Mathematical Literacy: Assessing Progress

Our Mathematical Literacy class is taking our first test today, which creates nervous students and concerned instructors. After 5 weeks of work (even some hard work), we get an opportunity to see how well students can apply the ideas we have been working on.

I might share later info on the kinds of scores students get on tests. At this point, I am thinking more about the outcomes in detail — assessing the class as a whole on important abilities.

One of the early items on the test is:

The base of a triangle is 4 feet, and the height is 18 inches. What is the ratio of height to base?

The major outcome here is knowing to have the same units when writing a ratio. About half of the students are showing that. Within class, this was somewhat of a minor topic; yes, we talked about it; we spent more time talking about percents requiring the units to be the same. The feet – inches comparisons came up primarily in the homework; I’ll check later, but I think the students getting this problem correct are generally those who have been doing their homework.

Another item on the test lists a table of values and students need to identify them as being linear or exponential. There are two tables provided, each with 4 ordered pairs; as you know, the 3rd ordered pair is sufficient to discriminate types (between these two). We never addressed this directly in class, though we spent one class entirely immersed in creating table of values for each type. Something like 80% of students are getting this correct (both items), which is fairly good.

A related item provides a verbal statement for linear change:

We have $200 in our savings account, and add $10 per month. Complete a table of values. Write a formula to find the balance in month T.

I am especially interested in whether students can create the more abstract model, as opposed to the table of values; in a beginning algebra course, we do a very similar problem — as part of a long sequence of topics related to slope & intercept. In Math Lit, this is not the case; we have been doing different models, and not focusing on the y=mx+b symbolism. I see this problem in Math Lit as being more difficult. It looks like about half of the students are getting the formula correct (balance = 200 + 10T), with a few having elements of the model but not all of it.

Overall, I am expecting students to do better on the concrete outcomes (numeric only) than on abstract (symbols, different representations). Of course, this is a statement about students in general. As the course progresses, I will watch to see if the gap remains wide — or if our course is having an impact on the gap.

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