Happy New Year 2020. We at ERC are excited to share news about a new partnership for our Innovation and Redesign Network. This one with What If Math, folks with big ideas, with huge potential to change the way we look at math. Read on!
I’m excited about math! For the first time in a long time. And it’s because I think I’ve seen a really significant next step for math education.
First, though, full disclosure: I had a tough time with math myself, almost all of it that I encountered after the 8th grade. My skill with arithmetic, which had won respect, now hardly mattered, and my standing on the math normative scale plummeted (even as it rose in world languages, history, writing, sports, music, etc). Years later, as a school leader and coach, I learned to bite my tongue about math --all the things I’ve seen, the missed opportunities, the foreclosure on numeracy, the use of math primarily as a sorter of young people. (Let me pause to say I greatly envy the skill of the able, deep, mathematical thinkers–you’ll meet two in a paragraph down the page—and I put a supremely high value on what engineers, scientists, programmers, and others have done and will do for our planet. So, math cognoscenti, bear with me, please.)
These days, apart from the beauty and utilitarianism of math, it’s most often referred to narrowly, as a tool for measurement of school performance. Math scores have come to represent a simple --and ineffective—approach to understanding schools and their improvement. Those scores, by the way, have been mostly flat for almost 3 decades while we keep doing pretty much the same thing. We make a little room for a marginally different, “new” math curriculum or “blended” approach every 4-5 years to show we are doing due diligence about those low math scores. But generally, the topic of math among policy makers is rare and elusive.
You don’t need me to tell you how most (lay) people react when the subject comes up again, math mavens, bear with me, please—“Oh, I didn’t do well in math”, “I really struggled with math”, “I’m not a math person”, or, “I’ve always had math anxiety”. A frequent disclosure runs something like, “I took History of Math to get through college”. We make it ok to feel this way—“Well, you really don’t need a lot of math to well in most jobs” or “you know, most math is really not related to the real world”,
Here’s a sample of routine commentary:
more kids fleeing from math, right from the start: from Psychology Today, link here
high-paying jobs for people who hate math, link here
teachers aren’t the problem, link here
Right? It’s this huge math irony we’ve learned to live with for generations. It’s there but it’s not a topic of discussion. We learn to live with it—until we have to discuss it with someone we care about in some capacity. Then, the vast majority of us, have to apply one of the above quotes. Additionally, I think we have to acknowledge the degree to which math, despite its critical role in critical fields, is a white elephant we can’t afford to keep feeding.
But bringing that discussion into a district, a school, a classroom, a Guidance suite, a PTA meeting? Never. Teachers? Who’s asking them? Besides, for any of these people, one has to know a lot of math to even dare to critique it.
Paul Lockhart’s A Mathematician’s Lament, 2002.
To help cope with my frustration, and to be clearer in my mind, about the rare earth of “school math” that disturbed me, I began to read and follow people with differing ways of seeing the world—Thomas West; Faraday; Eames; Kristina Lamour Sansone, whose Design Instinct Learning work in classrooms has always shined, and, of late, Froebel and Rhoda Kellogg. A dynamic Science teacher in Providence, David Evans, turned me on to Paul Lockhart’s A Mathematician’s Lament. A brilliant critique by a stellar mathematician and humanist. It inspired me that something might be done (although i must note it's almost two decades old now). So, I kept my math thoughts to myself, hunkered down, focusing on other deserving elements of the work, looking for an opening.
That opening came when I met the Math Guys. To be more specific, the What If Math guys—Peter and Art. These guys are seriously smart, have put a ton of sweat equity into ideas they want to share, and—I love it—they want us to think about math as a lab science! That got me right away.
Peter Mili is a long-time math instructor and coach with lots of years in a public-school setting. I like the chalk dust he brings, and he’s been recognized as a Teacher of Excellence by the NEA Foundation and a Pearson Foundation Global Learning Fellow. As well as thinking about the math involved, Peter has a sharp eye for when kids are engaged, and a deft touch for finding just the right starting point with teachers of varying experience and comfort.
Lamour Sansone showing child art researcher Rhoda Kellogg’s diagram illustrating the evolution of a child’s design development from scribbles to graphic form.
