WEBVTT 00:00:00.000 --> 00:00:01.000 music 00:00:01.000 --> 00:00:03.000 welcome to the 2019 00:00:03.000 --> 00:00:08.000 Mario and Alma Pastega Awards Event 00:00:08.000 --> 00:00:09.000 so pleased to see all of you 00:00:09.000 --> 00:00:11.000 here together to celebrate 00:00:11.000 --> 00:00:12.000 our colleagues accomplishments 00:00:12.000 --> 00:00:14.000 and recognition as you all 00:00:14.000 --> 00:00:15.000 probably know this is the 00:00:15.000 --> 00:00:17.000 highest award that we offer 00:00:17.000 --> 00:00:19.000 faculty at Western Oregon 00:00:19.000 --> 00:00:21.000 University I was looking back 00:00:21.000 --> 00:00:22.000 through how many how many 00:00:22.000 --> 00:00:24.000 award recipients do you think 00:00:24.000 --> 00:00:30.000 we've had for research? Any guesses? 00:00:30.000 --> 00:00:31.000 you quickly look in the 00:00:31.000 --> 00:00:33.000 brochure in cal this is the 00:00:33.000 --> 00:00:34.000 fortieth I think this is the 00:00:34.000 --> 00:00:35.000 fortieth one we used to call 00:00:35.000 --> 00:00:37.000 the faculty honors award 00:00:37.000 --> 00:00:40.000 six years later -- we develop 00:00:40.000 --> 00:00:42.000 the the award for teaching I 00:00:42.000 --> 00:00:43.000 believe the year after that 00:00:43.000 --> 00:00:46.000 we develop the staff award 00:00:46.000 --> 00:00:47.000 the Mario and Alma Patega 00:00:47.000 --> 00:00:50.000 Staff Award. so today we're 00:00:50.000 --> 00:00:51.000 going to honor both doctor 00:00:51.000 --> 00:00:53.000 Scott Beaver and doctor Rachel 00:00:53.000 --> 00:00:55.000 Harrington. They are going to have 00:00:55.000 --> 00:00:57.000 some presentations -- to share 00:00:57.000 --> 00:00:59.000 with us so I'm very excited 00:00:59.000 --> 00:00:61.000 to be able to introduce the 00:01:01.000 --> 00:01:02.000 Rachel Harrington my friend 00:01:02.000 --> 00:01:03.000 and colleague and I brought 00:01:03.000 --> 00:01:06.000 some notes because I could 00:01:06.000 --> 00:01:07.000 talk about Rachel for hours 00:01:07.000 --> 00:01:08.000 and also because I promised 00:01:08.000 --> 00:01:10.000 Rachel that I wouldn't cry 00:01:10.000 --> 00:01:11.000 and they wouldn't be could 00:01:11.000 --> 00:01:13.000 cry because we really have a long history of 00:01:13.000 --> 00:01:17.000 crying together actually 00:01:17.000 --> 00:01:19.000 think of academics as being 00:01:19.000 --> 00:01:21.000 people who are maybe specialize 00:01:21.000 --> 00:01:23.000 only in one thing or maybe not 00:01:23.000 --> 00:01:25.000 well rounded but Rachel Harrington is 00:01:25.000 --> 00:01:27.000 a very well rounded person I 00:01:27.000 --> 00:01:29.000 think is the renaissance women 00:01:29.000 --> 00:01:30.000 if you don't know Rachel 00:01:30.000 --> 00:01:33.000 very well we chose not only an 00:01:33.000 --> 00:01:34.000 amazing teacher and researcher 00:01:34.000 --> 00:01:36.000 bat she loves the Pittsburgh 00:01:36.000 --> 00:01:38.000 Steelers she will give you 00:01:38.000 --> 00:01:40.000 great canning recipes over the 00:01:40.000 --> 00:01:41.000 summer for how to make 00:01:41.000 --> 00:01:43.000 Zucchini relish and I think 00:01:43.000 --> 00:01:44.000 of her whenever I eat zucchini 00:01:44.000 --> 00:01:46.000 relish