Mathematical Literacy: Factoring in the Mathematics Curriculum

Some people will be surprised that our Mathematical Literacy course includes some factoring.  Over the years, the topic of factoring has been a focal point of conversations — almost with the assumption that a reform math course would not cover any factoring.  Sometimes, we go to the extreme view of “anything not practical right now … will be omitted”, and factoring is usually not very practical.

In our Mathematical Literacy course we covered factoring  last week — true, this is just the GCF (no trinomial methods nor special formulas).  Since we only include GCF as a method students have an easier time.  However, if we had time, I would not mind if we covered a little more factoring.

For language skills, it is important that people be able to express thoughts concisely (simplify); in some important situations, it is even more important to be able to express thoughts in a more complex way that maintains the equivalent message — persuasive writing and speaking are particular modes in this style.  In a general way, learning (or a process) that can only be used one direction is usually learned only partially.  Deeper learning depends upon a variety of experiences with objects or ideas.

Factoring plays a comparable role in any course emphasizing algebraic reasoning.  A basic issue in algebraic reasoning is “Adding or multiplying?”  Many of our students believe that parentheses always show two things — what to do first (under the curse of PEMDAS) and “this is a product”.  Our work with the GCF puts students right in the middle of this confusion; in other words, the GCF is a great opportunity for students to better understand basic algebraic notation.

Of course, one risk of this work with the GCF is that students get even more confused.  We need to be careful that assessments help students understand better; within the Math Lit class, I need more experience designing the class work so better assessments can be delivered to students.

Of the traditional developmental algebra content, factoring is not my lowest priority — it connects with basic issues of algebra.  I can’t say the same thing for radical expressions, where we deal with procedures only vaguely connected with exponents.  I also place ‘rational expressions’ lower in priority than factoring; outside of the very basic ideas of reducing simple rational expressions, our time on operations and equations with rational expressions list mostly wasted … the emphasis ends up on procedures, not concepts and understanding. Such topics have been included in developmental courses because they are seen as needed in pre-calculus courses … because they are seen as needed in calculus courses.  We should strengthen this flimsy curriculum design based on student needs AND content needs in deliberate ways.

All of us have a role in this process so that mathematics becomes an enabling process rather than a inhibiting process.  Factoring polynomials is not necessarily an evil to be avoided.

 
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1 Comment

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  By Sue Jones, April 25, 2013 @ 3:37 pm

  I was just reading yesterday in the NADE journal about the general condition of developmental mathematics and the conclusion of the article was: “We can no longer deny your weakest and poorest citizens the opportunity to obtain a college credential simply because we are unable to teach them how to factor polynomials.”
  The article itself said absolutely nothing about that topic, and absolutely nothing about teaching students to understand math (it was the usual focus on Getting Students to Meet Math Requirements). I have this sinking feeling that there are all kinds of assumptions and judgements behind that closing statement.
  I, too, have had a lot of students with a lot of confusion about multiplying vs. adding, and I start at the beginning of the year with stressing that the rules for adding and subtracting are really different than the rules for multiplying and dividing [interruption, I kid you not, to explain to a student that 1 2/3 is not 6/3 because where the plus sign is, you’re supposed to add, not multiply]…
  I think it’s worth spending the time on this, especially if I can build in time to show examples with good old fashioned numbers that yes, these are two ways of expressing the same thing.

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