Co-founding partner Art Bardige seems to me to be quite a polymath. He’s all about revolutionizing education, and math along with it, and he’s not shy about saying so. Art started out teaching physics, then moved on to develop education films, developed a middle school math curriculum, then started his first company, Learningways. He’s well-known as a premier independent educational software developer, so it’s no accident that he’s gone in big with What If Math. (Here’s a link to his new book—Make it Real )
I’m excited about what ERC and What If Math" can do together. We’re hoping to introduce and include them in our new “innovation space” conversations, places we work where the status quo experience of school is not good enough, where they are thinking more seriously about actual redesign.
So, just what’s in the secret sauce?
A core premise of What If Math (link here) is that, outside of schools, the tools of our digital age are enabling us, and increasingly forcing us, to rethink problem-solving. At What If Math, they’re using a problem-solving process out of the worlds of business and design. They call it Functional Thinking because it builds models using functions on spreadsheets. They think, and so do I, that their approach, applied consistently and systematically, is likely to foster many more proficient, creative problem-solvers, many of who right now don’t care for math or things associated with it. That’s a significant promise to math educators.
Something else I’ve noticed about the What If Math approach is the potential for young people to find joy in the struggle and the over-coming involved with numbers and logic. I love to watch the furrowed brows and occasionally confused looks convert to a slight smile or a high-five. Its catching. As Jacob Bronowski observed, "The most powerful drive in the ascent of man is his pleasure in his own skill. He loves to do what he does well, and having done it well, he loves to do it better." And of course, if relevance, something that Art and Peter quest for relentlessly, isn’t part of the learning recipe, it’s probably not going to stand up well with students. That drive for “real-world” is easily seen in their ideas of utilitarian lessons and concepts.
Mili’s answer regarding the What If name, says a lot about their approach:
“Much of the mathematics students are asked to do is school is focused on answering a question of the type ‘What is ….’ For example: What is: the value of this expression? the solution to this equation? the slope of this line? the area of this triangle? the vertex of this parabola?
“One of our ‘mottos’ became to ask, “What If…?” instead of “What is…?” Using spreadsheets to create mathematical models for expressions, equations, linear functions, geometric shapes, quadratics, more advanced functions, recreational mathematics, and problem solving allows for doing a “What if” kind of analysis. We use parameters in our models so students can explore mathematical topics, solve problems, and answer questions like, What if: you increase the coefficient in this equation?—how do the solutions change? is there a pattern? What if you want a see a steeper line in your graph?—which parameter do you change? what change makes the line steeper? What if the base of a triangle decreases by a factor of 2 but the height is constant? -does the area decrease by a constant factor?
“We believe that these are the kinds of questions that engage students, and then, more importantly, help them want to know and do more, and prepare them for using mathematics outside of the classroom.”
When I asked Art and Peter what I might see in a place where WhatIf Math had been around for a while, here’s what I heard:
“If we walked into a 10th-grade classroom that had been thinking about math as a lab science, I’d probably see that class would start with every student engaging in some task that builds on key prior learnings. This would be very individualized and/or small team based. The balance of classroom talk would be in favor of students sharing, connecting, critiquing, with seamless technology usage. In the What If approach, tech tools are there to develop critical thinking skills, including coding, with spreadsheets and access to the web in the forefront. One can imagine an art studio in which students are creating, doing quantitative reasoning and problem solving.”
“Teachers are much less in front of the classroom, and much more among the students, desk to desk, table team to table team, as they explore and experiment, guiding, clarifying, questioning, connecting. And, of course asking, ‘what if?” And, ideally, the teacher would be part of a teaching team, collaborating frequently with colleagues, with time to do just that.”
I wanted to know more about how the Math Guys had come on to these ideas and where they see it going. Art recounted some aspects of What If’s development:
“We found that even the most difficult concepts in Leonardo’s math, like variable and function, became transparent and concrete in Spreadsheet math and available to much younger kids. We visualize a function as a table of values, simply a row or column of numbers, concrete and easy to manipulate. We visualize and focus a function as paired columns, one containing input values, the other starting with an = sign to build a rule and thus producing an output. As students experiment and become familiar with functions, they can learn iteration where the output of a function becomes its input. We found the power of iteration when we discovered a new way to solve any quadratic equation without the quadratic formula. We’re convinced this math will turn students on because it turns us on. Students can think of math as a place they can also discover new things.”
That’s a key part of the vision—making learning environment a place for discovery. I relish Tyack and Cuban’s critique of our industrial classrooms as places where students encounter “proven facts and pre-determined answers to set puzzles they must solve”. What If gives us something different.
