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DataDoxy · 09-16-2014, 08:57 PM

Yes and no. We do want kids to draw the pictures of the two different sized groups of apples being joined together (4 apples and 5 apples). This way we can “see” they do in fact understand the concept of adding two different groups together. However, there is a little more to it…

It would be ideal to have the students actually perform the action of joining groups together with manipulatives even before they draw this and well before they learn the math symbols for simple addition. When adding 4 apples to five apples, students will use different strategies for this action as some kids will touch all the apples (or manipulatives) counting as they touch each one, others will know there are 4 in the first group and will count-on five more (5, 6, 7, 8, 9) touching the apples one by one, yet others will use fingers despite the manipulatives because they are still attached to this kind of concrete model. (There are many other strategies but I wanted to touch on a couple that showed concrete thinking and the need to touch to count).

We want students to move beyond these concrete strategies towards abstraction before we have them learning math symbols and being timed on quizzes to see if they know their addition facts. I would not have students learn the symbols (4 + 5) until I felt comfortable that the students understood the action and the process of adding. After I felt comfortable with this, I would go back and forth between symbolic questions, drawings or visual representations, and combinations of these questions (draw and do). Finally, when I was sure the students were ready, I would have them use symbols and would work on automatizing of their facts.

Traditionally, we have often taught the symbols and the picture together. Then we moved into timed tests of addition facts. For some kids, this jump to automaticity came way too early and they were still not clear about the process. Additionally, some of them need to learn more efficient strategies for adding (I.e. move from concrete touching to counting on, or skip counting, or perhaps abstraction seeing that 4 + 5 is 9) before they should practice automaticity.

Does this make sense? I know this was a pretty simple example... it gets more complex as the math gets more difficult as I know you can appreciate.

09-16-2014, 08:57 PM	#5
DataDoxy Bingo's Better Half Join Date: Jul 2014 Exp:	Yes and no. We do want kids to draw the pictures of the two different sized groups of apples being joined together (4 apples and 5 apples). This way we can “see” they do in fact understand the concept of adding two different groups together. However, there is a little more to it… It would be ideal to have the students actually perform the action of joining groups together with manipulatives even before they draw this and well before they learn the math symbols for simple addition. When adding 4 apples to five apples, students will use different strategies for this action as some kids will touch all the apples (or manipulatives) counting as they touch each one, others will know there are 4 in the first group and will count-on five more (5, 6, 7, 8, 9) touching the apples one by one, yet others will use fingers despite the manipulatives because they are still attached to this kind of concrete model. (There are many other strategies but I wanted to touch on a couple that showed concrete thinking and the need to touch to count). We want students to move beyond these concrete strategies towards abstraction before we have them learning math symbols and being timed on quizzes to see if they know their addition facts. I would not have students learn the symbols (4 + 5) until I felt comfortable that the students understood the action and the process of adding. After I felt comfortable with this, I would go back and forth between symbolic questions, drawings or visual representations, and combinations of these questions (draw and do). Finally, when I was sure the students were ready, I would have them use symbols and would work on automatizing of their facts. Traditionally, we have often taught the symbols and the picture together. Then we moved into timed tests of addition facts. For some kids, this jump to automaticity came way too early and they were still not clear about the process. Additionally, some of them need to learn more efficient strategies for adding (I.e. move from concrete touching to counting on, or skip counting, or perhaps abstraction seeing that 4 + 5 is 9) before they should practice automaticity. Does this make sense? I know this was a pretty simple example... it gets more complex as the math gets more difficult as I know you can appreciate.