My six and a half year old son Bruce has been doing Math Without Worksheets to earn screen-time recently. I write down a number problem, and he writes down a word problem to match. Then he solves the problems numerically on the left-hand side of the page, and in words on the right. This type of Constuctivist activity is the nidus of someday being able to write out proofs in higher level math.
Bruce has been solving problems this way once a week for three weeks in a row now, and you can already see a really big difference in his work. For one thing, he’s writing down his thinking himself now, whereas before I had to write down his answers for him. But there is still a lot of room for improvement. As a former teacher, these are the things I am looking for (rubric style):
- The word problem should match the number problem. (+3)
- The word problem should be neatly written and in its own space. (+3)
- Numerical work should be neat, tidy, and in its own space. (+3)
- The numerical work should clearly show the strategy being used. (+3)
- The answer should be circled. (+1)
- The written explanation should be neat, tidy, and in its own space. (+3)
- The written explanation should clearly show the strategy being used. (+3)
If I was a third grade teacher scoring Bruce’s work in the above example, I would give it 12 out of a possible 19 points. The word problem, as well as the written explanation, both need a lot of work. Numerically, Bruce is showing that he knows that since 20 divided by 5 = 4, then 20 divided by 4 is going to equal 5. That’s a solid strategy for solving the problem.
Here’s another example from the same day that shows a lot of improvement. In this next problem, Bruce’s numerical explanation is even stronger, but the written parts are still a bit confusing. I’d give this example 15 out of a possible 19 points.
For the twenty minutes Bruce spent working on these two pages I let him earn half an hour of Lego Ninjago on the computer. Am I a “Tiger Mom”? No. Am I looking for extra ways to boost my son’s academic potential? Yes! The best part of all of this is that it is free and rooted in solid Constructivist pedagogy. No matter what math curriculum your child is using at his or her school, this type of practice can help.