 Hi, so let me get this started. So I just want to say a few words before I'll turn it over to our speakers this afternoon. But so for those of you who have been here all week, I'm sorry for introducing myself yet again. And for those of you who are just here, I'm Ray from at SAO, the director of PCMI. And I just wanted to say a few words about how this particular event came into being. So one of the several activities that happen at PCMI is this workshop for equity in math education. And early on when we were planning this earlier in the spring, I got a couple of emails from some people at the University of Utah saying, we'd love to come, but we can't come sort of every day. And so we thought we started thinking hard about what would be a good way to at least try to bring people together. And this was kind of what we hit upon is hopefully a good solution for people from Salt Lake City and for people who've been here all week from all around the country to get together and talk. And so the workshop is being led this year by Jeronda Hughes, who's right here in the front row, and by Dina Khalil, who is right there, very good. And in any case, so I am very pleased to introduce Kelly MacArthur, who is gonna give the first of two presentations this afternoon. And the second one, Jeronda will be talking. And so let me turn it over to Kelly right away. I have like kid-sized ears, so we'll see. I think it's gonna fall off. Anyway, you'll tell me if you can't hear me anymore. Is that better? Great. So I got a call about two weeks ago maybe to give a talk and I was really excited to put together some information about some things that have been going on in the last several years, geared toward math equity. And I decided to call my talk, Answering the Call to Rehumanizing Mathematics. Two different projects that I'm going to talk about and I'll start with a couple quotes that are my favorite. We'll stick with old school. One of them is from Rochelle Gutierrez. Perhaps you're familiar with some of her work, especially the title comes from something that inspired by her. Play the game called Mathematics, but also change the game. Changing the game of mathematics means partly rewriting the narrative about who contributes to mathematics and who does well in it. This is from a paper she wrote, I don't remember, sometime in the last few years. And then there's something by Sunil Singh. And this was in response to a talk that Francis Sue had given at NCTM this year. He wrote in his blog, this great article, and this is probably my favorite quote from that blog. "'Human flourishing is for all. "'Sure, we might fail in reaching everyone. "'That is almost irrelevant. "'The magic lies in the attempt.'" You can read the rest of the quote there, but I think these are the things that really motivate me. The first project of the two projects I'll discuss is called Endahoa. This is a Navajo word that means re-learning or new learning, as it was explained to me. I don't speak Navajo, so hopefully I've got that right. The Endahoa program was started by Herb Clemens long time ago in 1994. And perhaps some of you have been around for a while. You know Herb. How many of you know Herb? A handful. He's just a great guy. And he was in the math department at the University of Utah for a long time, and now he's at Ohio State. He started this program with Pat Seltzer, who was the long-time principal at Monument Valley High School, which is on the Navajo Nation, down in the Four Corners area in Utah. And it was a great program that was a summer program. So it was designed to be a three-week program in the month of June, serving Navajo students from all around. So the buses would bring them in from all around the surrounding area, including in Arizona a little bit, because the way things are are restricted. Endahoa focused on bringing the old traditional craft learning from the Navajo elders, mixed with geometry and computer programming learning. So it was the old and the new mixed together. That was the idea of the program. It's really a beautiful program. Originally, it was meeting every day, Monday through Friday, for about six hours. The students would only spend about four hours there. No, that's not right. They would spend about five hours there. So originally, they had, in the morning, they would have, say, a two-hour section with the Navajo elders on the crafts. And then they would have lunch and a two-hour section with the math teachers that we would send down. So the University of Utah provided the math and geometry and computer programming teachers. And they would live there at the school for those three weeks. And there was a group of students who would do the crafts first, and then the math part second. And then another group of students who would do it in the opposite order. Over time, the program required a little more funding than what they had money for. You know, this is always kind of a challenge in any kind of educational setting. And so we had to get rid of the lunch portion. So we had to make it, say, from eight to 12 so the students were bringing their own snacks. I think they might have provided a snack, but not a free lunch. That actually decreased the attendance a little bit, but not substantially. This was a long-standing program. And when I came to the University of Utah as a full-time lecturer in 2003, when Herb left, I took over supervising this program for the math department. So our job in the summer was to get teachers for the math part or the computer programming part. They did all of that. This was a little bit challenging over the years because originally it started only for high school students. And then they added junior high students. And then they added the siblings. And so it ended up being over the years something that eight-year-olds were coming to as well as high schoolers. The high schoolers, a lot of times, we would be able to hire as, if they've already gone through the program a couple of times, we'd be able to hire as tutors. And this was very successful with the program because sometimes there was a culture clash a little bit, particularly because the teachers were coming in only for three weeks. And