“Discovering” Mathematics Vocabulary

September 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?



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  1. As we mentioned in class on September 25, 2009, there are alternative text sources. As brought up in Subjects Matter, not all textbooks are created equally. Although Daniels and Zemelman criticize all the stuffing but some do utilize pictures to help explain vocabulary (yet they can be overcrowded with excessive photographs and information to try to connect content to history). For example McDougal Littell’s Geometry textbook offers general pictures to illustrate definitions. I think some issues in the mathematics class stem from the definitions themselves—definitions are often difficult to understand. In class the definitions and vocabulary often are discussed in further detail and modeled. For example while student teaching, I utilized a chart (Word File) to organize properties of parallelograms in class. The properties reinforce definitions as well as contribute to deeper understanding. Another issue with understanding I believe is the theorems which are complicated for students to understand let alone prove to students. Going back to McDougal Littell, they utilize Venn diagrams to represent relationships among quadrilaterals, such as a square is both a rhombus and a rectangle.

    Verbal strategies mentioned by Thompson and Rubenstein are great examples. I know in LOTE classes, some teachers use these methods to drill students into learning correct pronunciation. But with math we obviously are looking at more than just pronunciation. In fact with memorization of facts, I have observed teachers utilize this. If you have ever watched Stand and Deliver, Jaime Escalante utilizes verbal strategies in getting students to learn that a negative times a negative is a positive, something that teachers in the field today do. But here we have transitioned, I feel from vocabulary to concepts and from potentially understanding to memorization.

    As we have mentioned (maybe I am thinking of GMST 522) but do we focus on the larger concepts or hitting everything? There are vocabulary words which from my experience I haven’t seen on NYS mathematics regents. So is it vital that students learn words such as “convex polygon”? Or to promote understanding do we discuss “base angles”?

    Many of the approaches mentioned by Cal I feel can be used in class but is it about memorization of vocabulary or is it about understanding terminology and concepts? There are other approaches to understanding vocabulary other than graphic organizers, verbal, etc. For example, take 4 drinking straws such that you have 2 congruent pairs and feed string through the straws (no too much and not too little) to form a parallelogram. Then play around with the angles to investigate properties of parallelograms. (Obviously I tried to quickly outline a hands on approach not utilizing organizers to learn vocabulary and concepts.)

    Chard seems to focus, I believe, more on elementary students. High school geometry students are asked to do exceedingly more with quadrilaterals for example, this is where we start incorporating algebra to solve equations using properties known.

    Not to criticize the choice of the Chard information but in light of what we have discussed in class and from reading Subjects Matter, what is everyone’s perception of this article? I noticed that Chard is a consultant for Houghton Mifflin. I wonder if this is a piece of stuffing that Houghton Mifflin includes in some of their textbooks. Also since both Cal and I are “math people,” what are our science people’s perceptions on these strategies in your classrooms?

  2. When I first started with my graduate studies, (eight years since my last semester), I forgot how to study. The traditional techniques that I first started to use were not working for me and it didn’t take long for me to remember and research techniques used for reading, retaining and vocabulary.

    There are many techniques out there that will assist you in teaching your students. As we have learned, no two students are created equal and there are numerous types of learning styles. This two minute video (http://www.youtube.com/watch?v=cX0teReijUk)entitled Learning Styles gives a brief overview of three main learning styles which include visual, auditory and kinesthetic. The video defines each learning style and gives examples of various study techniques for each style. As mentioned by Mr. Dupuis, it is important to utilize numerous vocabulary techiniques, and in doing so you will reach more students.

    I believe all tools can have benefits in the classroom, it is only a matter of finding a way to correctly utilize the technique. Graphic organizers can be used well in a mathamatics classroom. Think about how a step by step chart could help define terms like order of operations or can assit in memorizeing formulas with mulitple steps. After all, a formula is just as important to memorize as a vocabulary word, correct? A Venn Diagram can be considered a graphic organizer too, and could help catagorize vocabulary.

    Is there any reason to exclude a particluar literacy technique from your mathematics classroom?

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