Guest Post: Dennis Deets
In 1986, two years after graduating from college, I got picked up at The College Preparatory School in Oakland to teach all levels of math including AP Calculus (CPS, it is a prep school in the Oakland Hills between Berkeley and Piedmont.) My Department Chair, Dr. Joel Teller, had been a professor of Biochemistry at Berkeley, but left to help build CPS and focus on math curriculum development with Lew Douglas. CPS was, and still is, quite small, maybe 350 students. Getting in required some serious academic potential, but half our students were on full scholarship from areas all over Oakland and Berkeley.
Lew had connections with the Mathematical Sciences Research Institute (MSRI), and Lawrence Livermore Labs. Some of the professors and scientists were supporting a group of East Bay area math teachers through the Bay Area Math Project (BAMP). The BAMP was dedicated to trying new things in secondary math and collecting data on successes and failures. It was basically a clearing house with a bunch of sub-projects and a “throw it at the wall and see if it sticks” methodology. Lew was working with a number of teachers on developing geometry lessons that went beyond the T-column proofs standard at the time. He helped bring mirrors, tracing paper, straws, and other hands on relia into the high school geometry classroom. Lew was a regular presenter at the yearly Asilomar CMC North conference from the mid ‘80s through the last time he presented in 2017.
Joel had made connections with Dr. Sallee at UC Davis, and started attending a working group at UCDavis once a month or so. My memory is Dr. Sallee, Dr. Kasimatis, and their colleagues had an NSF or Eisenhower grant that would eventually turn into the CPM math program. There were drafts of the NCTM standards that would be adopted in 1989 floating around, and we were all pretty excited. This was well before California’s 1994 version of the Math Wars.
I got my two sections of AP Calc students (numbers were more like 1 ½ classes worth of students) and ¾ of the students were boys*. Lew asked me if I was interested in any of the working groups with BAMP. The group dedicated to getting more girls into higher math classes seemed like an obvious choice. I was a young teacher trying to remember as much calculus as I could. But at my first BAMP meeting, my colleagues let me have it. They asked me about the ‘situation’ and about what I had done. The situation, way more boys than girls, was abysmal and I had done nothing. How many girls are in your class? How many girls were there last year? How many in the past 5 years? Is this a trend or an anomaly? Imagine a bunch of math teachers wanting data.
Ok, step one: get more girls in class. This turned out to be mostly regular clerical work. I went to the registrar and got a list of all the students who were not in a math class (Yes we had computers in the ‘80s) I found all the female seniors without a math class and checked on their PSAT scores and what their class had been the previous year. This gave me about 15 girls with reasonable test scores and at least Algebra II already on their transcripts. I went to the counselor and asked about switching their classes around to make sure taking Calculus was even an option. This got me down to around 12 students. Time to hit the pavement.
If you are not familiar with CPS, it is a dream school, at least it was in the late 80’s. Class size was 20 students. Teachers had two prep periods, one to prepare, and one for office hours and tutoring. Students all had one open period to go around and get teacher support, work in the library, or hang out in the student center. The school also held daily ‘announcements’ in the multi-purpose room. All 350 students, teachers, and staff congregated for 15 minutes every day between 2nd and 3rd period. Admin, teachers, and students would line up to give their announcement at an open mic. So I got in line and gave my pitch, “I need more Calculus students, I still have 10 empty seats. If you are a senior without a math class, please talk with your counselor about taking my AP Calculus class. It will be the most fun you have ever had in a math class, 100% guaranteed. If you do not sign up today or tomorrow, please expect me to track you down. I will call your parents. Everyone needs to be in math their senior year.” Ding, my minute was up.
I was a young teacher trying to remember as much calculus as I could. But at my first BAMP meeting, my colleagues let me have it. They asked me about the ‘situation’ and about what I had done. The situation, way more boys than girls, was abysmal and I had done nothing. How many girls are in your class? How many girls were there last year? How many in the past 5 years? Is this a trend or an anomaly? Imagine a bunch of math teachers wanting data
I didn’t really wait. The next morning, I started on my sales pitch. I found my 12 students and explained about the difference between getting into college and actually graduating from college. I told them students who had taken AP Calc in high school were much more likely to graduate from college than students who didn’t. This was not the first or the last time I made up research to support my needs. (I had learned all about data manipulation in my undergraduate physics classes.) And, I was probably right.
Then I did something that turned out to be accidental genius. I asked my soon to be Calc students what were the reasons they didn’t sign up in the first place. Of course, most told me they had “math phobia” (a major disease of high school students well into the 21st century, later renamed “math anxiety”). “Ok, if you ever get that feeling in class, let me know and we will do what we need to do so it goes away. If you ever have that feeling while doing homework, write it down and I will give you credit for whatever you were unable to do at the time.” What else? “Grades!” Not a single student wanted her GPA to go down as a result of taking a math class. Specifically, they did not want a “C” or worse. Bad grades would be disastrous. Why risk it?
