Sunday, April 4, 2010

MAM Day 4: Math & language

I've thought about the connections between math and language a few times throughout my time at Boston Partners. Working with students, I find this connection quite often when we're doing word problems. I also notice that students don't read the instructions very often. Sure, we're doing math, but they skip the instructions (which always tell you how to approach the problem, what the problem is asking for, and sometimes hints to the solution) and then say "I don't know how to do this."

On one hand, math is universal. Pi is still approximately 3.14159 regardless of what country you are in. Numbers are the same in any language and math algorithms are just that, standard processes for getting certain answers. Multiplying 84 by 2 comes out with the same answer 168 no matter where you are.

However, understanding math word problems depends on knowing the language of math and the common terms that are used in conversation and language. Volume, area, and perimeter mean very specific things, but if students have learned them, they should be able to apply the correct formulas to get the right answer.

I just made up a word problem:
Alex bought a bag of oranges because she needed a dozen oranges to make orange juice. When she opened the bag, she had 5 more oranges than she needed. How many oranges were in the bag Alex bought?

In the problem, there are certain terms that help you figure out what the question is asking, and also some terms that may or may not be common knowledge. "A dozen" is a math term that we often know equals 12. If students don't know what a dozen means, they will probably not know how to figure out this question. "Five more oranges than" signifies she has extra oranges and that you should add 5 to 12 to get the total number of oranges.

This is why when I'm working with students I always emphasize that they read the instructions, either out loud or to themselves before asking me "how do I do this?" questions. If the questions are tricky or involve "intrinsic" terms (like a dozen), I tend to go over the vocabulary that will help the students. I point out or ask "what does 'more than' mean?" to help my students figure out the process for themselves.
On a different note:

My co-worker Karen and I had a conversation about the Chinese numbering system and how their number and math vocabulary is much easier in Chinese. One of her acquaintances told her they mentally compute in Chinese because it's much more efficient.

Math terms and language are also hidden in everyday conversations. These are just food for thought:

  • For example, "he and I" is simple addition! "A, B, C, and D went out last night" is also addition.
  • I use the phrase "more or less" quite often. "From time to time" is also another math phrase. I would also argue that "often" signifies frequency and is therefore math related.
  • Greater than / more than / less than
  • Questions of "How many times?" or "How much?" or "When" are all math related
  • Pairs of shoes or pants are math related
  • I've started phrases with "odds are..."
  • What does it mean to be an "average person?"

There are far more examples of the connections between math and language, but I'm done for today. More math tomorrow!


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