Teaching Stats in High School

An interesting thread came across my twitter feed, posted by the wonderful author Steven Strogatz. It was especially timely as I am hoping to find a way to add a Statistics class to our program here at Mid-Pen (while also hoping to reduce my classload from 6 to 5 classes – talk about needing a mathemagician! Anyone know a great math teacher who wants to teach 2 classes for free?) And it brought up an argument that I’ve thought a lot about over the last couple of decades.

I didn’t take statistics in high school. It wasn’t offered at my school at the time. When I entered Bates College, my first semester, one of the classes I enrolled in was BIO 244, an introductory class in Biostatistics. This was a long time ago, but I don’t remember being impressed by the class. I remember entering data into MATLAB, following recipes for statistical tests, and not feeling like it made a lot of sense. To be honest, I was also a very young first semester college student and probably didn’t take my academics as seriously as I should have. (Mind you, that had been true throughout middle and high school, and would continue through college. I finally learned how to be a student in grad school, but that’s another topic.)

logical-indexing-matlab-4-2c
MATLAB has come a long way since the 1990’s console window version!

My next exposure to statistics was MATH 215, a pure statistics class that had pre-requisites of MATH 206 (Multivariable Calculus) and MATH 214 (Probability). Here it was – the rich and theory based statistics that let you get your hands dirty with integrals and proofs and all the stuff that those non-math people couldn’t understand (or so I thought at the time, from my isolated and prestigious tower I imagined myself living in). Now this was the statistics class that I was looking for – nothing about data interpretation, except from a pure mathematical standpoint.

Finally, in my senior year in college, I decided to take a nice, easy class – and what do you know? There was PSYC 218, a statistics class in the Psychology Department. I figured it’d be an easy A – and if it was just about the math, I would have been right. In fact, I was that annoying student who had to show the professor that I knew the math better than he did, pointing out errors in the explanations of various tests and why they worked. I was also the student that lots of people came to in class when they didn’t get how to do the math. Unfortunately for me, there was a lot more in that class about how to design experiments, evaluate experiments, make conclusions based on the data, interpret results, and lots of other things that just didn’t seem to matter to me because they weren’t about the pure math. And (at the time) I was only about pure math. Applied math was a pointless waste for people who couldn’t live in my world of number theory and topology and elliptical curves.

Fast forward a few years, and I found myself teaching, which meant making the math relate to the real world for students, to make it meaningful and relevant. I was the only math teacher in a tiny high school program of 19 students, and was teaching Pre-Algebra, Algebra 1, Geometry, and Algebra 2…and U.S. History. (We had a math, science, and English teacher, and each of us had to take on a social studies class until the program grew.)

And grow it did…more than doubling in size over the next seven years that I was there. I started teaching calculus, and eventually was talked into teaching A.P. Statistics. And I was really wary of this – it didn’t require calculus, and how could you teach statistics without calculus? I had seen it go poorly1 for both biology and psychology classes at a very prestigious small college. But I decided to give it a try, and it worked well for students. A few years later, at a different school, I offered the same class, with some excellent results from students. And I realized that Statistics fits an important niche in the math education curriculum. It is a class that is taught exclusively as an applied course, which is different from how we teach Algebra and Geometry and Calculus. For those classes, even if we focus on how they can apply to the real world, that never seems to be our primary focus. And that’s okay I think. But statistics opens up the world of how to interpret data, whether in the sciences or social sciences. It’s power gives it validity and usefulness to many students I’ve had who, even when they come around to thinking that logarithms are cool and the Law of Cosines in vector form is amazing, have not experienced in other classes.

So, back to that thread in the beginning. Twenty-five years ago, I would have been firmly in the camp that calculus is required for statistics. And it’s true that knowing calculus may be required for understanding the theory of statistics. But a high school or introductory statistics class should be about how to use statistics, how to apply and interpret statistical tests, how to evaluate the use of statistics (especially in this era of fake news).

coxcombs
Florence Nightingale’s Coxcombs led to great advances in epidemiology.