There it was, handed to me on a platter. The college going teen’s worst nightmare, “a ‘C’ or worse”. “I promise you, if you do what I ask, you will get a ‘B+’ or better,” I said. It took a little more cajoling with some, but by the end of the first week, I had the rest of my two classes filled and my male/female ratio was pretty close to 50-50. I went back to my BAMP group all smug, thrilled I had already done my job for the year of getting more girls in Calculus. They all looked at me like I was indeed an idiot. “Anyone can get them enrolled, but can you keep them? Can you help with their math phobia? Can you get them to take the AP test at the end of the year? Can you repeat next year? Will they score as well as the boys? Nobody used the word “ubiquitous” before the 21st century, but had they, my BAMP team would have wanted to know about the ubiquity of girls in calculus. It was on.
Jaime Escalante had already made the news a few years prior with his inner city low income students “suspicious” AP scores.
So what did we need to ensure the students stayed in class, took the AP test, passed, and if all went well, overcame their math anxiety? And could I find something that was replicable?
Christianson, Johnson, and Horn, have one of the best essays on Educational Research ever published (as a chapter in the second edition of Disrupting Class) The point of the essay is simply, educational research is not done double blind, nor are all other variables held constant. Consequently, ed research does not really measure up to e.g., Carnap's ideal of the scientific method. I think my BAMP team, partly consisting of Livermore Lab scientists, understood this at least intuitively and possibly influenced the ‘try everything’ methodology.
“Anyone can get them enrolled, but can you keep them? Can you help with their math phobia? Can you get them to take the AP test at the end of the year? Can you repeat next year? Will they score as well as the boys? Nobody used the word “ubiquitous” before the 21st century, but had they, my BAMP team would have wanted to know about the ubiquity of girls in calculus. It was on.
The first step turned out to be something I was deeply embroiled in regarding all of my classes (I was teaching Algebra I, Algebra II, and AP Calculus that year). This was our transitioning from teacher lecture/student notes pedagogy to a student group discovery pedagogy and peer teaching. Joel and I were revamping the Algebra I curriculum, Lew and Joel were revising the Algebra II curriculum and giving it to me for my Algebra II sections, and that left me to write the Calculus curriculum.
We put all the curricula we wrote in Hypercard, a popular Mac software at the time. This allowed us to basically customize per day and per year without having to completely rewrite everything. Our attitude towards textbooks was to ‘borrow’ whatever worked for any particular concept. Joel, as department chair, had requested from all of the publishers teacher versions of all of their textbooks. We had a library of work to pull from with the luxury of mixing and matching and writing our own when something wasn't already published. It turned out reteaching myself first year calculus was particularly helpful for writing curriculum. I could use the AP syllabus and write lessons that guided students through discovery to important concepts and theorems. And it was quickly becoming our practice to have students work in pairs, threes, and/or groups of four based on the needs of the students and of the topic, project or activity. (Some of this transition was undoubtedly a consequence of Dr. Teller working with UCDavis. We had people from Davis visiting our classes regularly. Unfortunately, the relationship broke down sometime after I left CPS probably in the late 1990’s around the time the second edition of CPM math was being published.)
A few notes on discovery and girls in math. Discovery, as conceived in the late ‘80s, required verbal and especially reading skills. (Many years later, when teaching in Fontana CA, where EL population was almost 80% in the late 1990’s reading level was the most significant factor in math success using the CPM curriculum.) Having students work collaboratively is a social activity, and I need to add, one that must be taught. High school students are social, but not predisposed to work as an academic team without significant guidance i.e., they need to be taught how to collaborate productively. These aspects of discovery, or constructive, math helped keep the girls who did not expect to find themselves in a math class less disoriented than they might otherwise have been. When the girls were put into this collaborative setting, their relational skills, developed through years of gender construction, enhanced their ability to learn. Furthermore, the class structure was pretty new to all the students. Consequently all were on equally unfamiliar turf.
Back to my BAMP team’s expectations, I needed some allies if I was going to keep my students enrolled. I needed my students’ parents on my side. Historically, parents push their sons into advanced math classes. I needed this support for their daughters as well. I started teaching when I was much closer to the age of my students than to the age of my students' parents. Parents terrified me. I bit the bullet and held a meeting of all calculus student parents one evening. I did my song and dance. I told them all about the cost of a college class at a college, at Harvard. (why not start with the idea my class was going to get them all into Harvard) I told them about the cost of the textbooks. I had a mostly well educated parent group, they already knew about the Harvard cost, but they were a little surprised by the Calculus Textbook cost. I looked them all right in the eyes and told them their kids would pass the AP test and that was just as good as them earning $3000 (or whatever it was at the time). I explained that their kids may try to drop the class. “Don’t let them!” I said. I explained my grading practice and told them to call me if they ever needed any help with their kids and Calculus.
