Math’s Groundhog Day
When are we going to teach math understanding, and not just knowing?
by Ana Redmond
I keep reliving this conversation over and over again with different moms. One mom, who now runs an after school center for kids, said when her daughter was young she was behind in math. So, she took her daughter to one of the math centers that make kids do worksheets in a very strict progression. She was excited to see her daughter solve 3+6 one day on the worksheet.
Another day, she was driving with her daughter in the car, and asked her daughter a situational question. There are 6 cars in this parking lot, and 3 on the road, how many in total. She did not expect the answer she got: “I don’t know.” The mom eventually realized that her very smart daughter had memorized the math symbols and answers without understanding their meaning at all.
I met another mom, a very highly qualified Russian immigrant with advanced science degrees, at an event at which I was talking about math learning by doing. She described the time her son was in 3rd grade, and desperate and frustrated with math. The teacher required them to do math in a minute. And, if they weren’t able to, a note came home, to make sure the parents made him do so repeatedly. After several frustrating attempts at math memorization during which her son screamed in frustration, the mom took him out of school, gave up her job and started homeschooling.
Recently, I met another concerned mom and dad whose daughter is struggling with math. Her daughter is in 2nd grade and having trouble with math facts at school. She is frustrated. Her daughter is supposed to work on her math facts at home. She says teaching her daughter math is like Groundhog Day. Her daughter memorizes the math facts, and then the next day they start with the same facts all over again when she forgets them (just like Groundhog Day).
6 years ago, that was also my story. I started building math games for my daughter when she started falling behind in math in kindergarten. She was getting extremely frustrated and agitated when it was time to do math. Yet, she was an advanced reader, reading at 2nd grade level. It was not that she was incapable. The problem was how math is taught to young kids.
Adults seem to believe that if kids memorize enough math facts kids will figure out the meaning of the symbols without being told what it is. It is true that some kids do figure it out on their own. Many kids either don’t understand the meaning of the math or don’t do so till much later, by when they have already been branded as poor in math.
Jo Boaler, Professor of Mathematics learning at Stanford writes in this article:
“The irony of the emphasis on speed is that some of our world’s leading mathematicians are not fast at math. Laurent Schwartz — who won math’s highest award, the Fields medal, in 1950 — wrote in his autobiography that he was a slow thinker in math, who believed he was ‘stupid’ until he realized that ‘what is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.’”
Math is not computation. Math is patterns and symbols that have meaning. Math is a means of communicating complex ideas.
As a software developer, I also recognize the irony of forcing our children to learn math facts. I never use memorized math facts for calculations ever. I couldn’t even if I wanted. I don’t remember them. But, I constantly use math. I convert the real world to math. I convert requirements into equations and procedures that the computer then runs. The important part of math is understanding how to represent a real world problem using mathematical symbols. How math connects to everyday things. What math symbols mean.
That’s the math I taught my daughter. I built her games that explained concepts simply. She understood the meaning of the symbols by solving simulated problems. The understanding she gained built her number sense. I never again asked her to memorize facts. But, once she understood the meaning of the symbols, the memorization happened automatically. If she forgot the math fact, as she sometimes did, she just went back to basic principle to figure it out again. She developed a strong foundation in math along with her confidence in her ability to figure it out. Now, she is one of the best students in math in her 6th grade class.
Albert Einstein famously said:
“Any fool can know, the point is to understand.”
Then, why do we keep teaching math facts (knowing) instead of math concepts (understanding)? When will we all stop reliving Math’s Groundhog Day?