I have not been able to really think of beside some mental computation going on in my student teaching. I have seen one student work out a subtraction problem where they broke up the problem by a fact that they knew. The problem was 700-549. What the student did was subtract 700-550 to get 150 and then add one more to 150 to get 151. The only way I knew what the student worked out the problem like this was because I asked if they could explain what they did. I have seen this strategy before but I wouldn’t of known the student used this strategy if I didn’t ask. I was glad the student worked the problem out that way and encouraged the student to continue to use the strategy and to show what they thought that way I could see it when I looked at their work.
Based on the Student’s explanation the student solved the problem 700-549 like this:
700-549
Step 1) 700-550=150
Step 2) The student knows that 550 is 1 more than 549 so the student knows they need to add one more to 151.
Two other ways to solve the problem:
700-549=
Different Method
Step 1) 700-500= 200
Step 2) 200-49= 151
Jackie, I like how you explained what you student did to solve this problem. I think it is neat to see students making connections on different ways to solve math problems. I began to think, is the way your student solved the question a strategy that we as teachers need to know how to teach our students? At what point do we teach them something like this. And furthermore, does it's helpfulness outweigh it's potential to confuse students? This is something to think about always when trying to teach and introduce new strategies to our students.
ReplyDeleteJackie,
ReplyDeleteThat is an interesting way to think of solving subtraction problems. My math CT likes to teach the students this strategy, but I am not convinced the students quite grasp the concept. I know how frustrating it can be to see solely mental math. I have one student who simply stares off into space while thinking and then answers correctly. It is amazing to watch him mentally solve more difficult math problems. What I have done to get the student to explain his process is to have him write out his explanation on his white board. He solves the problem mentally first, then I ask him to write his process out on his whiteboard. Once he has done this, he "teaches" the class his process. I have found this helps not only me, but also him and the other students to understand the mental math process.
I have seen several students utilize this strategy, specifically in my GED setting. It seems to be effective at times but I'm not overly fond of it. In my 2nd grade classroom, the students used this strategy called Near Doubles: if I know that 8+8=16 then 8+7 is going to be one less than 16, 15. When I first had to teach this lesson I was terrified! I didn't think it made any sense!! But the students latched on to it like crazy. To them, thinking of the doubles facts that they knew so well, was very helpful for problems they deemed easier.
ReplyDeleteI guess because I am so stuck in my ways, that it is very strange to me for students to use these nonstandard algorithms. I just constantly think to myself OBVIOUSLY it's multiplication... I like how you went into detail to explain how he solved the problem in his mind but I'm curious, are your students allowed calculators? 700-459 is a large mental math problem (to me anyway) and it appears the student didn't utilize the standard algorithm and write it out, so does he normally have access to calculators?
Awesome post!
I had a similar experience to yours, Jackie, when I asked a student to explain her problem-solving-process to me on a three-digit subtraction problem. The strategy she used to break the problem down into smaller, more manageable parts would have been completely lost on me had I not employed the Talk Moves we've learned about in class. For my part, though I don't think I was ever taught how to use these strategies when I was learning math, I can really see their benefit in terms of teaching numeracy and number sense. For example, think about the level of understanding in terms of the relationships between numbers that was demonstrated by your student when she determined that 700-549 could be broken into two smaller, more manageable problems. As a response to Hattie's comment, I think teaching these "invented strategies" definitely has a place in the classroom. For many students I've worked with this semester, this idea of looking for parts of problems that are easier to understand and breaking problems apart into smaller problems doesn't appear to be a natural step in the problem-solving process for all of them. By incorporating instruction as to how this strategy can be used perhaps when teaching the students how to check their work on problems they've already solved, we can introduce them to the idea that math doesn't have to always be restricted to the algorithm laid in front of them.
ReplyDeleteAnother way I probably could've worked the problem would have been to expand all the numbers, add them by place values, and then add the sums from the place value. It is difficult to see the students solve problems because several times they will work it out in their heads, or use a strategy that I've never seen or can't see unless I ask to explain how they solved it. The way your student solved the problem is a way that I think even today I would have problems doing; only because I feel I would get lost with all the seperate equations. It'll be very interesting to see how their process changes as the problems and numbers increase, or if they keeps it the same.
ReplyDelete