it's hard for people to get bonded to a teacher in just three weeks time and not have the whole year to bond with them. So we did have some successes and difficulties. The pictures show you some of the successes. Most of the time what they were doing with the computer programming was in logo. I don't know if you all are familiar with logo. It's a really kind of a basic geometry programming platform that's very easy as far as programming goes. And the students would draw their rug, let's say if they were doing a rug for their craft, they would draw the design of their rug mathematically in logo. And they would have to learn mathematically not only how to program logo, but also how do you tell the turtle mouse in logo they have a little turtle that shows up as your cursor, let's say. So how do you tell the turtle to turn 30 degrees? And how do you decide that 30 degrees is the degree angle that you need for the rug that you're creating? So there was some nice mathematics in this. There were some difficulties as well. One of the difficulties I stated was having such a wide age range of students. Another difficulty I think is as I stated, having the teachers there for only three weeks, it's hard for the students to really bond with someone in that length of time. It did help quite a bit when we had the elder students who had already gone away to college and maybe were back for the summer and they had been through the program a couple of times, they would help. That was really a great plan. The other thing that was difficult, and this is the sad report that I have to give you is that currently this program is not happening. There were of course some political problems. I know this is not shocking for a lot of you. So we do have actually some funding set aside for our part of Endohoa, still sitting in the math department at the University of Utah, that we cannot access because Endohoa is not going. So what happened I think in 2013, Pat Seltzer had been the longstanding principal for many, many years. She bonded really well with the community and they respected her greatly and I think she was doing a really fabulous job, but the school district decided that they needed to go a different direction and they were very concerned about assessment scores and the rankings of the students' measurable success as they were looking at it. And so in the last few years they've gone through two or three different principles and unfortunately none of the principals have responded to my emails or are willing to meet. So the next thing that I'll probably try over either spring break or fall break is just to drive there and show up on their front door. Oh, I've done this before. That tends to work. So hopefully I can do that this fall break and get the program going again. I think the community on the Navajo Nation really liked the idea of Endohoa. It's just, it's a shame that we still have money to keep it going and the principals, I think perhaps they've been overwhelmed or your first year as a principal in a setting where everyone loved the previous principal that got ousted is a little bit difficult. So those are some of the difficulties and the current status. The next project I want to discuss is a project that I am just in the middle of that I started in the spring and it was a re-humanizing effort based on a talk or motivated by a talk that Rochelle Gutierrez gave at the University of Utah in maybe the end of January. I was very lucky to go to breakfast with her the morning of the talk and then even luckier to drive her back to the university after breakfast and in my drive time with her I asked her a very pointed question about what I could do in my calculus classes to humanize my classroom and she gave me one challenge and that was to look at assessments. So she didn't really say anything else, she didn't say change your assessments like this Kelly, she just said do something with assessments. And so I thought hard about this and changed my assessments quite drastically and the results were kind of phenomenal. So one thing I want to point out is in my calculus classes I was teaching two calculus classes in the spring. We always have this class mission statement written on the board and I tell you that the first time I started writing this statement on the board every day I felt a little awkward and goofy telling students but I have to tell you that when I forget momentarily to write this on the board, the students will say Kelly, where's our mission statement? And it started coming up in the evaluations as students are really embracing this. I mean, it comes up in class it's obvious in class that they're embracing it but they're referring back to it. The story that I like to start my class with every semester is this story that actually happened for my son who's now 27, this was when he was in second grade so it's a little while ago but he went to an elementary school in Utah that was an alternative program within the public school and it was a parent cooperative so the parents had to be there for three hours every single week so I taught math for three hours every week for seven years in this elementary school and the kids, the focus of the school was really very community minded. So when my son was in his second third blend I happened to be there one day and after recess the students came back in and sat in a circle on the floor as was customary in the classroom. They were discussing the goals for the rest of the afternoon and one student who would just join the class maybe a month before then so he hadn't been there since kindergarten. He raises his hand and he says I think I pooped myself a little and no one laughed in the classroom because this class, the kids had been so, what's the word I'm looking for? They had been so conditioned that this is a community effort that they immediately just started saying oh yeah that's happened to me before I totally know how that is and so then the teacher hardly had to do anything by the way the other parents also didn't really have to do much and the kids all solved the problem themselves one kid finally said oh I think I have an extra pair of pants in my backpack on my