Introduction
In 1976 Skemp published an important discussion paper spelling out the differences between relational and instrumental understanding as they apply to mathematical teaching and learning. Skemp highlights two faux amis, the first is understanding. Skemp defines understanding in two ways: 1) instrumental understanding and 2) relational understanding. The second faux amis is the word mathematics which he describes as two different subjects being taught. I have considered Skemp’s article in four sections.
1. Faux amis
2. Instrumental and relational understanding
3. The mismatch
4. Implication for mathematics teaching
Key terms: Schema; faux amis; Instrumental understanding; relational understanding; mathematics.
Setting the Scene
It is extremely difficult to define understanding. Skemp attempts to assimilate it into some form of an appropriate or inappropriate schema that is dependent upon many variables such as language, environment, belief, tradition and culture. Could understanding be an abstract thing, brain pattern or rule? Skemp uses the term ‘faux amis’ to mean that language can have different meanings to different people even though the root origins of words are the same. He looks at French and English and identifies what he calls a ‘mismatch’. He uses analogies and understandings based on his own experience and others in his community of practice (Mellin-Olsen, 1981). This mismatch, he believed, is the root of many difficulties in mathematics education including the word mathematics itself. This assignment attempts to appraise his arguments in relation to other literature and my own personal experience.
A schema is a mental structure we use to organize and simplify our knowledge of the world around u...
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The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
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The concept of Schema was first introduced by Jean Piaget (1926). This theory is used in the case study done by Brewer and Treyens (1981). The method of this study was simple subjects were told to wait in a psychologist's office for 3 minutes, and then moved into a another room and were asked what they saw in the office. They said that remembered things which would be in a office such as pens and books, this proves the schema theory. The Schema theory strengths are that it is testable, and their is a lot of evidence to back it up.
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Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
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