find

00:22:12.000 --> 00:22:13.000
a cool picture to put up here

00:22:13.000 --> 00:22:15.000
and the mathematics that came

00:22:15.000 --> 00:22:16.000
up on my screen was fascinating

00:22:16.000 --> 00:22:18.000
I would love to to go in and

00:22:18.000 --> 00:22:22.000
just look at that so anyway

00:22:22.000 --> 00:22:24.000
I want to transition now to

00:22:24.000 --> 00:22:25.000
talking more specifically

00:22:25.000 --> 00:22:27.000
about kind of my own research

00:22:27.000 --> 00:22:28.000
and some of the work that I've

00:22:28.000 --> 00:22:29.000
been doing over the last few

00:22:29.000 --> 00:22:32.000
years and in 2018

00:22:32.000 --> 00:22:33.000
I co authored a book called

00:22:33.000 --> 00:22:37.000
How Students Think When Doing Algebra and our goal with that

00:22:37.000 --> 00:22:38.000
was to synthesize all the

00:22:38.000 --> 00:22:40.000
research that's been done on

00:22:40.000 --> 00:22:41.000
teaching and learning algebra

00:22:41.000 --> 00:22:43.000
over the last forty fifty

00:22:43.000 --> 00:22:44.000
years we looked at around eight

00:22:44.000 --> 00:22:46.000
hundred research articles and I

00:22:46.000 --> 00:22:47.000
didn't look at eight hundred I

00:22:47.000 --> 00:22:48.000
looked at a small slice of them

00:22:51.000 --> 00:22:53.000
to focus on what how can we put

00:22:53.000 --> 00:22:55.000
the thinking back into algebra

00:22:55.000 --> 00:22:57.000
algebra is typically a subject

00:22:57.000 --> 00:22:58.000
that is it's easy to kind of

00:22:58.000 --> 00:22:60.000
reduced to procedures and just

00:23:00.000 --> 00:23:02.000
remembering and repeating the

00:23:02.000 --> 00:23:03.000
things that your teacher taught

00:23:03.000 --> 00:23:05.000
you so before we get into the

00:23:05.000 --> 00:23:07.000
research I want a flashy back

00:23:07.000 --> 00:23:08.000
to how algebra looks to first

00:23:08.000 --> 00:23:10.000
graders this is algebra in

00:23:10.000 --> 00:23:12.000
first grade we get these kinds

00:23:12.000 --> 00:23:13.000
of problems to first graders

00:23:13.000 --> 00:23:15.000
we ask them okay there's an

00:23:15.000 --> 00:23:17.000
empty box there and I'm gonna

00:23:17.000 --> 00:23:20.000
subtract fifteen and equals

00:23:20.000 --> 00:23:21.000
five what do you think should

00:23:21.000 --> 00:23:23.000
go inside that box in children

00:23:23.000 --> 00:23:24.000
are able to engage with this

00:23:24.000 --> 00:23:26.000
task they might look at it

00:23:26.000 --> 00:23:27.000
and say to themselves well

00:23:27.000 --> 00:23:28.000
you know like fifteen I can

00:23:28.000 --> 00:23:31.000
count on five sixteen seventeen

00:23:31.000 --> 00:23:32.000
eighteen nineteen twenty or

00:23:32.000 --> 00:23:34.000
maybe they put a pile blocks

00:23:34.000 --> 00:23:36.000
together and they have fifteen

00:23:36.000 --> 00:23:37.000
and they figure out how many

00:23:37.000 --> 00:23:38.000
would be left as they took away

00:23:38.000 --> 00:23:40.000
the five it there's lots of

00:23:40.000 --> 00:23:41.000
different ways first graders

00:23:41.000 --> 00:23:43.000
engage with this task and

00:23:43.000 --> 00:23:45.000
eventually you know most first

00:23:45.000 --> 00:23:46.000
grader second graders can tell

00:23:46.000 --> 00:23:48.000
you that twenty minus fifteen

00:23:48.000 --> 00:23:49.000
is what goes inside that box

00:23:49.000 --> 00:23:51.000
that little box the problem is

00:23:51.000 --> 00:23:52.000
though we get to high school

00:23:52.000 --> 00:23:54.000
algebra and that box becomes

00:23:54.000 --> 00:23:56.000
an X and we asked children

00:23:56.000 --> 00:23:57.000
this problem is they will

00:23:57.000 --> 00:23:59.000
x minus fifteen is five

00:23:59.000 --> 00:23:60.000
what do you think X.

00:24:00.000 --> 00:24:01.000
might be and they say well

00:24:01.000 --> 00:24:03.000
you know I'm thinking about

00:24:03.000 --> 00:24:04.000
it and I think I can I can

00:24:04.000 --> 00:24:06.000
just look at that and I know

00:24:06.000 --> 00:24:09.000
access twenty no no no no no

00:24:09.000 --> 00:24:11.000
we don't just think about it

00:24:11.000 --> 00:24:13.000
you have to show me your work

00:24:13.000 --> 00:24:15.000
I want to see a plus fifteen

00:24:15.000 --> 00:24:17.000
an a plus fifteen and I want

00:24:17.000 --> 00:24:18.000
you to draw the line and I want

00:24:18.000 --> 00:24:20.000
you to carry to no thinking

00:24:20.000 --> 00:24:23.000
please show your work and I

00:24:23.000 --> 00:24:24.000
did I'm guilty of it I do it

00:24:24.000 --> 00:24:26.000
all the time and the reason

00:24:26.000 --> 00:24:28.000
that we do it is this is the

00:24:28.000 --> 00:24:29.000
argument is the argument as

00:24:29.000 --> 00:24:30.000
well they're not always gonna

00:24:30.000 --> 00:24:32.000
be that easy right so we're

00:24:32.000 --> 00:24:33.000
gonna get problems that are

00:24:33.000 --> 00:24:35.000
more complicated Rachel and

00:24:35.000 --> 00:24:36.000
when you get to those you need

00:24:36.000 --> 00:24:37.000
to know the procedure so I

00:24:37.000 --> 00:24:39.000
want you to start now don't do

00:24:39.000 --> 00:24:41.000
anything so now I want to get

00:24:41.000 --> 00:24:42.000
back to the research that that

00:24:42.000 --> 00:24:45.000
we had done I stumbled across

00:24:45.000 --> 00:24:46.000
this article that was published

00:24:46.000 --> 00:24:47.000
in nineteen eighty three by

00:24:47.000 --> 00:24:49.000
Kumon on and it it really

00:24:49.000 --> 00:24:50.000
changed my trajectory on how

00:24:50.000 --> 00:24:52.000
I think about algebra and that

00:24:52.000 --> 00:24:54.000
what the task says is solve for

00:24:54.000 --> 00:24:56.000
X without using a pencil so

00:24:56.000 --> 00:24:58.000
that you can use a pencil to

00:24:58.000 --> 00:24:59.000
keep track but basically what

00:24:59.000 --> 00:24:61.000
it's saying is is don't use

00:25:01.000 --> 00:25:05.000
those formal procedures and so

00:25:05.000 --> 00:25:06.000
I want you to do that right now

00:25:06.000 --> 00:25:09.000
with me let's think about this

00:25:09.000 --> 00:25:11.000
What Kumon says is don't

00:25:11.000 --> 00:25:12.000
worry about adding fifteen to

00:25:12.000 --> 00:25:14.000
both sides -- undoing what's

00:25:14.000 --> 00:25:15.000
been done to X are all the

00:25:15.000 --> 00:25:17.000
procedures that we taught what

00:25:17.000 --> 00:25:18.000
he says is look at this task

00:25:18.000 --> 00:25:20.000
and asked children to cover

00:25:20.000 --> 00:25:22.000
up what's messy cover up what's 

00:25:22.000 --> 00:25:25.000
ugly and hard to understand

00:25:25.000 --> 00:25:26.000
and so what children will do is

00:25:26.000 --> 00:25:28.000
they will cover up that piece

00:25:28.000 --> 00:25:30.000
right that's messy and hard

00:25:30.000 --> 00:25:32.000
to understand but now I've got

00:25:32.000 --> 00:25:33.000
that problem that I had back in

00:25:33.000 --> 00:25:35.000
first grade right so now I know

00:25:35.000 --> 00:25:39.000
what's under the box twenty

00:25:39.000 --> 00:25:41.000
so whatever was under the box

00:25:41.000 --> 00:25:43.000
that's twenty okay so when I go

00:25:43.000 --> 00:25:46.000
from here cover up with messy

00:25:46.000 --> 00:25:47.000
ugly and hard to understand

00:25:47.000 --> 00:25:49.000
some a cover up the top I'm

00:25:49.000 --> 00:25:50.000
just not gonna think about it

00:25:50.000 --> 00:25:52.000
for now so now whatever is hard

00:25:52.000 --> 00:25:55.000
to understand divided by two is

00:25:55.000 --> 00:25:61.000
twenty so what's under my box

00:26:01.000 --> 00:26:03.000
and now I've got five time

00:26:03.000 --> 00:26:05.000
something is forty that feels

00:26:05.000 --> 00:26:06.000
like maybe a second or third

00:26:06.000 --> 00:26:07.000
grade problem right I can

00:26:07.000 --> 00:26:08.000
figure that out and I know

00:26:08.000 --> 00:26:10.000
that's eight the reality is

00:26:10.000 --> 00:26:12.000
almost every algebra problem

00:26:12.000 --> 00:26:14.000
in high school algebra one

00:26:14.000 --> 00:26:15.000
textbook can be solved in this

00:26:15.000 --> 00:26:16.000
way they're constructed that

00:26:16.000 --> 00:26:18.000
way and these are some examples

00:26:18.000 --> 00:26:20.000
for example you know because

00:26:20.000 --> 00:26:21.000
you might say well that works

00:26:21.000 --> 00:26:22.000
for that kind but let me give

00:26:22.000 --> 00:26:23.000
you some more examples for

00:26:23.000 --> 00:26:24.000
example let's look at this

00:26:24.000 --> 00:26:26.000
first one cover up with messy I

00:26:26.000 --> 00:26:27.000
don't know what's going on with

00:26:27.000 --> 00:26:29.000
that divide by X + 9

00:26:29.000 --> 00:26:30.000
that's making you stressed I

00:26:30.000 --> 00:26:31.000
can't remember how to undo that

00:26:31.000 --> 00:26:32.000
so I'm just going to cover it

00:26:32.000 --> 00:26:35.000
up so ten divided by something

00:26:35.000 --> 00:26:40.000
is one what's under the box

00:26:40.000 --> 00:26:42.000
ten ten divided by ten is one

00:26:42.000 --> 00:26:44.000
so now I can think about that

00:26:44.000 --> 00:26:45.000
X + 9 is 10

00:26:45.000 --> 00:26:48.000
X must be one okay let's look

00:26:48.000 --> 00:26:50.000
at the second one high school

00:26:50.000 --> 00:26:51.000
algebra one teacher Rachel

00:26:51.000 --> 00:26:52.000
would have said distribute the

00:26:52.000 --> 00:26:54.000
one half undo the parentheses

00:26:54.000 --> 00:26:56.000
everyone and then let's of

00:26:56.000 --> 00:26:58.000
Subtract three halves and blah blah blah

00:26:58.000 --> 00:26:60.000
no instead what I'm gonna say

00:27:00.000 --> 00:27:02.000
is coming up with messy half

00:27:02.000 --> 00:27:04.000
of something is six so what's

00:27:04.000 --> 00:27:07.000
that what's that something

00:27:07.000 --> 00:27:08.000
twelve so whatever's under the

00:27:08.000 --> 00:27:10.000
parentheses is twelve X.

