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).
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All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.
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However, one must remember that art is by no means the same as mathematics. “It employs virtually none of the resources implicit in the term pure mathematics.” Many people object that art has nothing to do with mathematics; that mathematics is unemotional and injurious to art, which is purely a matter of feeling. In The Introduction to the Visual Mind: Art and Mathematics, Max Bill refutes this argument by stati...
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Kirova, A., & Bhargava, A. (2002). Learning to guide preschool children's mathematical understanding: A teacher's professional growth. 4 (1), Retrieved from http://ecrp.uiuc.edu/v4n1/kirova.html
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
A schema is an abstract concept proposed by J. Piaget to refer to abstract concepts. For students, their schemas amount to what they already know about a concept. The most important rule for teaching based upon schema theory is: make sure the students’ existing schemas are up and running at a conscious