Have you ever wondered why it is so difficult to teach mathematics and why it is so difficult for students to grasp the meaning of the words we use in mathematics? If you pause and think about it, mathematics is a very technical subject, and it has a set of vocabulary words that have very precise meanings and sometimes multiple uses within mathematics. Outside of the math class, those same words take on a whole different meaning—oops, there is one of those words: “whole.” Get it?
Well, there are lots of them, and I would like for you to take the seat of the students for a few minutes as you read this and filter the conversation through their ears.
Jessie was asked to find the sum of 3 and 8. He said it was 6. When asked to explain his work, he responded “3 and 5 is 8, but you did not ask for all of it; you asked for some of it, so I put 6.”
Well, you just experienced homophonic partner-words with different spelling but the same sound. Imagine his thought process. Sounds like he was not familiar with the word sum, so he did a good job of problem solving as far as I am concerned! What do you think?
There are quite a few of these homophonic partners: weigh and way, weight and wait, eight and ate, one and won, to name a few. So, I always suggest identifying them in advance. Create a nice T-Chart and use a sentence as an exemplar for each use to make this clear at the onset of a lesson and help students keep up with the conversation and learn the language of math.
Then we come across those words that have multiple meanings or uses in math, like base. Oh, this one is really a pest. It actually fits into several categories. Remember homophonic partners? Well, base and bass go there! So, what does base mean in mathematics? Well, it all depends on the context. If you are using base to describe a 2-dimensional figure, the base is perpendicular to the height or altitude and is a one-dimensional measure. If base is used to describe a 3-dimensional figure, the base is now the area of a face that is perpendicular to the height.
The position of the figure does not affect what we refer to as the base. So if the triangular prism is resting on the rectangular face, as in the figure at left, the triangular face is still referred to as the base. The rule is that bases are opposite and parallel to one another in a prism, and the only faces that meet this rule are the triangular ones, so they get the special name of base. Now while that may not be a big deal at some lower grades, it is a big deal once we begin to find volume using the formula V=Bh where B represents the total area of the base of the figure. Confusing, right? Especially since, outside of math, base and bottom are often used synonymously! Now you are starting to see why the students have a struggle with the language of math!
When working with exponents, the base or base number is the number to be multiplied. For example 34 = 3x3x3x3 since the base number is 3 and the exponent is 4.
Now let’s move on to science where the students will encounter the word base again, but now it describes a pH balance—a measure from 0 to14 of how acidic or alkaline a liquid is. In music, bass is pronounced the same as base—ah, a homophonic partner. Oh, we are not finished yet with the word base. If you are part of a military family, base is often used to refer to a military installation. And, of course, there are sports, where you have a physical location: first base, second base, etc. No wonder many students are confused by the language of math … it keeps changing!
Enough with the bass, oh my mean base! My head is now officially spinning.
Moving on to round. At first glance, very nonthreatening, right? Just wait a minute. Yes, round. Hmm … I have a figure that is described as round like a circle, but then I need to round a number. This is a real challenge for English language learners because each of these situations actually shows the same word, round, used as a different part of speech in each instance—the shape is round (used as an adjective), and then we round the number (used as a verb). We use the words square and cube the same way.
Oh my, what is a student, and teacher, to do with these math words that keep me guessing? I love the use of graphic organizers to help flesh out these multiple meanings and uses and allow students to refer to them during instruction. Learning definitions just does not cut it and actually keeps the level of understanding at a superficial level at best.
In my upcoming webinar, “Unlocking the Language of Math,” I will further investigate the language of math and more of these challenges we face when attempting to teach a subject that is so dependent upon understanding and using content vocabulary to describe, justify, and explain definitions, solutions, and thinking. I will also provide simple-to-use strategies that support the use of interactive student notebooks and word walls.
Looking forward to continuing the conversation with you!
View Bea's complimentary, interactive webinar exploring more ways to unlock the language of math!
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