Tag Archives: testing

‘You must keep track of inventory’: Story-problem stories

brandi_math_2014

A friend recently posted this photo to Facebook, and, as I am a Matt, I was drawn to it. But I found this story problem to not accurately represent my desires. I don’t really want any flag at all, but given the choice of the two, I’d much prefer the Mondrian-esque flag on the right rather than the one with “4 equal parts.”

But then, story problems are all too often mere fiction. Students are expected to apply some math processes to situations that, while plausible (like realistic fiction) are not actually, you know, real.

I see some problems here with story problems that have fictional set-ups. One, if the situations are fictional, doesn’t that also suggest that the math is fictional (see also here), too? And if so, why should I spend any more time learning math than I do learning the names of all the dwarves in The Hobbit? And, two, if I’m an imaginative person, I might get so interested in the fictional situation and/or the fictional text that actually doing the math might seem damn boring in contrast, or even besides the point. Who cares about an equally sectioned red flag, if green better matches my living room decor?

Below are some examples (found here, questions that are in the style of the exam given to high school juniors in Illinois) of fictional math situations that seem strange and wonderful.

4. A customer in the music shop where you work purchases 3 cassette tapes. One costs $8.99, one costs $7.99, and one is on sale for $3.99. Excluding taxes, how much does the customer owe?

First, let me ask why the test writers either, A., know preternaturally much about my afterschool employment, or B., are asking me to pretend a whole lot here: I work in a “music shop” — what is this, 1998? Nope, wait, a customer is purchasing “cassette tapes,” so this is 1985. These prices certainly suggest those of the ’80s, but even then, who is selling a cassette for $3.99? Is this a good deal? I mean, is this cheap cassette Led Zeppelin IV or is it the Bullet Boys? If it’s the latter, should I harass the customer for his terrible taste?

So many questions: Why would I exclude taxes — isn’t that included in what the customer has to pay? I mean, am I gonna offer the customer numerous nonfinal tallies, say, giving a subtotal after every item? And why doesn’t this 1985 “music shop” have a cash register to do this work for me? Is the power out? It’s store policy to ask patrons to leave and we lock the store until the lights are back on.

The word “owe” — is the customer taking out a loan to buy these cassettes? Should I, as a math student of the future, advise the buyer not to buy cassettes at all, as the vinyl that now seems inconvenient will be cool again in just a few years, and the CDs that are coming soon will be usable long after cassette players become scarce, but the cassettes he buys will just be stored in some box in a closet in his mother’s house, to be thrown away when she moves out? Would the customer find my future-perspective frightening, as he did not know he would be buying items from a test-taker who was born long after 1985?

6. You must keep track of inventory in an office supply warehouse. This week, 8 computers of a particular model have been shipped out of the warehouse to a local store, while 4 more computers of the same model have been received by the warehouse from the factory. What is the overall change in the number of these computers in inventory this week?

I “must.” Ha, such imperatives. Am I a slave in this office supply warehouse? Or is it a family obligation, like maybe my manager is my wife’s uncle, who was kind enough to give me a job when I got fired (for asking too many questions and frightening the customers) from the “music shop” in question 4 above — and I had to spend some purgatory time in Question 5,  where I was told to Calculate the missing values so as to complete the chart — and so now I feel like I owe the guy, even though our warehousing business isn’t doing so well. It’s these damn Kaypros. I keep telling him that everybody wants IBM or Apple computers, but he won’t listen, and half the computers we send out come back. He just tells me to stick with the strategic plan, but I really think he’s just jealous of my intellect. My wife tells me to bide my time, that the resumes I’m sending out to get a job in my field will eventually pay off, but until then, I’m stuck in the logistics biz. No kid ever grows up and says he wants to be in “logistics” — but here I am. Ah, well, at least I got a place to go and a paycheck to keep my home warm. And thanks to all these Kaypros we keep getting returned, I don’t have to do the inventory myself. Lotus 1-2-3, take it away.

After Question 7 — Calculate the missing values so as to complete the chart — ignores the spreadsheet the Kaypro made, I’m apparently moving to the health care field. Such career whiplash:

8. In the hospital where you work, one of your duties is to take pulse counts. One patient has a pulse count of 21 beats in 15 seconds. At this rate, what should this patient’s pulse count be for 60 seconds?

Man, oh, man, do I hate taking pulse counts. Having to hold the bony wrists while keeping a finger on the sagging flesh of these old arms, it’s the worst. Plus, are we really sure that it should be my “duty”? I mean, I have no experience except selling cassettes and inventorying computers. But around this place, man, you never know. But that’s why sometimes, just to keep myself amused, I’ll count a pulse beat for 10 seconds, and then scream, “OH MY GOD, WHAT’S THAT ON YOUR HEAD?” at the patients just to see how much faster their heart rates can get. I go for unpredictable. But even if I don’t scare them on purpose, how do we know that their heart will beat at an even rate for the next 45 seconds? I mean, dead people’s hearts once worked, too, until they didn’t. And once a person’s dead, at least they don’t have to do these stupid story problems.