“We keep being surprised at the power inherent in this relatively new technology, but then we should not be surprised because new technologies make hard things easy. We have to bring that simplicity, that power of functional thinking, to our students,” says Bardige.
WhatIf Math? spreadsheets.
There it is again, Bronowski’s theorem – that learning and growing are innate and dynamic. The fact that students see so little of this kind of joyous struggle underlies headlines such as these from Education Week and USA Today a few years ago – “Gallup Student Poll Finds Engagement in School Dropping by Grade Level”. (link here)
For Bardige, the idea of math as a laboratory science is only the point of the lance of their strategy. Bardige shares in his book that he stands for a complete rethinking of the math curriculum:
“The old stuff, Leonardo's Math, that we teach our kids is obsolete. There is no serious reason for our kids to learn it. On the other hand, the math used in business, science and industry in the 21st century, is largely spreadsheet math, with functions as the primary math element and thus functional thinking—model building—as the essential method of problem solving. The What If Labs we’ve designed so far represent a significant step in representing that vision. Recapturing the time spent today in classrooms on paper algorithm practice, we open the way to focus on the future, preparing students to be problem solvers and to use functional thinking as an essential quantitative part of that process. Moreover, it will integrate the disciplines. STEM will be thought of not as a a club of four --science, technology, engineering, and mathematics—but as an integrated approach to creatively solving interesting problems.
“Until that Utopian future arrives I like to think about What If Math as part of a “STEM Problem/Project-Based” approach, where spreadsheet math and functional thinking are used to enable students to deal with big databases and to build and experiment with quantitative models and modeling. Tools like Google Sheets and Microsoft Excel are free to schools and enable students to not just build models but to communicate and collaborate as well as to experiment which enables them to think creatively and critically. In addition, spreadsheets are coding and model building platforms. Problems and projects using spreadsheets—powerful computational tools—allow students to explore authentic issues and to test real world models. Such projects can be done as separate courses or as a portion of science or even math courses.”
Mili, however, would not limit the use of What if Math Labs and spreadsheets to only “revolutionary settings”, commenting “I believe they can be used in any classroom setting, given a teacher with the mindset to do it. He is cautious about “curriculum overhaul wars” with math educators, having seen them before. He believes a deeper focus on the how of K-12 mathematics teaching could be more productive for many schools, and move the dial in a bigger way,
“What I feel is missing is in the field is a coordinated effort to understand how the ongoing revolution of digital technology should inform our mathematics education efforts, and how to integrate technology into the practice of teaching and learning mathematics in an effective, authentic way. He, like Bardige, is particularly excited about rethinking the use of all the time spent in today’s classrooms on paper algorithms.”
This future oriented What If Math vision has resonated strongly with me and with the ERC team, the notion of strategic “letting go” of unproductive practices and replacing them with better structures and systems. That’s the essence of our growing network of innovation and redesign -IRN- people and places committing to what Ted Sizer challenged us to do in 1993- to evolve the systems, structures and practices that promote learning. It’s about time we got back to that. Now that we’re fully aware of the Math Guys, we’re talking about how to move forward together, both in and around schools. As a part of that growing collective, we’re driven to help schools find new ways to think about math, about school innovation and redesign, and about school (and policymaker) accountability.
Sir Isaac Newton’s mathematical thinking.
What If Math Labs are free, and work on Google Sheets and Microsoft Excel, and there’s no sign-in required for students and teachers. There are 125 now across all age and grade ranges and the team is constantly developing new ones. Art and Peter encourage and support any teachers who want to use their Labs in their classrooms, and if you register you can receive blog posts on mathematical problem- solving and the new Labs they publish. A Spring 2020 event will bring interested explorers together.
I’m also fond of What If Math because its so consonant with ERC’s vision of an emerging, dynamic curriculum approach, The Grand Challenges (link here) Thinking differently about what a “core curriculum” is and should do, is way overdue, something funders and innovators should ponder and use to press policy-makers. What If Math is just the kind of approach to help propel that redesign work in STEM fields and beyond.
Check out the What If Math website. It’s wonderfully abundant in ideas to get your mind going. Their work can be a huge catalyst at a time its most needed. If you want to engage with them directly, it’s easy. Or I’m happy to tell you more and have ERC be a connector. I’ve seen a big chunk of the future of math education. Come on down.
Dr. Larry Myatt
Co-Founder
Education Resources Consortium