Gail Burrill is currently an Academic Specialist in the Program for Mathematics Education at Michigan State University. She was a secondary teacher and department chair in suburban Milwaukee, Wisconsin for over 28 years. She is the Immediate Past President of the International Association for Statistical Education, served as President of the National Council of Teachers of Mathematics and as Director of the Mathematical Sciences Education Board. Burrill co-chaired the College Board Commission on the Calculus Framework and is currently chair of the College Board’s Advanced Placement Calculus Development Committee.
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Rosemary Pennington: Here on Stats and Stories we spend a lot of time talking about research involving statistics, the practical applications of statistical data, and how news media covers statistical stories. What we spend less time talking about is statistical education. That is the focus of this episode of Stats and Stories, where we explore the statistics behind the stories and the stories behind the statistics. I’m Rosemary Pennington. Stats and Stories is a production of Miami University’s Departments of Statistics and Media, Journalism and Film, as well as the American Statistical Association. Joining me in the studio are regular panelists John Bailer, Chair of Miami’s Statistics Department and Richard Campbell former Chair of Media, Journalism and Film. Our guest today in the studio with us is Gail Burrill, Burrill is a mathematics specialist in the program in mathematics education at Michigan State University. Her research interests are statistics education, the use of technology and teaching secondary mathematics and the issues related to what it means to teach math. She’s also the former president of the International Association for Statistical Education. Gail, thank you so much for being here today.
Gail Burrill: Thanks for having me.
Pennington: What inspired you to get involved in statistical education?
Burrill: So, I was teaching high school and my junior and seniors were- had a study hall two days a week, three days a week, actually, and they were bored and causing problems and so I was like okay, how about if I teach a class? And so, I thought well, why don’t I try statistics? It sounded intriguing and I like numbers and data, and so we made a class happen. And they weren’t bored anymore, and I thought it was really fun. That led me to be one of the few statistics teachers in those days, and when they had a Woodrow Wilson summer institute for four weeks at Princeton, I was lucky enough to be one of the people who was chosen to go there a couple years after I started teaching stats, and then that’s where I met John Tukey. And was one of the all-time kind of renowned recent figures in innovations in stat education, or actually the field of statistics not just the education part, and then that eventually a couple years later led to me meeting Deming, and that was also very cool thing and he was all about teaching. And so, it was just great, and once I started I never stopped, and we kept having classes in statistics and it was fun.
Pennington: How did you decide what you were going to teach these high school students? Because you know – I have a high schooler and I imagine if I said instead of doing study hall we’re going to teach you statistics, I can imagine the eye-roll I would get from her, so I’m just wondering how did you choose what you taught these students in order for them to be engaged? Because math is something that so many students in stats are sort of scared of or wary of…
Burrill: Well they really didn’t know enough to be scared or wary about it and so we just started with data. I mean, we got to do things like okay, so it turns out that Milwaukee is, or was at that time, a place where advertising people did their marketing tryouts, so we- so the kids did things like they went to – they tracked down what kind of ads they had gotten from the Milwaukee Journal, and the Milwaukee Journal would tell us what they were doing and we could get these big books about stuff, and they could go to places. Like they could go to the shopping mall on one side of town and price out certain things and go to the shopping mall on the other side of town and price out certain things and discover that the prices were different. And that fascinated them. And we could do the same thing with groceries in stores, and so we did stuff like that. They go to do a lot of their own- I mean I didn’t know what I was doing. I didn’t have anybody- I don’t think I ever had a formal statistics course before. So, we just did whatever seemed like fun and kind of analyzing data as we went along and looking at what the data had to tell us about cool things.
