Math, but not what you remember
In my career as a teacher, I have always shied away from the canvas-book-bag-clichés, but the truth is I LOVE MATH. And more so, I believe that WHEN YOU DO MATH, YOU CAN DO ANYTHING. Despite my enthusiasm, I am not naive to the fact that this is not a popular passion. I find any expression of this passion often met with, at best, eye-rolling and at worst, ire and disdain. It comes from fellow educators, from parents, from the public.
In a recent article in the Atlantic, Here’s How Little Math Americans Actually Use at Work, the data suggests that less than a quarter of Americans use mathematics beyond arithmetic. The more basic arithmetic topics (any math, basic operations and fractions) are clearly valued much better than the middle and high school topics (Algebra, Geometry, Statistics, Calculus). These results, though, are dependent on the public’s definition of these subjects as they experienced as students, which often is nothing more than a list of vocabulary words and forgotten formulas.
In truth, we math educators can only blame ourselves. The mathematics of my heart is not equal to the set of all the procedures we have practiced, assigned, and board-raced for decades. It isn't the strange and mysterious feast that we have force-feed our students one bite at a time as they sit in quiet and compliant rows. The mathematics of this definition could not possibly be one of meaning or of use. We have spent a long time emphasizing how to use the tools, like equations and formulas, rather than on the real goal of solving problems. We have been running drills without ever asking the students to play the game. Imagine if baseball was only batting practice! Sadly, it is what many people have experienced. Even more sadly, it is the model of practicing mathematics that most math teachers experienced themselves as students and perpetuate, doing what we know to do.
The real magic in the Common Core Standards is that they articulate a different definition of school mathematics and what DOING math looks like. The Mathematics in this definition is a body of understanding, a discipline of sense-making. Mathematicians use reason to solve problems and logic to develop arguments. Within this body of knowledge, the old unit headings of our textbooks serve as tools that help to clarify and analyze the complex relationships and systems that we observe. Skills like factoring and solving equations are not the end, but rather the means by which we arrive at solutions. I wonder how the data in the study would be different if people were asked how often they solve problems, critique arguments, use models, look for patterns, consider precision, etc.
How do we learn to engineer experiences for students in this new world with these new goals? How do we evaluate if the experiences we are engineering fit the definition? I have been asking myself – and all the friends who might tolerate the conversation – for four years. The bullets below summarize three truths that have surfaced for me. And the inevitable questions that follow.
- The Math Practice Standards are not what students should be able to do AFTER they have learned, but are in fact WHAT they should be learning and HOW they learn the best. (Are my students engaged in MP1, MP2 and MP3 everyday? Each of the others every unit?)
- The Core Ideas tell the story of the Mathematics students experience across their careers and are the cross-cutting concepts (thank you, NGSS) that thread together their learning. (Can I define what the big ideas of my content are? Have my students connected today’s learning to one of the big ideas, like Equality or Proportional Reasoning?)
- What we assess is what we value. We have to assess the thinking of mathematics, not the mimicry and minutia of answer-getting or procedures. (Do my assessments provide students an opportunity to show me the depth of their reasoning and sense making?)
Certainly, I do not have the answers, but have discovered some truths that have helped me in the journey so far. I am going to share my thoughts on these three more here in the blog and on twitter, and I hope you will share yours! Follow us @the_explicator (Chris) and @kastidham (me).