Vocabulary
In researching volumes and volumes of math word problem strategies for preparation of this unit, I found one particular common theme. Vocabulary is important. It is essential to teach basic vocabulary pertaining to math word problems.
Clearly there is some overlap in the wording for addition and multiplication. That is bound to happen. Usually the problem must be looked at as a whole and a decision of addition or multiplication must be made. There are numerous synonyms for the basic math functions. It is a good idea to know those words. If you don't understand individual words in a word problem, you have little chance of grasping the overall meaning. However, memorizing the following list of words is not a complete solution. The goal is exposure to vocabulary and an awareness of general meaning. Whatever words come up regularly in your classroom should be reviewed with the students so they can understand what is being asked in the problem.
It is important for students to understand the language when reading a math word problem. Many times the simple words of add, subtract, multiply and divide do not even appear in the problem. Instead words such as sum, difference, product, etc. are used instead. This can become confusing to a student if they are unfamiliar with the vocabulary. The first step in helping students to read math word problems more clearly is to equip them with the necessary vocabulary they will likely come across in word problems.
Bluman has provided a short list of synonym vocabulary for help in deciphering words in word problems. The following list is taken from his book. "Use addition when being asked to find: the total, the sum, how many in all, how many altogether" (2005, p. 6); "Use subtraction when you are asked to find: how much more/less, how much larger/smaller, how much more/fewer, the difference, the balance, how much is left, how far above/below, how much further" (p.7); "Use multiplication when you are being asked to find: the product, the total, how many in all, how many altogether" (p. 8).
Wingard-Nelson also suggests reviewing words that have the same meaning in regards to mathematical function. For addition she uses the same words Bluman uses and also adds the following list: "add, additional, all, and, both, combined, exceeds, gain, greater, in addition to, more than, plus, raise, and together" (Wingard-Nelson, 2004, p. 46). It should be noted however, that some of these are for addition, some for subtraction, and some can be used in calling for either addition or subtraction. It is necessary to note that mathematics vocabulary is not an exact science. For subtraction Wingard-Nelson suggests "changed, comparison, decreased by, dropped, lost, minus, reduced, remain, subtract and take away" (p. 48). It is important to read problems carefully. You can do a service by providing examples of problems, where the language suggests subtraction, but addition is actually called for, and vice versa. Particularly in comparative groups, this could be a powerful lesson. Multiplication synonyms are offered as "at, every, multiply, of, per, rate, times, and twice" (p. 50). Division words were not offered by Bluman, however Wingard-Nelson suggests "average, cut, divided, divisor, each, equal parts, evenly, every, out of, quotient, separate, shared, and split" (p. 52).
It should be noted that phrases and words have different meanings depending on the context of the word problem. The point should be made that these words can be thought of as helpful hints as to what a problem might be about, but that memorizing lists of words is not a substitute for developing the habit of careful reading. Correct interpretation of a problem often depends on a more global understanding of what it says. This presumably is one reason why word problems are difficult. If it were a matter of memorizing key words, the issue would have been settled long ago.
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