Consider this math problem:

In 1974, the state that had the highest population density was New Jersey with a population density of 1305 people/sq. mi. In the years that followed the decline of the auto industry, the populations began to shift away from the major industrial centers (like many of the cities in New Jersey). By 2015, New Jersey’s population density had dropped to 1210 people/sq. mi. If New Jersey has a total size of 8700 square miles, how many fewer people live in New Jersey in 2015 than in 1974?

Okay…

The math of this problem isn’t really that sophisticated. Take your densities, multiply them both by the area to get total populations. Subtract the bigger population from the smaller population and there you go.

However, what is making me struggle with this problem is the undeniable literacy component. When I consider the reasons a student might get this problem wrong…

- Made computational errors
- Did computations correctly, but computed the wrong numbers.
- Didn’t know how to set up the computation because they got lost in the vocabulary or notation.
- Didn’t know how to set up the problem because the task was unclear.
- Got frustrated and skipped it because the US Census keeps records of state populations that can be referred to instead of having to crunch numbers.

From an assessment standpoint, what does a correct answer from a student reveal to us about what that student understands and is able to do?

- We know that student can work with rates and units in context.
- We know that student can multiply and subtract strategically and accurately.
- We know that student has the ability to accurately comprehend a piece of reading equivalent to about a seventh or eighth grade level.

I want to talk about that last one. The reading one.

If that question appeared on a math test, what would be the value of exploring their ability to read? It seems like we have tests for that. Won’t they reveal those things? Shouldn’t the result a math test be based simply on a student’s ability to do math?

Well, I’m going to go ahead an add a wrinkle. Michigan just adopted the SAT as the state-sanctioned offering to the legal requirement that all juniors in the state of Michigan will take a college-readiness test before they leave high school. (From 2008-2014 it was the ACT.)

The literacy component of the SAT Math test is quite heavy. The problem that I highlighted (which I made up… along with most the data in the problem) resembles the SAT Math questions pretty well.

So, the College Board (authors of the SAT and most the AP Tests) seem to be making the statement that college readiness includes the ability to read. I’m not sure there would have been much argument for that in general, however, there are SAT portions for reading comp and an essay. The literacy bases seem covered.

So, why put such a high emphasis on reading in math?

Perhaps The College Board is making the statement that math proficiency includes the ability to fluently read mathematical scenarios.

I’m of two minds on this issue, so I’d really like some reader participation in the comments. I’m not at all attempting to challenge the value of reading, but some students really struggle with reading. Does a reading struggle apply a ceiling to future math growth?

And if there is an essential connection between math and reading, what role do math teachers play in teaching reading? Should we be developing strategic interventions for math-based reading?

I hope you’ll feel comfortable adding a comment, idea, or question that I’m not thinking about.

In my next post, I’m going to further break down this idea with respect to my limited understanding of Universal Design for Learning.

Reading in math: yes, in school math understanding is entwined with being able to read with comprehension- as evidenced in the testing questions, like your example, used for formal assessment. I personally think many of the questions are unnaturally complicated, in attempt to give context to the problem.

If we want to know if children understand a content or process, why use such a lengthy question? Why can’t the questions be more direct?

To use your question as an example:

The amount of people per square mile living in New Jersey has changed from Xx to xx over the last xx years. New Jersey has an area of 8700 square miles. How would you calculate the population of New Jersey now, and xx years ago? Set up the problem, and solve for the original population….

What happens here is a clear statement of what is, the change, and what is needed. That will tell us if the student understands the Math relationships found in the problem. As a bonus, it is stated the way a problem will be stated at work, except that the employee would have to get the numbers himself, before finding the answer!

There is no black and white in these things- I don’t want math to just be numbers- the world doesn’t give us clean numbers already set up in an equation to solve. As I told one of my students, who has difficulty with word problems, math IS word problems. All math starts out with words – numbers are shorthand for working out the solutions. I look forward to hearing more of your thoughts on this.