Greetings Colleagues,
I currently teach a basic skills course in reading, writing, and mathematics. One student, in a very small class (3-6 students) experienced difficulties in determining whether to use multiplication or division in transforming 60 inches into feet and 7 feet into inches.I sensed that some graphics or illustrations would help. I wonder what specific suggestions or ideas you may have in working with someone for whom these measurement transformations (inches, feet and yards) seemed too abstract for her to internalize.
A broader concern when teaching math is that i can explain and illustrate a procedure fairly well, for example, in going over ratios, but am often at a loss when I need to draw on a broader pedagogical explanation for someone who is either "not getting it," or who can mechanically complete a computation, but does not understand why the procedure in a given way.
Math is far from my first language, but I have had the opportunity to teach it in a number of contexts, which I've come to enjoy. However, I seem to be scratching my head in searching for adequate explanations that I sense would help my students better internalize what they are learning.
George Demetrion
Hartford, CT
Comments
My 2 cents: When learners get stuck in Math, it's usually because they don't understand the concept of what's happening. My go to strategy is always to explain the underlying concept with a concrete example and then model a few applications.
There's two concepts in your example: unit equivalences and multiplication/division. "If I want to convert inches to feet, should I end up with more or less than when I started?" is the key question. A ruler makes the answer pretty clear if you take the time to look at it: There are always more inches and less feet. "So do we divide or multiply if we want less?" Then a student can answer that question. You can't convert units well without a sense for them. I recommend real-world items as benchmarks: Your thumbnail is an inch (ish). Your foot is a foot(!). You have to be a yard (ish) tall to ride the roller coaster. If you ask, "Convert 60 thumbnails into human feet." They might multiply at first, but when you say, "60 thumbnails equals 720 human feet?!" They'll say, "Oh, I should have divided. Right?"
Josh:
Your direction to think about "more" or "less" is important. However, the student needs to realize that you have the SAME DISTANCE or SAME AMOUNT, just with a different name.
On the other hand, your emphasis on "more" or "less" is false when multiplying or dividing my fractions or decimals less than 1. But that is another whole issue...
Dorothea Steinke
Lafayette, CO
Many times, when students are struggling, I will give them a very basic problem that mimics what they need to do on the other problem. It is usually a problem that they can solve in their head. After a few examples, I ask them how they did the math for the simpler problem. Often times, they can then make the connection to what they need to do in the other problem. A note of caution though, some students may get confused when you bring up a similar problem, trying to make what you just said relate to the problem they are struggling with. When that happens, I usually tell the student to stop and look at me and tell them this is a different problem and we will return to what they are working on in a minute.