1.1.3 Teachers' questioning, and changing
. and adding representations The activity shows the importance of teachers' questioning and representations to promote children's mathematical thinking, which will be re-explained in Part I. When teachers represent the relationship by arrows, it is possible that children can explain the pattern regarding why a 37 x (3 x _) involves using the 3s row of the multiplication table for the multiplier. The reason the digits come up to be the same is that this is 37 x (3 x _) = 37 X 3 x _, and 37 x 3 = 111, and so this can be explained as being the same as 111 x _. This is the chance to recognize that we can explain patterns based on the first step of the pattern.2 It is interesting to see how what one has already learned in mathematics can be used to explain the next ideas. Using what we here learned/ done before is one of the most important reasonings in mathematics. To recognize and understand the reason, the arrow representation is the key in this case. Since the arrow representation makes it possible to compare the relationship between mathematical sentences. To understand and develop mathematical reasoning, we usually change the representation for an explanation in order to represent mathematical ideas meaningfully and visually. It is also a good opportunity for children to experience a sense of relief upon finding the solution to this mystery using the idea of the associative law. Even if they do not know the law, they will understand well the significance of changing order in multiplication.
1.1.3 Teachers' questioning, and changing. and adding representations The activity shows the importance of teachers' questioning and representations to promote children's mathematical thinking, which will be re-explained in Part I. When teachers represent the relationship by arrows, it is possible that children can explain the pattern regarding why a 37 x (3 x _) involves using the 3s row of the multiplication table for the multiplier. The reason the digits come up to be the same is that this is 37 x (3 x _) = 37 X 3 x _, and 37 x 3 = 111, and so this can be explained as being the same as 111 x _. This is the chance to recognize that we can explain patterns based on the first step of the pattern.2 It is interesting to see how what one has already learned in mathematics can be used to explain the next ideas. Using what we here learned/ done before is one of the most important reasonings in mathematics. To recognize and understand the reason, the arrow representation is the key in this case. Since the arrow representation makes it possible to compare the relationship between mathematical sentences. To understand and develop mathematical reasoning, we usually change the representation for an explanation in order to represent mathematical ideas meaningfully and visually. It is also a good opportunity for children to experience a sense of relief upon finding the solution to this mystery using the idea of the associative law. Even if they do not know the law, they will understand well the significance of changing order in multiplication.
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