now she grew up in 00:01:46.000 --> 00:01:48.000 a tiny town in Southeastern 00:01:48.000 --> 00:01:50.000 Alaska and she comes from a 00:01:50.000 --> 00:01:52.000 big family and she worked in 00:01:52.000 --> 00:01:53.000 the cannery and has worked shift 00:01:53.000 --> 00:01:54.000 work and then all sorts of 00:01:54.000 --> 00:01:56.000 interesting things and I think 00:01:56.000 --> 00:01:58.000 because of that many of our 00:01:58.000 --> 00:01:59.000 students here at Western really 00:01:59.000 --> 00:01:61.000 you can relate to that meant 00:02:01.000 --> 00:02:03.000 they relate to you and you 00:02:03.000 --> 00:02:05.000 know you just bring a practical 00:02:05.000 --> 00:02:07.000 common sense no nonsense 00:02:07.000 --> 00:02:09.000 notion to so many things 00:02:09.000 --> 00:02:11.000 you do and frankly academia 00:02:11.000 --> 00:02:12.000 really needs that. 00:02:12.000 --> 00:02:14.000 I love that about you but 00:02:14.000 --> 00:02:16.000 at the same time Rachel is 00:02:16.000 --> 00:02:17.000 one of the most talented 00:02:17.000 --> 00:02:18.000 teachers I've ever known 00:02:18.000 --> 00:02:22.000 And I know a lot of teachers. 00:02:22.000 --> 00:02:25.000 She can take advanced concepts and make them accessible to students 00:02:25.000 --> 00:02:28.000 in really amazing ways. She leads graduate students through 00:02:28.000 --> 00:02:32.000 advanced research projects and thesis work. 00:02:32.000 --> 00:02:35.000 She builds their identities as writers and researchers. 00:02:35.000 --> 00:02:38.000 Many of her students have published in professional journalism 00:02:38.000 --> 00:02:42.000 and newsletters and just the other day she was running down the hall 00:02:42.000 --> 00:02:45.000 Showing us a published article from one of her 00:02:45.000 --> 00:02:48.000 former students, in Teaching Children Mathematics which is 00:02:48.000 --> 00:02:52.000 the journal in mathematics education 00:02:52.000 --> 00:02:55.000 And when I suggested to Rachel that that was part of the 00:02:55.000 --> 00:02:58.000 seeds she had planted with this student she refused 00:02:58.000 --> 00:02:65.000 to take any acceptance for that, but I know that teachers are inspired by Rachel. 00:03:05.000 --> 00:03:12.000 To not only be math teacher but also mathematicians and teacher researchers. 00:03:12.000 --> 00:03:13.000 Rachel is an amazing colleague and many 00:03:13.000 --> 00:03:14.000 her colleagues here in the 00:03:14.000 --> 00:03:16.000 division and outside of the 00:03:16.000 --> 00:03:18.000 division are here today. 00:03:18.000 --> 00:03:20.000 she's the type of friend and colleague 00:03:20.000 --> 00:03:21.000 Who pays attention when 00:03:21.000 --> 00:03:22.000 people are having a bad day 00:03:22.000 --> 00:03:23.000 and she suggests that you go 00:03:23.000 --> 00:03:25.000 get a coffee treat to make 00:03:25.000 --> 00:03:27.000 it better she's always the 00:03:27.000 --> 00:03:29.000 first one to use fractions 00:03:29.000 --> 00:03:30.000 to make everything just a 00:03:30.000 --> 00:03:34.000 little bit better. Don't worry Marie were one fourth 00:03:34.000 --> 00:03:35.000 Of the way through EDTPA 00:03:35.000 --> 00:03:38.000 We have almost graded two thirds of the lit reviews. 