It also offers some great historical stories about the development of statistics, and gives the opportunity to talk about Florence Nightingale’s contributions during the Crimean War.

Statistics can be a great class for the math student who has already taken calculus, and they can be encouraged and guided through some of the theory behind statistics. It can also be the perfect class for the student who is sure they are not going on in math or science but has finished Algebra 2 and wants a math class on their transcript. Make no mistake – I’m not calling this a math class for non-math people. What I am calling it is a chance for students to make a choice to take a math class that they see as relevant, that they will buy into, that they won’t question when they’ll use it because it is clear in every lesson just how it can be used. In the end, doesn’t this give them a greater appreciation for the richness of math?

 

1In retrospect, it is clear that my memories of those classes were colored by my biases about math as well as my poor student skills – they may have been outstanding classes, after all.

Working on Feminism in Math Class

My college adviser in math, Professor Bonnie Shulman, has been one of my biggest influences in my math education career. She inspired me as a teacher who could help s35dd7datudents find the excitement and joy that mathematics could bring them. I had entered Bates as a relatively young first year student, definitely over-confident, and with no real idea for what I would do with my life – probably become a doctor since I liked the idea of helping people, and it seemed like it would be a nice challenge. After my first semester, I realized that I really didn’t like chemistry and there would be a lot of chem required for pre-med, it would be hard for me to not major in music after having devoted so much of my life to writing and performing in various ensembles, and most significantly, that math wasn’t just easy for me – it was actually a lot more interesting and fun than I ever gave it credit.

Much of Bonnie’s focus was how to get more girls and women involved in math and science. As I started my teaching career, I made a conscious decision to give all of the girls in my math classes the most encouragement, the highest expectations, and the best future in STEM careers. And I failed miserably. Well, maybe not miserably, but I didn’t have them leaving my class and going straight into prestigious colleges and universities and graduating with math and science degrees. And I was sure the problem wasn’t me, because you know what I found? None of my female students had confidence. At least, that’s what I saw. When I asked a question in class, they didn’t raise their hand. If I called on them anyway, they would mumble, or say they didn’t know. If they did answer, they did so in a questioning voice. And what would I tell them? “Speak up! Speak confidently! Don’t answer with a tone that keeps going up!” And that fixed none of the problems. That is, maybe they would answer in that moment with a louder and less questioning tone, but their lack of confidence hadn’t really changed.

This isn’t to say that there weren’t issues of confidence that these girls had learned over the previous 8, 9, 10, or 11 years of classes before they got to me. And yet, despite my best intentions, all I was doing was pointing out their lack of confidence. Any progress that they were making in improved confidence was incremental, and probably being undone by my pointing out how they weren’t being enough like the male students.

I don’t pretend that I have all the answers now. I still have high expectations for my students, regardless of gender (male, female, trans, non-binary, fluid), and I make every effort to let each student know that I believe in them. But I don’t call on students when they aren’t volunteering. I don’t demand that they answer with confidence. In fact, I now relish the questioning, since doubt allows us to develop deeper and more interesting explorations into the mathematics. And with more time for reflection, I’m sure that I could figure out other things that I do that help.

One thing I do know is that I am surrounded by Dr. Johanna Nelson at SLAC's SSRL synchrotron facilityamazing girls and women in my life, many of whom absolutely love and appreciate math and science (including a large number of my previous students). I am also grateful for having my wife in my life, for many other reasons of course, but for the purpose of this post, because I find myself talking about a woman who is a successful physicist on probably a weekly basis in my classes.

Now, sixteen years after having started my teaching career, I have two (very different) young daughters, and a whole new lens to look through when I think about how I approach my teaching style for my non-male students, and also for my male students. I want to encourage all of the positive behaviors that students can have, regardless of their gender and regardless of gender stereotypes. I also want to remember to meet each student where they are, and to do everything I can to help them see the exciting things that math can tell us about the world and ourselves. Or sometimes, show them how we can just have fun with math.