00:27:10.000 --> 00:27:12.000
must be nine this last one

00:27:12.000 --> 00:27:14.000
I love because I would have

00:27:14.000 --> 00:27:15.000
told my students to you know

00:27:15.000 --> 00:27:17.000
distribute the threes combine

00:27:17.000 --> 00:27:18.000
like terms get your X's onto

00:27:18.000 --> 00:27:21.000
one side do all those things

00:27:21.000 --> 00:27:23.000
Coverup what's messy and since

00:27:23.000 --> 00:27:25.000
I understand about the equal

00:27:25.000 --> 00:27:27.000
sign I can cover up things on

00:27:27.000 --> 00:27:29.000
both sides of the equation I'm

00:27:29.000 --> 00:27:31.000
covering up equal things and

00:27:31.000 --> 00:27:34.000
what's left behind X.

00:27:34.000 --> 00:27:35.000
equals negative one I don't

00:27:35.000 --> 00:27:37.000
even need to distribute and

00:27:37.000 --> 00:27:38.000
I would argue that in each

00:27:38.000 --> 00:27:41.000
of these cases I'm thinking

00:27:41.000 --> 00:27:42.000
through the procedure I'm not

00:27:42.000 --> 00:27:43.000
carrying out a procedure I'm

00:27:43.000 --> 00:27:45.000
not remembering and repeating

00:27:45.000 --> 00:27:47.000
instead I'm thinking but I will

00:27:47.000 --> 00:27:48.000
tell you that this makes a lot

00:27:48.000 --> 00:27:49.000
of folks very uncomfortable

00:27:49.000 --> 00:27:51.000
a lot of algebra 1 teachers

00:27:51.000 --> 00:27:53.000
very uncomfortable we want you

00:27:53.000 --> 00:27:54.000
know we've pushed kids in the

00:27:54.000 --> 00:27:56.000
past so much to just remember

00:27:56.000 --> 00:27:60.000
and repeat so as I say -- going

00:28:00.000 --> 00:28:03.000
through my work -- I have had

00:28:03.000 --> 00:28:05.000
to ask myself how do I get my

00:28:05.000 --> 00:28:07.000
pre service teachers set to

00:28:07.000 --> 00:28:09.000
move away from this idea that

00:28:09.000 --> 00:28:10.000
math teaching is remembering

00:28:10.000 --> 00:28:12.000
and repeating and how do I get

00:28:12.000 --> 00:28:14.000
them to move towards thinking

00:28:14.000 --> 00:28:15.000
in mathematics so I give them

00:28:15.000 --> 00:28:17.000
problems like this and you

00:28:17.000 --> 00:28:18.000
might say well that's not a

00:28:18.000 --> 00:28:19.000
problem that's an exercise and

00:28:19.000 --> 00:28:20.000
I would agree one ninety eight

00:28:20.000 --> 00:28:21.000
times twenty five but I don't

00:28:21.000 --> 00:28:23.000
give it to them that way I start

00:28:23.000 --> 00:28:25.000
this way I also think about

00:28:25.000 --> 00:28:29.000
what is two hundred times five

00:28:29.000 --> 00:28:31.000
right now what do you think

00:28:31.000 --> 00:28:33.000
Eva? A thousand all right let's

00:28:33.000 --> 00:28:35.000
see if Eva can do this one

00:28:35.000 --> 00:28:36.000
your try it Eva?

00:28:36.000 --> 00:28:39.000
Seamus will back you up. 

00:28:39.000 --> 00:28:40.000
if I know two hundred times

00:28:40.000 --> 00:28:43.000
five is a thousand what would

00:28:43.000 --> 00:28:46.000
two hundred times twenty be

00:28:46.000 --> 00:28:47.000
it takes and thinking what

00:28:47.000 --> 00:28:50.000
do you think do you think you

00:28:50.000 --> 00:28:52.000
know Krissy got an excited

00:28:52.000 --> 00:28:55.000
face. What do you think Seamus

00:28:55.000 --> 00:28:61.000
four thousand, how did you know that

00:29:04.000 --> 00:29:07.000
so it's four thousand so two

00:29:07.000 --> 00:29:09.000
thousand Chrissy's problem was

00:29:09.000 --> 00:29:11.000
a thousand and and the next one

00:29:11.000 --> 00:29:13.000
was four thousand two hundred

00:29:13.000 --> 00:29:16.000
times twenty five be I know

00:29:16.000 --> 00:29:17.000
the first one thousand and

00:29:17.000 --> 00:29:21.000
the second one's four thousand

00:29:21.000 --> 00:29:24.000
any ideas because we know

00:29:24.000 --> 00:29:26.000
the first one we got five

00:29:26.000 --> 00:29:27.000
two hundred some about twenty

00:29:27.000 --> 00:29:29.000
two hundred so now we've got

00:29:29.000 --> 00:29:31.000
twenty five two hundred so now

00:29:31.000 --> 00:29:32.000
my question for the audience

00:29:32.000 --> 00:29:34.000
as if I know that two hundred

00:29:34.000 --> 00:29:35.000
times twenty five is what's one

00:29:35.000 --> 00:29:39.000
ninety eight times twenty five

00:29:39.000 --> 00:29:42.000
it's two twenty five west right

00:29:42.000 --> 00:29:43.000
SO four thousand nine hundred

00:29:43.000 --> 00:29:45.000
fifty the thing is if I had

00:29:45.000 --> 00:29:46.000
given you this problem and just

00:29:46.000 --> 00:29:48.000
said Hey can you figure out

00:29:48.000 --> 00:29:49.000
what one ninety eight times

00:29:49.000 --> 00:29:51.000
twenty five is I bet most of

00:29:51.000 --> 00:29:52.000
you including myself would

00:29:52.000 --> 00:29:53.000
have set it up like we did on

00:29:53.000 --> 00:29:55.000
the right hand side but what I

00:29:55.000 --> 00:29:57.000
challenge students to do is to

00:29:57.000 --> 00:29:59.000
engage with thinking about how

00:29:59.000 --> 00:29:61.000
we can create multiplication

00:30:01.000 --> 00:30:03.000
strings addition strings these

00:30:03.000 --> 00:30:05.000
are called strings that allow

00:30:05.000 --> 00:30:07.000
children to logically think

00:30:07.000 --> 00:30:08.000
about what the mathematics is

00:30:08.000 --> 00:30:10.000
because honestly when a child

00:30:10.000 --> 00:30:11.000
encounters one ninety eight

00:30:11.000 --> 00:30:12.000
times twenty five I don't

00:30:12.000 --> 00:30:13.000
want them doing it that way I

00:30:13.000 --> 00:30:14.000
don't want them doing it the

00:30:14.000 --> 00:30:15.000
way on the right I want them

00:30:15.000 --> 00:30:17.000
to think through it and reason

00:30:19.000 --> 00:30:20.000
less than two hundred twenty

00:30:20.000 --> 00:30:22.000
five I can figure that out

00:30:22.000 --> 00:30:23.000
and the reason I want them to

00:30:23.000 --> 00:30:24.000
do that is if they forget the

00:30:24.000 --> 00:30:26.000
procedure are they maybe carry

00:30:26.000 --> 00:30:28.000
out the procedure incorrectly

00:30:28.000 --> 00:30:29.000
if they know how to do what's

00:30:29.000 --> 00:30:30.000
happening on the left they

00:30:30.000 --> 00:30:32.000
have strategies for going back

00:30:32.000 --> 00:30:33.000
in figuring out if they're

00:30:33.000 --> 00:30:35.000
correct or they have the

00:30:35.000 --> 00:30:37.000
ability look at all of you

00:30:37.000 --> 00:30:39.000
some of whom think you're not

00:30:39.000 --> 00:30:41.000
good at math they just figured

00:30:41.000 --> 00:30:42.000
out what one hundred ninety

00:30:42.000 --> 00:30:43.000
eight times twenty five was in

00:30:43.000 --> 00:30:45.000
your head and you wouldn't have

00:30:45.000 --> 00:30:46.000
been able to do that if you

00:30:46.000 --> 00:30:47.000
hadn't been thinking through

00:30:47.000 --> 00:30:49.000
this recently okay I'm about

00:30:49.000 --> 00:30:50.000
to wrap up I I think I'm going

00:30:50.000 --> 00:30:52.000
to long and I hesitate to

00:30:52.000 --> 00:30:54.000
ends my presentation with

00:30:54.000 --> 00:30:55.000
a wall of text because I

00:30:55.000 --> 00:30:57.000
know powerpoint rules tell me

00:30:57.000 --> 00:30:59.000
not to do that but I am very

00:30:59.000 --> 00:30:60.000
very proud of this wall of

00:31:00.000 --> 00:31:03.000
text these are five articles

00:31:03.000 --> 00:31:04.000
that have been published by my

00:31:04.000 --> 00:31:05.000
elementary math instructional

00:31:05.000 --> 00:31:07.000
leader candidates -- graduates

00:31:07.000 --> 00:31:09.000
now elementary math specialist

00:31:09.000 --> 00:31:12.000
graduates and Cheryl and Laurie

00:31:12.000 --> 00:31:14.000
and I have worked really hard

00:31:14.000 --> 00:31:15.000
with the students to help them

00:31:15.000 --> 00:31:17.000
engage in thinking about what

00:31:17.000 --> 00:31:19.000
problem solving means and what

00:31:19.000 --> 00:31:20.000
thinking means and these are

00:31:20.000 --> 00:31:22.000
fine I I'm probably more proud

00:31:22.000 --> 00:31:23.000
of the scholarship than I am

00:31:23.000 --> 00:31:24.000
of any of the other things

00:31:24.000 --> 00:31:26.000
that I've done and each one of

00:31:26.000 --> 00:31:28.000
these articles represents an

00:31:28.000 --> 00:31:29.000
article that they have written

00:31:29.000 --> 00:31:30.000
that somehow deals with problem

00:31:30.000 --> 00:31:32.000
solving and somehow deals with

00:31:32.000 --> 00:31:33.000
putting that thinking back

00:31:33.000 --> 00:31:35.000
into mathematics and I've I

00:31:35.000 --> 00:31:38.000
am very very proud of that

00:31:38.000 --> 00:31:39.000
I'm ending my slide with the

00:31:39.000 --> 00:31:40.000
title slide because this was

00:31:40.000 --> 00:31:42.000
my alternate title I was trying

00:31:42.000 --> 00:31:43.000
to decide what my title should

00:31:43.000 --> 00:31:46.000
be for this session I really

00:31:46.000 --> 00:31:48.000
I think it's really important

00:31:48.000 --> 00:31:50.000
that we all acknowledge this

00:31:50.000 --> 00:31:51.000
that you actually are good at

00:31:51.000 --> 00:31:53.000
math once you can know that

00:31:53.000 --> 00:31:55.000
math is about thinking and

00:31:55.000 --> 00:31:56.000
not remembering and repeating

00:31:56.000 --> 00:31:57.000
once you know that math is

00:31:57.000 --> 00:31:58.000
about problem solving and

00:31:58.000 --> 00:31:60.000
not working on exercises

00:32:00.000 --> 00:32:02.000
once you know that I think we

00:32:02.000 --> 00:32:03.000
can help people recover from

00:32:03.000 --> 00:32:06.000
the traumatic experience and

00:32:06.000 --> 00:32:07.000
And help them undo this notion that

00:32:07.000 --> 00:32:08.000
they're either math people

00:32:08.000 --> 00:32:10.000
are not math people and then I

00:32:10.000 --> 00:32:11.000
think we can all be confident

00:32:11.000 --> 00:32:13.000
that everyone including

00:32:13.000 --> 00:32:18.000
you is good at math. Thank you.