00:03:38.000 --> 00:03:41.000 but she's also the first 00:03:41.000 --> 00:03:44.000 person to arrange meals for a 00:03:44.000 --> 00:03:46.000 colleague in need or to go to 00:03:46.000 --> 00:03:47.000 bat with leadership for someone 00:03:47.000 --> 00:03:50.000 who deserves a fair shake -- I 00:03:50.000 --> 00:03:51.000 just simply listen when people 00:03:51.000 --> 00:03:54.000 need good advice she's also 00:03:54.000 --> 00:03:55.000 an excellent adviser entry 00:03:55.000 --> 00:03:57.000 leader for students she'll sit and 00:03:57.000 --> 00:03:58.000 counselor teacher candidating 00:03:58.000 --> 00:03:60.000 crisis and listen to them so 00:04:00.000 --> 00:04:03.000 carefully and carrying but she will 00:04:03.000 --> 00:04:05.000 also give students a straight 00:04:05.000 --> 00:04:07.000 talk when they need to hear it 00:04:07.000 --> 00:04:09.000 a few years ago Rachel and I 00:04:09.000 --> 00:04:10.000 right before we were going on 00:04:10.000 --> 00:04:11.000 sabbatical and had a little bit 00:04:11.000 --> 00:04:13.000 of senioritis ourselves 00:04:13.000 --> 00:04:15.000 We lead a group of lively 00:04:15.000 --> 00:04:18.000 MATers here you were finishing 00:04:18.000 --> 00:04:20.000 their action research project 00:04:20.000 --> 00:04:21.000 each week Rachel and I would joke 00:04:21.000 --> 00:04:24.000 about to be good cop or bad 00:04:24.000 --> 00:04:26.000 cop to motivate the students to 00:04:26.000 --> 00:04:28.000 finish their projects the end 00:04:28.000 --> 00:04:30.000 result can wear both hats well 00:04:30.000 --> 00:04:32.000 she knows how to give that pep 00:04:32.000 --> 00:04:34.000 talk when students need it but 00:04:34.000 --> 00:04:36.000 she also knows how to gently 00:04:36.000 --> 00:04:37.000 and firmly direct students back 00:04:37.000 --> 00:04:40.000 on the path she's an amazing 00:04:40.000 --> 00:04:42.000 teacher I know because I could 00:04:42.000 --> 00:04:43.000 Co taught with her probably a dozen 00:04:43.000 --> 00:04:46.000 times now -- every time I learn 00:04:46.000 --> 00:04:47.000 something new and I become a 00:04:47.000 --> 00:04:48.000 better teacher for working with 00:04:48.000 --> 00:04:50.000 her she's creative, she's 00:04:50.000 --> 00:04:52.000 organized, she's well prepared 00:04:52.000 --> 00:04:55.000 she student centered, she is 00:04:55.000 --> 00:04:56.000 beloved by her students I see 00:04:56.000 --> 00:04:58.000 a couple of her students here 00:04:58.000 --> 00:04:62.000 today and for good reason and it's not jus the "mathies" 00:05:02.000 --> 00:05:03.000 these as I like to call them 00:05:03.000 --> 00:05:05.000 who love Rachel. Rachel 00:05:05.000 --> 00:05:07.000 teachers are future elementary 00:05:07.000 --> 00:05:08.000 students many of whom will 00:05:08.000 --> 00:05:10.000 come in and say well I don't 00:05:10.000 --> 00:05:11.000 think I'm very good at math 00:05:11.000 --> 00:05:15.000 I can't do math and she will not allow that. 00:05:15.000 --> 00:05:18.000 she helps them to love and 00:05:18.000 --> 00:05:19.000 have a rich tool box and then 00:05:19.000 --> 00:05:21.000 Amazing ways to make math 00:05:21.000 --> 00:05:23.000 meaningful and transformational 00:05:23.000 --> 00:05:25.000 to children and she