This math sheet was part of a math packet that was given for homework. The students had to use mental math in order solve each problem. This worksheet does not elicit students problem solving or thinking. IT is a worksheet that they have seen numerous times before and they automatically know how to go about filling it out.
This student did well with this particular task. She often can complete math tasks quickly in her head as long as she does not have to read and follow directions. Although I think that is important to practice many subtraction problems I do think that this worksheet was redundant. Not only are all of these problems practicing the same skill but this is not the first time these students have completed this worksheet. There is a worksheet that looks like this in almost every math homework packet given out every week.
Some of the students look at the worksheet and say that they do not know how to subtract. A common mistake is that students start to do addition rather than subtraction. Other students count on their fingers to solve each problem. There are a few students who use a number line which can be difficult because they might not have a number line at home to use when completing the homework. Students that are more advanced have some of these problems memorized and can answer quickly.
Although this girl does well with this worksheet there are many students who still have not mastered this skill. I think that most likely more work needs to be done in class with subtraction where struggling students can get immediate feedback before doing the problem wrong 20 times in a row. Another thing I would change about this worksheet would be to give students more individualized work. For example since this student gets each answer right every week she should start to get worksheets with more difficult subtraction problems.
It is very important to deconstruct what you mean by "subtraction". As you talk about in this post, there are different ways to represent subtraction: the algorithm / procedure for two-digit subtraction; using the number line; etc. It is important to think about all the different ways to approach the problem and the key is to think about what the connections between those different approaches / representations are. This is what will help you as a teacher understand student thinking better and also be better able to facilitate their advancement in understanding.
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