Richard Campbell: This is like one of your tips for introducing students to statistics I read because this is how you kind of started out. You don’t start out with definitions and formulas, you start out with hands-on activities and just getting them into the concepts right away. So that’s something you just sort of had an instinct that this was the way to get them in, so my question as a follow up on that- so how do you get college students, how do we get college students- and journalism students are very much like this; they may have had a bad experience with math classes in high school and they’ve got this phobia and they don’t want to take statistics. We really encourage our students to take statistics, so this is- so how do you- so you talked about when you met them, they didn’t know enough. So, we have a different problem I think at the college level and you’ve probably seen that too.
Burrill: So, my students at the college level are mostly in the college of education and so they do have that kind of aversion to taking statistics. But I think, again, what I am trying to do with those is to show them why they need it by engaging them in different kinds of fun things, but also things that are important to what they are about to do. I mean we just had a story just yesterday one of our graduate students was a high school teacher in California and he taught AP stats, and his school got involved in data. Everybody had to have data; data was a big thing so your school will be better. So, the data came back on algebra and his students did so well that he was charged with taking the other algebra teacher and helping the other algebra teacher learn what he was doing so she could become better. What he was – he was a pretty smart guy, and he said let’s look at these data and see what’s going on, and it turns out that it had nothing to do with his teaching it had to do with the lunch period and who the kids- so the lunch period so the juniors taking algebra were in one lunch period and got one teacher and the sophomores or freshmen in algebra were in another lunch period and the juniors had mostly failed the algebra course already. So, it had nothing to do with his teaching ability but a story like that y students sat up and they go really? You know, I need to pay attention? I don’t know if that helps but you got to give them something that they care about like how many pets do people have in their family? What kind of answers do you think kids would give?
John Bailer: You know, I find that when you said you started with data that was pretty revolutionary at the time. I know that just in the time I’ve been watching the intro stat book world, it has evolved dramatically from things that were more formulaic to those that are more data motivated. So, you know you had insights very early; I’m quite impressed that is really awesome.
Burrill: Well it was the analyzing data part that was fun it was working with the data. Remember I didn’t really have a formal statistics course, so I didn’t know all the formulas that I needed to learn. And I have to tell you that I did get a book I forget the name of it it was little and yellow and I think it was written by NTTN president, but I taught the probability section in the book and all the answers were wrong the first year. And the second year, not so many answers were wrong. And the third year almost all the answers in the book were right.
Bailer: That’s progress.
Burrill: That is progress, but I didn’t really know a whole lot. And you know, when I finally got them all right, I kept thinking, think of all the kids I’ve ruined in terms of their understanding of probability but I didn’t come up with all those formulas that I was supposed to know how to use so.
Bailer: I would love to hear a Tukey story about kind of one of the you know so John Tukey clearly was this luminary in the history of our statistics profession and the impact of things like exploratory data analysis and more. So, what was it like to interact with him as someone who was coming into the teaching of statistics and encountering this person?
Burrill: Scary.
[Laughter]
Burrill: I mean he was a really interesting person so I- the one thing- I remember a couple things, but one thing I remember so, he did a talk with us, there were 50 of us in the teachers at Princeton, and one of my friends asked him a question at the end of the talk and I can’t even remember the question. I just remember that he was sitting, and he leaned back in his chair to the back two legs, closed his eyes and put his arms across his chest, and silence and silence… And pretty soon we’re all looking at each other, I mean you could have heard a pin drop in this auditorium. We’re all looking at each other and then Pam whispered did I say something bad? Like what did I do? And all of a sudden he went, and he put his chair back down and he sat up and he answered her question. And that’s how he thought; he was processing. And his answer, when it came out, there was no hesitancy was very complete, but he was processing, and he scared us all.
[Laughter]
Burrill: I still a couple of us still get together and we still talk about that.
Campbell: It reminds me about the fictional detective Nero Wolf, he used to do that in his books, and he would sit, and you could see his lips moving, and everything would go quiet and then he would come up with the answer.
Burrill: And since then I have discovered some of my other friends are like that, especially some mathematicians. I have some really awesome mathematician friends and one of my dear colleagues and I could see him start to zone out. If I ask him an interesting question, he zones out while he’s processing and then he’ll come back to life once he’s finally figured it out.
