Math and Science, Bass-Ackwards

In one of my jobs, I’m a paraprofessional in a high school science classroom. Last week in Biology we were in the unit on carbohydrates, lipids and proteins as polymers. Of course, the students have been struggling because we’re touching on biochemistry concepts, and they’ve not had chemistry.

So I asked the teacher, “If biology depends upon chemistry, and chemistry depends upon physics, then WHY don’t we start with physics, and then go to chemistry and then biology?”

(I mean like, duh!)

And he replied, “Because most of these students don’t have the math background for physics; they’re only in geometry.”

That’s Geometry as the class that for some reason is inserted between Algebra 1 and Algebra 2, before they get to Trigonometry. Actually, a person can get through basic physics without using calculus. But you do need algebra. And you especially need to be willing and able to tackle “story problems”.

I think this whole issue with “story problems” illustrates a very basic problem in a great deal of American maths instruction. Mention “story problems” and the students groan and whine, if not almost break out in a rash because “they’re confusing and hard and [we] don’t understand them”. Unfortunately, a lot of textbooks (and educators) focus too much on rote drills using the particular method for that lesson, for example, “how to use distribution” by multiplying 5(3x-2). The problem with such approaches is that it focuses the students upon recognising a particular “kind” of problem, and then using whatever method was taught with those kinds of problems in that section. The students often lose out on when to use particular methods, and why.

(The most daring and illuminating thing a mathematics teacher ever told me was in my college algebra class, when she said to us, “If you don’t like it, then change it!” Meaning, if the way the problem is set up is difficult to do, then you can manipulate it into an easier form. Naturally, that’s what a lot of algebra is really about — juggling the knowns to figure out the unknown — but it had never been explained as something where each of us were allowed to change things around to what we needed, rather than trying to guess what some anonymous person thought should be done to the problem.)

Another thing that students often miss when learning too much rote mathematics is determining how to identify and then create their own equations (& inequalities). You know, the “When am I ever gonna do THIS in real life!” whine. Well, that is to some degree a valid complaint; everyone wants to learn things that have some use in their own lives.

But in real life, no one is ever handed a textbook of problems to solve, much less one with the answers to the odd-numbered problems in the back of the book. This is my answer to those who complain (about any subject), “I don’t care how it’s done, just tell me the right answer.” Because the really important part of the instruction is not the answer, but knowing how to get the answer! (The teacher doesn’t really need dozens of students to tell them the answer; the teacher could calculate the answer, or look it up in the teacher’s textbook, assuming there’s not a typo. I’m always amazed at how many typos were in the answer keys!)

In real life, we don’t have ready-made equations, aside from various bookkeeping functions. Rather, we have an assortment of situations where we need to figure something out, usually as a part of a much larger project we’re working on. For example, this weekend I will have to calculate area of a yard, then do a concentration conversion, then calculate the amount of material to spread on my lawn. Of course, in real life I can’t go down to the hardware store with a number like “3.6666667.” In real life, I would end up buying a 5-pound or 2-kilogram bag of whatever.

That’s a story problem; I have to identify which variables I need, and which formulae to use, select conversion factors (if needed), and then create my own equations using whatever quantities I know, to figure out which quantities I will need.

Regardless of whether or not we use calculators, we still have to know how to set up the problems, and how to solve them. Calculators enable us to do the drudge-work more easily and quickly, so we don’t lose sight of what step we’re on, or what we’re trying to solve for. I have no quibble with using calculators for most kinds of mathematics or science instruction. Regardless of what kinds of tools you use, you still have to know when and how to use them. No matter what some students think, the calculator doesn’t tell you the answer to the problem; it only displays the result of what you punched into it.* GIGO, Caveat emptor, et cetera.

Back to teaching science. So in this simplistic sense, we can’t teach our science in a sensible physics-chemistry-biology order because our students can’t do the maths. At our local schools, the state has decided to start doing science assessments, which if I understand correctly, will have one particular grade getting a physical sciences assessment, and another grade getting a biological sciences assessment, but because the current biology students didn’t do the physical sciences assessment last year, they have to do it and the biological sciences assessment this year. (I don’t understand the rationale for that, either.) Which of course means that the science teachers are taking time from teaching the curriculum for doing assessment preparation.

As the saying goes, “No one ever grew by being measured.” Although I think most everyone agrees that we need good teachers, and that we need to hold schools accountable for providing the educations that our students need, I don’t think that the constant focus upon assessment tests is the way to achieve that. We end up placing too much focus on test-preparation instead of teaching, and reciting or identifying the “right answer” instead of knowing how or why it’s the right answer.

Bug Girl has a nice little piece, “We’re taking our math and going home in a huff” about the Bush administration not wanting to participate in the next global test of advanced math and science, quite possibly because US students don’t compare well to their peers in many other countries, and the results wouldn’t reflect well upon the 2002 No Child Left Behind Act.

When all is said and done, we still end up placing too much focus on getting the “right answer” on the NCLB stats, instead of knowing how or why it’s the right answer, or more importantly, if it answers the questions we’re asking, or if we’re even asking the right questions.

