This past weekend, I was at our state affiliate conference. MichMATYC has a long history (relatively), and we have had a number of AMATYC leaders from our state (including three AMATYC presidents). We’ve been heavily involved with the AMATYC standards (all 3 of them). However, you can still see some bad stuff among our practitioners.

One of the sessions I attended focused on lower levels of dev math — pre-algebra and beginning algebra. The presenter shared some strategies which had resulted in improved results for students; those improved results were (1) correct answers and (2) understanding. That sounded good.

However, the algebra portion was pretty bad. The context was solving simple linear equations, and the presenter showed this sequence:

- one step equations (adding/subtracting; dividing)
- two step equations (two terms on one side, one on other)
- equations with parentheses, resulting in equations already seen

All equations were designed to have integer answers; the presenter’s rationale was that students (and instructor) would know that a messy answer meant there had been a mistake. All equations were solved with one series of steps (simplify, move terms, divide) — even if there was an easier solution in a different order.

When asked about the prescriptive nature of the work, the presenter responded that students understood that it was reversing PEMDAS (which, of course, makes it even worse for me).

The BAD PART of dev math is:

- Locking down procedures to one sequence
- Building on memorized incomplete information (like PEMDAS)

As soon as students move from linear equations taught in this way to any other type (quadratic, exponential, rational) they have no way to connect prior knowledge to new situations. In other words, the student will seem to ‘not know anything’ in a subsequent class.

To the extent that this type of teaching is common practice, developmental mathematics DESERVES to be eliminated. Causing damage is worse than not having the opportunity to help students. When we offer a class on arithmetic (even pre-algebra), the course is very likely to suffer from the BAD PART; offering Math Literacy to meet the needs in ‘pre-algebra’ and ‘basic algebra’ will tend to avoid the problem — but is no guarantee.

All of us have course syllabi with learning outcomes. Those outcomes need to focus on learning that helps students, not learning that harms students. Reasoning and applying need to be emphasized, so that students seldom experience the BAD PART.

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