hook outside in the hallway so they got up went to get an extra pair of pants brought it back to the little kid and he said okay he went to the bathroom changed his clothes came back that was the end of the conversation because really the problem was solved right but this is the way it was in that school and my point of bringing this story up to my students every semester is not that I want them to poop their pants in class but that I want them to feel like this is a failure tolerant place this is a place where we can say I totally don't understand this or here's my answer but I'm not sure it's correct or any sorts of things mathematically but they will have the community mindedness of the rest of the class to not laugh at their jokes and not their jokes but not laugh at their comments or their answers or their questions or any kind of contribution mathematically that they're making so this is why I think it's a brave inclusive kind and failure tolerant classroom and to me the most important word there is failure tolerant. So what did I do with my assessments? I went through some research that I've heard about and read about perhaps giving students time to redo some of their tests I'm sure some of you have read some of this research where students will redo some of their work on an exam to get partial points earned back because of course assessments are a learning tool in themselves and I really like this idea except that I typically teach very large classes and I only have so many greater hours available to me and this scaling issue was huge so I calculated it would be an additional 40 worker hours for each exam which was just too much so I didn't go with that what I did the other thing is I wanted to really create a community atmosphere in the classroom so I split my tests into two pieces I have two days to do the exam this takes up a little more class time but I was willing to give up a little class time so that I could try this assessment strategy out so I have a group portion of the exam on one class day and the following class day I have the solo portion of the exam and the group portion is typically somewhere between 30, 38% of the points and then the solo portion is the rest of the points so students still have to perform on their own on a test as they would normally but the group portion really allows them to talk with other students I picked the groups by the way they are the first couple midterms the groups were picked randomly and after that I did partial random I put them in the top third, the middle third and the bottom third based on either their previous midterm score or their overall grade so far and then randomized each of the three groups and put one from each group together into a group of three so the students got twice as long to do the test right because they get two class periods the tests were in general about the same length as the previous semester for the final exam this didn't seem this particular scenario for assessment didn't seem like it would be a good idea because we only have two hours for the final exam and the last class day was almost a week before the final it just didn't seem like it flowed very well to have a part of the final exam the last class day and then a week later the rest of the exam and so I came up with this idea to do one intact final exam for two hours the first 45 minutes were silent and solo the next 30 minutes was group conversation and the last 45 minutes was silent solo the idea of this is that this is more like real life this is how we do mathematics it's rare that we sit in our office and do mathematics all on our own and we don't go talk to someone when we get stuck and so I was trying to mimic that community-mindedness idea of how we do mathematics and in 30 minutes the students really didn't have enough time to copy the entire exam from someone for instance but it really did help them get unstuck so if they were looking at an integral and they weren't quite sure even where to get started and they had some group time they could at least say oh well someone else suggested integration by parts oh why didn't I think of that right they know how to do integration by parts they just got stuck on that particular integral so in this way it helped them get unstuck and it helped them be able to showcase their abilities a little bit better and I think these results kind of speak for themselves one thing I want to point out is in the fall of 2017 I taught one large Calc 2 class that ended with 144 students in spring of 2018 I taught two Calc 2 classes that totaled between the two of them around 167 to start so notice that the first midterm we had about the same number of students and by the end of the semester for the final scores do you see that we lost fewer in the spring than we did in the fall now I haven't done this is these are all really preliminary results so I should put this caveat out there that I have not yet done the statistical analysis on this but I still find it compelling for me I think one of the most compelling things is to look at the standard deviation and if you look at the low scores they went up remarkably there are other things that I think are not measurable with these scores of course part of the things that I think are not measurable are things like how anxious are the students how well are they able to articulate their mathematical thinking so what happens in the class and what I noticed over the semester is that students were even more interested in voicing their ideas than in previous semesters and I've been doing that class remission statement for a while now but this group portion of the test made them even more invested in being able to talk about their mathematical ideas and as an educator to be able to walk through a classroom and hear people debating mathematics is really quite lovely that was probably one of my favorite parts also the other thing I want you to see did you see midterm two from 60 something so I've been teaching calc two for many many years and calc two that second midterm it's pretty commonly around the 65 mean and median mark and that went up to the 80s that's just remarkable and the standard deviation