If students develop a good mathematical vocabulary it helps them understand exactly what the question is asking. As mentioned before, many mathematical terms have both a general meaning and a specialized meaning and it is important for the student to know both. Many times, there are students in the class who are English Language Learners who may not yet have acquired all the vocabulary needed to do well in mathematics. When students have a good vocabulary, they are able to participate in mathematical discussions with more ease because they can express their ideas properly.
When teaching vocabulary in class, it is important to begin with the vocabulary they already know before introducing the mathematical vocabulary. The vocabulary they have may be informal in that they describe a rhombus as a diamond due to the shape. The teacher would then affirm it did look like a diamond and was called a rhombus. In other words, repeat back the language used by the student to include the correct mathematical terms because it acknowledges the student has some base knowledge. It is important to use the mathematical language even if it is paired with a regular description such as area or the inside part of the shape so they build an association between the word and a definition.
Second, the words must be taught explicitly to the student and they must be given a chance to use the new vocabulary so they learn it. The words can be introduced in a pre-teaching session, taught during the actual session by using definitions, pictures, drawings, and examples. Post the vocabulary on a word wall or have students write them into their personal dictionaries they are making. Afterwards, review the words by having students define each new word and provide both an example and non example of the word. Always teach and use the words in context.
Next, have a classroom word wall to post the new words along with pictures and definitions of each word if the picture is not enough. For instance, if the chapter has the word line, you might draw a straight line all the way across the page. Most high school students know what a line looks like so you may not need a definition but you might need to include a definition for the word "betweenness".
Another possibile activity is have students fill out vocabulary cards using the Freyer Model. If you haven't used them, they are great because they have students have students create definitions, list characteristics of the new world, provide examples and non-examples to show what it is and what it isn't. The word always goes in the middle. If you do a quick search, you can find templates that have several on each page.
Finally, use math journals to help reinforce the use of mathematical vocabulary. At the end of class have students use a writing prompt to think about the lesson itself. One such prompt could have students begin "Two ways to solve this problem are........." or "One problem I solved was........". These types of prompts have students reflecting on what they learned and on the concept taught in class. It encourages self reflection.
Sometime in the near future, I'll talk about ways to use word walls and writing prompts in class to help them develop a better mathematical vocabulary. Let me know what you think, I'd love to hear. Have a great day.
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