problems clearly and accurately, using whatever words are comfortable for them. However, as you use mathematical terms frequently, students will become used to hearing them and will begin to use them naturally. Even young children can learn to use mathematical vocabulary accurately when they hear it used correctly and in the context of meaningful activities. (Using Mathematical Vocabulary, Mathematical Thinking at Grade 5, page 14.)
What does this look like in the classroom?
To think about what this might actually look like in the classroom, consider this vignette from a teacher on the CGI-Investigations listserve:
My students had been stumbling over terms as we worked with the Picturing Polygons unit. We've explored and defined polygons, triangles, and angles, and are moving on to quadrilaterals and other polygons. My students expressed a need for reminders around the room to help them with terminology. So we made a list of 16 terms we'd been using, and the kids worked in partners to create posters with definitions and illustrations... They were very engaged, worked hard to make the posters visible from a distance, and tweaked their definitions for both clarity and brevity. For example, the pairs who were working on triangle and quadrilateral came to me and said they knew they could use polygon as part of the definition because the poster for polygon listed its attributes, and anyone in our class reading the word polygon would know those attributes too! In addition, because it's a pet peeve of mine, I wouldn't let them use the word to define the word. For example, they couldn't define right angle as "an angle that measures 90 degrees." It forced them to focus on synonyms and clear meanings, turned out to be a great review and solved the problem of confusing terms for lots of kids. -- Debbie Sauer, 5th grade teacher, Duluth, MN
In this classroom:
- Students can base their definitions on the many experiences they have already had with shapes, angles, etc. (during the first part of the unit Picturing Polygons).
- Students do the work of generating the definition and drawing pictures/examples that illustrate; they also respond and react to each other's work. (Note that students are also developing ideas about mathematical definitions -- they are working towards clear, concise definitions that don't use the word they are defining, or define words that others are defining.)
- Students are deepening and consolidating their knowledge of those shapes and attributes by discussing, comparing, and refining definitions.
- Students have created resources they can continue to use and refer to and adapt.
The goal is that children gain a working knowledge of math ideas and terms, not that they memorize definitions. The mathematical activities in Investigations provide students with numerous opportunities to hear, gain knowledge of, and use mathematical vocabulary in context.
A final note regarding vocabulary lists and glossaries:
The Investigations units do not include a list of vocabulary words. However, when people are looking to create one, the vocabulary support for second language learners IS a good place to start. (This includes the Preview for the Linguistically Diverse Classroom in the Front Matter of each unit, Vocabulary Support for Second Language Learners towards the back of each unit, and an additional, separate support package.
Note that some of the words and terms included in these sections are less about math and more about other words students will need to know and understand about a particular context in order to make sense of the math.
Megan Murray, TERC
Thanks to Kathy Silman and Beth Perry, TERC, and to the members of the CGI-Investigations Listserve, especially Debbie Sauer