for the final exam I think is also remarkable a standard deviation of less than 10 for 156 students let's see I think I've gone through most of these the spring exams were a little bit harder than the fall exams I did that on purpose just to make sure that I wasn't going too easy on them in 2017 in the fall the final exam did have a take home portion and also in 2017 they had three hours to complete the exam whereas in spring of 2018 they only had two hours and I made sure the exams were of comparable difficulty in both semesters they had the opportunity to earn some extra credit for the final exam and for midterm so in that way they were very similar and of course besides the numbers I wanted to share some quotes with you from students about the group and solo exam portion so I'll read one of them and leave the others for you to read the top one says the group portions are excellent for me I have a well that's a typo from the student but it's their exact quote tough time starting choosing the methods or tests but after I discuss with other I gain a better understanding of which one and why and then I can go forth with my process and usually complete it on my own so this kind of gets back to what we think assessment is getting at right or are we trying to test their skill in an anxiety-ridden situation by themselves or are we trying to test their skill with some anxiety still present there but other students kind of helping them get unstuck so that they can showcase what they really do know so I don't know where you lie on that fence it's something to ponder I'm not sure exactly where I lie as well and I think those things change over time but it's certainly something to ponder and of course a lot of students commented how it helps with the solo portion especially to start with the group portion so here's some other quotes I like the middle one they give me more room to make mistakes and discuss them without destroying my grade other people in your group may notice your errors and correct long-standing mistakes and that in itself I think is part of the beauty of the group portion of the exam is that students are helping correct others mistakes and in order to even be able to recognize someone else's mistake you have to understand it at a deeper level than just being able to produce the computation and I included the last quote because I wanted you to see that most of the quotes are fairly positive about the group portions but of course I get some of these quotes that students are like but wait I don't like it when other people talk me out of my right answer I get some of these all the time and I am teaching a Calc 2 class right now and I did this survey again last week and I actually had one student say that the group portions are great for other people because he explains everything to them like okay well eventually that's gonna fall away and you're gonna need them to help you but perhaps not yet here's some noteworthy points to make or questions that I'd like to ask from the data that I haven't yet analyzed the standard deviation I've already pointed out if the scores if you notice from the spring and the fall they started out fairly similar in midterm one and then the story drastically changed by the final exam so that was interesting to me the low scores and the overall scores are quite different and then I have done nothing yet to figure out how this breakdown affects gender or students from different races or ethnicity so I haven't done any analysis of the data as far as who's doing better all I know right now is that in general the class is doing better and then I wanted to end on this note so I've gone over two different projects that I've done the end-to-hoa and then the rehumanizing assessments and I want to end with this because this is a little bit different tack but in the spring I was so interested with these survey results that I was getting that I decided to also ask the students so there's this math educator Dr. Rochelle Gutierrez who is doing talks about rehumanizing math I didn't give them any more information than that I just said, tell me what you think that means to you what does rehumanizing math mean to you so I've done one pass of coding through all that data I have about 150 responses so and at the end of this week I'll have about 35 more there are two quotes that I'll share with you honestly I think it means to make having a mathematical tool set something that is attainable and desirable for people in general I think that a lot of mathematics is taught by teachers in such a way that the majority of people are put off by it not the discipline itself but by the people they associate it with not no offense I think teachers and educators can rehumanize math by making better learning environments in class and by learning how to connect better with people the reason I like this quote so much is because it really gets at the heart of humanizing mathematics is about connecting with people and making it a people thing and not just computational thing that students sometimes view it as and this is another quote that I really liked I especially liked it because this one has the word robotic in it and I saw that word robotic at least five times so it was really, that's not a word I would think about when I think about mathematics I think it's one of the most creative endeavors of humankind but students kept coming up with this word robotic, cold when thinking about mathematics in my opinion the idea of rehumanizing mathematics seems to be the idea of making math less robotic cold and conspicuously heartless I think the problem is less making math more human and more getting people to see that math is human I think teachers could move towards this goal of rehumanizing mathematics by helping their students see that it is not a genius subject that only someone with a computer for a brain could do and that mathematics is actually a really fun cool subject invented by humans to help us with our everyday lives I think one good way to do this would be by pointing out that even people who are good at math have to try hard to be good at it and that even they make mistakes and to me I think this is