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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