It’s nearly impossible to separate mathematics and language. We can’t teach math and students can’t ‘do’ math without naming mathematical objects and concepts and without language to express mathematical ideas. In the October, 2020 issue of Mathematics Teacher: Learning and Teaching PK–12, the authors of the article, Developing and Writing Language Objectives, state “the role of language development in the mathematics classroom must be at the forefront of instruction.”
My purpose in this blog is not to discuss this article, but to suggest 3 ‘unusual’ mathematics vocabulary, language function and language skills activities that my graduate math methods students have found useful and engaging for their students.
The first activity is ‘finding’ everyday words with a mathematical root. Some of these words are obvious, such as tricycle. Children use words like bicycle or tricycle without noticing their mathematical roots, but those roots are not hard to find or determine. The root of the word ‘twin’ is not so obvious, but maybe it’s clear that it’s related to ‘two’. ‘Twine’ is also related to ‘two’ and refers to two or more strands twisted together. ‘Mile’ comes from the Latin word ‘milli’ (as in millimeter or milligram) which means 1000, and ‘mile’ is the distance traveled by a 1000 Roman soldier steps.
Some words have only an obvious or only a mathematical meaning, e.g. semicircle, pentathlon. Whereas the math root of other words is more hidden. Finding these words can be very engaging. Words such as ‘ounce’ (derived from the Latin ‘uncia’ meaning 1/12) or ‘atone’ (at one – become one or reconciled) have lost their mathematical roots.
If you know of others, please let us know in the Comments below.
The second activity is to use word clouds. My graduate math methods students use vocabulary specific to a content unit, and/or expect their students to make word clouds which can be used to ‘decorate’ an assignment or as a graphic for video creations. Some word cloud software can be programmed to conform to a particular shape (rather than a more general cloud). Here’s a word cloud in the shape of the United States (interdisciplinary?) created by one of my elementary education math methods students who were given the prompt ‘Divisor’.
And, here’s another created by one of the students in my History of Math for Teachers course.
These clouds make great graphics for bulletin boards – both real and virtual. How could you and/or your students use word clouds? You can tell us by leaving a Comment below.
My third, and final, suggestion of a mathematical language activity is to use Frayer models. The Frayer model, named after the late Dorothy Frayer (at the time of the U of Wis) is a graphic organizer that was traditionally used for language concepts. However, graphic organizers are great tools to support thinking through problems in math. The Frayer organizer has 5 sections with the center section reserved for the key word.
Here’s an example focusing on the word ‘quadrilateral’.
Notice that this could be created by students for each ‘new’ vocabulary word and, more importantly, notice how this organizer focuses on mathematical thinking/concept development rather than only on vocabulary.
More interactive uses are giving students with one of more of the 5 sections blank and expecting students to complete them accurately. The example below has the center word blank, but other sections could be blank too. Perhaps you could make this a group activity in which each group is ‘responsible’ for one of the sections of the Frayer model. In my courses, I’ve had students create their own after I give them the center word prompt, and then the other students comment/improve them.
And, here’s another with very few words.
These Frayer models can be used for bulletin boards – both real and virtual, for ‘vocabulary’ notebooks, etc. How could you and/or your students use the Frayer model to focus on academic/mathematical language and content?
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Have a question for the authors? Email us at congruentthoughts@nl.edu or tweet me @GeorgeLitman1.
Congruent Thoughts with Aleks & George 
Yes, these posts are so helpful! Especially since we want our students to think mathematically, and math is everywhere!! I would love if you had more like this, thank you so much!
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