Musings on Algebra

For our first specific concept post (see the schedule), I thought I’d offer some general thoughts on a part of math that confused me for years: algebra. Hopefully, this will help you see God’s handiwork amid the xs and ys.

What is algebra?
Algebra is the process of using letters and symbols to describe general quantities and relationships.

For example, say I head into a store with $20 and come out with $5. I would have spent $15.

$20 – $5 = $15.

My starting dollars minus my ending dollars showed me how much I spent in the store.

starting dollars – ending dollars = dollars spent

Let’s use letters to represent this relationship. We’ll use z to represent the starting dollars, y for our ending dollars, and x for the dollars spent.

z – y = x

We now have represented a general relationship that holds true for more than one situation! (We could use it to see how much we’d spent in any store.)

The above is one example of using letters to describe a relationship. By recording a relationship rather than a specific situation, we’re able to solve for unknowns and discover other relationships. This process proves useful in MANY areas (electricity, interest rates, gravity, laws of motion, etc.)

Algebra is based on the idea that certain relationships consistently hold true–that objects operate in a predictable fashion. Dollars do not mysteriously multiply in our wallets. Objects fall in a predictable way. The relationship between the power and voltage and current in an outlet remains the same. Why do things operate so predictably?

Because an unchanging God holds every aspect of this universe together! If God were not keeping everything together in an amazingly predictable manner, algebra would be completely useless. But because of God’s unchanging hand over creation, we can use letters and symbols to name and describe the predictable world around us.

What about all the rules?
A large portion of algebra textbooks focus on rules and conventions. Each “rule” is one standardized convention to represent a real-life consistency.

For years men did not use our current conventions at all! The graphic shows some different ways an algebraic equation has been expressed.

Why does algebra often seem so meaningless?
So often, algebra students completely miss seeing the amazing consistency algebra records because they get lost in the mechanics. As Morris Kline points out, “The usefulness of the techniques of algebra has caused many people to mistake the means for the end and to emphasize these menial techniques to the exclusion of the larger ideas and goals of mathematics. The students who are bored by the processes of algebra are more perceptive than those who have mistakenly identified algebraic processes with mathematics.” [Morris Kline, Mathematics and the Physical World (1959; repr. and slightly corrected, Mineola, NY: Dover Publications, 1981), p. 68.]

Conclusion
As you teach algebra, beware of emphasizing the means (i.e., the rules and conventions) to the point that your student loses site of algebra’s purpose–to record consistent relationships. Remember to let your mind pause and consider the greatness, power, and consistency of the God who, day in and day out, governs all things consistently enough for us to record general relationships and expect them to hold true in various situations. His power, might, and faithfulness truly know no bounds!

“I am the LORD: that is my name: and my glory will I not give to another, neither my praise to graven images.” Isaiah 42:8 (KJV)

Note: Watch for more on algebra soon!