Demystifying Math
May 14, 2008
Let me expand on yesterday’s post about a poorly written math standard in Michigan, because that standard is just one way in which we make math much more inaccessible than it should be.
Take multiplication: the most common way of saying 4 x 7 is “four times seven.” But to a third grader, honestly, what does that phrase really mean? Why not say “four groups of seven” instead?
Similarly, we should read 5 + 6 as “six more than five” (or “five added to six”) as opposed to the inherently meaningless “five plus six.”
10 - 4 is “four less than ten,” not “ten minus four.”
When we change 4/10 into 2/5, we did NOT “reduce” that fraction (at least not according to the standard definition of ’reduce’), yet that’s exactly what we often say.
And when we solve a problem like 28 + 24, what exactly are we “carrying?”
My plea: Ban words like plus, minus, times, borrow, carry, and reduce from your elementary math classroom, and replace them with genuine phrases that represent what is actually occurring.
Entry Filed under: Education, Elementary Education, Fifth Grade, First Grade, Fourth Grade, Learning, Math, Second Grade, Students, Teaching, Third Grade, school. .
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1.
Liza Lee Miller | May 14, 2008 at 10:03 pm
I don’t disagree with you however I have found that my 5th graders (and I teach low achieving 5th graders) can learn the concepts AND the same vocabulary that they’ll be expected to learn later in life. Math should absolutely be demystified. But, vocabulary doesn’t have to be a roadblock as long as it’s carefully and explicitly taught. I don’t want them to get to middle school and high school and be lost when the teacher asks them what 10 minus 4 is.
2.
eyeingtenure | May 15, 2008 at 12:40 am
Teach both.
3.
mpullen | May 15, 2008 at 7:06 am
I can live with the “teach both” philosophy so long as we use the meaningful words as students are actually learning that math concept, and then we only slip into the “mathy” language once we are sure that learning has already occurred.
4.
totally3rdgrade | May 15, 2008 at 9:29 am
I don’t agree with the notion of “banning” words from any context; the words themselves are not the problem. You have, however, raised an important issue that hasn’t received enough examination.
Much of the language used in education is crafted in terms of convenience or convention. It’s just easier to continue presenting material as it’s always been presented than it is to carefully examine the semantic implications of our word choices.
I am an educational music songwriter and first became sensitized to this issue when I started penning lyrics that need to convey abstracted thought. I, too, was searching for the best way teach multiplication facts and (fortunately) realized that one of the reasons that kids struggle with multiplication tables is that the facts are being presented in a backward, confusing and non-intuitive way.
As Mark points out, “4 x 7” should be correlated with the concept of “four groups of seven.” That’s exactly what the number sentence is trying to convey.
But here’s where the breakdown occurs: “4 x 7” as an expression doesn’t tell you if you’re studying the “4” times tables or the “7” times tables. Ultimately, it won’t matter, but when you’re trying to gain mastery it matters a lot.
If you asked most adults to write out the “4” times table, I can guarantee you that virtually every one of them will write 4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, 4 x 4 = 16, etc.
Did you see what just happened? Out of convenience and without semantic regard, the concept that we’re trying to convey has been reversed!
Conceptually, we want kids to understand that “one group of four = four; two groups of four = eight; three groups of four = twelve, four groups of four = sixteen, etc.”
Why then didn’t we write our 4 times table as “1 x 4 = 4, 2 x 4 = 8, 3 x 4 = 12 and 4 x 4 = 16?”
This revelation led me to seek out clear examples of “groups” that could be used in verse to clarify this concept. (See examples http://www.totally3rdgrade.com/six_skinny_bug_legs.html
http://www.totally3rdgrade.com/five_holes_in_my_head.html
http://www.totally3rdgrade.com/eight_hours_a_day.html )
In short, I think it’s time we challenge convenience and convention and ask ourselves, “what am I really trying to accomplish here and am I really supplying the best information I can to achieve that goal?”
5.
j smith | May 15, 2008 at 5:02 pm
I think we’re making this way too complicated. Very young students do need to understand what “3 groups of 4″ truly means. That is the foundation. After they understand the concept, students will naturally be ready to apply the vocabulary words that are commonly used, such as plus, minus, times, borrow, carry, and reduce.