"Helping students generalize their mathematical thinking by routinely expressing and justifying their generalizations will develop students’ capacity to think algebraically and can lead to greater students’ achievement." Maria L. Blanton and James J. Kaput
This was always difficult for me as a student to grasp. I mean, why in the world are there letters in math anyway! I am looking forward to hearing ideas.
How we develop students' conceptual understanding of equality in the early years is so important. For example, tell first graders the whole story about numbers! Positive and Negative numbers are a part of the number system. I think we need to clarify what we mean by "algebraic thinking." I believe too much emphasis is placed on patterns (which is an important idea). As I look learn more about the Japanese curricular materials, what seems to be missing in the typical US approach is the emphasis on writing equations. We rarely discuss the importance of expressing our mathematical thinking using mathematical expressions and equations, Thus, for too many children expressions like 1x(2+3) simply means to calculate and find the answer
Another thing we should do..is help students make connections to their experiences to mathematical ideas.
In looking at ways to really help students get to the heart of algebraic thinking. One key is really forcing students to do the thinking piece. Unfortunately, too many time math is reduced to a series of pre-determined steps to arrive at an answer. Having students to conducts investigations and come up with their own steps would really solidy their understanding.
"Helping students generalize their mathematical thinking by routinely expressing and justifying their generalizations will develop students’ capacity to think algebraically and can lead to greater students’ achievement." Maria L. Blanton and James J. Kaput
ReplyDeleteThis was always difficult for me as a student to grasp. I mean, why in the world are there letters in math anyway! I am looking forward to hearing ideas.
ReplyDeleteHow we develop students' conceptual understanding of equality in the early years is so important. For example, tell first graders the whole story about numbers! Positive and Negative numbers are a part of the number system. I think we need to clarify what we mean by "algebraic thinking." I believe too much emphasis is placed on patterns (which is an important idea). As I look learn more about the Japanese curricular materials, what seems to be missing in the typical US approach is the emphasis on writing equations. We rarely discuss the importance of expressing our mathematical thinking using mathematical expressions and equations, Thus, for too many children expressions like 1x(2+3) simply means to calculate and find the answer
ReplyDeleteAnother thing we should do..is help students make connections to their experiences to mathematical ideas.
In looking at ways to really help students get to the heart of algebraic thinking. One key is really forcing students to do the thinking piece. Unfortunately, too many time math is reduced to a series of pre-determined steps to arrive at an answer. Having students to conducts investigations and come up with their own steps would really solidy their understanding.
ReplyDelete