Wednesday, September 20, 2017
Skemp and relational understanding
In order to have deep understanding of mathematics it must be seen as a language as opposed to a set of rule and operations. Language is created by assigning a symbol to an abstract concept. We traditionally understand these to be words and grammar but in the context of mathematics it becomes notation. In Skemp's article they rightfully point out that many students have the ability to perform operations and memorize notation, but often times the effects of this are short-term and do not bring about progression and retention. Students often times do not actually have a clear idea about what the abstract concepts that are being represented by notation and thus can perform very well in the setting of examinations but not when being asked to think and build on material that has already been taught.
In the article there was an interesting discussion on the difficulties in changing the focus in math education on a true meaning of understanding- what they call "relational understanding"- due to the advantages of "instrumental understanding". One of the advantages of instrumental learning that was mentioned was the evaluation schemes in the status quo for math. In my opinion it is not adequate to exclusively test a student's ability to perform rules and operations. There must be a way to equally evaluate the actual relational understanding of the subject, and the article presents a very good example with units in relation to area. Evaluations ought be thought-provoking and help students discover the nuances of the abstractions we define using notation. The article also pointed out different approaches one can take in introducing theoretical concepts and having the importance of that inclusion be known. Abstract concepts are difficult for everyone to understand, but especially children. The article's focus on accessible ways of relating abstract math with concrete math is a good first step toward bringing about the necessary components of mathematics that bring about true deep understanding in students.
In the article there was an interesting discussion on the difficulties in changing the focus in math education on a true meaning of understanding- what they call "relational understanding"- due to the advantages of "instrumental understanding". One of the advantages of instrumental learning that was mentioned was the evaluation schemes in the status quo for math. In my opinion it is not adequate to exclusively test a student's ability to perform rules and operations. There must be a way to equally evaluate the actual relational understanding of the subject, and the article presents a very good example with units in relation to area. Evaluations ought be thought-provoking and help students discover the nuances of the abstractions we define using notation. The article also pointed out different approaches one can take in introducing theoretical concepts and having the importance of that inclusion be known. Abstract concepts are difficult for everyone to understand, but especially children. The article's focus on accessible ways of relating abstract math with concrete math is a good first step toward bringing about the necessary components of mathematics that bring about true deep understanding in students.
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