Welp, Wednesday and Thursday were both Too Busy To Breathe days. TOday I said “No” to subbing ( it’s been so long that I’ve “taught a class” that I have this insane idea that I wouldn’t know what to do…) and it’s been quieter — it’s also raining hard. (Left early on the bicycle to get in before it really got rolling.)

I’m making an annotated list of articles and I … thought I had already blogged about WHAT COMMUNITY COLLEGE DEVELOPMENTAL MATHEMATICS STUDENTS UNDERSTAND ABOUT MATHEMATICS .

It explores and explains… starting with this:

Most of what we know about the mathematical knowledge of community college students we learn from placement tests (Accuplacer, Compass, MDTP). But placement test data is almost impossible to come by due to the high-stakes nature of the tests and the need to keep items protected. Further, the most commonly used tests (Accuplacer and Compass) are adaptive tests, meaning that students take only the minimal items needed to determine their final score, and so don’t take items that might give a fuller picture of their mathematical knowledge. Finally, most of the items on the placement tests are procedural in nature: they are designed to assess what students are able to do, but not what students understand about fundamental mathematical concepts.

Then this:

Currently there is great interest in reforming developmental mathematics education at the community college. Yet, it is worth noting that almost none of the reforms have focused on actually changing the teaching methods and routines that define the teaching and learning of mathematics in community colleges.

… and then, yes, the hypothesis I’d like to explore as well:

In particular, we are interested in exploring the hypothesis that these students who have failed to learn mathematics in a deep and lasting way up to this point might be able to do so if we can convince them, first, that mathematics makes sense, and then provide them with the tools and opportunities to think and reason.

There’s a healthy sample size here. 1643 in algebra readiness, 1856 in Elementary Algebra, 1651 in Intermediate Algebra and 680 in Pre-calc.

So, from the “algebra readiness” here’s just the top part of analysis of the questions causing the most trouble:

Note: that’s the percent who got it *right.*

Patterns? Fractions … bad news. Students did something that sort of looked right. “it appeared as though students sometimes fell back on their knowledge of how math questions are typically posed.” So asked for least common multiple of 6 and 9 … answer would be “3.”

The ten questions answered correctly by students… students could get them right by plugging a few things in and doing what looked right.

The article went on with a whole lot of conceptual problems and … ouch. Ouch.

They also interviewed some students. Consistent with my experience, students who knew that “half of something” was the same as dividing by two couldn’t apply that to other fractions well. Students did not expect to use “common sense” in math class. There were no connections between their intuitive understandings and … math problems.

“Roberto, in our case study, asked at one point:

‘Am I supposed to do it the math way, or just do what makes sense (paraphrased)?’

Let’s fix that, okay?

Stigler, J.W. et al. (2010) What community college developmental mathematics students understand about mathematics. MathAMATYC Educ. 10, 4–16

*article, Uncategorized*

Posted on August 24, 20180