Back to the Future
I’ve been a cook since I was big enough to kneel on a chair to reach the kitchen table. I remember my father teaching me to measure flour, a small cloud rising above the canister as I leveled the measuring cup with the back of a butter knife. A quick sift, cut in some ice-cold butter, roll and cut the dough into rings, bake for 15 minutes at 450°. I couldn’t wait to taste those fresh biscuits, the flaky, buttery crust dripping with even more melting butter. Before I’d ever really heard of Paradise, I already knew its official food.
Dad wasn’t my only cooking teacher. My mom was equally talented in the kitchen, and in a house with books in every room, cookbooks dominated the shelves. On weekends, Julia Child and the Frugal Gourmet were like extended family members.
In school, my first love was always math. Solving a difficult problem has always been satisfying. I started elementary school towards the end of the “New Math” movement, so we learned about set theory and base 8. By the time I entered high school, though, the “back to basics” shift was in full swing and my schooling was much more traditional.
Evolution of Math
Skip ahead to 1996. This was an important year for me, personally and professionally. A blizzard dumped 30 inches of snow on the Philadelphia region, closing schools for a full week. After four years of teaching third grade, I moved to fifth. Pennsylvania gave its very first state assessment. I turned 30. My second child, Timothy, was born, as was the Google search engine and the TI-83 graphing calculator.
Things were also beginning to change again in mathematics education. In this same year, the US Department of Education established the Mathematics and Science Educational Panel, tasked with evaluating the quality of K‑12 mathematics programs.
1996 was also the year that Laurie Kreindler (@LaurieEDU) and Tom Laster founded IT’S ABOUT TIME™ (IAT), publisher of the Interactive Mathematics Program® (IMP). In the NSF-funded video above (Life by the Numbers with Danny Glover), an exuberant Danny Glover (@mrdannyglover), fresh from a successful run of Lethal Weapon movies, introduces IMP to an audience conditioned to teaching and learning traditional math. IMP, however, was anything but traditional. When this video was produced, featuring teachers and students from Philadelphia Central High School, IMP was only being taught to35,000 students in approximately 200 schools nationwide. IMP was a radical new way of thinking about high school mathematics instruction. With an emphasis on problem solving and understanding of deep concepts, IMP set a new standard.
“You might not realize it, but mathematics can unlock incredible power! Mathematics is a powerful tool for exploring life on earth and discovering our place in the universe. Why would anyone teach you what the tools are without helping you learn how to use them? That’s exactly how mathematics have been taught in this country for decades. All around the country, dynamic educators and innovative professionals are finding a way to make math make sense. Who knows, you just might discover that you are really pretty good at math because you’ve had the tools all along!” — Danny Glover (Life by the Numbers, 1996)
Today, my son Tim is a college freshman. It’s enlightening to compare how math instruction (and cooking!) have evolved in the years he’s been alive.
Nerdy is the New Cool
Twenty years ago, there were only a few chefs in popular culture: Julia Child, Wolfgang Puck, Emeril Lagasse. Their television shows were primarily about making sophisticated techniques accessible to untrained cooks using the equipment available in most home kitchens. Still, to admit you were a fan of cooking shows was to embrace the label of “nerd.”
Math in school was in a similar place. The “math nerds” didn’t hang out with everyone else. In fact, it was cool to proclaim that math just wasn’t your thing. And nearly everywhere, school math focused on computational fluency and getting the right answers.
But 1996 was at the cusp of changes in both fields. The NCTM standards had started a movement away from rote learning towards an emphasis on problem solving and application, exemplified byIMP. And the fledgling TV Food Network was beginning to change the way America thought about cooking.
Today, popular media and culture are filled with cooking competitions and festivals. Artisanal pickles and small-batch craft beers are mainstream. Chefs are celebrities, and they even have live touring shows. It’s cool to be nerdy about food.
Math sadly hasn’t made as much progress. Danny Glover told us about popular nineties icons bad-mouthing mathematics, and today Hollywood still hates math. Even when Hollywood shows it a little love, math is almost always the domain of the quirky genius or the mentally ill one. It’s math as spectator sport, still not something mere mortals should attempt.
Understanding Is Engaging
The PSSA test in Pennsylvania brought with it a new kind of test item my colleagues and I hadn’t seen before on standardized tests: the open-ended question.
For me and my students, the most challenging part of these questions was the requirement to explain reasoning. For the first time, it wasn’t enough to pick the right answer out of a list. My students had never been asked to answer the questions “Why?” or “How do you know?”