does 00:05:25.000 --> 00:05:26.000 this because she has a huge 00:05:26.000 --> 00:05:28.000 passion for math education 00:05:28.000 --> 00:05:30.000 in mathematical thinking and 00:05:30.000 --> 00:05:32.000 she builds advocacy in future 00:05:32.000 --> 00:05:34.000 teachers she's just a can do person 00:05:34.000 --> 00:05:36.000 And students leave her 00:05:36.000 --> 00:05:37.000 class with the how and why of 00:05:37.000 --> 00:05:40.000 math education so like I said 00:05:40.000 --> 00:05:41.000 she's about growth mindset 00:05:41.000 --> 00:05:42.000 you are not allowed to tell 00:05:42.000 --> 00:05:43.000 Rachel that you're not good 00:05:43.000 --> 00:05:45.000 at math she will not listen 00:05:45.000 --> 00:05:47.000 to that it's not allowed and 00:05:47.000 --> 00:05:49.000 she will humbly but I also think a little b 00:05:49.000 --> 00:05:50.000 bit probably share her own 00:05:50.000 --> 00:05:53.000 AP math test score with her 00:05:53.000 --> 00:05:57.000 future students to show that it's not where 00:05:57.000 --> 00:05:58.000 you start it's where you 00:05:58.000 --> 00:05:60.000 end up and then standardized 00:06:00.000 --> 00:06:02.000 assessments are not indicative 00:06:02.000 --> 00:06:06.000 of potential even as a mathie she 00:06:06.000 --> 00:06:07.000 knows why children should 00:06:07.000 --> 00:06:09.000 never be accessed only through 00:06:09.000 --> 00:06:11.000 quantitative measures and are 00:06:11.000 --> 00:06:12.000 you strongly for why qualitative 00:06:12.000 --> 00:06:14.000 details matter her teaching 00:06:14.000 --> 00:06:16.000 and research illustrate this 00:06:16.000 --> 00:06:18.000 learners are so much more 00:06:18.000 --> 00:06:19.000 than numbers in her classroom 00:06:19.000 --> 00:06:22.000 And in her research she makes 00:06:22.000 --> 00:06:23.000 math fun and meaningful and 00:06:23.000 --> 00:06:24.000 important to everyone who 00:06:24.000 --> 00:06:26.000 knows her and certainly to our 00:06:26.000 --> 00:06:28.000 students she wears fun math pun t-shirts 00:06:28.000 --> 00:06:31.000 has geometry themed Toms 00:06:31.000 --> 00:06:34.000 and she owns several "pi" P-I 00:06:34.000 --> 00:06:38.000 inspired pie plates. PI day March 14 00:06:38.000 --> 00:06:41.000 for those non mathies out there 00:06:41.000 --> 00:06:42.000 national holiday and Rachel's 00:06:42.000 --> 00:06:44.000 life and now in the 00:06:44.000 --> 00:06:46.000 college of education students 00:06:46.000 --> 00:06:49.000 Sing pi themed carols, create pi themed art 00:06:49.000 --> 00:06:51.000 and of course devour pi treats 00:06:51.000 --> 00:06:54.000 In her classes. Back to that Renaissance woman 00:06:54.000 --> 00:06:55.000 She makes all of her pie crust. 00:06:55.000 --> 00:06:58.000 from scratch it's like a family pride. 00:06:58.000 --> 00:06:62.000 Thank you Maria. 