Campbell: John’s zones out, but he’s not really processing.
[Laughter]
Bailer: Oh man, not nice Richard.
Burrill: Oh man, I’m not entering into this at all.
Bailer: And he was one of my friends. So, what ideas are- you know, as you’ve been teaching this over the years, you started with data, what are some of the hardest for students to grasp and what are some of the strategies that you found to be effective in trying to then teach those?
Burrill: So, when I started doing this I didn’t really understand they were really hard things to teach, I was just teaching stuff. And then the world of advanced placement statistics came along and it got a little more organized and a little more formal, and then so then now I have to teach at the university where there are some expectations about what kids are going to learn, and so I really started to think hard about what’s going on here? And so, one of the things that I am figuring out is that there’s certain concepts that kids really don’t understand. I’m pretty sure you could go to a class you have of undergraduates and ask them what the mean is, and you’re probably going to get an answer like you add them up and divide. So, there’s really not a conceptual foundation.
Bailer: That’s a recipe.
Burrill: It’s a recipe; there’s really no conceptual understanding. And the more I take apart some of these things, the more I discover there really is a lack of conceptual understanding about random, about distribution. And I’m thinking that we go too fast. Everybody goes too fast over these, supposedly, very simple ideas. The idea of the fact that you reason from the known; how known things behave, to conjecturing about the unknown. That’s a big idea and I don’t think kids get it, because we don’t talk about that enough. We get into the doing we start giving them the formula, we start processing it, we don’t get into the doing. So that’s what I found hard and we’ve been working with interactive applets to try to leverage better conceptual understanding. And I think it’s promising for my work.
Pennington: You’re listening to Stats and Stories and today we are talking to Michigan University’s Gail Burrill about how people learn about statistics. I was actually going to ask you about the applet and new technology after the break, so I’m glad you brought it up before. So, I wonder what is this applet you’re using? And I wonder if you could also talk a bit about how technology- the way you use technology to teach statistics has maybe evolved as well.
Burrill: So, at the beginning when I started using technology I didn’t understand that it would mean somewhat of a different way in what I was doing. For instance, I’m very used to walking around the room looking at what my students are writing. Now they’re all using software; everybody has a computer and they’re all using software and there are these applets on the software. I can’t see what they’re writing. I have to find other ways to get what they’re thinking out by having them talk with each other and me listening to their discussion or things like that, which was a surprise to me; there’s probably other changes I had to make. But basically, these applets are designed for them to respond to certain questions that will develop this understanding. So, they might, for example, right now they just spent yesterday- they are moving trying to find lines that will be appropriate models for linear data. Starting like they only know what an equation of a line is from mathematics, these are elementary preservice students. So how do I know when I have a good line what are some possible approaches and so they came up with the fact that they are going to try to find one that minimizes the deviations. They didn’t quite use that language, but that’s what they- so now they’re moving lines and looking at the sum of the absolute deviations, and so they’re talking with each other and they’re asking and answering certain questions, but they’re all on these applets. And they move these little clicks and things and they don’t have to understand the programming, they just click and drag, and they can kind of see the sum of these absolute deviations change. And then they have a contest to see who can get them the smallest and then we magically go okay, well there ought to be a better way. Well, we can just use this regression and what does it do? Well, it minimizes the sum of the squares, not the absolute, whatever. But they work on that and the technology lets them think about the ideas, rather than focusing on some formula or something else. I don’t know if that answers the question. I could give you more examples because that’s what I do.
Bailer: Well I think that the idea of the technology letting the focus on the ideas is really useful and very important. I find that your earlier comment about everyone goes too fast over the simple ideas, it seems like that might even be getting worse. And if I look at students coming into college now, the expectation is they will have seen ideas at the high school level They may not understand them they may not have the conceptual grounding, they may be pretty proficient with the recipes, but yet they are going to be starting here and we will probably be saying well we assume that you’ve had this. So, how do you fight that pressure to push forward? You know, this pressure to cover the syllabus, if you will, when really what you want is this deeper conceptual understanding that they could build on.
