What good is algebra?

Developmental algebra is the most studied course in American colleges … well, at least the most enrolled! Studying is another thing. 🙂

Why? What value does this activity add?

I’ve noticed something about students who have passed our beginning algebra course, and I am not happy about this. We have several math courses that can be used to meet the requirement for an associates degree, and one of these math courses is a mathematical literacy course. This course involves a lot of problem solving, based on understanding relatively few concepts.

Consider this sequence of problems and typical student responses:
Item: A company has $38 million in sales this year, and expects it to rise by 10% for next year. What will the sales be next year?
Student: Okay, 10% is 0.10 … we better multiply … 0.10 times 38 is 3.8. That’s too small for the sales, so we add 38 + 3.8. The sales next year are $41.8 million.
Item: A company has $38 million in sales this year, and expects it to rise by 10% per year for the next several years. Write an expression for the sales based on the year n.
Student: What? 38 times 0.10. Where does n go? Is it 0.10n + 38?
Me: Okay, let’s look at a simpler problem.
Item: A company has $38 million in sales this year, and expects it to rise by 10% per year for the next several years. Estimate the sales for the next 4 years.
Student: Okay, the first year is like the one we did earlier … $41.8 million. Do we do the same thing again? [me: might be — would that make sense?] Yes, I think so … {calculates}.
Me: That is looking good. How about the expression … does your work here have anything to do with the expression we need?
Student: You got me!

Of course, our beginning algebra course has a lot of applications, and students see like terms and a lot of exponents. We cover percent applications, including some where we know the value after the 10% increase and need to find the original. In spite of the appearance of ‘mastery’, most students do not connect their knowledge with the concepts in a novel situation. Quite a few students will actually deny the connection between the algebraic expression and the computations they do.

We often ‘sell’ our courses because of a belief that passing a math course indicates a better capacity to reason and to think logically.

However, the traditional courses do not deliver on this promise (in my opinion). Almost all textbooks have repetition of skills, and we cover too much material to work on applying anything to novel situations. Sadly, almost all useful applications of mathematics (in life and in occupations) begin as novel situations.

I personally dislike (strongly!) the phrase “a mile wide and an inch deep” (for one thing, we are all adept at 90 degree rotations to get “an inch wide and a mile deep”). Slogans like that do not help us. What might help us is thinking about what we believe is valuable in mathematics … and delivering courses that build this value for our students.

As long as we attempt to ‘remedy the deficiencies’ of our students, we will miss the benefits. Their deficiencies are many; most adults have similar deficiencies (even those employed in occupations that our students are preparing for). Our attention should be on “what mathematics is needed for community college students” or “what mathematics is needed for university students”.

I really believe that we can provide courses that students will see the value of, and that we can be proud of as mathematicians. I think that the New Life model is a good starting point, and I hope you will consider becoming a supporter of this work … and consider offering these types of courses at your college!

Developmental Mathematics Revival!

Bringing a new vitality to college mathematics 2011 to 2019