00:32:18.000 --> 00:32:20.000
so good afternoon my name is

00:32:20.000 --> 00:32:23.000
Hamrid Bernard, I am as serving as the

00:32:23.000 --> 00:32:25.000
chair of the national science

00:32:25.000 --> 00:32:27.000
and mathematics division but

00:32:27.000 --> 00:32:28.000
but I'm also faculty in the 

00:32:28.000 --> 00:32:31.000
mathmatics department and so it's

00:32:31.000 --> 00:32:33.000
my pleasure today to introduce

00:32:33.000 --> 00:32:35.000
Doctor Scott Beaver  

00:32:35.000 --> 00:32:38.000
this year's recipient of the 

00:32:38.000 --> 00:32:41.000
Pastega Award for excellence in

00:32:41.000 --> 00:32:43.000
teaching so Scott joined us in

00:32:43.000 --> 00:32:46.000
two thousand five I believe --

00:32:46.000 --> 00:32:49.000
so we got lucky you know I I

00:32:49.000 --> 00:32:51.000
Can not really say we bought

00:32:51.000 --> 00:32:54.000
one we got one for free but

00:32:54.000 --> 00:32:55.000
We got really lucky with

00:32:55.000 --> 00:32:57.000
The couple that we 

00:32:57.000 --> 00:32:60.000
got here and -- Scott's been

00:33:00.000 --> 00:33:03.000
Really from the moment 

00:33:03.000 --> 00:33:05.000
that he  join our department and

00:33:05.000 --> 00:33:07.000
hit the ground and running 

00:33:07.000 --> 00:33:10.000
being active in all parts of

00:33:10.000 --> 00:33:12.000
the department and university

00:33:12.000 --> 00:33:15.000
all of you know this and 

00:33:15.000 --> 00:33:17.000
Scott been teaching all of

00:33:17.000 --> 00:33:18.000
levels of mathematics

00:33:18.000 --> 00:33:22.000
That we have. I don't know if 

00:33:22.000 --> 00:33:23.000
there are any courses that

00:33:23.000 --> 00:33:24.000
you haven't really taught maybe

00:33:24.000 --> 00:33:27.000
maybe abstract algebra 

00:33:27.000 --> 00:33:28.000
and group theory

00:33:28.000 --> 00:33:29.000
under the two so there is a

00:33:29.000 --> 00:33:36.000
share a teaching them so between the two of them it really...

00:33:36.000 --> 00:33:38.000
so Scott also

00:33:38.000 --> 00:33:39.000
been teaching some of our pre

00:33:39.000 --> 00:33:41.000
service and in service classes

00:33:41.000 --> 00:33:45.000
but yeah mainly -- teaching

00:33:45.000 --> 00:33:48.000
math major students that

00:33:48.000 --> 00:33:50.000
are there and Scott

00:33:50.000 --> 00:33:51.000
is really passionate about

00:33:51.000 --> 00:33:54.000
teaching and this is a

00:33:54.000 --> 00:33:56.000
confession I have to make so

00:33:56.000 --> 00:33:58.000
Scott is never happy with any

00:33:58.000 --> 00:33:59.000
of the textbook that to be

00:33:59.000 --> 00:33:61.000
have and at the very beginning

00:34:01.000 --> 00:34:04.000
a kind of annoyed because I'd say Oh my gosh this

00:34:04.000 --> 00:34:06.000
guys never happy with any book

00:34:06.000 --> 00:34:07.000
then once I got to know him

00:34:07.000 --> 00:34:10.000
I realized that the way that he is

00:34:10.000 --> 00:34:11.000
thinking that the Math should be

00:34:11.000 --> 00:34:14.000
taught it's not in those books

00:34:14.000 --> 00:34:15.000
and that's the reason that he

00:34:15.000 --> 00:34:17.000
is not happy with the books

00:34:17.000 --> 00:34:19.000
that we have. And this really

00:34:19.000 --> 00:34:21.000
shows in his teaching math at

00:34:21.000 --> 00:34:24.000
that -- he really doesn't have

00:34:24.000 --> 00:34:27.000
a lecture class it's mostly

00:34:27.000 --> 00:34:30.000
taught by doing activities some

00:34:30.000 --> 00:34:32.000
of the hardest courses that

00:34:32.000 --> 00:34:33.000
at least I think Scott and I

00:34:33.000 --> 00:34:34.000
believe that the some of the

00:34:34.000 --> 00:34:36.000
hardest courses that we have

00:34:36.000 --> 00:34:38.000
in mathematics department is

00:34:38.000 --> 00:34:40.000
advanced calculus and I

00:34:40.000 --> 00:34:41.000
believe the two of us are the

00:34:41.000 --> 00:34:44.000
only one who's teaching that

00:34:44.000 --> 00:34:46.000
and so Scott teaches it for

00:34:46.000 --> 00:34:48.000
five six years and I says Scott

00:34:48.000 --> 00:34:49.000
I think I'm ready to teach and

00:34:49.000 --> 00:34:51.000
then I did it for one year and

00:34:51.000 --> 00:34:52.000
say okay I think I'm done you

00:34:52.000 --> 00:34:55.000
can pick it out again and 

00:34:55.000 --> 00:34:58.000
it's it's a very abstract two

00:34:58.000 --> 00:34:60.000
semester course two term courses

00:35:00.000 --> 00:35:03.000
and -- these are very difficult

00:35:03.000 --> 00:35:05.000
because it's so abstract

00:35:05.000 --> 00:35:07.000
and you have to solve these

00:35:07.000 --> 00:35:10.000
problems at all proves and 

00:35:10.000 --> 00:35:12.000
so besides being colleagues we

00:35:12.000 --> 00:35:14.000
are also neighbors our offices

00:35:14.000 --> 00:35:16.000
are next to each other and 

00:35:16.000 --> 00:35:19.000
the department being so small you

00:35:19.000 --> 00:35:21.000
really hear everything in each others

00:35:21.000 --> 00:35:22.000
others offices what's happening

00:35:22.000 --> 00:35:25.000
with the students so this is

00:35:25.000 --> 00:35:28.000
how it goes in Scott's office

00:35:28.000 --> 00:35:30.000
hours so first term that's

00:35:32.000 --> 00:35:35.000
one student come knock the door

00:35:35.000 --> 00:35:37.000
Dr. Beaver you have time

00:35:37.000 --> 00:35:38.000
can I ask you a question 

00:35:38.000 --> 00:35:41.000
Scott says oh yes come on in and

00:35:41.000 --> 00:35:42.000
I just don't know how to do

00:35:42.000 --> 00:35:44.000
this problem and then Scott

00:35:44.000 --> 00:35:46.000
says okay let's do an example

00:35:46.000 --> 00:35:47.000
and they start doing working

00:35:47.000 --> 00:35:50.000
on the board and so this goes

00:35:50.000 --> 00:35:53.000
on and as time progresses you

00:35:53.000 --> 00:35:55.000
see these students come in

00:35:55.000 --> 00:35:58.000
with a lot more confident and

00:35:58.000 --> 00:35:60.000
big part of it is because when

00:36:00.000 --> 00:36:03.000
they come and they come with

00:36:03.000 --> 00:36:04.000
an idea on how to solve the

00:36:04.000 --> 00:36:07.000
problem Scott doesn't say well

00:36:07.000 --> 00:36:08.000
that's good he says that's

00:36:08.000 --> 00:36:10.000
a great idea I didn't think

00:36:10.000 --> 00:36:12.000
about it this way it gives students 

00:36:12.000 --> 00:36:14.000
wings. They really feel 

00:36:14.000 --> 00:36:17.000
like they're gonna fly that's

00:36:17.000 --> 00:36:18.000
that's how and another part of

00:36:18.000 --> 00:36:20.000
it is that they never feel

00:36:20.000 --> 00:36:24.000
that Scott is thinking

00:36:24.000 --> 00:36:26.000
that he's above them he thinks

00:36:26.000 --> 00:36:28.000
they are equal and that's give

00:36:28.000 --> 00:36:30.000
such a confident to students

00:36:30.000 --> 00:36:34.000
that he can do whatever they

00:36:34.000 --> 00:36:35.000
that Scott is giving them to

00:36:35.000 --> 00:36:38.000
do and I'm really proud to

00:36:38.000 --> 00:36:40.000
introduce my colleague Dr Scott

00:36:40.000 --> 00:36:42.000
Beaver without further ado.

