Skip to main content
Mathematics Educators

Return to Question

edited title
Link
marco trevi
marco trevi
  • 805
  • 9
  • 22

Does there exist a (statisticstatistical) topology induced by students on the space of algebraic formulas? :)

added 1 character in body
Source Link
marco trevi
marco trevi
  • 805
  • 9
  • 22

It's kind of a serious question even if the title seems silly. As math educators, we all know that students link together different algebraic expressionexpressions thinking that they mean the same thing, e.g. \begin{equation} (a+b)^2 = a^2+b^2 \end{equation} or \begin{equation} \frac{x+2}{2} = x \end{equation}

These errors can be grouped statistically in categories, such as "false linearity" as in the $(a+b)^2$ case. This student-induced grouping leads to a kind of student-induced topology on the space of all algebraic formulas, where the "student-distance" between two expressions is small if statistically a lot of students think that they are the same expression.

My question is this: has this "topology", i.e. the organization of student errors in algebra, been studied sistematically? Is there any reference in literature that thoroughly deals with the issue of really categorizing and understanding errors in basic algebraic expression manipulation?

I think it would be extremely beneficial to know how to traverse the formula space in order to optimize learning (Of course this taxonomic approach has a sense only for algebraic manipulation, not for complex problems).

It's kind of a serious question even if the title seems silly. As math educators, we all know that students link together different algebraic expression thinking that they mean the same thing, e.g. \begin{equation} (a+b)^2 = a^2+b^2 \end{equation} or \begin{equation} \frac{x+2}{2} = x \end{equation}

These errors can be grouped statistically in categories, such as "false linearity" as in the $(a+b)^2$ case. This student-induced grouping leads to a kind of student-induced topology on the space of all algebraic formulas, where the "student-distance" between two expressions is small if statistically a lot of students think that they are the same expression.

My question is this: has this "topology", i.e. the organization of student errors in algebra, been studied sistematically? Is there any reference in literature that thoroughly deals with the issue of really categorizing and understanding errors in basic algebraic expression manipulation?

I think it would be extremely beneficial to know how to traverse the formula space in order to optimize learning (Of course this taxonomic approach has a sense only for algebraic manipulation, not for complex problems).

It's kind of a serious question even if the title seems silly. As math educators, we all know that students link together different algebraic expressions thinking that they mean the same thing, e.g. \begin{equation} (a+b)^2 = a^2+b^2 \end{equation} or \begin{equation} \frac{x+2}{2} = x \end{equation}

These errors can be grouped statistically in categories, such as "false linearity" as in the $(a+b)^2$ case. This student-induced grouping leads to a kind of student-induced topology on the space of all algebraic formulas, where the "student-distance" between two expressions is small if statistically a lot of students think that they are the same expression.

My question is this: has this "topology", i.e. the organization of student errors in algebra, been studied sistematically? Is there any reference in literature that thoroughly deals with the issue of really categorizing and understanding errors in basic algebraic expression manipulation?

I think it would be extremely beneficial to know how to traverse the formula space in order to optimize learning (Of course this taxonomic approach has a sense only for algebraic manipulation, not for complex problems).

Became Hot Network Question
Source Link
marco trevi
marco trevi
  • 805
  • 9
  • 22

Does there exist a (statistic) topology induced by students on the space of algebraic formulas? :)

It's kind of a serious question even if the title seems silly. As math educators, we all know that students link together different algebraic expression thinking that they mean the same thing, e.g. \begin{equation} (a+b)^2 = a^2+b^2 \end{equation} or \begin{equation} \frac{x+2}{2} = x \end{equation}

These errors can be grouped statistically in categories, such as "false linearity" as in the $(a+b)^2$ case. This student-induced grouping leads to a kind of student-induced topology on the space of all algebraic formulas, where the "student-distance" between two expressions is small if statistically a lot of students think that they are the same expression.

My question is this: has this "topology", i.e. the organization of student errors in algebra, been studied sistematically? Is there any reference in literature that thoroughly deals with the issue of really categorizing and understanding errors in basic algebraic expression manipulation?

I think it would be extremely beneficial to know how to traverse the formula space in order to optimize learning (Of course this taxonomic approach has a sense only for algebraic manipulation, not for complex problems).