The picture above is a sample of an addition worksheet that I worked on with my students this week. The students were to work individually on these 20 problems. Depending on what their skill level was on, they were encouraged to use cubes, or without the cubes. For the duration of the past two weeks, these second graders have been working on two digit addition and regrouping. The students in my classroom have had a very hard time with this concept of regrouping, however. I have been pulling groups of 4 students outside of the classroom to spend more time working on this concept for the past two visits I have been to the school.
The example provided was completed by a very advanced student. She did not have to use cubes, and she understood the "regrouping" or "carrying" tactic of this assignment. This is outstanding for my classroom, because roughly 18 out of the 23 students have to use the cubes to even attempt to answer these questions. She understood the difference between the "ones place" and the "tens place" and where to start with the addition. Most students in the classroom start by adding the tens place, or start with the ones place, but instead of carrying the number in the tens place, they carry the number in the ones place. Another common mistake that I observed my students making, was how to align the numbers to add properly.
To help my students, I feel as though my MT needs to spend more time focusing on the very basic steps of the problem. She barely emphasized the importance of how to set the problem up, which was concerning for me to see. That was a very common mistake among the students, so I think going back to the basic steps would help a lot. Steps to take to advance the students who have understood the concept might include providing very basic word problems for the students to set up themselves. This would allow these advanced students to pull information out of the context of the sentence and show that they truly understand the question that is being asked.
Think of other ways to represent this problem other than going over the basic steps of the procedure again. One of the lessons of CGI is that there are multiple ways to approach / represent a problem. What might be some other ways, other than the basic steps of the standard procedure? (those are the critical questions to ask)
ReplyDeleteIt is very good how you note the common mistakes that the students are making. Analyze these mistakes. What do you think they reveal about their mathematical thinking / understanding at this point? How might you channel this type of thinking into a new type of task / representation? Again, these are the key questions, and you are setting yourself up perfectly to ask them.
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