00:36:42.000 --> 00:36:44.000
Thank you Hamrid. I would also like

00:36:44.000 --> 00:36:47.000
to thank the Pastega Awards

00:36:47.000 --> 00:36:49.000
Committee for both of their

00:36:49.000 --> 00:36:50.000
selections today it is an honor

00:36:50.000 --> 00:36:52.000
to share the stage with Rachel

00:36:52.000 --> 00:36:54.000
today I'd like to thank my

00:36:54.000 --> 00:36:55.000
family Doctor Cheryl Beaver

00:36:55.000 --> 00:36:57.000
and future doctors Elizabeth

00:36:57.000 --> 00:36:60.000
Beaver and doctor Evan Beaver

00:37:00.000 --> 00:37:01.000
for the support that they've

00:37:01.000 --> 00:37:03.000
given me -- not just for the

00:37:03.000 --> 00:37:05.000
past several weeks and months

00:37:05.000 --> 00:37:07.000
but -- for an awful long time

00:37:07.000 --> 00:37:08.000
and I really appreciate that

00:37:08.000 --> 00:37:09.000
I also like to thank Hamrid again

00:37:09.000 --> 00:37:11.000
for nominating me and and

00:37:11.000 --> 00:37:12.000
writing a letter of support

00:37:12.000 --> 00:37:14.000
on my behalf and in that they

00:37:14.000 --> 00:37:16.000
had also like to thank doctor

00:37:16.000 --> 00:37:18.000
Lori Burton and doctor Bryan

00:37:18.000 --> 00:37:20.000
Denton for writing the letters

00:37:20.000 --> 00:37:22.000
a couple of former students

00:37:22.000 --> 00:37:23.000
have written letters for me as

00:37:23.000 --> 00:37:24.000
well and I like to call them

00:37:24.000 --> 00:37:26.000
by name Erica Stockard who's

00:37:26.000 --> 00:37:27.000
in attendance  today thank you for

00:37:27.000 --> 00:37:29.000
coming Erics I appreciate that

00:37:29.000 --> 00:37:31.000
Britney Johnson as well Jose

00:37:31.000 --> 00:37:35.000
Sosa Vasquez and at the time

00:37:35.000 --> 00:37:37.000
she wrote the letter it was

00:37:37.000 --> 00:37:39.000
Ariel Setnicker and now

00:37:39.000 --> 00:37:40.000
it's Doctor Ariel Setnicker

00:37:40.000 --> 00:37:41.000
so that's pretty cool I'm awful

00:37:41.000 --> 00:37:44.000
proud of that so I'm gonna talk

00:37:44.000 --> 00:37:46.000
a little bit about my pedagogy

00:37:46.000 --> 00:37:47.000
today and I think you know

00:37:47.000 --> 00:37:50.000
that's relevant but I'd like to

00:37:50.000 --> 00:37:52.000
warm us up with a math problem

00:37:52.000 --> 00:37:54.000
because you know you know what

00:37:54.000 --> 00:37:55.000
you got into and you decide to

00:37:55.000 --> 00:37:57.000
come here today so if you know

00:37:57.000 --> 00:37:59.000
about the Monty hall problem

00:37:59.000 --> 00:37:60.000
and you've already thought

00:38:00.000 --> 00:38:01.000
carefully through the solution

00:38:01.000 --> 00:38:02.000
please don't chime in too

00:38:02.000 --> 00:38:05.000
early here so goes as follows

00:38:05.000 --> 00:38:08.000
Monty Hall was a game show host

00:38:08.000 --> 00:38:09.000
in the sixties seventies and

00:38:09.000 --> 00:38:10.000
eighties and in particular he

00:38:10.000 --> 00:38:12.000
was the host for a show called

00:38:12.000 --> 00:38:14.000
Let's Make A Deal and in this

00:38:14.000 --> 00:38:17.000
particular problem that 

00:38:17.000 --> 00:38:20.000
A reader for a magazine column 

00:38:20.000 --> 00:38:24.000
wrote in to Marilyn

00:38:24.000 --> 00:38:26.000
about and Marilyn answered it

00:38:26.000 --> 00:38:30.000
correctly and was just laid out

00:38:30.000 --> 00:38:31.000
by a bunch of people who later

00:38:31.000 --> 00:38:33.000
had to apologize and admit they

00:38:33.000 --> 00:38:34.000
were completely wrong about it

00:38:34.000 --> 00:38:36.000
but that so the problem goes

00:38:36.000 --> 00:38:38.000
as follows there are three

00:38:38.000 --> 00:38:40.000
doors they're obscuring 

00:38:40.000 --> 00:38:41.000
contents there's a car behind

00:38:41.000 --> 00:38:43.000
one of the doors and in my

00:38:43.000 --> 00:38:46.000
version or two donkeys because

00:38:46.000 --> 00:38:47.000
the graphic on the next page it

00:38:47.000 --> 00:38:49.000
has that so they're two donkeys

00:38:49.000 --> 00:38:50.000
and will assume that you don't

00:38:50.000 --> 00:38:51.000
want the donkeys and that you

00:38:51.000 --> 00:38:53.000
do want the car just for

00:38:53.000 --> 00:38:55.000
concreteness take the red door

00:38:55.000 --> 00:38:56.000
Monty asks you to pick a door

00:38:56.000 --> 00:38:58.000
if you pick the right one you

00:38:58.000 --> 00:38:59.000
get to keep the car and I and

00:38:59.000 --> 00:38:61.000
I suppose is an added incentive

00:39:01.000 --> 00:39:03.000
if you picked the wrong one

00:39:03.000 --> 00:39:04.000
you get to keep the donkey

00:39:04.000 --> 00:39:07.000
right so all right so one out

00:39:07.000 --> 00:39:10.000
of three right okay here's the

00:39:10.000 --> 00:39:14.000
wrinkle the donkey behind door 1, you picked door 2,

