I brought in a few samples of students' two-digit multiplication problems. I brought in samples from two different students. This was their exit slip and there were two different problems. One of the students got both of the answers correct, following a correct method of multiplication. The other student got both of the problems wrong. It was clear to see that this student did not understand the correct way to multiply two-digit numbers. The student would do the steps correctly, multiplying the two numbers furthest right, but instead of carrying the tens-place number, the student would put the full number below the line. It was easy to see where and why the errors were being committed which was good in that there was some mathematical sense behind the student's thinking. This makes it easier to help the student when we can see what he/she was thinking. After class, I took the student aside and did a complete problem while he/she watched in order to illustrate the correct way. I highlighted where I carried a number and left the ones number under the line. Then I did a few problems with guided practice so that the student could get used to the pattern of the method. Then I had the student do a few problems on his/her own. Another way that I could have advanced the student's understanding was have another student help him/her out. The students love working together and not only would this benefit the student in need, but it would also benefit the student that was doing the teaching. I could ask this student why he/she is doing what they are and after further instruction if they understand why this works and how to do it independently. There are many tasks this student could find fruitful because in 5th grade, multiplication is in a lot of the other topics so it is important to grasp the concept early on.
Remember that one of the best ways to engage students in mathematical thinking is not to teach them an algorithm or have them repeat a procedure, but to have them make sense of the problem however they choose. It is important to start where they are at. From there, you can compare their method with other methods, and they will, through this scaffolding, begin to make the connections and see the logic of the more standard procedure.
ReplyDeleteSo, if these students cannot multiply two digit numbers, it is most likely difficult for them to understand what is going on (how does one make intuitive sense of 36 x 25?). You might even ask students to make up a real world scenario where the problem 36 x 25 applies (without solving it). This will help the students make sense of what the mathematics actually represents, and the procedure itself will make intuitive sense, rather than having to blindly remember a step-by-step procedure that means nothing to them.