Amy B. Ellis and Paul Grinstead have written an article that was published in The Journal of Mathematical Behavior last week. The article is entitled Hidden lessons: How a focus on slope-like properties of quadratic functions encouraged unexpected generalizations. Here is a copy of their article abstract:
This article presents secondary students’ generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax2 + bx + c. Students’ generalizations about these connections led to a surprising finding: two-thirds of the students interviewed identified the parameter a as the “slope” of the parabola. Analysis of qualitative data from interviews and classroom observations led to the development of three focusing phenomena in the classroom environment that inadvertently supported a focus on slope-like properties of quadratic functions: (a) the use of linear analogies, (b) the rise over run method, and (c) viewing a as dynamic rather than static.
Yesterday, there was an interesting article in The Spectrum. The title of the article is “Algebra: Use it or lose it?“, and the claim that is put forth by author Sarah Clark was that algebra teachers all over the world are lying when they tell students that algebra is important because they’ll use it in their daily life.
Clark (32) describes herself as a non-traditional student:
(…) who hasn’t taken an algebra class in 15 years. If, for the past 15 years, I had been using algebra in my everyday life, I would be blowing through my algebra homework with ease, thinking, “Hey! I just did this yesterday while I was washing laundry,” or, “I’m so glad I’ve known this all along. I’d never be able to drive anywhere without it!” or “Wow! I just used this formula last week to calculate the ratio of jazz to classical music on my iPod.
Apparently, this is not what she has experienced. On the contrary, she has never experienced using algebra in her daily life, and she now finds herself uncapable of doing it. She also proposes an algebra revolution, where we should share the truth with every student who is struggling with algebra: these skills will not be crucial for you in adult life.
There are lots of things to comment on these statements, for sure. And lots of people did comment on it already (so be sure to read the comments below the article as well!). Deb Peterson at About.com made an interesting (external) comment to the article, that might be worth reading.
Myself, I think all these claims about how mathematics is/can be useful in your everyday life is a mixed bag. I think Clark’s article illustrates a common issue as well: when teachers claim that mathematics is useful in everyday life, it might be their own everyday life they think of rather than their students’. (Lots of people have written about the connections with everyday life, and if you are interested, you might want to take a look at my own PhD thesis: Mathematics in everyday life: a study of beliefs and actions.)