Sues entry-slip: Mathematical Representation
Mathematical Representation
What convinces (or doesn't convince) you in the author's argument? I fully agree with the author in that representation is fundamental to the development of a student's mathematical understanding. What convinced me was the simple fact that pictures help kids (and adults)understand. I have to confess, I was unfamiliar with the terminology before starting the article and had a very difficult time getting through it. Had I googled the terminology before reading, I would have seen all of the pictures and examples and better understood the context and direction of the material. On further exploration, I realized that the author is really explaining what is, to my mind, the easiest and clearest way to work.
What kinds of mathematical representations are included and excluded in the artcle? The article includes references to representations such as: numerals, algebraic equations, graphs, tables, diagrams and charts, and an example of simplifying using patterns, among other things.
Can you think of an example of a mathematical representation of a particular math concept (from secondary or elementary school curricula) that is not included, but that might be helpful for students in developing understanding? Describe briefly how you might teach using this representation.
An example of a math concept that one could use in both elementary and secondary school is use of a chart to track data points that can later be manipulated. One idea for teaching using this representation is to have the students first gather some data points in the context of a game or other relevant activity and then ask them to determine how best to group the data so that it can be used to do more work. Then I would suggest plotting the points so they can see visually what conclusions can be drawn.
What convinces (or doesn't convince) you in the author's argument? I fully agree with the author in that representation is fundamental to the development of a student's mathematical understanding. What convinced me was the simple fact that pictures help kids (and adults)understand. I have to confess, I was unfamiliar with the terminology before starting the article and had a very difficult time getting through it. Had I googled the terminology before reading, I would have seen all of the pictures and examples and better understood the context and direction of the material. On further exploration, I realized that the author is really explaining what is, to my mind, the easiest and clearest way to work.
What kinds of mathematical representations are included and excluded in the artcle? The article includes references to representations such as: numerals, algebraic equations, graphs, tables, diagrams and charts, and an example of simplifying using patterns, among other things.
Can you think of an example of a mathematical representation of a particular math concept (from secondary or elementary school curricula) that is not included, but that might be helpful for students in developing understanding? Describe briefly how you might teach using this representation.
An example of a math concept that one could use in both elementary and secondary school is use of a chart to track data points that can later be manipulated. One idea for teaching using this representation is to have the students first gather some data points in the context of a game or other relevant activity and then ask them to determine how best to group the data so that it can be used to do more work. Then I would suggest plotting the points so they can see visually what conclusions can be drawn.
Good thoughts and commentary, Sue! I'm glad that you were able to find examples and definitions of the terminology -- I know it can be frustrating to read a piece full of unfamiliar terms.
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