00:39:14.000 --> 00:39:16.000
right now the donkey behind

00:39:16.000 --> 00:39:17.000
one of the other two doors in

00:39:17.000 --> 00:39:18.000
this case door one tries to get

00:39:18.000 --> 00:39:22.000
out and and -- reveals himself

00:39:22.000 --> 00:39:23.000
so now Monty want to ask you if

00:39:23.000 --> 00:39:28.000
you want to switch your guess

00:39:28.000 --> 00:39:30.000
take a couple minutes argue

00:39:30.000 --> 00:39:33.000
with the people at your table

00:39:33.000 --> 00:39:34.000
again don't don't reveal if

00:39:34.000 --> 00:39:36.000
you already know how this works

00:39:36.000 --> 00:39:37.000
but yeah hammered out think

00:39:37.000 --> 00:39:38.000
about it. Should you switch your

00:39:38.000 --> 00:39:39.000
guess? There are three answers

00:39:39.000 --> 00:39:41.000
right you should you should

00:39:41.000 --> 00:39:48.000
or doesn't matter... decide 

00:39:48.000 --> 00:39:50.000
so why don't we just do a

00:39:50.000 --> 00:39:52.000
show of hands just out of

00:39:52.000 --> 00:39:53.000
curiosity remember there are

00:39:53.000 --> 00:39:56.000
three possible and then you

00:39:56.000 --> 00:39:57.000
got to pick one of them all

00:39:57.000 --> 00:39:58.000
right there's no not voting

00:39:58.000 --> 00:39:60.000
stuff to get pick one either it

00:40:00.000 --> 00:40:01.000
doesn't matter where you should

00:40:01.000 --> 00:40:03.000
definitely not switch or you

00:40:03.000 --> 00:40:05.000
should definitely switch so for

00:40:05.000 --> 00:40:07.000
definitely not switch how many

00:40:07.000 --> 00:40:09.000
hands who says yeah all right

00:40:09.000 --> 00:40:11.000
we got a couple all right very

00:40:11.000 --> 00:40:15.000
good. Doesn't matter raise

00:40:15.000 --> 00:40:18.000
your hand quite a few more or

00:40:18.000 --> 00:40:20.000
maybe we got half between those

00:40:20.000 --> 00:40:21.000
two answers and then you should

00:40:21.000 --> 00:40:24.000
definitely switch okay you

00:40:24.000 --> 00:40:25.000
know it's remarkable whether

00:40:25.000 --> 00:40:29.000
it's a an audience of -- non

00:40:29.000 --> 00:40:30.000
mathematicians or if it's a

00:40:30.000 --> 00:40:32.000
class in math two forty three

00:40:32.000 --> 00:40:34.000
or even at three eleven it

00:40:34.000 --> 00:40:35.000
really does kind of split down

00:40:35.000 --> 00:40:37.000
the middle it's it's consistent

00:40:37.000 --> 00:40:38.000
I've been talking about this

00:40:38.000 --> 00:40:40.000
and in class -- for maybe

00:40:40.000 --> 00:40:41.000
twenty years off and on when I

00:40:41.000 --> 00:40:43.000
get to teach a statistics class

00:40:43.000 --> 00:40:44.000
or something or probability

00:40:44.000 --> 00:40:46.000
class and it really does split

00:40:46.000 --> 00:40:48.000
right down the middle do you

00:40:48.000 --> 00:40:50.000
want to know the answer you do

00:40:50.000 --> 00:40:52.000
Do you want to know the answer? okay are you

00:40:52.000 --> 00:40:53.000
should definitely switch it

00:40:53.000 --> 00:40:55.000
turns out there's a probability

00:40:55.000 --> 00:40:57.000
of two thirds that you'll

00:40:57.000 --> 00:40:58.000
pick the right door if you're

00:40:58.000 --> 00:40:59.000
interested in the car if you

00:40:59.000 --> 00:40:61.000
switch your guess and only one

00:41:01.000 --> 00:41:02.000
third if you don't switch your

00:41:02.000 --> 00:41:04.000
guess so let me just twice as

00:41:04.000 --> 00:41:06.000
likely up for you to succeed

00:41:06.000 --> 00:41:08.000
if you switch your guess now to

00:41:08.000 --> 00:41:10.000
explain that would take a look

00:41:10.000 --> 00:41:12.000
us a little farther afield

00:41:12.000 --> 00:41:13.000
and then I want to go except

00:41:13.000 --> 00:41:16.000
to say that if you wrote out

00:41:16.000 --> 00:41:18.000
okay let's put the the car and

00:41:18.000 --> 00:41:20.000
door one and list out all the

00:41:20.000 --> 00:41:21.000
possible ways that could go

00:41:21.000 --> 00:41:23.000
but the car door to list out

00:41:23.000 --> 00:41:25.000
all the ways that could go and

00:41:25.000 --> 00:41:26.000
so on you would notice the two

00:41:26.000 --> 00:41:28.000
out of three of those if you

00:41:28.000 --> 00:41:30.000
switch you land on the car so

00:41:32.000 --> 00:41:33.000
those out comes out everything

00:41:33.000 --> 00:41:34.000
but I won't bore you about

00:41:34.000 --> 00:41:37.000
doing that now that explanation

00:41:37.000 --> 00:41:38.000
probably only convinced about

00:41:38.000 --> 00:41:39.000
half for you that raised your

00:41:39.000 --> 00:41:41.000
hand it said it didn't matter

00:41:41.000 --> 00:41:44.000
so what I often do then is --

00:41:44.000 --> 00:41:45.000
well let's simulate it right

00:41:45.000 --> 00:41:46.000
if we can similarly properly

00:41:46.000 --> 00:41:48.000
using index cards or something

00:41:48.000 --> 00:41:49.000
and we can sort of you know try

00:41:49.000 --> 00:41:51.000
this and do it over and over

00:41:51.000 --> 00:41:53.000
and over after some reasonable

00:41:53.000 --> 00:41:54.000
number of trials we're gonna

00:41:54.000 --> 00:41:55.000
get pretty close to two thirds

00:41:55.000 --> 00:41:56.000
as our chances of victory

00:41:56.000 --> 00:41:58.000
in that and that convinces

00:41:58.000 --> 00:41:59.000
everybody because we can do you

00:41:59.000 --> 00:41:61.000
know three hundred four hundred

00:42:01.000 --> 00:42:03.000
simulations and class and if

00:42:03.000 --> 00:42:04.000
the real probability is a half

00:42:04.000 --> 00:42:06.000
that you'll get the car it's

00:42:06.000 --> 00:42:07.000
not going to be that far away

00:42:07.000 --> 00:42:09.000
you end up finding out pretty

00:42:09.000 --> 00:42:11.000
quickly that it is in fact more

00:42:11.000 --> 00:42:14.000
advantageous to switch your gas

00:42:14.000 --> 00:42:16.000
so one up so now we're gonna

00:42:16.000 --> 00:42:19.000
dive into just a few -- just

00:42:19.000 --> 00:42:21.000
sort of principles I have that

00:42:21.000 --> 00:42:25.000
I -- try to engage in when when

00:42:25.000 --> 00:42:27.000
I'm teaching math here will

00:42:27.000 --> 00:42:29.000
As Hamrid said I do I do respect

00:42:29.000 --> 00:42:31.000
students as equals essentially

00:42:31.000 --> 00:42:32.000
they certainly don't know as

00:42:32.000 --> 00:42:34.000
much math as I do that there's

00:42:34.000 --> 00:42:35.000
no point saying they know

00:42:35.000 --> 00:42:38.000
that's that's my job right but

00:42:38.000 --> 00:42:39.000
they're people just like me

00:42:39.000 --> 00:42:41.000
and and their time is just as

00:42:41.000 --> 00:42:44.000
important as mine is so you

00:42:44.000 --> 00:42:45.000
know I treat them that way and

00:42:45.000 --> 00:42:46.000
that that to me is a point I

00:42:46.000 --> 00:42:47.000
want to make them comfortable

00:42:47.000 --> 00:42:49.000
the other thing we have going

00:42:49.000 --> 00:42:51.000
on -- in math is we have a big

00:42:51.000 --> 00:42:53.000
language barrier -- as we go

00:42:53.000 --> 00:42:55.000
through math right it has its

00:42:55.000 --> 00:42:57.000
own nouns its own verbs its own

00:42:57.000 --> 00:42:58.000
adjectives that it's part of

00:42:58.000 --> 00:42:59.000
the English language or German

00:42:59.000 --> 00:42:60.000
or whatever you're studying

00:43:00.000 --> 00:43:02.000
but it's a big barrier and then

00:43:02.000 --> 00:43:04.000
we get to the symbols right

00:43:04.000 --> 00:43:05.000
that the mathematical symbols

00:43:05.000 --> 00:43:07.000
which were a huge advance

00:43:07.000 --> 00:43:10.000
in the way that people talked

00:43:10.000 --> 00:43:11.000
about mathematics but it came

00:43:11.000 --> 00:43:13.000
at a cost prior to you know

00:43:13.000 --> 00:43:15.000
maybe sixteen fifty or so

00:43:17.000 --> 00:43:18.000
written out in words and it

00:43:18.000 --> 00:43:21.000
was clear but it was not sure

00:43:21.000 --> 00:43:23.000
and now when we have our nice

00:43:23.000 --> 00:43:25.000
notation to work with what

00:43:25.000 --> 00:43:27.000
we have is a paragraphs worth

00:43:27.000 --> 00:43:29.000
of information crammed into

00:43:29.000 --> 00:43:31.000
maybe half a line or less right

00:43:31.000 --> 00:43:33.000
so that is an improvement it

00:43:33.000 --> 00:43:34.000
allows us to more efficiently

00:43:34.000 --> 00:43:37.000
talk about math but it also

00:43:37.000 --> 00:43:38.000
allows us to blast through

00:43:38.000 --> 00:43:39.000
a lot of math kinda 

00:43:39.000 --> 00:43:41.000
quickly but if we're going through

00:43:41.000 --> 00:43:43.000
a paragraphs worth of concepts

00:43:43.000 --> 00:43:44.000
in just a second or two of

00:43:44.000 --> 00:43:46.000
notation students can suffer

00:43:46.000 --> 00:43:48.000
from that so it's part of my

00:43:48.000 --> 00:43:49.000
job to make sure that that

00:43:49.000 --> 00:43:51.000
barriers breached as much and

00:43:51.000 --> 00:43:53.000
as soon as possible basically

00:43:53.000 --> 00:43:55.000
we want students to build

00:43:55.000 --> 00:43:56.000
their skills there is that

00:43:56.000 --> 00:43:57.000
left handed the diagram that Dr

00:43:57.000 --> 00:43:59.000
Harrington was talking about I

00:43:59.000 --> 00:43:60.000
also want them to have a nice

00:44:00.000 --> 00:44:01.000
view from thirty thousand feet

00:44:01.000 --> 00:44:03.000
when the opportunity presents

00:44:03.000 --> 00:44:05.000
itself if there's concepts in

00:44:05.000 --> 00:44:07.000
math two fifty four that are

00:44:07.000 --> 00:44:09.000
very parallel to concepts in

00:44:09.000 --> 00:44:10.000
math three forty one I want

00:44:10.000 --> 00:44:11.000
students in that three forty

00:44:11.000 --> 00:44:12.000
one to know that I want them

00:44:12.000 --> 00:44:14.000
to be able to come back and

00:44:14.000 --> 00:44:16.000
re look at the things that

00:44:16.000 --> 00:44:17.000
they didn't have to fifty four

00:44:17.000 --> 00:44:19.000
which have parallels in in math

00:44:19.000 --> 00:44:21.000
three forty one for example

00:44:21.000 --> 00:44:23.000
I mean math is not fun if you

00:44:23.000 --> 00:44:25.000
You are not reasonably confident

00:44:25.000 --> 00:44:27.000
so it's important to me that

00:44:27.000 --> 00:44:29.000
students have repeated triumphs.

00:44:29.000 --> 00:44:31.000
as they go forward they can't

00:44:31.000 --> 00:44:32.000
just struggle and not get

00:44:32.000 --> 00:44:33.000
anything out of it so that's

00:44:33.000 --> 00:44:34.000
a big deal at the builder

00:44:34.000 --> 00:44:36.000
confidence that way and finally

00:44:38.000 --> 00:44:40.000
up there one slide too early

00:44:40.000 --> 00:44:41.000
and you've all been staring

00:44:41.000 --> 00:44:42.000
at it I'll explain now it's

00:44:42.000 --> 00:44:44.000
one of the most beautiful I

00:44:44.000 --> 00:44:45.000
think it is the most beautiful

00:44:45.000 --> 00:44:47.000
equation in math it has the

00:44:47.000 --> 00:44:50.000
five most important constants

00:44:50.000 --> 00:44:51.000
in in the whole alphabet

00:44:51.000 --> 00:44:52.000
of math right so you've got

00:44:52.000 --> 00:44:54.000
that attitude identity zero

00:44:54.000 --> 00:44:56.000
the multiplicative identity

00:44:56.000 --> 00:44:58.000
one these other things right

00:44:58.000 --> 00:44:60.000
there's a pie we all recognize

00:45:00.000 --> 00:45:01.000
pie that's the ratio of the

00:45:01.000 --> 00:45:02.000
circumference to the diameter

00:45:02.000 --> 00:45:04.000
of every circle the base for

00:45:04.000 --> 00:45:05.000
the natural logarithm that's a

00:45:05.000 --> 00:45:07.000
little more obscure it's E.

