Eula E. Monroe and Professor Leslie Huber, Teacher Education
According to Benjamin Whorf, a language philosopher, language shapes thought (1). Based on this premise, the language of mathematics must be known in order to think about mathematics. The National Council of Teachers of Mathematics (NCTM) recommends that teachers monitor students’ use of mathematical language to enable them to communicate in mathematics (2). Since the requisite meaning vocabulary is necessary to speak the language of mathematics, it is vital that teachers help students learn mathematics vocabulary. This study attempted to test the effectiveness of a certain teaching method, called a graphic organizer, in teaching mathematics vocabulary to pre-algebra students.
In 1996 Michelle Pendergrass, then a BYU undergraduate student examined the effects of teaching mathematics vocabulary to fourth grade students using a graphic organizer called the integrated Concept of Definition-Frayer model (see Figure 1). The CD-Frayer model guides students to think about examples, attributes, and category of a given concept. It follows schema theory, which dictates that the brain organizes information into hierarchical frameworks called schemata, with each schema containing generic information about a single concept (3).
Two intact pre-algebra classes from a junior high school in Orem, Utah were selected for this study. One group was randomly assigned the control group, and the other group was designated the treatment group. A two-week unit on ratio and proportion was taught to the students, with each class receiving the same lessons, except for the last five minutes of daily instruction. During this time the relevant vocabulary was taught-by definition to the control group, and by a graphic organizer to the treatment group. The groups were given a pretest and a post-test at the beginning and end of the two-week unit consisting of two parts: a written assessment and an objective test.
The MANOVA procedure in SPSS was used to perform two separate, repeated measures analysis of variance, one for the objective test scores and one for the written assessment scores. Statistical analysis of the pre- and posttest scores revealed no significant differences between the means of the two groups. The two groups were not initially equivalent. The control group mean exceeded the experimental group by one-half (.48) of a standard deviation on the pre-written assessment and .27 of a standard deviation on the pre-objective test, though neither of these differences were statistically significant. However, the average posttest score of the two groups combined was significantly higher than the average pretest score of both groups combined, on both the written assessment and the objective test. This difference supports the conclusion that both groups learned.
Vocabulary instruction in the experimental group always lasted a few minutes longer than vocabulary instruction in the control group. Thus, one implication of this study is that the CDFrayer model provides a meaningful context for discussion in the classroom. This concurs with the NCTM standards, which emphasizes teaching mathematics as communication.2 Further research needs to be conducted concerning the effectiveness of the CD-Frayer model in teaching mathematics vocabulary to pre-algebra students.
References
- Carroll, J.B. (ED.). (1956) Language, thought, and reality: Selected writings of Benjamin Lee Whorf. New York: Technology Press of Massachusetts Institute of Technology, John Wiley & Sons.
- National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: Author.
- Dunston, P.J. (1992). A critique of graphic organizer research. Reading Research and Instruction, 31(2), 57-65. Figure 1. CD-Frayer model for the word ratio.