Side note, after the first student unsuccessfully dropped the class a few weeks into the semester, I realized I needed to contract with my students and parents. The contract had all sorts of wonderful smiley face language about success, but the bottom line was that counselors and parents would not drop a student from my calculus class without first having a meeting with me and the student. Counselors are mostly amazing human beings, but sometimes they can be talked into things. Side to the side note, after the first student dropped, and I threw a total fit, the student was put back into the calculus class with parental support. This might also have helped with retention in the long run. Word got out, “Don't drop his class, he will just get the counselor to put you back in.”
These aspects of discovery, or constructive, math helped keep the girls who did not expect to find themselves in a math class less disoriented than they might otherwise have been. When the girls were put into this collaborative setting, their relational skills, developed through years of gender construction, enhanced their ability to learn. Furthermore, the class structure was pretty new to all the students. Consequently all were on equally unfamiliar turf.
Let’s talk about the hard times dealing with math anxiety. As mentioned, I had the luxury of having an office hour in the middle of the school day. I was even more lucky in that students took advantage of this time for one on one or small group instruction. But no one told me while I was working on my credential I would have students crying in my office. And they did. I didn’t have any boys crying in my office. I did have some girls, not a lot, but some once or twice and some regularly. Real tears. I was horrified. 4) “I can’t do this.” “It doesn’t make sense.” “I'm not smart enough.” “It is too hard.” So there it was, I was teaching math, but it was clear I was also needing to teach patience, perseverance, self-esteem, confidence, and so much more. And I really didn’t want anyone crying in my office. I really didn’t want anyone hating math or hating school or hating learning.
That these girls had the courage and fortitude to share their frustrations had tremendous benefit for my classes as well. It was not too hard to generalize, if Riemann sums are making one student’s life miserable, they are probably making many students’ lives miserable. I could work on developing some reteaching activities for the next day. I could also make use of my rule, “If you do what I say, I guarantee a B+ or better.” Depending on the situation and the crisis, what I often said was, “Put your math away. Do your other school work, sports, whatever, tonight, don’t open your math book. Stop by 15 minutes before school starts tomorrow or at snack break after assembly and we will start again.” Riemann sums are not something to learn while crying.
When the student came back the next morning, I did not assume she had somehow learned the concept while doing her history homework. Although my general method of teaching was through discovery and peer teaching, there is a time for clear explanation, the “I do” part of “I do, we do, you do”. Depending on the time, I would spend a few minutes with “I do” letting my student follow along and or take notes as she liked. That day in class, we were likely doing the reteach lesson and so she would now be one step up on many of her peers with this one-to-one pre-teaching. Math anxiety hits students, and probably adults, all at once. Things are fine and then they are not. Of course, taking some deep breaths, etc. works sometimes and to some extent. Taking a short walk works sometimes and to some extent. But for me, showing compassion was probably the best.
Side note. My one-to-one and small group sessions during office hours helped me learn a lot about aloud self-talk and making sure students had some idea what I was thinking while thinking about math. I would not be so bold as to think I cured my students of math anxiety, but I do know by the time the AP exam came around, none of my students panicked. They were emotionally prepared for their exam.
Plato argues math has two primary functions: (1) math can help us build better catapults, i.e., it has a pragmatic function, and (2) math helps us learn how to think abstractly, i.e, it trains our minds how to think about universal concepts like: justice, beauty, virtue, etc. We still believe (2), but we think our students will somehow intuit abstract reasoning skills from math class. Thinking clearly about abstract concepts was rarely the focus of any lesson even in the ‘80s before TIMSS and all the testing. But I needed a way to keep the students engaged and invested in class. I had what amounted to negative reinforcements from parents, counselors, and my contracts. I needed some positive reinforcements. At the time, my own prejudices about women emerged. Because there were almost no females in my high school and college physics classes, I assumed girls didn’t like physics. I thought, I need something other than velocities of rockets and volumes of toruses to keep my students, especially my girls, wanting to come to class. I had the good fortune to be living with a Berkeley math grad student at the time. He told stories about his weird topology class where the professor gave World War II history analogies throughout the topology seminar. This made me think maybe calculus didn’t need to be about the tree shadow lengths or the path of basketballs. Maybe it could be about finding love, living forever, the origin of the universe, The Cure. Maybe I could push Plato’s second function more. Of course, at some point the right length of ladder and the right distance for the rocket needed to be computed, but these were bad places to start for most teens.
