“Discovering” Mathematics VocabularySeptember 25, 2009 at 9:31 am | Posted in uncategorized | 2 Comments
(post authored by Cal Dupuis)
One of the most challenging tasks faced by mathematics teachers is how to best introduce new vocabulary to students so that they understand the concepts. Traditional techniques of having students just look up words such as “perpendicular” or “asymptote”, or even asking the students to extract the meaning of the words from context in textbooks or other materials, are not effective enough methods in mathematics. Textbooks are too vocabulary-dense and often lack visual representations in presenting new vocabulary in mathematics.
Various effective learning strategies for vocabulary in mathematics are described by Dr. David Chard at http://www.eduplace.com/state/pdf/author/chard_hmm05.pdf and by Denisse R. Thompson and Rheta N. Rubenstein at http://www.erusd.k12.ca.us/ProjectAlphaWeb/index_files/MP/Learning%20Mathematics%20Vocabulary.pdf. Generally speaking, the most effective approach involves teaching a variety of strategies because there are many types of student learning styles and to pre-teach vocabulary so the students to get a grip on the concepts prior to using them to solve problems. It’s important to model vocabulary first when teaching new concepts in math.
In my opinion, the most effective strategy is to enable the students to evolve into or “discover” new vocabulary through the use of manipulatives. I would allow students to explore concepts first by playing with pertinent objects and then attach vocabulary to the ideas that result. An example would be to ask students to build a number of different types of quadrilaterals out of simple materials or on Geometer sketchpad software and then to sort out and identify different kinds of quadrilaterals. Vocabulary is then attached to these shapes. The words are fortified by having the students say, write and spell them.
Another proven strategy is the use of visual techniques to understand terms and their relation to each other. I think the most effective scheme uses a vocabulary tree concept. There is an excellent example for terms in statistics in the second resource mentioned above. Subjects Matter (Daniels and Zemelman, 2004) provides another vocabulary tree example for polynomials. Such a method could be used very successfully for triangles and quadrilaterals, where these terms are the trunk of the tree and other words branch out from there.
A third approach is to take advantage of word origins. Mathematics has been around a long time and many terms are composed of the roots of words with known meaning from prior languages that can be applied to surmise the meaning of the word in question. For instance, “perpendicular” comes from a root, pend, meaning to hang, because when a weight hangs freely on a string, it forms a perpendicular to the ground. In addition, by exploring the meanings of words such as acute and obtuse in a non-mathematical sense, inferences can be made for the meanings of acute and obtuse triangles.
There are other techniques for teaching vocabulary such as graphic organizers like the Frayer model and vocabulary word sorting and labeling techniques. I think that these methods are better suited for English, history or science. But can you think of how to use these strategies effectively to learn math vocabulary? Why are some techniques of teaching math vocabulary better than others?