00:45:07.000 --> 00:45:09.000
as a value about two point

00:45:09.000 --> 00:45:11.000
seven eight irrational there's

00:45:11.000 --> 00:45:13.000
a number that's not even real

00:45:13.000 --> 00:45:14.000
in there that's all I that's

00:45:14.000 --> 00:45:16.000
the square root of minus

00:45:16.000 --> 00:45:17.000
one and so that's not a real

00:45:17.000 --> 00:45:18.000
number but it is a number

00:45:18.000 --> 00:45:20.000
it is an awesome number it's

00:45:20.000 --> 00:45:21.000
incredibly useful in math

00:45:21.000 --> 00:45:23.000
and there they are all five

00:45:23.000 --> 00:45:24.000
of them in one place anybody

00:45:24.000 --> 00:45:25.000
knows where to get a bumper

00:45:25.000 --> 00:45:28.000
sticker that I would love that

00:45:28.000 --> 00:45:30.000
I want to challenge students

00:45:30.000 --> 00:45:31.000
but again I want them to be

00:45:31.000 --> 00:45:33.000
able to succeed so I set high

00:45:33.000 --> 00:45:36.000
bars for them in and then I 

00:45:36.000 --> 00:45:37.000
essentially asking to get

00:45:37.000 --> 00:45:39.000
there but I I don't set is so

00:45:39.000 --> 00:45:40.000
high that the struggle is not

00:45:40.000 --> 00:45:43.000
productive that's a big deal

00:45:43.000 --> 00:45:45.000
then finally once I give them

00:45:45.000 --> 00:45:46.000
enough to go with I get out of

00:45:46.000 --> 00:45:48.000
the way I want to keep talking

00:45:48.000 --> 00:45:49.000
you know I could show them

00:45:49.000 --> 00:45:50.000
an example in that could show

00:45:50.000 --> 00:45:52.000
more complicated example that's

00:45:52.000 --> 00:45:54.000
not really useful they can do

00:45:54.000 --> 00:45:55.000
the more complicated example

00:45:55.000 --> 00:45:57.000
with just a little nudge in in

00:45:57.000 --> 00:45:58.000
their seats so they don't need

00:45:58.000 --> 00:45:61.000
me to show them how to do four

00:46:01.000 --> 00:46:02.000
them before they start their

00:46:02.000 --> 00:46:04.000
homework so I used to lecture

00:46:04.000 --> 00:46:07.000
I love to lecture I'm so smart

00:46:07.000 --> 00:46:08.000
I write all this great stuff

00:46:08.000 --> 00:46:10.000
up on the board and it's it's

00:46:10.000 --> 00:46:12.000
beautiful it's flowing and

00:46:14.000 --> 00:46:17.000
time more than I would like

00:46:17.000 --> 00:46:18.000
to admit in two thousand five

00:46:18.000 --> 00:46:20.000
or six or seven so now I'm a

00:46:20.000 --> 00:46:21.000
lecture but it's probably only

00:46:21.000 --> 00:46:22.000
for ten or fifteen minutes at

00:46:22.000 --> 00:46:24.000
the beginning class at most

00:46:24.000 --> 00:46:26.000
if at all possible. My favorite

00:46:26.000 --> 00:46:29.000
quote I mean there are origins

00:46:29.000 --> 00:46:30.000
to this I don't think anybody

00:46:30.000 --> 00:46:32.000
agrees on them so but I think

00:46:32.000 --> 00:46:34.000
it's true of most people if

00:46:34.000 --> 00:46:35.000
you're doing something you

00:46:35.000 --> 00:46:36.000
get a lot better training that

00:46:36.000 --> 00:46:38.000
just listening about it I think

00:46:38.000 --> 00:46:39.000
Richard would agree with me

00:46:39.000 --> 00:46:40.000
on that one based on her talk

00:46:40.000 --> 00:46:44.000
as well so that leads me to

00:46:44.000 --> 00:46:46.000
sign a piece of the title of

00:46:46.000 --> 00:46:48.000
the talk today is positioning

00:46:48.000 --> 00:46:49.000
the material in this is an

00:46:49.000 --> 00:46:51.000
abstract notion of you know

00:46:51.000 --> 00:46:53.000
more or less how far away do I

00:46:53.000 --> 00:46:55.000
put the material from students

00:46:55.000 --> 00:46:57.000
and so they are sufficiently

00:46:57.000 --> 00:46:59.000
challenged -- but not challenge

00:46:59.000 --> 00:46:61.000
too much if we put it to close

00:47:01.000 --> 00:47:02.000
if we make it look too easy

00:47:02.000 --> 00:47:03.000
for them than they blast

00:47:03.000 --> 00:47:05.000
they don't learn much everybody

00:47:05.000 --> 00:47:06.000
gets an A and nobody takes

00:47:06.000 --> 00:47:07.000
anything away from it really

00:47:07.000 --> 00:47:09.000
they learned too little so a

00:47:09.000 --> 00:47:11.000
little too far away like maybe

00:47:11.000 --> 00:47:12.000
I did in the first couple years

00:47:12.000 --> 00:47:14.000
of advanced calculus then it's

00:47:14.000 --> 00:47:16.000
demoralizing for students and

00:47:16.000 --> 00:47:17.000
that's no good either I mean

00:47:17.000 --> 00:47:18.000
that the best students may it

00:47:18.000 --> 00:47:20.000
may get through it but why put

00:47:20.000 --> 00:47:21.000
everybody else through that

00:47:21.000 --> 00:47:24.000
as well so productive struggle

00:47:24.000 --> 00:47:26.000
it's got to be a struggle for

00:47:26.000 --> 00:47:27.000
it students to the steam the

00:47:27.000 --> 00:47:29.000
material sufficiently man it

00:47:29.000 --> 00:47:31.000
has to be productive or or the

00:47:31.000 --> 00:47:34.000
it just sinks the idea is to

00:47:34.000 --> 00:47:36.000
provide continual infrequent

00:47:36.000 --> 00:47:38.000
reliable moments of discovery

00:47:38.000 --> 00:47:39.000
so that students can build a

00:47:39.000 --> 00:47:41.000
very positive math self image

00:47:41.000 --> 00:47:42.000
and carry that forward so

00:47:42.000 --> 00:47:44.000
let's do another one of those

00:47:44.000 --> 00:47:45.000
discoveries we did the Monty

00:47:45.000 --> 00:47:47.000
hall problem let's let's do

00:47:47.000 --> 00:47:48.000
another one I love baseball

00:47:48.000 --> 00:47:50.000
so I managed to shoehorn a

00:47:50.000 --> 00:47:52.000
baseball reference into my

00:47:52.000 --> 00:47:54.000
talk here -- for those of you

00:47:54.000 --> 00:47:56.000
who are not familiar with --

00:47:56.000 --> 00:47:58.000
the batting average -- it's

00:47:58.000 --> 00:47:59.000
the number of hits over the

00:47:59.000 --> 00:47:60.000
number of it back so player

00:48:00.000 --> 00:48:01.000
goes up to the plate and if

00:48:01.000 --> 00:48:03.000
they have an at bat they

00:48:03.000 --> 00:48:05.000
Either get a hit or they don't and so

00:48:05.000 --> 00:48:06.000
we can look at the proportion

00:48:06.000 --> 00:48:08.000
of hits they got basically all

00:48:08.000 --> 00:48:10.000
right expressed a three decimal

00:48:10.000 --> 00:48:12.000
places and we don't pronounce

00:48:12.000 --> 00:48:14.000
the decimal place so we say

00:48:14.000 --> 00:48:16.000
it so for example last year

00:48:17.000 --> 00:48:19.000
the Red Sox led the Majors in

00:48:19.000 --> 00:48:21.000
batting average with hundred

00:48:21.000 --> 00:48:22.000
eighty hits five hundred twenty

00:48:22.000 --> 00:48:24.000
at bats divide those and get

00:48:24.000 --> 00:48:26.000
three forty six to the third

00:48:26.000 --> 00:48:27.000
decimal place notice I didn't

00:48:27.000 --> 00:48:30.000
pronounce the decimal okay so

00:48:30.000 --> 00:48:31.000
that's that's batting average

00:48:31.000 --> 00:48:33.000
how we calculated so here's the

00:48:33.000 --> 00:48:36.000
puzzler suppose Bryce that's

00:48:36.000 --> 00:48:37.000
three hundred good batting

00:48:37.000 --> 00:48:39.000
average first half of the

00:48:39.000 --> 00:48:41.000
year second half of the year

00:48:41.000 --> 00:48:42.000
that's four hundred that's a

00:48:42.000 --> 00:48:43.000
great batting average that's

00:48:43.000 --> 00:48:44.000
not gonna happen over a whole

00:48:44.000 --> 00:48:46.000
year again I think we'll see

00:48:46.000 --> 00:48:49.000
all right now suppose Rhys

00:48:49.000 --> 00:48:51.000
Bats a less than the Bryce

00:48:51.000 --> 00:48:53.000
to eighty in the first half

00:48:53.000 --> 00:48:54.000
and again really well but a

00:48:54.000 --> 00:48:57.000
little less than Rhys in the

00:48:57.000 --> 00:48:60.000
second half three eighty take

00:49:00.000 --> 00:49:03.000
a minute see if you can parse

00:49:03.000 --> 00:49:06.000
this out think about it is it

00:49:06.000 --> 00:49:08.000
possible reasonable chat about

00:49:08.000 --> 00:49:13.000
it we'll come back in a minute

00:49:13.000 --> 00:49:15.000
is it possible what do you

00:49:15.000 --> 00:49:17.000
think yes or no raise your hand

00:49:17.000 --> 00:49:19.000
if you say yes that's good you

00:49:19.000 --> 00:49:21.000
guys are smart this is awesome

00:49:21.000 --> 00:49:23.000
yes I'm glad you raised your

00:49:23.000 --> 00:49:27.000
You hand Joe. So here is a nice sample of how this can happen. Take a look at