How about that B plus or better thing? I did a lot of rubric grading. That made it pretty easy to start, four piles of work, A, B, C, redo. everyone with B or C got the option to redo. On tests, students who did not do well were told to do test corrections and sometimes were told to do make-up tests. They were told to come to office hours. the B+ or better was always contingent on doing what I asked them to do. In short, my students did not have to go into high stakes situations worrying about failing. I also developed with my fellow CPS teachers, a win-win grading system. We figured some students would do well on tests and maybe not well on projects, problem sets, etc. We also figured some students would not do well on tests but could do well in all these other situations. Students had a weekly assessment grade, a final assessment grade (the final assessment was a full released AP exam given on a Saturday under test conditions two weeks prior to the actual exam), and an everything else grade. The highest of the three was recorded on their transcripts. I was using the ‘and everything else’ grade to my advantage in my contract.
I thought, I need something other than velocities of rockets and volumes of toruses to keep my students, especially my girls, wanting to come to class. I had the good fortune to be living with a Berkeley math grad student at the time. He told stories about his weird topology class where the professor gave World War II history analogies throughout the topology seminar. This made me think maybe calculus didn’t need to be about the tree shadow lengths or the path of basketballs. Maybe it could be about finding love, living forever, the origin of the universe, The Cure. Maybe I could push Plato’s second function more. Of course, at some point the right length of ladder and the right distance for the rocket needed to be computed, but these were bad places to start for most teens.
That contract at the beginning of the year, thanks to my BAMP group, also included Take the AP Test. Someone had the good sense to warn me to get students and parents to commit at the beginning of the year not after winter break. But it was still some work to make sure everyone signed up. I had the idea I would explicitly not teach to the test until the month prior to the AP test, and then only teach to the test. So, during the month of April, I cut up and photocopied old test questions. And probably like every AP class everywhere, my students worked on moving their conceptual understanding of the material into rote skills demonstration.
My students did well. Much better than I expected. During my years at CPS, I had 100% of my students take the AP Calc AB test with 100% scoring 3 or better. Today, just under ½ the students taking the AP Calc AB test are female, but still for those taking the AP Calc BC test, it is closer to 40% female. I collected data and presented it to my BAMP colleagues. We shared lessons and stories and provided support to one another. With Dr. Teller and Lew Douglas, I wrote up presentations for CMC North. And a few years later, because I was too young at the time to have the perfect job, I left CPS and went to grad school.
My BAMP group was always emphasizing cognitive coaching, “What did you learn?” “What will you try next?” “What can you recommend as best practice?” “Are you going to present at CMC?” Eventually, at one point in my career, I had a job working for the CDE presenting on the CCSS Math Standards all over the state, but what I learned that year at CPS was fundamental to my teaching. Feminist theory posits: a wider diversity of perspective improves the quality of life for all people. We need people of different races, different sexes, and different cultural heritage to be able to provide their perspective without it being marginalized. These people's perspectives are necessary for human flourishing.
When I was a child in the ‘60s, elementary school spelling bees made me cry. Elephant was obviously spelled “elifant” which always turned out to be wrong. I never imagined math could make someone cry. It was not in my experience. The girls in my math class taught me that for some people, math resembled spelling. I had to change my thinking about lessons to accommodate this fact. It changed my pedagogy significantly. Loving math problems put me in the minority, which was fine, except it wasn’t fine when writing curriculum and teaching students.
The girls in my classes also taught me that with sufficient background knowledge, they could learn and master exactly the same math skills as the boys. And in the bigger picture, pushing academic research forward at its core depends on seeing the world in new ways. Primatology, zoology, and even biology had a renaissance in the 70s because Jane Goodall saw chimpanzees differently. I imagine history will one day show planetary physics and astrophysics will make huge conceptual growth in the coming decade due to the influx of women and other minorities into the field (in combination with new JWST data - new perspectives on new data). Finally, I think Plato is right. I often hear people say, “I am not a math person.” This is like saying “I am not a person who thinks about abstract concept.” Firstly, I think it is probably false. But it is also dangerous, especially to society. People, all people including women and minorities, benefit from thinking critically about abstract concepts, be it about limits or about justice. People, all people including women and minorities, need good math education that supports their competency and their happiness.
*Through this essay, I try to use the gender/sex language I would have used in the 1980s. Appropriate gender/sex terms, esp for teens and young adults, is the topic of a different essay. At the time, I remember thinking my students were too old for ‘boys and girls’ and too young for ‘men and women’. Still, gender neutral language is difficult and evolving.
Current BAMP groups:
BAM-C (Bay Area Math Collaborative)
BATMATH (Bay Area Teachers and Mathematicians
Dennis Deets retired recently after working 35 years as a teacher and school administrator. Career highlights include working as liaison between school districts and the California Department of Education and on CCSS implementation.