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Math…It’s Not One Size Fits All
Since I majored in mathematics in college, I obviously have a love of numbers, but I am not Rain Man. I can’t multiply two digit numbers by two digit numbers in my head quickly, and I figure out the lowest unit cost at the grocery store by using my calculator. However, I do have a pretty good conceptual understanding of mathematical processes and how they can be applied to solve problems. I’m not saying mental math is useless, but if we constructed a mathematical skills hierarchy, it wouldn’t be anywhere near the top. Unfortunately, teachers often focus on memorizing multiplication tables and mental computation to the detriment of many students.
A very good friend of mine, Sally, recently asked me for suggestions that might help her son in his elementary math class. He was driven to tears daily from the frustration he felt when he couldn’t keep pace with the activities. Sally, also an educator, was at her wit’s end, unsure of how to help him succeed in class and eliminate the drudgery his math homework time had become for both of them.
That evening I asked to help “Bret” with his homework to see if I could identify the root cause of his struggle. Bret had been assigned eight problems. Each problem was different and they all involved linking math to the real world…so far, so good. I read the first problem aloud and asked Bret if he had any ideas where to start. He not only had ideas about where to start, but he had a plan for the problem. He dove in and began working. At one point, he said to me that he needed to multiply 63 by 27. He was right, he needed to do that, but he stopped. He had written down and lined up everything correctly but could go no further. I could tell he was thinking so I asked, “Bret, what’s wrong?”
He said, “I know what seven times three is, but I am trying to remember what seven times six is.”
The light bulb went on for me. I printed out a multiplication table and put it on the desk. He went back to work. In no time, we had all eight problems completed. It was obvious from Bret’s demeanor as he left my office that this homework session went much better than usual. His mother was annoyed when she saw him because she knew there was no way he was finished, but she was wrong.
I did three things to help him: I read the problem aloud, at the end of each question I asked if his answer made sense, and I provided a multiplication table for him. HE completed the eight problems in less than 20 minutes. Why do I tell this story? I tell it because as math teachers, we need to identify every “Bret” in our classrooms so we can intentionally remove the barriers to success in math. As a former high school math teacher, I had plenty of students that were efficient with mental math, but they had no idea when to use what in problem solving. In this case, Bret knew how to apply his math skills, but needed help with calculating accurately.
Teachers also need to be intentional about deciding the outcome for each lesson and activity. Is the goal to develop mental math skills or is it to persevere in problem solving? Both are important and fluency plays a role in both.
Bill McCallum, lead writer for the CCSS math standards wrote in a blog comment on April 2, 2012, “Fluent means “fast and accurate” and mental means “in your head”. A fluent calculation is not necessarily mental; a student could be fluent with a paper and pencil algorithm, for example. And a mental calculation is not necessarily fluent…”
Sally’s son is a student with an IEP. He has a learning disability in written expression, reading and math computation, and his IQ is 115 (that puts him in the superior intelligence range). We cannot leave him, or any other student, behind because they are not fluent in mental math calculations. I’m the perfect example of how someone can be a successful mathematician without a supernatural ability in mental calculations, and if you will excuse me now, it’s time to watch Judge Wapner.