Stronger Subtraction Strategies
See below for Steve Brown’s (Grade 4C) blog post on subtraction strategies.
When I was teaching in the UK (back in 2001), I remember attending a Math workshop for teachers where we were shown how to teach computation strategies. The presenter gave a simple addition problem, e.g. 45 + 67, and showed us a half dozen ways it could be solved. At the time, it was completely revolutionary to my understanding of how to add and subtract multi-digit numbers. I only knew one way – stack the 45 on top of the 67, add 5 and 7 to make 12, write the 2 and carry the 1, etc. The workshop revealed a whole other world outside the traditional vertical method algorithm I was taught at school.
Last week, 4C encountered a similar revelation. Students were asked to solve 6 simple subtraction problems involving two 2-digit numbers (those that felt more confident worked with two 3-digit numbers). They had to solve them using a mental strategy (one that’s performed without pencil or paper) while being timed. We then reviewed the strategies that students used. I was surprised at how many students were using a mental version of the vertical method. We all agreed there were more efficient ways to solve subtraction problems.
We inquired into the different types of questions we encounter. There were those that had two numbers quite close together and those that had numbers far apart. For the former, we proposed a counting up strategy to find the difference, i.e. start at the lowest number and count up to the higher number. For the latter, we did the opposite, or a counting down strategy, i.e. start at the higher number and count down the value of the smaller number.
With a week’s worth of practise, students were becoming more proficient at applying these strategies and started to adapt them based on the numbers in the question. Their thinking became more flexible as they moved away from the rigidity of using one strategy, vertical method. By the end of the week, they were retested on the original six questions. Everyone improved. Have a look at the graphs in the below posts, the data speaks for itself.
Horus’ blog post titled Subtraction Strategy Post-Assessment Results
Kiana’s blog post titled An Exciting Math Test