Mathematical Literacy: One third is less … or is it more than?
Our Math Lit class is dealing with a network of algebraic concepts, including some basic problem solving. As we often find, students don’t see the point of an algebraic method for simple problems and then have great difficulty using algebra when the problem is a bit more complex.
A simple problem was something like:
The IV is supposed to deliver 50 mL/hr, and the patient is supposed to get 400 mL. For how many hours will the patient be on the IV?
Most students ‘just divided’, even though they could not explain why that would provide the answer. When asked for an equation, they could see why ’50n = 400′ would provide a solution; students just did not see the value of the equation.
The next problem was something like:
A house is listed as having an assessed value of $42,000. The assessed value is one-third of the true value of the home. What is the home actually worth?
Every student started off finding one-third of 42000, with a few then adding this ‘one third’ to the 42000. Those that added-on were doing a ‘one-third more than’ (a more complicated relationship) rather than a simple factor of 1/3. In other words, some students thought that the answer should be less than $42000 … and some thought that the answer was 4/3 of $42000.
Students were doing these problems in groups, as they often do in this class. In this case, however, students did not question each other about their thinking. Hints and ‘simpler case’ finally got most people to the correct representation. I suspect that a few students said that this made sense just to be polite.
I suspect that students are being trained to look at “one-third of” as always meaning multiply the numbers — instead of usually meaning that there is a multiplying relationship being stated. This seemed so strongly held a belief that writing “1/3*n = 42000” did not make sense to them. Yes, this ‘of’ means multiply — but not ‘multiply by the number stated’. In addition, I suspect that students are having trouble with the conceptual part of using variables. This problem is very easy if the ‘one-third of the true value’ is seen as one-third of a variable; this view was difficult for this class of students.
Some similar problems show up in traditional algebra courses, including my intermediate algebra course. The good thing (or not so good) is that the Math Lit students are not really having that much more trouble with this than students in a ‘higher’ course. There seems to be a larger baseline ‘desperation’ triggered when a problem involves a fractional relationship, with students reverting to ideas with little or no validity.
This particular relationship (a number is one-third of another) is not that important within the mathematics of this course. The more important thing, to me, is students avoiding those bad ideas in a desperate move to answer a question with fractions. To help with that, I may approach this problem with more scaffolding next time.
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Mathematical Literacy Course | Jack Rotman | 
March 25, 2013 6:29 pm
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Jack Rotman
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By Laura Bracken, March 25, 2013 @ 7:08 pm
My students, dev math and otherwise, definitely have been trained (deliberate use of trained) in the past to multiply the numbers in the problem when they see the word “of”. There isn’t any extraneous information and so the students just take the numbers and multiply them. Number plucking at its finest. I wonder if this is a consequence of pressure to improve student scores on standardized tests in which the word problems are all of a “type.” Since I’m teaching Math for Elementary School Teachers this year and I’m struggling to improve my students’ efforts in problem solving, I also wonder if this is a consequence of teachers who also always multiply when they see “of.”
By schremmer, March 26, 2013 @ 6:49 am
Well observed. So, since it is well known that these students have a terrible time going through x, why do we keep on trying to find “new ways” to get them through x when we know perfectly well that, no matter what we do, it is not going to work and they won’t get through x.
Why not get * around* the issue and begin by reconstructing the students’ ability to think on some other ground. Once that’s done, they will wonder what the problem was with x.