Link: Teaching reading is crap-detecting

This New York Times article, saying it’s harder to raise students’ test scores in reading than it is in math, indirectly raises some cultural/epistemological questions about the differences between math and reading.

The article opens with this anecdote from someone who has apparently taught both:

David Javsicas, a popular seventh-grade reading teacher known for urging students to act out dialogue in the books they read in class, sometimes feels wistful for the days when he taught math.

A quiz, he recalls, could quickly determine which concepts students had not yet learned. Then, “you teach the kids how to do it, and within a week or two you can usually fix it,” he said.

Helping students to puzzle through different narrative perspectives or subtext or character motivation, though, can be much more challenging. “It could take months to see if what I’m teaching is effective,” he said.

I have taught high school science and English, and I’m not sure I’d say it’s easier to teach science, because of what it means to “teach science.” The expectation (as I was informed after I pursued a different goal) is for students to learn and apply the set of science ideas (theory of evolution, atomic theory, Newton’s Laws, etc.) that are provided in the textbooks. The discipline of science observes and tries to explain the physical world, but most science classes don’t allow this. Students take notes, do equations, take tests. Real research is not done by most students (though some high school science competitions, such as this one, show that students are capable of doing impressive work).

Science classes, then, just teach a set of ideas — let’s call it a story, Science Stories — and so do math classes. Math classes could be theoretical explorations of these abstract ideas, but many high school math classes simply teach procedures (algorithms) for doing things: to find the area of a rectangle, multiply the base times the height. Sure, that’s useful information, but hardly intellectually all that challenging. Math, as taught to high school students, is a tidy system of right and wrong methods for arriving at an answer. What mathematicians do is far more abstract and creative, of course, but we don’t generally let students see that.

In English, however, we’re actually asking students to do the same things (though obviously adapted to younger minds) that English professors do — read and analyze texts and write about them. What I love about teaching writing is that students are truly CREATING texts. Students in our science and math classes are not making anything — they are just taking in the ideas that others have made.

Of course, creating something is more intellectually demanding than just memorizing and applying an idea (even Bloom’s Taxonomy, that education cliche, says so). So we writing and literature teachers give our students guidelines and models to help them “scaffold” (in the teachers’ vernacular) their way to completed projects.

But of course, there are very few right or wrong essays or literature interpretations — there are worse ones and better ones, and judging which is which is highly subjective. The student essays I like best are those that go beyond what is merely stated in a text to make connections that are not obvious. In other words, I like essays that are interesting, that say things I hadn’t read or thought of before.

Lately I’ve been suspecting that maybe the best way to teach this kind of creative thinking and individual judgment is to model it for my students. As a teacher, I have my own biases and peculiarities, and so I’m not an ideal (Platonic?) model — but maybe learning to be analytical and/or creative is really more of an apprenticeship anyway, rather than something that has set standards for students to adhere to.

And here’s where teaching the study of literature gets interesting and/or controversial. The recent Common Core State Standards for teaching literature include statements such as the following:

CCSS.ELA-Literacy.RL.11-12.2 Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text.

The very use of the the word “objective” in relation to a text is nearly an absurd statement to someone familiar with the critical theories used to interpret literature that arose in the last few decades. Taking undergrad literature classes in the mid-1990s, I gained just a limited understanding of some of these approaches, but judging by the enthusiasms of the younger professors and by the resistance of the older ones, I understood these ideas to be important.

But the Common Core standards seem written in ignorance of these developments in interpretation, as if the standards writers were just gonna elide the last 50+ years of criticism. And though the standards are careful to call their lists of texts for use in classes “illustrative” rather than “recommended,” this listing shows 14 texts, only two of which were published in the last 50 years.

So the act of reading and interpreting texts is something that, in addition to necessitating word-processing skills, also “requires background knowledge of cultural, historical and social references” (as the Times article states), and from these basic skills and resources, we ask students to make coherent, logical statements of analysis. That’s asking a lot of anybody. But then, all too often, standardized reading tests ask students to select an interpretation from multiple choices, which requires students to also analyze the test to see which of the many possible interpretations of a text is the one that the test will honor as the “right” answer. The student has to match minds both with the text-writer and with the test-writer. In the Times article,

But when [the teacher] asked [students] to select which of two descriptions fit Terabithia, the magic kingdom created by the two main characters, the class stumbled to draw inferences from the text.

Uh, yeah. Why only two descriptions? We ask students to make this complex, creative, personal interpretation, and then ask them to compare theirs to an adult’s?

This might all be despair-inducing, except for the fact that when we teach interpretation skills to students, we also empower them to see the tests and the standards as the bullsh*t they so often are. This reminds me of the Hemingway quote featuring his one standard of education:

“Every man should have a built-in automatic crap detector operating inside him.”

(One, too, might employ such a crap-detector while reading Hemingway.)