Consider the following problem: "Norton earns $80,000 per year as a professor. His wife earns $120,000 per year as a physician. How much more does his wife earn?" Instead of saying "Subtract the numbers and find the answer," you could say "Subtract the subtrahend from the minuend to find the difference. The number 120,000 is the minuend and 80,000 is the subtrahend. The equation becomes 120,000 -- 80,000 = 40,000. The difference between the two salaries, which we found by subtraction, is $40,000." This problem reminds students of the meaning of "subtrahend," "minuend," and "difference." It also illustrates that the number following the word "from" in a subtraction problem is the minuend.
Proofs found in geometry textbooks provide an excellent example of how to teach geometry vocabulary using worked examples. In the left column, the steps of the proof are given. In the right column, the reasons for the steps are given. Those reasons are usually postulates or theorems that contain the math vocabulary students need to learn. In this way, the meaning of the words is illustrated by their actual use in problems.
Some students learn better through reading and writing. Others learn better through listening. Try to provide methods that allow for multiple earning styles. Ask an artistic student to make a poster illustrating the concepts. A student who loves music could write a silly song teaching the vocabulary. A child with a literary bent could write a poem or short story illustrating how these words are used.
When English teachers want to teach vocabulary, they use several strategies. They create worksheets asking students to match vocabulary words on the left with definitions on the right. This strategy gives students reminders without actually telling them the answers.
English teachers also instruct students to write sentences using vocabulary words. Often, teachers construct analogies that force students to understand the logical connections between various words. For example, you could create a question like "Sum is to difference as product is to (blank)" to elicit the answer "quotient."
Some teachers quiz students orally and offer a small piece of candy as a reward. Others use an online crossword-puzzle maker to produce puzzles containing math vocabulary words. Teachers or parents with several children can hold a spelling bee and quiz students on math words. Adolescents love games and it takes only a little imagination to hold a mathematical version of "Jeopardy!" or some other favorite game show.