ARCHIVED School Mathematics Glossary - Introduction

Nunavut Arctic College, Nunatta Campus (Iqaluit, Nunavut)

Teaching of school mathematics, whatever the language of instruction, has traditionally employed a strikingly limited, if specialized, vocabulary: names for numbers, for process instructions ("add," "multiply"), for computational components ("dividend," "quotient," "remainder"), and for a minimum of content-related concepts ("cancel," "invert," "check," "odd," "even," "triangle," "cube"). Such vocabulary, with its limitations, has then tended to influence teaching and learning. What could and often did result was a mathematics of "worksheets" and of routine textbook "exercises," with a minimum of new terms and limited scope for deviation from an essentially linear plan.

Yet, over recent years in and beyond Baffin Region, Inuktitut speakers and others have repeatedly shared with me astute observations on how mathematics learning could be hampered by lack of vocabulary. This I see as a reflection of growing awareness, across Canada and internationally, that—whatever the language of instruction—mathematics learning is best rooted in rich language usage. One-page word lists, however resourceful, could not suffice in Inuktitut any more than they could have in English or in French.

Such recognition of vocabulary need can be seen as reflecting the spirit and intent of major professional documents of interprovincial and international import. The range of terminology selected for inclusion in the pages that follow, accordingly, has been influenced, on the one hand by Curriculum and Evaluation Standards for School Mathematics, 1989, and Professional Standards for Teaching Mathematics, 1991, of the (United States) National Council of Teachers of Mathematics, in particular the associated Curriculum standards for Grades K-4 and 5-8. (These documents are well extracted in Billstein, Libeskind, and Lott, A Problem Solving Approach to Mathematics for Elementary School Teachers, 5th ed. (Addison-Wesley, 1993), a text reference currently used in Eastern Arctic teacher preparation. The second influence on choice of terminology has been The Common Curriculum Framework for K-12 Mathematics of the Western Canadian Protocol for Collaboration in Basic Education: an "Interim NWT Version" of this forward-looking document has been widely available since 1995. The Grade 10 to Grade 12 supplement, 1996, should be studied to grasp the full scope of the program, but some of its vocabulary requirements necessarily are beyond the scope of this work.

The vocabulary of school mathematics should enrich and should be reinforced by thematic and interdisciplinary experiences. "Many possibilities for integrating learning experiences across the curriculum" are acknowledged in Mathematics K-9: Goals and Objectives, the recent (1990) Northwest Territories curriculum guide, which goes on to caution that "mathematics is a sequential discipline and concepts should be developed in the contest of mathematical instruction."

The plan of this glossary is to present the vocabulary and ideas for a rich and imaginative presentation of school mathematics through middle grades, with terms in Inuktitut, English, and French, and descriptions if not rigorous definitions of topics involved. Working with the Inuktitut-translation team at the Interpreter-Translator Program at Nunavut Arctic College has been a fascinating adventure of seeking—or creating—the mot juste to present meaningfully a mathematical concept to young people of Nunavut at a time when mathematical maturity will be vital to the realization of full potential.

Don Allen
Coral Harbour, Nunavut