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Unformatted text preview: Angela Dobbins February 25, 2011 MTH 211 Relational Understanding VS. I nstrumental Understanding in Mathematics All my life when I thought I understood something, I understood it that was until, recently when I learned that there are two different types of understanding. I learned this when I was introduced to the topics of relational and instrumental understanding in my math class when we had to read Richard Skemps 1976 paper on the subject. It took me several reads to understand the concepts he spoke of, as it probably would most. Although I must say, once understood his concepts and ideas make perfect sense, and I realized I have actually experienced what he discusses in my own school life. Throughout elementary school, I wondered why I always got my math problems wrong when I had the right answer; I just had not gotten the answer the way they wanted. I could never grasp the concept that it had to be done a certain way for a certain reason, because when I would ask my teachers why they never had an answer for me. Mr. Skemps article starts by introducing the reader to the term Faux Amis (Skemp) which is a french term defined as a word in a second language that closely resembles a word in somebody's first language but means something different. (Dictionary) Skemp goes on to state the the word understanding in mathematics is a Faux Amis, because there are two current uses and meanings of the word, instrumental and relational. Wow, who knew? Angela Dobbins February 25, 2011 MTH 211 Skemp defines relational understanding in his paper as follows; By the former (rational understanding) is meant what I, and probably most readers of this article, have always meant by understanding: knowing both what to do and why (Skemp Pg 2 Paragraph 4). What I precieve he means by this is the every day knowledge we all have in simple mathematics combined with the knowledge of why we do things a certain way in mathematics. For example we have all experienced asking our math teachers why every now and then, a teacher that is teaching relational mathematics will answer that why for you. Instrumental Understanding on the other hand is defined by Skemp as Instrumental understanding I would until recently not have regarded as understanding at all. It is what I have in the past described as `rules without reasons', without realizing that for many pupils and their teachers the possession of such a rule, and ability to use it, is what they mean by `understanding' (Skemp Pg 2 Paragraph 4). If I were to break his definition down more, I would say he meant that instrumental understanding is the way most of us were taught math in our elementary school...
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- Spring '11