Burrill: I think you have to stop and ask. What do you guys really understand? When I say random, what’s in your head? Even though they come to you as if they know all these ideas, I think you need to stop and ask, and it might mean some back peddling while you try to develop that understanding. When you get them here, it would seem to me that you backpedal and then you help them build the linkages between where they came from to where you eventually want them to go, but it doesn’t help if you tell them. You have to let them build the linkages because just telling- nobody gets it. Nobody gets it. I mean really, I can tell them anything I want and then fifteen minutes later I can say what did you- and right. I mean I just told them I do not want to see the mean equals the median equals the IQR equals I want a story about the numbers. What is the context? And I get the mean equals twelve, the median is two, the whatever whatever.
Campbell: So, I saw in a talk you gave at Drexel you had tips for teaching statistics and one of your tips was about randomness and you say randomness is awesome, so how do you get that across to students? Here’s what is awesome about randomness.
Burrill: Okay so one of the things I did is- accidentally, actually. My students in calculus weren’t handing in their homework and I had too many of them to collect their homework every day, this was back in high school. So, I said okay I’m going to put your names in a bag and I’m going to draw out four names every day and that’s who’s homework I’ll correct. So I did this and it was really- when the same kids name got drawn three times in a row, they were like sure I was cheating, and I’m like no, this is randomness, you guys want to draw the names out of the bag to show- so that- so we have an applet you can look at the class of 30 kids and you choose four of them and you will see that in a week’s time, almost every single week, one kid has to hand in the paper three times. That’s randomness, that’s awesome, right? Do you want the end of the story?
All: Yes.
Burrill: Okay, so I’m walking down the hall at the other end of the building one day, and sometimes the largest smiles on teachers because I looked down and there was this little piece of paper on the ground, way far from my classroom. And I picked it up because teachers are supposed to keep the halls clean. And it was one of my student’s names; Kwong’s name. I’m like, so I go back, and I look in my bag and Kwong’s name wasn’t in the bag, so the next three days Kwong’s name got called.
[Laughter]
Bailer: Yeah randomness is awesome, but also sometimes determinism is fun too. I think of it as more than awesome; I think of it as job security. You know this is, you know you’ve been also very active in international statistics education. How does the teaching and learning of statistics differ, if at all, across countries?
Campbell: And is somebody doing it better than we are in the states?
Burrill: Oh yes. I, sorry. So, two things-
Bailer: Don’t be sorry this is-
Burrill: So I have not been to New Zealand, but I have read of the work, I’ve talked with Chris Franklin, I have colleagues in New Zealand, I’m not sure how pervasive it is and how well it’s hit the schools in the K-12 world, but I clearly think they are way ahead of us in the kind of ways that they’re thinking about teaching statistics- I mean there’s a project that they did Wild did about rethinking what you do in intro stats, and basing it more on simulation-based inference; that is part of what New Zealand as a country is doing. It’s not just something that one university or one researcher is doing, but it’s as a country that they’re trying to rethink what’s important, and how to teach it so that better learning takes place. But there are countries, I mean when we were in Kuala Lumpur, at the ISI World Congress just last summer, my colleagues from Slovenia readily admitted that their statistics is really not so databased. We did a panel on that and that they are still pretty much doing a mathematical-statistical approach, and I guess that’s right for them. But it’s way different from the kind of data-driven things we’re thinking about in the United States.
Pennington: I wonder, this is something we’ve asked a few of our guests, but there seems to be this climate where data and stats feels suspect like it feels like there is less trust. Has it made it more difficult for you to sort of engage with stats in the classroom? Or do you feel like there is – had it made your job more difficult? This sort of climate of skepticism around data and numbers ad statistics?