one of the best quotes to end with because it shows how students have by and large a strange misconception about mathematics that it's just something that we sit down and we do perfectly we produce a good proof and voila it's like this amazing thing we don't have like a whole bunch of scratch papers scribbled up and thrown in the garbage or we haven't sat in the fetal position on the floor crying because our math skills are not what we think they should be please tell me I'm not the only one who's done that so I like this one because it gets at the heart also of the failure tolerant and that's what we're trying to get out with students is be failure tolerant get used to failing and embrace it at some point so that we can keep going and eventually get to where we need to be and be okay with making mistakes along the way because that is expected well it's expected for me I don't know maybe you all are the brilliant mathematicians where that doesn't happen anyone in here wanna own up to that no and that's the end any questions yeah so most of these students in Calc 2 at the University of Utah anyway most of them are not math majors most of them are engineering physics computer science maybe a few math majors but not the majority of them I do have an IRB application approved to gather more data so what I would like to do especially with the spring students is to follow them for the next couple of years and gather all the data on how they're continuing to do I don't know what to expect from that data but I think that's what you're asking am I gonna gather that data yeah I've also done a lot of interviews and focus groups with the students and I'm still in the midst of doing that probably for another six months yeah good question so I do not use the same groups so what happened is I was doing the groups for three midterms and then the final exam so the first midterm I created the groups in Canvas which has this awesome tool that you can just randomly create groups of three for the entire class and then it tells students which groups they're in and I have a seating chart that I make at the beginning of class so students know group one sits here in the classroom, group two sits somewhere else, et cetera so they are the first midterm group they were randomly created and each midterm and final exam they were in different groups by the final exam I was hand picking the groups a little bit so as I described for the final exam when I created the groups I grouped them based on their overall scores in the class at that point with the top group, the middle group and the bottom group of scores and then I randomly, I randomized each of those three groups and then put one from each of the three groups into a group of three the one thing that I did massage a little behind the scenes is that in part of the surveys that I had students fill out about how the group portions were working I had a handful of women say that when they were in a group with two men it didn't go well so I made sure there were no groups with only one woman so I moved things around a little bit I also had a small handful of students who had some anxiety issues and so I grouped for the final exam especially I grouped them with people I knew they would be comfortable working with to take care of decreasing their anxiety as much as possible does that answer your question? Oh, they don't sit together every day so every day they sit wherever they'd like I make sure the groups are set up at least two weeks before the exam so that the students can work with their group partners if they'd like to outside of class or sit with them during class and usually the day before the group exam I would have them sit in their groups so they knew where to go and they knew who their group was the other thing I forgot to tell you is that the very first time for the midterm one when we did the groups I had them work with their group the entire class hour which was 50 minutes and I found this kind of interesting I did a survey after that to ask them how is it going well actually I didn't think about doing the survey first but I got two complaints from men in email within two days of the exam saying that they were the ones carrying their group and they didn't think that their group they wanted to do the test on their own in the future because their group wasn't helping them and they didn't really like this setup and so I decided to do a survey anonymous survey and see how this was going what I noticed from the comments was that students were saying that two things they were either saying that they carried the groups and their group they used some interesting deficit thinking so they would say things like I had slackers in my group or I had people who weren't studying and I don't know if you've talked how to but most people in Calc 2 are not slackers they actually are interested invested students and then I had more students than that saying things like I am a slow processor so when we went straight to the groups I didn't have time to think about the problems before I was expected to talk and so the other people just took over the conversation and I didn't have time to actually contribute anything even though I was well prepared and so what I noticed was that the groups where people thought they were carrying the group they were coming to an erroneous conclusion about the other students and so from then on the group portions had 15 minutes of silent time and then the rest of the time was open talking to your group so that way everyone had enough time to really process on their own before they started discussing things does that answer your question? Yeah, well it just I mean I just did this in the spring so I don't know that people are aware enough yet to have pushback so no not yet, should I be braced for this? So I don't know if that's going to happen I don't know if it will happen I don't know if it won't happen I'm just kind of crossing my fingers for now that it won't happen but in our department there is a pretty strong concern that faculty members have academic freedom to run their classes as they think is reasonable so I don't really suspect that I'll have huge pushback yeah