00:07:02.000 --> 00:07:03.000 I just wanted to start off today 00:07:03.000 --> 00:07:05.000 by a first acknowledging my 00:07:05.000 --> 00:07:07.000 colleague Scott Beaver it's 00:07:07.000 --> 00:07:09.000 an honor to be speaking with 00:07:09.000 --> 00:07:10.000 him today Scott and I actually 00:07:10.000 --> 00:07:12.000 have a lot in common we were 00:07:12.000 --> 00:07:15.000 both from Alaska we both lived 00:07:15.000 --> 00:07:16.000 in Pennsylvania for awhile we 00:07:16.000 --> 00:07:18.000 both studied math and we both 00:07:18.000 --> 00:07:21.000 think Cheryl Beaver is awesome 00:07:21.000 --> 00:07:23.000 I've noticed that about us 00:07:23.000 --> 00:07:24.000 I also want to acknowledge the 00:07:24.000 --> 00:07:25.000 Pastega family I don't 00:07:25.000 --> 00:07:27.000 know if they're any one of 00:07:27.000 --> 00:07:28.000 them was able to make it today 00:07:28.000 --> 00:07:30.000 but once a month I 00:07:30.000 --> 00:07:32.000 go to a support group at the 00:07:32.000 --> 00:07:34.000 Pastega Cancer Research Center 00:07:34.000 --> 00:07:36.000 in Corvallis my mother in 00:07:36.000 --> 00:07:38.000 law hooked up her RV 00:07:38.000 --> 00:07:40.000 into the Pastega house for 00:07:40.000 --> 00:07:41.000 three weeks while her husband 00:07:41.000 --> 00:07:42.000 was in the hospital my children 00:07:42.000 --> 00:07:43.000 go through the Pastega 00:07:43.000 --> 00:07:45.000 Christmas lights every year 00:07:45.000 --> 00:07:48.000 for five times and I just we 00:07:48.000 --> 00:07:51.000 We have a Pastega room in our building I just I've considered 00:07:51.000 --> 00:07:52.000 a great honor to be associated 00:07:52.000 --> 00:07:54.000 with this family and I'm very 00:07:54.000 --> 00:07:57.000 very proud of this award today 00:07:57.000 --> 00:07:59.000 I also want to think -- Marie 00:07:59.000 --> 00:07:61.000 Marie is probably my closest 00:08:01.000 --> 00:08:03.000 friend here at Western over the 00:08:03.000 --> 00:08:04.000 years and we've been through 00:08:04.000 --> 00:08:06.000 a lot together a lot of tears 00:08:06.000 --> 00:08:07.000 I was nervous about today's 00:08:07.000 --> 00:08:09.000 preparation -- presentation so 00:08:09.000 --> 00:08:10.000 I made the mistake of watching 00:08:10.000 --> 00:08:12.000 Marie's talk from last year 00:08:12.000 --> 00:08:14.000 and -- when it got done they 00:08:14.000 --> 00:08:16.000 told my husband I do not want 00:08:16.000 --> 00:08:18.000 to do this now I just watched 00:08:18.000 --> 00:08:20.000 I just watched Marie's and I feel way worse and he 00:08:20.000 --> 00:08:21.000 said well what was her research 00:08:21.000 --> 00:08:22.000 on and I said it's about 00:08:22.000 --> 00:08:24.000 how children interact with 00:08:24.000 --> 00:08:26.000 storybooks and picture books 00:08:26.000 --> 00:08:27.000 and my husband the librarian 00:08:27.000 --> 00:08:29.000 said your research can't 00:08:29.000 --> 00:08:30.000 compete with that argument just 00:08:30.000 --> 00:08:33.000 just just do what you need to 00:08:33.000 --> 00:08:35.000 do it'll be fine just don't try 00:08:35.000 --> 00:08:36.000 to compete so Marie I'm not 00:08:36.000 --> 00:08:37.000 going to try to compete today 00:08:37.000 --> 00:08:39.000 I'm gonna try to keep up a 00:08:39.000 --> 00:08:41.000 little bit and I can finally I 00:08:41.000 --> 00:08:43.000 want to mention my husband Ryan 00:08:43.000 --> 00:08:46.000 I I have a lot of presentations 00:08:46.000 --> 00:08:47.000 and publications on my CV and 00:08:47.000 --> 00:08:50.000 everyone of those presentations 00:08:50.000 --> 00:08:51.000 is a weekend where he was 00:08:51.000 --> 