These past few weeks have been some of my most enjoyable in my over thirty years in education. This semester I have the privilege of re-imagining the content and teaching methods used in a developmental mathematics course at MSU. With failures rates hovering around or above 50% in this course change is needed.
I have watched my students as they have become accustomed to my methods and been vulnerable enough with me to share their personal math journeys. Many feel like math has damaged them and one theme that emerged as they shared their stories is that it started with learning multiplication facts by taking timed multiplication tests. Their stories include frustrated parents, missed recess time, missed sundae parties, teacher scorn, and downright embarrassment because "other kids got it and I didn't!"
This past week I was sitting with a student helping her review for our first test. Despite showing me great thinking she began to cry. I asked her what was a matter. She said, "I am worried that if I do not pass this test, I might not pass this class, I won't make it through school, and I won't get a good job! I have just struggled with math for so long I just don't know if I will ever get it!" As tears flowed down her face I asked her how long she had felt this way. She said, "Since we learned times tables." She shared, in great detail, that she had been slow to learn them, could never do them as fast as the other kids, and missed out on going to the sundae party with the rest of her class. She said her parents would try to help her by doing flash cards with her, but it did not help. She said it made her feel stupid, hate math, and she stopped trying because she believed she would never figure it out.
I am not opposed to fluency with multiplication facts and practicing those facts, but why do we have to time the process? Do there need to be winners and losers based on speed?
As we talked more I asked her if she could tell me what 8 * 6 was? She nodded her head that she couldn't. I asked, "How about 4 * 6?" She nodded again that she couldn't. I asked, "What about 2 * 6?" She said it was "12". I wrote the problem on a sheet and asked, "study 2 * 6 and tell me what 4 * 6 would be?" She said "24". I asked what did you notice? She said it "doubled". Then I asked, "What about 8 * 6?" She took a moment but said "48". I did not do my best work to uncover her thinking, but I pressed her to think about what 16 * 6 would be. She wrote out 16 + 16 + 16 = 48 and doubled that to get an answer of 96. I knew she was starting to see something. I finished by asking her if she could use all her work to tell me what 15 * 6 would be? She paused a bit, and finally said "90". She smiled from ear to ear in a way that made might heart grow "10 times larger!"
If you ask a mathematician, in general, what their work entails they would tell you it is about "looking for patterns and finding relationships." I believe there is a mathematician in every child, but it is slow thinking, not fast thinking, that wins the prize because often patterns and relationships take time to see. Are we giving our students an opportunity to do this? Think for a moment the power of the following sequence of multiplication problems. Oh the places you could go!
2 * 6
4 * 6
8 * 6
16 * 6
15 * 6
I think we are all wired to think this way. We just need the right sequence of problems, a little time, and the opportunity to explore. I know we want to do what is best for our children, but as this story exemplifies, and is repeated many times as I talk to other students, timed multiplication tests seem to be doing more harm than good. If that is the case, why does it continue?
