Teachers of mathematics need to recognize that there is a strong link between language, writing, and problem solving. In most of the assessments that states use to determine student and school success, a student must demonstrate math reasoning abilities through writing. This skill is not automatic, though. It develops through a recursive process:
Vocabulary & Language <—> Reasoning <—> Talk <—> Writing
Beginning with vocabulary and language, a student learns to reason, then to communicate those thoughts verbally, and finally to write. Each of the levels feeds back to the previous one, reinforcing and further developing it.
Thus if we’re going to teach reasoning skills effectively, it follows we need to carefully consider the vocabulary we use.
It isn’t uncommon, especially in the primary grades, for teachers to simplify the language we use with children to explain complex concepts. Although this is useful, it can also lead to sloppy language if we aren’t careful. It is particularly important that we don’t permit students to use precise math terms improperly and that we teach the “real” terms as quickly as possible. Even if students don’t use them right away, they should be hearing the correct terminology in context from the beginning.
Here are a few examples of sloppy math language that I often hear from older students. If these go uncorrected, students will have a very difficult time communicating well when they need to explain their thought process–a skill that is essential to upper level math.
|Instead of these…||Use these…|
|answer||sum, difference, product, quotient|
|amount||length, height, volume, number, etc.|
|number||digit, addend, factor, dividend, etc.|
|bigger, smaller||greater than, less than|
I believe it’s essential to require students to be precise when they communicate. Often when students don’t use the correct term, or use a valid term improperly, it is a sign they just don’t have the right words.
I’ve heard teachers argue that young children just aren’t capable of such sophisticated language yet. My father, a retired professor of speech/language pathology, has often said, however, that if second graders can learn and correctly use terms like “Tyrannosaurus Rex” and “Diplodocus”, why on earth can’t we teach them to say “subtracted” instead of “minused”? Vocabulary instruction should be as much an integral part of mathematics as it is of reading, writing, and other content areas.
Tomorrow I will tackle a more challenging vocabulary-related issue in mathematics: verbal and written explanations of a student’s cognitive process.
(This article is based on material I originally posted in Grandé With Room.)
@Bill No, I haven’t, but I will certainly be looking it up! Thanks for the tip.
Have you read Writing to Learn? It contains excellent examples of using writing to teach mathematics, among other things. I highly recommend it!