00:49:27.000 --> 00:49:29.000
the numbers for a minute and

00:49:29.000 --> 00:49:31.000
see where we land Bryce ninety

00:49:31.000 --> 00:49:33.000
out of three hundred in the

00:49:33.000 --> 00:49:34.000
first half of the season to

00:49:34.000 --> 00:49:35.000
that division you get three

00:49:35.000 --> 00:49:38.000
hundred as the average forty

00:49:38.000 --> 00:49:39.000
out of a hundred in the second

00:49:39.000 --> 00:49:40.000
half that's a four hundred

00:49:40.000 --> 00:49:41.000
batting average Rhys on

00:49:41.000 --> 00:49:42.000
the other hand twenty eight

00:49:42.000 --> 00:49:45.000
at a hundred and one fourteen

00:49:45.000 --> 00:49:46.000
out of three hundred to get

00:49:46.000 --> 00:49:48.000
the history eighty one we add

00:49:48.000 --> 00:49:49.000
the hits for Rhys we got a

00:49:49.000 --> 00:49:51.000
hundred forty two when we had

00:49:51.000 --> 00:49:52.000
the hits from Bryce we had a

00:49:52.000 --> 00:49:54.000
hundred and thirty also them

00:49:54.000 --> 00:49:56.000
at the same number of at bats

00:49:56.000 --> 00:49:58.000
so there we go how did this

00:49:58.000 --> 00:49:60.000
happen right there average is

00:50:00.000 --> 00:50:01.000
lower in the beginning lower in

00:50:01.000 --> 00:50:03.000
the end but when we aggregated

00:50:03.000 --> 00:50:04.000
together it's higher that's

00:50:04.000 --> 00:50:07.000
crazy well the mystery comes

00:50:07.000 --> 00:50:09.000
from or the solution to the

00:50:09.000 --> 00:50:12.000
mystery arises as a result of

00:50:12.000 --> 00:50:15.000
noticing that Rhys is higher

00:50:15.000 --> 00:50:17.000
average has a big weight attached to it

00:50:17.000 --> 00:50:18.000
there's three hundred at bats

00:50:18.000 --> 00:50:20.000
that go along with that three

00:50:20.000 --> 00:50:22.000
eighty and that tends to pull

00:50:22.000 --> 00:50:24.000
his average up farther and what

00:50:24.000 --> 00:50:27.000
Bryces biggest number of at bats

00:50:27.000 --> 00:50:28.000
go with the lower average down

00:50:28.000 --> 00:50:30.000
here at three hundred so in

00:50:30.000 --> 00:50:31.000
the end that's that's what

00:50:31.000 --> 00:50:32.000
happens this is an example

00:50:32.000 --> 00:50:35.000
of of Simpson's paradox which

00:50:35.000 --> 00:50:37.000
occurs when a trend shows up

00:50:37.000 --> 00:50:39.000
within groups of data but when

00:50:39.000 --> 00:50:40.000
you aggregate and get rid

00:50:40.000 --> 00:50:42.000
Of the group structure of it and

00:50:42.000 --> 00:50:44.000
the trend either vanishes or 

00:50:44.000 --> 00:50:47.000
even worse reverses and you

00:50:47.000 --> 00:50:48.000
don't have to look too far in

00:50:48.000 --> 00:50:50.000
in things like this the sports

00:50:50.000 --> 00:50:53.000
stuff to find these things okay

00:50:53.000 --> 00:50:56.000
so back to a little pedagogical stuff

00:50:56.000 --> 00:50:59.000
 so yeah in two

00:50:59.000 --> 00:50:60.000
thousand five I came here and I

00:51:00.000 --> 00:51:02.000
lectured quite a bit that first

00:51:02.000 --> 00:51:03.000
year -- but I noticed some

00:51:03.000 --> 00:51:05.000
things were going on in some

00:51:05.000 --> 00:51:06.000
of the classes that were really

00:51:06.000 --> 00:51:08.000
making me wonder whether 

00:51:08.000 --> 00:51:09.000
lectures the right thing and

00:51:09.000 --> 00:51:11.000
the reason I noticed those is

00:51:11.000 --> 00:51:13.000
partly because of the content

00:51:13.000 --> 00:51:15.000
itself. It's reasonable to

00:51:15.000 --> 00:51:17.000
think that the course content

00:51:17.000 --> 00:51:19.000
may help us figure out how

00:51:19.000 --> 00:51:21.000
to teach certain classes and

00:51:21.000 --> 00:51:23.000
this is no exception these two

00:51:23.000 --> 00:51:26.000
particular classes for me --

00:51:26.000 --> 00:51:27.000
each gave me a different kind

00:51:27.000 --> 00:51:29.000
epiphany about how

00:51:29.000 --> 00:51:31.000
I ought to teach in in most

00:51:31.000 --> 00:51:34.000
circumstances so -- let me talk

00:51:34.000 --> 00:51:35.000
briefly about both of those

00:51:35.000 --> 00:51:36.000
and then I'll leave you with

00:51:36.000 --> 00:51:39.000
another puzzler. In sequences

00:51:39.000 --> 00:51:40.000
and series this is this is

00:51:40.000 --> 00:51:42.000
calculus three and I'm not

00:51:42.000 --> 00:51:44.000
going to show you any sequences

00:51:44.000 --> 00:51:45.000
or series these are you know

00:51:45.000 --> 00:51:46.000
they're great mathematical

00:51:46.000 --> 00:51:49.000
objects and everything -- but I

00:51:49.000 --> 00:51:51.000
have been persuaded by several

00:51:51.000 --> 00:51:52.000
folks to leave that stuff

00:51:52.000 --> 00:51:57.000
out I think they were right

00:51:57.000 --> 00:51:58.000
calculus one calculus two in

00:51:58.000 --> 00:51:60.000
calculus four and five which

00:52:00.000 --> 00:52:01.000
we don't offer here at Western

00:52:01.000 --> 00:52:03.000
but one two and four they're

00:52:03.000 --> 00:52:05.000
very algorithmic problems those

00:52:05.000 --> 00:52:07.000
problems where you're doing

00:52:07.000 --> 00:52:08.000
some sort of calculation you're

00:52:08.000 --> 00:52:10.000
finding an area under the curve

00:52:10.000 --> 00:52:12.000
or finding the slope of some

00:52:12.000 --> 00:52:14.000
curve at a point of order or

00:52:14.000 --> 00:52:16.000
maybe some pressure to you know

00:52:16.000 --> 00:52:17.000
some physics stuff involved in

00:52:17.000 --> 00:52:19.000
it those are algorithmic those

00:52:19.000 --> 00:52:20.000
are you're you're gonna end up

00:52:20.000 --> 00:52:21.000
crunching some numbers during

00:52:21.000 --> 00:52:23.000
the procedure and coming up

00:52:23.000 --> 00:52:25.000
with a numerical or perhaps an

00:52:25.000 --> 00:52:27.000
answer that's a function at the

00:52:27.000 --> 00:52:28.000
end that is not what is going

00:52:28.000 --> 00:52:30.000
on in sequences and series

00:52:30.000 --> 00:52:32.000
sequences and series there is

00:52:32.000 --> 00:52:35.000
a class in which the students

00:52:35.000 --> 00:52:37.000
have to draw conclusions about

00:52:37.000 --> 00:52:39.000
some property of the sequence

00:52:39.000 --> 00:52:40.000
or the series right does it

00:52:40.000 --> 00:52:42.000
converge whatever that means or

00:52:42.000 --> 00:52:43.000
diverged opposite of whatever

00:52:43.000 --> 00:52:45.000
the first thing meant there is

00:52:45.000 --> 00:52:48.000
not calculation problems those

00:52:48.000 --> 00:52:49.000
are not algorithmic those are

00:52:49.000 --> 00:52:51.000
things where you have to apply

00:52:51.000 --> 00:52:52.000
reasoning and it's not to show

00:52:52.000 --> 00:52:55.000
your work your work is the work

00:52:55.000 --> 00:52:56.000
that's the whole point of the

00:52:56.000 --> 00:52:57.000
problem is to try to make some

00:52:57.000 --> 00:52:60.000
argument and unfortunately at

00:53:00.000 --> 00:53:01.000
every university there's not

00:53:01.000 --> 00:53:04.000
a proof training class that

00:53:04.000 --> 00:53:06.000
comes before calculus three

00:53:06.000 --> 00:53:09.000
so if we're going to adhere

00:53:09.000 --> 00:53:10.000
to the way this material is

00:53:10.000 --> 00:53:12.000
constructed and help teach

00:53:12.000 --> 00:53:13.000
students proofs we have two

00:53:13.000 --> 00:53:15.000
choices you can either put

00:53:15.000 --> 00:53:17.000
an introduction to proofs

00:53:17.000 --> 00:53:18.000
course in front of it as a

00:53:18.000 --> 00:53:20.000
prerequisite to help train them

00:53:20.000 --> 00:53:21.000
for the logical work they're

00:53:21.000 --> 00:53:22.000
going to need to do in that

00:53:22.000 --> 00:53:24.000
class or you can train them

00:53:24.000 --> 00:53:26.000
in the class right and so --

00:53:26.000 --> 00:53:29.000
as the curriculum process goes

00:53:29.000 --> 00:53:31.000
here it just didn't seem right

00:53:31.000 --> 00:53:33.000
to put it two eighty in front

00:53:33.000 --> 00:53:34.000
of the two fifty three so I

00:53:34.000 --> 00:53:37.000
instead decided that I would

00:53:37.000 --> 00:53:38.000
help train the students in

00:53:38.000 --> 00:53:43.000
that at the time and so it's

00:53:43.000 --> 00:53:45.000
still problem solving it's

00:53:45.000 --> 00:53:46.000
just a really different kind

00:53:46.000 --> 00:53:48.000
of problem you're not solving

00:53:48.000 --> 00:53:49.000
a problem looking for a new

00:53:49.000 --> 00:53:51.000
medical or function answer you

00:53:51.000 --> 00:53:54.000
your product is an argument

00:53:54.000 --> 00:53:55.000
and that's a different deal

00:53:55.000 --> 00:53:56.000
and students are not they don't

00:53:56.000 --> 00:53:58.000
see that very often geometry

00:53:58.000 --> 00:53:59.000
in high school to headline

00:53:59.000 --> 00:53:60.000
proofs right you may have

00:54:00.000 --> 00:54:01.000
seen a few of those but that's

00:54:01.000 --> 00:54:05.000
it these aren't line proof either

00:54:05.000 --> 00:54:10.000
so yeah to me talked about this

00:54:10.000 --> 00:54:15.000
so I stand by that statement

00:54:15.000 --> 00:54:17.000
so I went ahead and first I

00:54:17.000 --> 00:54:18.000
published a short paper about

00:54:18.000 --> 00:54:21.000
how this would work and then I

00:54:21.000 --> 00:54:22.000
took that paper and I got rid

00:54:22.000 --> 00:54:23.000
of all the words and started

00:54:23.000 --> 00:54:25.000
adding you know more and more

00:54:25.000 --> 00:54:27.000
Theorems and definitions to

00:54:27.000 --> 00:54:28.000
it, and in the end after

00:54:28.000 --> 00:54:30.000
about four years it had turned

00:54:30.000 --> 00:54:32.000
into a text book thanks work

00:54:32.000 --> 00:54:34.000
works very well it does focus

00:54:34.000 --> 00:54:36.000
on in some elementary logic

00:54:36.000 --> 00:54:37.000
in it and then it focuses on

00:54:37.000 --> 00:54:39.000
the rigor of argument

00:54:39.000 --> 00:54:40.000
since that they are at the

00:54:40.000 --> 00:54:42.000
center of the material another

00:54:42.000 --> 00:54:43.000
thing I put in this book that

00:54:43.000 --> 00:54:45.000
I think is is really important

00:54:45.000 --> 00:54:47.000
is I put more stuff than is

00:54:47.000 --> 00:54:48.000
really necessary to make the

00:54:48.000 --> 00:54:50.000
arguments that what that means

00:54:50.000 --> 00:54:52.000
is that students that take this

00:54:52.000 --> 00:54:53.000
course with that text they have

00:54:53.000 --> 00:54:55.000
an opportunity for multiple

00:54:55.000 --> 00:54:57.000
different passed to a solution

00:54:57.000 --> 00:54:58.000
and that's a big deal right

00:54:58.000 --> 00:54:59.000
that allows them to use the

00:54:59.000 --> 00:54:61.000
right brains and be a little

00:55:01.000 --> 00:55:03.000
creative so I'm particularly

00:55:03.000 --> 00:55:04.000
proud of that notion and I

00:55:04.000 --> 00:55:05.000
love to hear students argue

00:55:05.000 --> 00:55:07.000
about which of the methods is

00:55:07.000 --> 00:55:08.000
better when they're working

00:55:08.000 --> 00:55:09.000
on worksheets in class that

00:55:09.000 --> 00:55:12.000
makes me happy so and in

00:55:12.000 --> 00:55:14.000
particular this sets us up for

00:55:14.000 --> 00:55:16.000
first year students -- getting

00:55:16.000 --> 00:55:18.000
practice at proving theorems

00:55:18.000 --> 00:55:19.000
making these arguments earlier

00:55:19.000 --> 00:55:20.000
than they otherwise would and

00:55:20.000 --> 00:55:22.000
that's a big deal for anybody

00:55:22.000 --> 00:55:23.000
who's taught in upper division

00:55:23.000 --> 00:55:25.000
classes in the room proving

00:55:25.000 --> 00:55:27.000
skills do not come easily they

00:55:27.000 --> 00:55:29.000
take experience and practice

00:55:29.000 --> 00:55:31.000
in the earlier we start on that

00:55:31.000 --> 00:55:32.000
the better and so we can get

00:55:32.000 --> 00:55:34.000
this happening for freshmen I

00:55:34.000 --> 00:55:36.000
think it's a big deal now we

00:55:36.000 --> 00:55:39.000
move to -- advanced calculus

00:55:39.000 --> 00:55:40.000
now this is a completely

00:55:40.000 --> 00:55:41.000
different type of thing I

00:55:41.000 --> 00:55:43.000
lectured as I mentioned in two

00:55:43.000 --> 00:55:44.000
thousand five at a terrific

00:55:44.000 --> 00:55:46.000
textbook, Elementary Analysis

00:55:46.000 --> 00:55:48.000
the Theory of Calculus by

00:55:48.000 --> 00:55:49.000
Ken Ross at the University of

00:55:49.000 --> 00:55:50.000
Oregon it's really well written

00:55:50.000 --> 00:55:52.000
it's a terrific textbook and

00:55:52.000 --> 00:55:54.000
so I took the stuff from that

00:55:54.000 --> 00:55:56.000
I put it up on the board I made

00:55:56.000 --> 00:55:58.000
these beautiful presentations

00:55:58.000 --> 00:55:59.000
for students and then they

00:55:59.000 --> 00:55:60.000
would go off and dutifiy if we do

00:56:00.000 --> 00:56:01.000
their homework and they would

00:56:01.000 --> 00:56:03.000
return it to me and it brought

00:56:03.000 --> 00:56:04.000
all the harm hallmarks of just

00:56:04.000 --> 00:56:05.000
praying to the gods of partial

00:56:05.000 --> 00:56:07.000
credit and that and they just

00:56:07.000 --> 00:56:09.000
weren't getting there and so

00:56:09.000 --> 00:56:10.000
I double down right at work

00:56:10.000 --> 00:56:12.000
hard on my lectures and I tried

00:56:12.000 --> 00:56:13.000
to make them smarter and show

00:56:13.000 --> 00:56:15.000
the students more and nothing

00:56:15.000 --> 00:56:16.000
else happened it was exactly

00:56:16.000 --> 00:56:18.000
the same and so by the end of

00:56:18.000 --> 00:56:20.000
the third year I realize that

00:56:20.000 --> 00:56:21.000
something else had happened

00:56:21.000 --> 00:56:24.000
in this course so what I did I

00:56:24.000 --> 00:56:25.000
decided to try to use the Moore

00:56:25.000 --> 00:56:27.000
Method. The Moore Method was a

00:56:27.000 --> 00:56:29.000
a method of teaching and I use

00:56:29.000 --> 00:56:31.000
that term loosely -- invented

00:56:31.000 --> 00:56:32.000
by or discovered no one knows

00:56:32.000 --> 00:56:33.000
which it is right it's a

00:56:33.000 --> 00:56:35.000
math thing so it's invented

00:56:35.000 --> 00:56:37.000
or discovered I don't know what it is

00:56:37.000 --> 00:56:38.000
L.L. Moore of the University of Texas

00:56:38.000 --> 00:56:40.000
at Austin has produced more

00:56:40.000 --> 00:56:44.000
PhD -- mathematicians as his

00:56:44.000 --> 00:56:47.000
advicees than anyone still

00:56:47.000 --> 00:56:48.000
to this day by a factor of a

00:56:48.000 --> 00:56:51.000
lot. So it works really well

00:56:51.000 --> 00:56:54.000
to produce PhD mathematicians

00:56:54.000 --> 00:56:56.000
but after a couple years it

00:56:56.000 --> 00:56:57.000
became clear that it didn't

00:56:57.000 --> 00:56:61.000
work really that well -- for --

00:57:01.000 --> 00:57:02.000
helping undergraduate students

00:57:02.000 --> 00:57:04.000
get to the end of the advanced 

00:57:04.000 --> 00:57:06.000
calculus so I modified right

00:57:06.000 --> 00:57:08.000
So the idea then is I took

00:57:08.000 --> 00:57:09.000
this long list of the theorems 

00:57:09.000 --> 00:57:11.000
that I used in the Moore Method

00:57:11.000 --> 00:57:14.000
and I tweaked it into a list of

00:57:14.000 --> 00:57:16.000
definitions, theorems, axioms and

00:57:16.000 --> 00:57:18.000
all that so that some of them

00:57:18.000 --> 00:57:19.000
Were homework problems and some

00:57:19.000 --> 00:57:21.000
of them are ones that students

00:57:21.000 --> 00:57:22.000
have to present in front of

00:57:22.000 --> 00:57:27.000
the class without notes and

00:57:27.000 --> 00:57:30.000
get critique that is a big step

00:57:30.000 --> 00:57:32.000
that's a big step students --

00:57:32.000 --> 00:57:35.000
are terrified frankly but for

00:57:35.000 --> 00:57:36.000
that first one and then they

00:57:36.000 --> 00:57:37.000
get up there and they know

00:57:37.000 --> 00:57:38.000
they're in front of friends

00:57:38.000 --> 00:57:40.000
in the in the you know they

00:57:40.000 --> 00:57:41.000
see that we critique them

00:57:41.000 --> 00:57:43.000
gently everybody's professional

00:57:43.000 --> 00:57:45.000
there's a sort of set of rules

00:57:45.000 --> 00:57:46.000
that we have applied in that

00:57:46.000 --> 00:57:48.000
class to make sure nobody takes

00:57:48.000 --> 00:57:50.000
it on the chin too hard that's

00:57:50.000 --> 00:57:51.000
most of the time by the time

00:57:51.000 --> 00:57:53.000
they get to advanced calculus

00:57:53.000 --> 00:57:54.000
they've done enough work that

00:57:54.000 --> 00:57:56.000
they can handle this material

00:57:56.000 --> 00:57:58.000
they're just not sure of that

00:57:58.000 --> 00:57:60.000
in the first week or two maybe

00:58:00.000 --> 00:58:01.000
three or four it depends on

00:58:01.000 --> 00:58:03.000
the students and the material

00:58:03.000 --> 00:58:05.000
so but those present up in

00:58:05.000 --> 00:58:06.000
front of the class and that's

00:58:06.000 --> 00:58:08.000
about half the grades the six

00:58:08.000 --> 00:58:09.000
or seven presentations is non

00:58:09.000 --> 00:58:12.000
trivial but -- it is in some

00:58:12.000 --> 00:58:14.000
sense a trial by fire and

00:58:14.000 --> 00:58:16.000
eventually it works for every

00:58:16.000 --> 00:58:17.000
single student I've had in

00:58:17.000 --> 00:58:19.000
those classes it it gets you

00:58:19.000 --> 00:58:22.000
there it's just an incredible

00:58:22.000 --> 00:58:24.000
struggle for them and it's such

00:58:24.000 --> 00:58:26.000
a struggle you know when they

00:58:26.000 --> 00:58:27.000
they have to go think deeply

00:58:27.000 --> 00:58:29.000
about a problem for several

00:58:29.000 --> 00:58:32.000
days maybe weeks this is what

00:58:32.000 --> 00:58:35.000
happens right you get it you

00:58:35.000 --> 00:58:37.000
got to school and don't remember how you got there because you were

