Pi Day is an annual fun day when people employ a homophone connection and celebrate the day with pie. Irrational? It has taken me by surprise a few times. The most notable was when a popular breakfast restaurant publicized that they were honoring Pi Day. My family begrudgingly put on the Sweetie-Pi and Cow-Pi t-shirts I had purchased at an NCTM conference and wore them to the restaurant. Not a single employee of the restaurant even noticed we were dressed for the occasion (I had to ask a waitress to notice them). Still, I am a fan of Pi Day. In 2015, in fact, I had quite an irrational party, in which we all toasted with champagne at 9:26. (If you are wondering why, consider that Pi is infinite and look at its digits beyond 3.14) But wouldn’t it be great if we could celebrate a little bit of the value of Pi and other mathematical ideas? At the very least, can we take on some of the irrational ideas that people hold about today’s mathematics and replace them with more rational ideas befitting the 21st century? Here are my top three irrational ideas I regularly hear from lay people and educators, and my suggestion for what is a more rational perspective.
Irrational Idea #1: The new strategies in math are silly/not needed/a political agenda. First of all, none of the strategies for doing this level of mathematics are new. What is new is that many newer standards in Grades K-8 ask students to “use strategies” to do mathematics. Let’s pause for a moment and do some math ourselves.
Let’s debrief. For #1, stacking the two numbers and regrouping is an irrational idea for a mathematical thinker. A mathematical thinker would notice that 98 is really close to 100 and use that idea to more quickly add those two numbers. One strategy is to add 100 + 45 and then subtract 2 from the answer. Another strategy is to move two over from the 45, making a new problem of 100 + 43. Done. It is certainly irrational to stack and regroup for number 2. Those numbers are only 9 apart. If your child or students are stacking and borrowing or regrouping, they aren’t thinking. Finally, fractions. Creating improper fraction(s) here is irrational. You have two and a half, maybe dollars. Two of those make 5, double again, and you have 10. So, the not-new strategies, now explicit in our standards, are there in order to help us create students who can select a reasonable strategy given the numbers in the problem. This flexibility is central to procedural fluency and a must for mental math, which is 90% of all the mathematics we do.
Rational Idea #1: Explicitly teach strategies, with a focus on making good strategy choices.
Irrational Idea #2: Timed tests make students faster. The only thing that gets faster with timed tests is students’ heart rates. Yes, timed tests cause math anxiety. And the anxiety they have leads to avoiding mathematics, not being good test takers, not pursuing mathematics-related professions, and so on. The most effective way to learn basic facts is through strategies (aha, see #1!). To add 9 + 6, for example, students first count up, then they learn to use a strategy like moving one from the 6 to re-imagine the problem as 10 + 5 and add. This strategy initially takes time to think through (in fact, at first it is slower than counting), but eventually the student masters this “move 1 over” idea and not only can they answer 9 + 6 automatically, they are set to do #1 above and beyond! When under time pressure, it is hard to think, and students resort back to counting. [Sidebar: a 1-minute timed drill is not the same as the end-of-year timed assessments in which a fluent child has plenty of time to do all the problems.]
Rational Idea #2: Never use timed facts tests. Instead, play facts games to allow time for students to practice strategies.
Irrational Idea #3: Mathematics is genetic. In science, the nature/nurture debates are fascinating. So, here is one for the masses. How is it that math could be inherited (imagine hearing a parent saying “I wasn’t good at math either”), but that science, reading, and social studies are not? Mathematics is something everyone can do, but we struggle with a few cultural realities that have stood in our way. First and foremost, elementary teachers and parents must stop immediately with saying things like, “I was never good at math.” “I don’t like math.” “Math is hard.” Just stop. If you don’t like it or don’t feel good at it, you were probably a victim of the two irrational ideas above (only learning standard algorithms with no conceptual understanding behind them and timed skills tests). Math does make sense and it is learned well by anyone who has the opportunity to see why procedures work (and when to put them to use). Second, we have to quit grouping students by ability. Tons of research indicates that all students do better when put in mixed groups. Can we learn from our high-performing countries on this point?
Rational Idea #3: Communicate to all audiences, including yourself: Everyone can make sense of and do mathematics.
In the year 2020, when we might think of having a clear vision of our futures, the most rational way to proceed is to consider that mathematics is meaningful and useful. In the 21st century, computation is almost always completed mentally or using technology. Mathematics is used everywhere. We need every child to be competent and confident in mathematics. That idea may seem radical, but it should not seem irrational, as it is the way that we can ensure a future generation able to navigate the technology-rich, constantly changing world in which they will live.
Jennifer M. Bay-Williams is a national leader in mathematics education who has written over a dozen books and many articles about K–12 mathematics teaching, most recently Math Fact Fluency and On the Money. She is a mathematics teacher educator at the University of Louisville, Kentucky.