In the conclusion, a general approach to teaching arithmetic was laid out. Small-group work followed by whole-class discussions of pupils’ solutions would be a cognitively guided instruction approach for teaching multiplication and division as well. Shorter, teacher-led activities could be done as described below.
The progression began with the “Double ten-frame activity.” An activity that would allow students the same type of situations for thinking and discussion would be flashing groups of numbers. I like Investigation’s “Quick Images” in that the progression gets deeper and deeper. It starts with 9 groups of 4 dots and progresses to 3 groups of 10 dots but the 10 dots are in groups of 2.
The “Balance Activity” taught students relational thinking. The Investigations curriculum also does a nice job with its flash cards in this instance. Students are asked to use a known problem to help them to solve an unknown problem. Knowing 2x6 for example could help them with 4x6, as it is 2x6 doubled. Having students share the problems they use to help them solve unknown problem would help other students in solving problems they haven’t mastered yet.
I agree with Nick that the conclusion laid a general approach out, and multiplication and division would follow along the same lines.
I also think that with addition and subtraction the students get progressively sophisticated in their thinking and reasoning. I think the same would happen in multiplication and division. In the beginning they talk about counting by ones to get an answer with addition. That would be like counting by 3s to get 3x7. Later on, they start to use doubles, and know those from memory. After that, the students start to relate problems; similar to what Nick talked about in the last paragraph with the balance activity.
In the conclusion, a general approach to teaching arithmetic was laid out. Small-group work followed by whole-class discussions of pupils’ solutions would be a cognitively guided instruction approach for teaching multiplication and division as well. Shorter, teacher-led activities could be done as described below.
ReplyDeleteThe progression began with the “Double ten-frame activity.” An activity that would allow students the same type of situations for thinking and discussion would be flashing groups of numbers. I like Investigation’s “Quick Images” in that the progression gets deeper and deeper. It starts with 9 groups of 4 dots and progresses to 3 groups of 10 dots but the 10 dots are in groups of 2.
The “Balance Activity” taught students relational thinking. The Investigations curriculum also does a nice job with its flash cards in this instance. Students are asked to use a known problem to help them to solve an unknown problem. Knowing 2x6 for example could help them with 4x6, as it is 2x6 doubled. Having students share the problems they use to help them solve unknown problem would help other students in solving problems they haven’t mastered yet.
I agree with Nick that the conclusion laid a general approach out, and multiplication and division would follow along the same lines.
ReplyDeleteI also think that with addition and subtraction the students get progressively sophisticated in their thinking and reasoning. I think the same would happen in multiplication and division. In the beginning they talk about counting by ones to get an answer with addition. That would be like counting by 3s to get 3x7. Later on, they start to use doubles, and know those from memory. After that, the students start to relate problems; similar to what Nick talked about in the last paragraph with the balance activity.