Thursday, March 5, 2009

Multiplication & Division Algorithms

I have a student who is very good in mathematics. But he does not follow the steps like regrouping to divide and multiply. He writes down his answer directly. My question is must he follow the steps? Must he show the working in vertical format?

Tia, a teacher from Indonesia

He should not need to. After all we want them to use mental strategies for computations. He has been able to do that. The use of paper and pencil should be a temporary help for children who cannot do it using mental strategies (because their number sense and metacognition are not yet well developed). For example to divide 96 by 8, we want students to see that 96 is 80 and 16. Both 80 and 16 can be divided by 8 mentally to give 10 and 2. hence, 96 divided by 8 is equal to 12. A 12-year-old should not need to use paper and pencil to do a computation such as this. Similarly, to multiplyu 39 and 6, we want children to use the product of 40 and 6 to obtain the product of 39 and 6. The ability to do so tells us that the child is able to make connections between the two and has a strong number sense.