Such as the important question about the most sensible order to present different science subjects.

* No matter what some students think, the calculator doesn’t tell you the answer to the problem; it only displays the result of what you punched into it.

“Seven!” he crows, shoving the calculator in my face.
“And what does ‘seven’ mean?” I ask.
“That’s the answer — seven.”
“No, seven-what? What do you have seven of?”
Cross retort: “I dunno.”
“Well, what’s the problem asking?”
Student recites, “How many [blah-blah-blah]…”
“Okay, so what do you have seven of?”
“I dunno,”
I wait a moment, letting the mental cogs catch up.
“Oh,” he realises, “Seven pizzas.”
“Right.” I then model translating the numeric result into a verbal answer, “To feed everyone at the party you would need seven pizzas. This is what you use math for.”
“Hah! I would just buy a bunch of pizzas and eat them ALL MYSELF!” comes his grandiose reply, accompanied by exuberant arm-waving and squirming at the desk.
I sigh at this last response; this is a program for students with emotional and behavioural issues, after all…

(See my additional comment below.)


  1. qw88nb88 said,

    4 October 2007 at 22:39

    There are several interesting points raised here in your comments, folks.

    About a century ago, one of the main foci of American public education was to help create a moderately literate and obedient labor force; part of the education was about turning various immigrant children into Good Citizens by instilling the right moral values and work ethics into them. The skills and knowledge they were to learn was to prepare girls to be good wives, and boys to be good workers in factories or offices.

    Only a small percentage of the graduates went on to college, and certainly the high school graduation rate itself was not high — that’s why graduating high school was such a Big Deal, with diplomas, gowns & mortarboards, and class rings. Even as late as the early 1960’s, barely over half of workers had high school diplomas. Now just into the 21st century, we have a high school graduation rate around 90%, and about a fourth of the adults have college degrees.

    This education level in the population is WHY it is important for us to be sure that our high school graduates gain an understanding of how science works, how to identify junky pseudoscience, and know how to use mathematics to understand and answer things in their own lives, such as budgets, loans, work-related calculations, and whatnot.

    As for mathematics and intelligence, this is indeed a tricky issue. While it’s true that someone with really low abstract cognitive abilities will not be able to progress far in mathematics, that’s not the same thing as saying that people who struggle with the maths are necessarily stupid. There are indeed plenty of smart people out there with dyscalculia, or people who have dyslexia-type problems with numbers, or who (like myself) found that “the easy things are hard and the hard things are easy”. I was in 8th grade (13 years old) before I had fully memorised my multiplication tables. Moving from one state to another left gaps in my maths education (for those outside the US, each state creates its own educational plans and selects which textbooks to use, so there’s not a lot of consistency). Algebra was something I struggled to pass, but then much later on I found the concepts of calculus to be much easier to grasp:


  2. codeman38 said,

    3 October 2007 at 17:01

    Related to the issue of the education system focusing on rote drills rather than serious stuff…

    I still can’t do arithmetic in my head; even fairly simple problems I need pen and paper for (and even then, I sometimes mess things up, like, for instance, writing down 6 as the sum of 2 and 3, or inadvertently transposing digits).

    Yet the school system seems to be designed so that all manner of rote drilling in arithmetic is necessary before one can go on to algebra and the like.

    Now I’m not saying that basic arithmetic shouldn’t be taught; I am, however, saying that if a student has trouble with basic arithmetic, he or she shouldn’t necessarily be held back from going on to higher math! It may very well be that that student fully grasps the ideas in algebra, but just doesn’t have a brain that’s suited for raw arithmetic computations… and a cheap dollar-store calculator can easily be used to work around that handicap.

  3. Norah said,

    3 October 2007 at 11:23

    Interesting piece, but I hope not everyone here thinks that people who are unable to do even basic math will definitely end up in factory lines and are also unable to do logical problem solving?
    Sheesh, I shouldn’t insult people, but… (ok, I’ll hold it in).
    Not to mention equating inability to do math with stupidity.

  4. tekel said,

    3 October 2007 at 3:15

    You know, the “When am I ever gonna do THIS in real life!” whine. Well, that is to some degree a valid complaint; everyone wants to learn things that have some use in their own lives.

    That’s what we call a self-fulfilling prophecy. If students don’t learn algebra, they won’t use it in their real lives, and they’ll spend those real lives doing menial tasks and following simple orders given by people who took the time to learn math, because their failure to learn has made them incapable of solving problems.

    Or as we used to cheer in college when our basketball team was getting beat (i.e. at every game): That’s allright, that’s OK, you will work for us some day!

    This is perhaps a rant for another day, but I think in some sense that churning out a pliant and unquestioning work force was and is the major motivation for NCLB. Somebody has to assemble all of those ugly American cars, and once those jobs don’t come with health benefits, you’re going to need a bunch of dumb kids who can’t do math to keep the assembly lines moving. If you teach everyone how to think effectively for themselves, who will work at the Ford plant?

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