Let's Stop Making Wrong Turns with Math Education
Note: Last week and this week RHSU is featuring guest bloggers from the National Network of State Teachers of the Year. For more on NNSTOY, check them out here. Today's post is from Mike Flynn. Mike is a director of Mathematics Leadership Programs (formerly SummerMath for Teachers) at Mount Holyoke College, and was Massachusetts teacher of the year in 2008.
In the wake of a Canada's drop to 13th place in the PISA rankings in December, there has been a proverbial angry mob made up of parents, pundits, and the general public writing letters, signing petitions, and openly calling for Canadian teachers to return to the basics in mathematics. It's an all too familiar story that we have seen in the United States. National or international test scores are published and people panic, point fingers, and call for sweeping changes in how we teach math (or anything, for that matter). However, in the rush to apply quick-fix solutions to very complex problems, the voices of those most knowledgeable about how to best educate kids in mathematics (teachers, math specialists, teacher educators, and researchers) often get drowned out by the masses who are not in the education field, but have strong opinions nonetheless. The result is a misguided attempt at reforming the way we teach math in our country.
Ironically, the "traditional" approach some are calling for is actually one of the reasons we have problems with math instruction in the first place. Traditional math, the kind you or I experienced as a student, is procedural mathematics where students are shown specific methods to solve problems. This approach relies on rote memorizing rather than building conceptual knowledge and often leads to a fragile understanding of key mathematical ideas. An example of this occurred when I tutored a group of third graders who were well-versed in the traditional subtraction algorithm. I asked them to use mental math to solve 200-198. To my amazement each student told me they could not do this mentally because it was impossible to keep track of all that borrowing in their head. They had only one way to think about the problem. Our students deserve better than that.
When talking to people about math reform, I often use a metaphor of trying to navigate Boston in my car. For years, I relied on MapQuest, with a series of step-by-step directions to find my way from point A to point B. I drove in a constant state of panic because I never had a sense of where I was, knowing if I took one wrong turn I would be completely lost. That feeling of dread was the same I experienced in traditional math classes as a child. I was always operating with just a vague notion of the mathematics and was completely reliant on the teachers' procedures, tricks, and shortcuts. When I remembered the steps and followed them correctly, I usually got the right answer, but I had no understanding of what I was doing. Even worse was when I forgot a procedure or made some error, I had no other strategies to solve the problem and had to ask for help. Being lost in math is a lot like being lost in Boston: it's no fun.
Tired of getting lost all the time, I enlisted the help of my brother (who was very familiar with Boston) to help me make sense of it. He rode shotgun as I drove and together we took the time to explore the area. He helped me discover key landmarks, learn the traffic patterns, and gain a sense of the layout of the city. It wasn't pretty at first. I made lots of mistakes, took roundabout routes when there were shortcuts, and got frustrated more than once. Scott was very patient and supportive. He let me figure things out, but didn't leave me floundering if I needed help. After a while, things started to click and I was able to navigate the city with relative ease.
This is the same intention behind reform math. Students need to explore mathematics, much like I explored Boston, so they develop a deep understanding and no longer have to rely on tricks or mnemonic devices. We want them to have multiple, efficient strategies to solve a wide array of problems. We want math class to be a place where students interact with each other as they work on complex and engaging problems. Most importantly, we want students to love math and feel successful with it.
Makes sense, right? Yet some are quick to criticize the reform movement as they're doing right now in Canada, and I think it's an unfair critique. Too often school districts simply hand teachers a new curriculum and expect them to change their teaching without support. It's like asking someone who's only used MapQuest to suddenly teach others how navigate Boston but not giving them time or training to explore the area. It's not fair to teachers and it's certainly not fair to students.
If we want to see improvement in math education, then school districts need to invest in ongoing, sustainable professional development for their teachers so they can deepen their own mathematical content and pedagogical knowledge. Then we need to support them as they begin to make shifts in their teaching. Just like my brother sitting shotgun, we need coaches and instructional leaders to help teachers as they begin implementing these new ideas with students. Finally, we need time to see results without kneejerk reactions after one short year of implementation. True learning takes time, space, and room for errors (and learning from them). We must give our teachers and students room to explore the area of mathematics so that math is no longer about memorizing procedures, but about developing strong mathematical ideas and understandings that benefit students for life, not just one test.