Burrill: No. mostly because schools seem to operate independent of the world. I mean at least the K-12 environment does. The world kind of reaches in- it pretends to, but as a matter of fact one of the things I would say is not the teaching of statistics, but this pervasive notion that if we collect a lot of data, it will make my school a better school; that our achievement will rise. And the evidence is just not there that that’s the case there was a great article by Heather Hill that just came out that says, you know, all this data doesn’t buy improvement. And so, to make all of the professional development that happens in schools, that administrators have teachers doing is really not a productive use of their time.
Bailer: So, what are you most excited about for the future of statistics education?
Burrill: Oh, my goodness.
Bailer: That’s a softball. [Laughter]
Burrill: Most excited about or really want to see what happens?
Bailer: Yes. You get to answer both.
Burrill: Alright okay, so most excited about is probably the idea that we can really do a lot with simulation-based inference and that the technology can really do the kinds of things I’m working on with this concept building, I think that can make a whole lot of difference if we can get enough people to play the game. I think it can make a lot of difference. What am I most excited about? The potential and I got this from some of my self-American people who are trying to do statistics, the potential for statistics to help change the economic plight in situations of countries. The idea of being able to make a difference in your country because you can get statistics on how we are using water and what we can do to make better use of it, what kinds of things we’re doing with waste. There are statistical things that can actually help countries make a difference. I they have the ability and support that they need in order to make that statistical education really a part of what they do in those countries.
Campbell: In this country are there states that are doing a better job with statistics training? I mean you’ve seen it sort of gradually grow. I mean I just know when my students when we were recruiting students, a lot of them had never had a statistics class in high school and today many more are coming in with statistics courses. So, what is your feeling about what we’re doing here?
Burrill: The common core is actually- which is our common core state standards, which not all states use, but they have something close to them, actually, made a bigger emphasis on statistics, and so that has been very useful and helpful. The American Statistical Association has a statistics ambassador, Chris Franklin, which I think was on your show at one point.
Bailer: Yeah.
Burrill: And she is doing a great job of working with schools, so I am thinking states maybe not so much, but districts I think are really taking it to heart and getting the support they need to help their teachers. I couldn’t identify a particular one, but I think there are pockets where they really are taking this seriously.
Bailer: So, Rosemary gave me permission to ask one little question.
[Laughter]
Bailer: I have to always ask permission at the end because she gets mad at me. So right now, there’s a lot of discussion about data science. As a matter of fact, there’s this international data in schools project that ASA and ISI and many other organizations are involved with- including, I don’t know, including Chris Wild has been involved in this and Nick Fisher has been a leader in this. I’m just curious what is your take on- how does data science get wrapped up in terms of stated at multiple levels?
Burrill: Well so remember I started in data. I didn’t know it was data science I just started playing with data. And it probably wasn’t data science then. But I’m thinking that it’s going to become a more important part. I’m hearing schools start now data science statistics courses that are not advanced placement but they’re adding them into the curriculum as an option. Even though I think a lot of people really haven’t figured out yet what this data science really would look like, but I think it’s got huge potential and things like census at school that you can get from ASA is a great place to start for what we do in the K-12 world. So, I think it’s an awesome thing, I think it’s got a lot of potential.
Bailer: Great. Thank you.
Pennington: Well Gail thank you so much for being here it’s been a pleasure talking to you.
Burrill: Thank you I was really happy. It was fun. Pennington: Stats and Stories is a partnership between Miami University’s Departments of Statistics and Media, Journalism and Film, and the American Statistical Association. You can follow us on Twitter or Apple podcasts or other places you can find podcasts. If you’d like to share your thoughts on the program send your email to statsandstories@miamioh.edu or check us out on statsandstories.net and be sure to listen for future editions of Stats and Stories, where we discuss the statistics behind the stories and the stories behind the statistics.