The *language of mathematics: A functional definition and the development of an instrument to measure teacher perceived self -efficacy.

摘要

Mathematics is permeated with language; it appears in the form of new words and some old words with new meanings. There are new symbols to be able to read and consume; much information is presented in tabular or graphic form, and finally the language in a mathematics class has its own semantics, syntax and traditions of argumentation and expression. It is this language, used in the mathematics classroom, which students must absorb and develop fluency with---all while learning the mathematics expressed by this language. Traditionally, the language of mathematics has been overlooked in the classroom, as if students could learn it by just being exposed, rather than having explicit instruction. Numerous professional organizations have called for a focus on language in mathematics education, yet it appears that this important topic is overlooked in the classroom. This research project concentrated on developing a working definition of the language of mathematics and then, speculating that the reason teachers avoid teaching the language of mathematics, it developed the Language of Mathematics Teacher Self-Efficacy Scale (LoMTES), a measurement instrument to measure teacher perceived self-efficacy regarding the teaching of the language of mathematics. Bandura's socio-cognitive theory was the guiding force in developing this instrument. Bandura indicates that self-efficacy is predictive---that teachers with high perceived self-efficacy on a topic are generally capable of teaching it, while teachers with low perceived self-efficacy on a topic tend to skip over the topic or teach it in a minimal way. Self-efficacy, however, is a changeable construct; thus, this instrument could be used to identify teachers with low perceived self-efficacy regarding the teaching of the language of mathematics, which would enable the mathematics education community to explore possible interventions designed to improve student learning by improving teacher perceived self-efficacy.