So we developed some rudimentary techniques to start building those muscles. We gave students a challenging problem and asked them to work on it for a week. We encouraged them to work together and talk to each other. We spent time teaching writing and vocabulary. We even gave them problems to which we didn’t know the answer.
Although student engagement has today achieved buzzword status, it was hardly talked about twenty years ago. Nonetheless, when our students were working on complex problems, they were more deeply engaged. Our math class was being transformed into one focused on big mathematical concepts; without realizing it, we were inventing in our elementary classrooms what IMP was doing for high school math.
A similar transformation was happening in the world of cooking. As we turned to the 21st century, Alton Brown created Good Eats. Equal parts Julia Child, Mr. Wizard, and Monty Python, Brown did far more than just walk his audience through a recipe. He taught us why it worked. And did it in a way that was deeply engaging. My son Tim has probably seen all 252 episodes of Good Eats at least twice. Though he and I did spend a fair amount of time together in the kitchen, I suspect Tim learned far more from Mr. Brown.
Defragmenting the Curriculum
For my entire school career, first as a student and then as a teacher, math class was fragmented into two-week segments. We’d spend two weeks learning, say, how to add three-digit numbers. One day we’d add without regrouping. The next we’d add with regrouping. Eventually, we’d take a test with all the kinds of three-digit addition mixed together.
The day after the test, we’d start a new unit: perimeter and area. Two weeks later: fractions. And so on. Many schools institutionalized this with scripted programs and tight pacing calendars. Thanks in large part to a ten-year experiment called Project Follow Through, direct instruction was touted as vastly superior to any other method.
This design was the epitome of what David Perkins calls “elementitis”: teaching a subject by breaking it down into its smallest elements and teaching them in isolation. The instruction is more manageable, but it sacrifices understanding for simplicity.
By far the biggest change in school mathematics is now happening as a result of the Common Core State Standards. Instead of fifteen topics to cover at breakneck speed, we now have three or four major topics each year. The explicit intention of the Common Core standards is to allow teachers and students to spend more time and go into more depth.
This does not go far enough, however. The groundwork has been laid, and if the next twenty years are going to be better than the last, it is time to reinvent mathematics.
The Future of Math
While some schools may still choose scripted programs despite more recent evidence that direct instruction is ineffective, more reflective schools, like Etowah High School (“What Does Math Look Like in Today’s Classroom?”), will embrace this opportunity to rethink their instructional practices. Three things need to happen for school math to be relevant and meaningful in the twenty-first century:
Bypass the Busywork
One thing that hasn’t changed at all in the past twenty years: high school math classes still use the TI-83 calculator, even though today there are more options, like Photomath, Desmos, and Wolfram Alpha. Look at that Danny Glover video again: what was once state-of-the-art in video production today looks dated and even a bit cheesy. It’s well past time for us to have high def math.
Our reliance on old tools and methods just allows students to lose even more ground. “It’s not so much that maths education is worse than it was;” says mathematician Conrad Wolfram, “instead, real life is much more demanding and we’re running in the wrong direction to catch up.”
Wolfram’s approach to math is radical: stop asking students to do computations that can be done more easily by a computer. Although many schools may not be ready to dive head first into this deep end of the curriculum pool, we all must shift instructional time significantly towards mastering the few things that humans still do better than computers.
Understand the Brain
Any professional educator should be an expert in learning, and to do that you must understand the brain. We know far more today about how the brain learns than we did twenty years ago (as Sherry Fraser explains in an interview, “Sherry Fraser Doles Out Mental Ice Cream with Problem-Based Math.” Math educators must understand the mental processes involved in subitizing, number sense, and how the brain processes different kinds of learning experiences. They need to be aware of developmental and emotional factors and be able to recognize different causes for a student misconception. Teachers also must understand how to gain and maintain a student’s attention, when to shift gears, and how to design instruction so it aligns with the brain’s natural timing and patterns.
Design Whole Learning Environments
Connected with understanding the brain, math teachers must realize the importance of the entire learning environment on a student’s learning. Curriculum isn’t enough, nor is it adequate to rely on an instructional bag of tricks. Physical space has a significant effect on learning, as does the culture of the classroom. Math teachers must be intentional about not just designing lessons but designing the entire environment in which those lessons will take place.
The more I learn about cooking, the more complicated it becomes. Every new idea, technique, and ingredient carries with it a raft of other things to learn about making good food. I find the same is true for math: transformation will take time. We’ve come a long way since IAT and Danny Glover made that film. Programs like IMP are helping teachers do the hard work of thinking differently about what math class should look like.
But we still have work to do. Edward Begle said in 1972, “Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.” If he were alive today, I suspect he might say this is an understatement.