## Algebra for Everybody, and Algebra for Nobody

Algebra is so basic that all students need to have a good grasp, and adults without this capability will be limited in their economic and social choices.  Algebra is so esoteric compared to daily life and work that only those in STEM careers need to bother learning it.  Both of these statements can be true; the apparent inconsistency is based on what is meant by the word ‘algebra’.

As such things normally happen, there is another article suggesting that nobody needs algebra (see Andrew Hacker’s article at http://www.huffingtonpost.com/2012/07/30/in-new-york-times-op-ed-c_n_1719947.html) and a response by Borwein & Bailey (see http://www.huffingtonpost.com/david-h-bailey/algebra-is-essential-in-a_b_1724338.html).  Reflecting our society in general, we tend to view issues as a binary choice — if it is good, all people must; if it is not good, nobody should.  The Bailey & Borwein response is well written, and reflects a balanced point of view.

As a mathematician, I view algebra as a language system used to describe and manipulate features (whether known or not) of the physical world based on arithmetic operators .  Basic literacy in this language system is essential in both academia and ‘real life’; translations into and out of algebra are the most basic literacies, followed by different representations (symbolic, numeric, graphic).

Unfortunately, the algebra of mass education tends to focus on procedures and complexity of limited value to anybody combined with a focus on solving algebraic puzzles, as if completion of a crossword puzzle is a basic skill for a language.    True to our current binary approach, people who agree with a literacy approach will invest great effort to avoid all procedures, complexities, and puzzles.  The truth is that we undertake these problems ourselves just for fun, and this is one element in our transition to being mathematicians; how are we to capture the attention of potential STEM students if we avoid the fun stuff?

As a language system, basic literacy in algebra means that a person can read the meaning of statements; transformations to simpler forms is based on that meaning.  I failed to help my students in the algebra class this summer … I know that because students could distribute correctly in a product but failed routinely with a quotient.  [In case you are wondering, the problems involve a 3rd degree binomial and a 1st degree monomial; in the division case, many students 'combined' the unlike terms in the binomial instead of distributing.  This is a basic literacy error; very upsetting!]

Hey, I know … nobody needs to distribute algebraic expressions on their ‘job’ (except us!).  That type of  reason is enough for me to conclude that we do not need to cover additional of rational expressions (prior to college algebra/pre-calculus); that process is complex, and is based on a higher level of understanding of the language.  Distributing is a first-order application of algebraic literacy; avoiding that topic means that we present an incomplete picture of algebra as a language.  A pre-college mathematical experience needs to provide sound mathematical literacy — including algebra.

Everybody needs algebraic literacy, as part of basic mathematical literacy.  We can design courses that provide the needed mathematical literacy as a single experience — no need for a numeric literacy course (‘arithmetic’) and an algebra course and a geometry course; all of that, plus some statistical literacy, can be combined into one course.  This is the approach of the New Life model, and is imbedded within the Quantway & Statway (Carnegie), and in the New Pathways (Dana Center).  I encouage us all to include some transformations (‘simplifications’) in the algebraic language.

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### 1 Comment

• By schremmer, August 3, 2012 @ 12:45 pm

Most everybody does NOT need “algebraic literacy”.
However, when appropriately design, an algebra course can be an area where people can learn when to stop and consider, how to conjecture and how to act on said conjectures, how not to be taken in by appearances, when to insist on a case being made, etc. All of which everybody needs.
The specific contents of such a course are relatively unimportant. But the contents’ architecture is paramount for the students to learn focussing on the “connective tissues”.
Regards
–schremmer