## Vocabulary and the Language of Mathematics

Mathematics is a language of its own, with not only specific vocabulary but also symbols and a continual translation between mathematical notation and English language. Learning mathematics can be compared to learning in a bilingual setting, therefore the importance of building vocabulary must not be overlooked. Hattie notes that vocabulary programs in math have a significant impact (effect size 0.67).^{1} Indeed, we cannot expect students to deepen their understanding through mathematical discourse or to explain their reasoning if we do not give them the language to do so.

Marian Small reminds us that the thinking matters more than the vocabulary^{2}. See this link for more information with respect to developing classroom discourse.

If math language isn’t explicitly taught, children learn to disregard math words and only pay attention to the numbers.^{3}

An effective vocabulary program involves student contributions as well as teacher modelling. The comprehension strategies that teachers use for literacy instruction also apply to literacy in math (making connections, summarizing, note taking, reading and writing responses, etc.). For example, mathematical word walls are effective if they are incorporated into the topic being taught and referred to continually. This is significant because commercial word walls can be purchased and posted without reference and context.

The Saskatchewan Math Curriculum^{4} suggests teaching new math words explicitly, meaningful construction and understanding of mathematical terminology by involving the students experientially. Then individually and as a group, determine the how the definitions will be used within the class. At that point, the students are then prepared to consider published definitions and to read and critique them.

Students also need to communicate their learning using mathematical terminology, but only when they have had sufficient experience to develop an understanding for that terminology.

**Generative Vocabulary Instruction:**

- refers to highlighting root words and sources of words for students, and discussing where they may encounter those words outside of math class. It involves making and strengthening connections. For example: quadrilateral, quadratic, quad (ATV with 4 wheels), quadriceps (a muscle group of 4), quadrant, quadruple, etc. Expanding vocabulary exploration across other subject areas will strengthen students’ understanding. Front-loading vocabulary is an effective way to provide context and connections.

Because math involves translating back and forth between spoken language to mathematical symbols (for example decreased by, less than, diminished, difference, etc), consider introducing symbolic writing with a “we write” and “we say” notation.

For example we say “four less than a number is seven” and we write:

n -4 = 7

For example, we write:

and we say “Find the sum of all the terms generated by the expression 4n, starting at the first term, where n=1, and stopping at the 6th term”.

^{1}Hattie, J. Visible learning for mathematics, grades K-12. 2016

^{2}Small, Marian Personal Communication, January 25, 2021

^{3}Uscianowski, C. (2018). Use these 5 actionable strategies today to grow your students’ math vocabulary. Retrieved 10 December 2020, from https://luminouslearning.com/blogs/sped-math/teaching-math-vocabulary.

^{4}Grade 2 Curriculum Page 11.

^{5}See footnote #3 above (https://luminouslearning.com/blogs/sped-math/teaching-math-vocabulary.)

^{6}Templeton, S., Bear, D., Invernizzi, M., & Johnston, F. Vocabulary their way. Pearson.

^{7}Learn Alberta. Interactive Mathematics Glossary. Retrieved 5 July 2020, from http://www.learnalberta.ca/content/memg/1_A/index.html.

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