n fit right on top of the yellow one.
Luis noticed that three of these diamonds can fit right on top of the hexagon. Did anyone notice any other pieces that can fit together on the hexagon?
You don't need to insist that students use the conventional terms. They will begin to learn them naturally, the same way they learn other vocabulary -- by hearing them used correctly in context. In geometry activities in later units, the students will have many experiences in classifying, describing, and defining shapes. (Talking about Shapes, Mathematical Thinking at Grade 1, page 11.)
Students learn mathematical words the same way they learn other vocabulary -- by hearing them used correctly, frequently, and in context. Young children learn words by hearing their families use language appropriately. When they make mistakes -- "Look at the big doggie," says a young child pointing at a horse -- family members use the correct word, and the child gradually learns the distinctions among all the four-footed animals that at first look like "doggies."
We don't ask young children to memorize definitions of horse or dog; rather, we find opportunities for them to hear words being used in meaningful ways. Learning mathematical vocabulary is no different.
When you speak to students, try to use mathematical vocabulary as often as you can. Connect mathematical terms with more familiar words that students may know, and use these terms in context that make sense to students. For example:
Antonio and Kevin made a rectangle from 24 tiles. The rectangle is 8 tiles across and 3 tiles down. Its dimensions are 8 by 3.
While we counted around the class by 25's, Toshi listed the numbers we said on the board. Look at what she wrote. Do we have the multiples of 25 on the board?
Throughout the Investigations curriculum, we will point out mathematical terms that are important for you to use in context. Don't insist that the students use these terms. What's important is that they express their ideas and describe their strategies for solving mathematical 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).
- S