Arithmetic before algebra?

In our college ‘developmental’ mathematics curriculum, we place arithmetic before algebra … and tell students that they need to know their arithmetic before they have a reasonable chance of passing an algebra course. In many ways, we have this backwards!

Think about this: Arithmetic, as normally taught, involves ideas relating to multiple sets of numbers (whole, fraction, decimal, integers) and procedures for multiple operations (binary operations in particular, and some unary operations), with concepts from geometry and dozens of cultural contexts for ‘word problems’. Within these topics, few direct connections exist; students are faced with a problem learning (remembering, as they would call it) the diverse material.

Algebra brings a structure and connections between topics that makes the learning easier. Of the arithmetic topics, only a limited number are directly prerequisites to some algebraic learning. Fractions have little to do with the concepts of solving linear equations or combining like terms; we might force those issues to come up with some contrived problems, but the algebra itself is quite basic.

Another point of view: A 8 hour sequence of class time in an arithmetic course is likely to involve a wider variety of problems than an 8 hour sequence in a beginning algebra course. Furthermore, the algebra course will provide a clearer logic for the work as well as connecting material to prior learning compared to the arithmetic course.

I’d also point out that arithmetic is not nearly as practical as it once was. Current occupations have a greater need for quantitative sense and reasoning, and we could dump much of an arithmetic course to make room for these topics … and help students in the process (with no harm done to any student).

Take a step back, and really think about your developmental math curriculum. Do you have the important stuff in the right order to help your students?

Developmental Mathematics Revival!

Bringing a new vitality to college mathematics 2011 to 2019