00:08:54.000 left home alone with kids I'm 00:08:54.000 --> 00:08:56.000 gonna get emotional -- and I 00:08:56.000 --> 00:08:57.000 appreciate all of his support 00:08:57.000 --> 00:08:59.000 in this process they didn't 00:08:59.000 --> 00:08:61.000 identify him as the love of my 00:09:01.000 --> 00:09:03.000 life so -- they'll biography 00:09:03.000 --> 00:09:06.000 like Scott did. That was my mistake 00:09:06.000 --> 00:09:07.000 and finally I want to thank 00:09:07.000 --> 00:09:08.000 the audience thank you for 00:09:08.000 --> 00:09:10.000 being here today signing up 00:09:10.000 --> 00:09:11.000 for it to listen to two talks 00:09:11.000 --> 00:09:13.000 about mathematics on a sunny 00:09:13.000 --> 00:09:15.000 Thursday afternoon is a big 00:09:18.000 --> 00:09:20.000 snacks that we have but I I 00:09:20.000 --> 00:09:22.000 appreciate you being here when 00:09:22.000 --> 00:09:24.000 people ask me -- what I do for 00:09:24.000 --> 00:09:26.000 a living I often just say that 00:09:26.000 --> 00:09:28.000 I work in teacher preparation 00:09:28.000 --> 00:09:30.000 I don't typically say that I'm 00:09:30.000 --> 00:09:31.000 a math educator because I find 00:09:31.000 --> 00:09:33.000 that when I say I'm in math 00:09:33.000 --> 00:09:35.000 education people want to tell 00:09:35.000 --> 00:09:36.000 me about all of the horrible 00:09:36.000 --> 00:09:38.000 experiences they've had over 00:09:38.000 --> 00:09:39.000 he hears and sometimes I just 00:09:39.000 --> 00:09:41.000 want to stand in the line it 00:09:41.000 --> 00:09:42.000 WinCo and buy my groceries 00:09:42.000 --> 00:09:45.000 so I I fully acknowledge that 00:09:45.000 --> 00:09:46.000 there are some great mathies 00:09:46.000 --> 00:09:47.000 in the audience today but 00:09:47.000 --> 00:09:48.000 they're also a lot of people 00:09:48.000 --> 00:09:50.000 who have some really bad 00:09:50.000 --> 00:09:53.000 experiences and frankly some 00:09:53.000 --> 00:09:55.000 trauma in their past related 00:09:55.000 --> 00:09:57.000 to mathematics so when I was 00:09:57.000 --> 00:09:59.000 thinking about things to talk 00:09:59.000 --> 00:09:61.000 about today I I realized I 00:10:01.000 --> 00:10:02.000 have a little bit of imposter 00:10:02.000 --> 00:10:04.000 syndrome when it comes to my 00:10:04.000 --> 00:10:05.000 scholarship and I struggled 00:10:05.000 --> 00:10:07.000 with what to talk about but I 00:10:07.000 --> 00:10:08.000 also knew that this audience 00:10:08.000 --> 00:10:09.000 didn't really want your thirty 00:10:09.000 --> 00:10:11.000 minutes of me talking about how 00:10:11.000 --> 00:10:12.000 teachers engage with web based 00:10:12.000 --> 00:10:14.000 curriculum in the classroom 00:10:14.000 --> 00:10:15.000 and so I started thinking to 00:10:15.000 --> 00:10:16.000 myself I'm going to have this 00:10:16.000 --> 00:10:18.000 room full of really interesting 00:10:18.000 --> 00:10:20.000 people and they have to listen 00:10:20.000 --> 00:10:22.000 to me for twenty five minutes 00:10:22.000 --> 00:10:23.000 this is my chance to advance 00:10:23.000 --> 00:10:25.000 my agenda that and then I 00:10:25.000 --> 00:10:26.000 realize no that's kind of a 00:10:26.000 --> 00:10:28.000 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.