00:58:38.000 --> 00:58:39.000
thinking how to prove some

00:58:39.000 --> 00:58:42.000
function is uniformly continues

00:58:42.000 --> 00:58:43.000
you know they wake up

00:58:43.000 --> 00:58:44.000
with ideas in the middle of the

00:58:44.000 --> 00:58:45.000
night and that's when I know I

00:58:45.000 --> 00:58:47.000
got out that's that's that's a

00:58:47.000 --> 00:58:49.000
mathematician so that's that's

00:58:49.000 --> 00:58:51.000
a terrific thing I think --

00:58:51.000 --> 00:58:53.000
and they are wiped they don't

00:58:53.000 --> 00:58:55.000
want to see me again until they

00:58:55.000 --> 00:58:56.000
come back to the next alumni

00:58:56.000 --> 00:58:58.000
picnic and that's fair but

00:58:58.000 --> 00:58:59.000
when they do come back most

00:58:59.000 --> 00:58:61.000
of them thank me for putting

00:59:01.000 --> 00:59:02.000
them through that that always

00:59:02.000 --> 00:59:04.000
makes me feel good and I do

00:59:04.000 --> 00:59:06.000
appreciate that so that's the

00:59:06.000 --> 00:59:08.000
pedagogical stuff let's let's

00:59:08.000 --> 00:59:13.000
dive into one more puzzler

00:59:13.000 --> 00:59:14.000
again if you seen this one

00:59:14.000 --> 00:59:15.000
don't blurted out right

00:59:15.000 --> 00:59:20.000
away how can this happen

00:59:20.000 --> 00:59:22.000
all the same components so

00:59:22.000 --> 00:59:24.000
I guess we could call them

00:59:24.000 --> 00:59:28.000
all right in triangles A and B

00:59:28.000 --> 00:59:30.000
get the two little Tetris pieces right. Two and five for the

00:59:30.000 --> 00:59:32.000
yellow and three and five for

00:59:36.000 --> 00:59:37.000
and the two tri in the red

00:59:37.000 --> 00:59:41.000
in the the blue triangles

00:59:41.000 --> 00:59:47.000
how do you rearrange them and lose a square?

00:59:47.000 --> 00:59:51.000
take a minute or two

00:59:51.000 --> 00:59:54.000
take a careful look at the blue

00:59:54.000 --> 00:59:56.000
and the red triangle now if

00:59:56.000 --> 00:59:59.000
they fit perfectly into the big

00:59:59.000 --> 00:59:60.000
triangle they have to have the

01:00:00.000 --> 01:00:02.000
same rise over run they they

01:00:02.000 --> 01:00:04.000
have to have the same you know

01:00:04.000 --> 01:00:06.000
the length and height right so

01:00:06.000 --> 01:00:09.000
so if we look at triangle A when

01:00:09.000 --> 01:00:11.000
we gonna look at it over here because

01:00:11.000 --> 01:00:12.000
it's not that wide like I'm

01:00:12.000 --> 01:00:14.000
looking at their what we have

01:00:14.000 --> 01:00:16.000
we have five in the base of

01:00:16.000 --> 01:00:18.000
of the blue in triangle A

01:00:18.000 --> 01:00:20.000
and then and then two. 

01:00:20.000 --> 01:00:22.000
So then that slope is then 

01:00:22.000 --> 01:00:23.000
I guess two fifths rise over

01:00:23.000 --> 01:00:26.000
run. so the ratio of the hight of the

01:00:26.000 --> 01:00:28.000
triangle to the base is two over

01:00:28.000 --> 01:00:32.000
five but look at the red one

01:00:32.000 --> 01:00:33.000
with that three over eight

01:00:33.000 --> 01:00:35.000
You have three vertical and

01:00:35.000 --> 01:00:37.000
eight horizontal so those

01:00:37.000 --> 01:00:38.000
don't have the same slope so

01:00:38.000 --> 01:00:40.000
what you are seeing there is

01:00:40.000 --> 01:00:43.000
two not triangles if you look

01:00:43.000 --> 01:00:45.000
carefully the the the triangle A

01:00:45.000 --> 01:00:47.000
has a little cusp in it

01:00:47.000 --> 01:00:50.000
just barely and triangle

01:00:50.000 --> 01:00:51.000
B has a little bump in it

01:00:51.000 --> 01:00:55.000
the hypotenuse so yeah it just

01:00:55.000 --> 01:00:56.000
careful examination will always

01:00:56.000 --> 01:00:58.000
get you this now if you did

01:00:58.000 --> 01:00:59.000
this with triangles that over

01:00:59.000 --> 01:00:61.000
thousands of good things it

01:01:01.000 --> 01:01:02.000
would you know it's harder but

01:01:02.000 --> 01:01:03.000
the small ones we could parse

01:01:03.000 --> 01:01:05.000
out if we pay careful enough

01:01:05.000 --> 01:01:07.000
attention okay again thank

01:01:07.000 --> 01:01:09.000
you -- for listening today

01:01:09.000 --> 01:01:14.000
I appreciate it. 

01:01:14.000 --> 01:01:15.000
What's obvious is that 

01:01:15.000 --> 01:01:17.000
I need more coffee this time of day

01:01:17.000 --> 01:01:18.000
 to do these puzzlers

01:01:18.000 --> 01:01:20.000
but it's a really enjoyable

01:01:20.000 --> 01:01:21.000
to be a student a classroom

01:01:21.000 --> 01:01:23.000
and that's what we saw 

01:01:23.000 --> 01:01:25.000
this afternoon. It's also a

01:01:25.000 --> 01:01:27.000
great time of the year to 

01:01:27.000 --> 01:01:29.000
a celebrate this award

01:01:29.000 --> 01:01:31.000
here after year after year

01:01:31.000 --> 01:01:32.000
in a beautiful spring day as

01:01:32.000 --> 01:01:34.000
well and it also on server

01:01:34.000 --> 01:01:36.000
launch pad for next week --

01:01:36.000 --> 01:01:37.000
with our academic excellence

01:01:37.000 --> 01:01:39.000
showcase and it's a example 

01:01:39.000 --> 01:01:41.000
of what makes Western so

01:01:41.000 --> 01:01:44.000
special. I also want to

01:01:44.000 --> 01:01:46.000
before bring Cheryl up

01:01:51.000 --> 01:01:52.000
Rachel talked about Cheryl so 

01:01:52.000 --> 01:01:56.000
but I'd like to ask those

01:01:56.000 --> 01:01:57.000
committee members who are here

01:01:57.000 --> 01:01:59.000
to -- stand to be recognized

01:01:59.000 --> 01:01:60.000
for the selection process so

01:02:00.000 --> 01:02:02.000
feel to be recognized for their

01:02:02.000 --> 01:02:06.000
Award. Thank you and stay standing.

01:02:06.000 --> 01:02:08.000
I know we have a number of

01:02:08.000 --> 01:02:09.000
other previous award winners

01:02:09.000 --> 01:02:11.000
in the room when I like those

01:02:11.000 --> 01:02:12.000
individuals stand and join

01:02:12.000 --> 01:02:13.000
the the previous selection

01:02:13.000 --> 01:02:16.000
committee because it's so

01:02:16.000 --> 01:02:18.000
this is a this is the legacy

01:02:18.000 --> 01:02:21.000
thank you talk about going

01:02:21.000 --> 01:02:22.000
back forty years this is the

01:02:22.000 --> 01:02:24.000
legacy upon which the DNA of

01:02:24.000 --> 01:02:26.000
Western is so proud and

01:02:26.000 --> 01:02:28.000
and makes it so special to

01:02:28.000 --> 01:02:30.000
be here and and celebrate 

01:02:30.000 --> 01:02:31.000
teaching and scholarship 

01:02:31.000 --> 01:02:32.000
together and I think that's

01:02:32.000 --> 01:02:34.000
what is part of our mission

01:02:34.000 --> 01:02:35.000
which makes us distinctive in

01:02:35.000 --> 01:02:37.000
so many different ways and 

01:02:37.000 --> 01:02:39.000
so I don't know if...

01:02:39.000 --> 01:02:41.000
Learned new terms, Mathies, I haven't

01:02:41.000 --> 01:02:42.000
heard that in awhile so it was

01:02:42.000 --> 01:02:44.000
great at the love that -- and

01:02:44.000 --> 01:02:46.000
then pi day knew about -- but

01:02:48.000 --> 01:02:51.000
the year but one puzzle within a

01:02:51.000 --> 01:02:53.000
puzzle and I'll ask Rachel 

01:02:53.000 --> 01:02:55.000
And Scott to come forward is

01:02:55.000 --> 01:02:57.000
in Rachel's presentation 

01:02:57.000 --> 01:02:59.000
there was a little indicator

01:02:59.000 --> 01:02:61.000
of what was in her bio and also

01:03:01.000 --> 01:03:03.000
in the introduction and that

01:03:03.000 --> 01:03:05.000
was in the first photograph of

01:03:05.000 --> 01:03:06.000
a family you may have noticed

01:03:06.000 --> 01:03:08.000
or not noticed that she was

01:03:08.000 --> 01:03:13.000
wearing the Steelers t-shirt

01:03:13.000 --> 01:03:15.000
yeah yeah yeah and so that

01:03:15.000 --> 01:03:16.000
that was that was evidence

01:03:16.000 --> 01:03:18.000
of that that was true and

01:03:18.000 --> 01:03:19.000
and so the question for Scott is

01:03:19.000 --> 01:03:20.000
which baseball team's your

01:03:20.000 --> 01:03:22.000
favorite? Phillies. Phillies okay.

01:03:22.000 --> 01:03:24.000
good good and and that was a

01:03:24.000 --> 01:03:26.000
great story I'm a baseball fan

01:03:26.000 --> 01:03:27.000
as well so I actually got the

01:03:27.000 --> 01:03:28.000
RBI one right the other one not

01:03:28.000 --> 01:03:31.000
so much better but I I would

01:03:31.000 --> 01:03:32.000
like to ask both Rachel 

01:03:32.000 --> 01:03:33.000
and Scott to come forward and receive

01:03:33.000 --> 01:03:37.000
their certificates as

01:03:37.000 --> 01:03:40.000
well as their awards.

01:03:41.000 --> 01:03:47.000
So Scott, this is yours. Thank you so much I appreciate it.

01:03:47.000 --> 01:03:54.000
Rachel, and this is yours.

01:03:54.000 --> 01:03:55.000
and please join me in one

01:03:55.000 --> 01:03:57.000
last round of applause for Scott and

01:03:57.000 --> 01:03:59.000
Rachel and all the other award

01:03:59.000 --> 01:03:60.000
winners who are part of this

01:04:00.000 --> 01:04:02.000
the legacy as we add two

01:04:02.000 --> 01:04:04.000
more this year and so it's a

01:04:04.000 --> 01:04:05.000
wonderful opportunity for us to

01:04:05.000 --> 01:04:07.000
celebrate the accomplishments

01:04:07.000 --> 01:04:09.000
of two of our best faculty 

01:04:09.000 --> 01:04:10.000
in the work that they do both

01:04:10.000 --> 01:04:11.000
in teaching and scholarship

01:04:11.000 --> 01:04:13.000
and  it's what

01:04:13.000 --> 01:04:15.000
makes the university so

01:04:15.000 --> 01:04:23.000
vibrant so thank you for that.

01:04:23.000 --> 01:04:25.000
Great day to celebrate

01:04:25.000 --> 01:04:26.000
this accomplishment

01:04:26.000 --> 01:04:28.000
thank you for coming out.