Response to: Learning Algebra in a Computer Algebra Environment

Do you ever read an article and then wonder what you just read?  That's how I felt after reading Learning Algebra in a Computer Algebra Environment, by Paul Drijvers of Utrecht University, which summarizes his doctoral thesis.  Often I find that reading articles like the above mentioned are not a good use of my time as the article is written for the purpose of building a resume and publishing for the sake of publishing. Additionally, in my opinion one of the most important considerations of being a preservice teacher is the ability as an educator to explain material at a lower level, a skill that I feel differentiates a satisfactory teacher from an above average educator.  With that said, this article is difficult to read and comprehend and to be blunt, is written to sound smart and not actually deliver valuable insight to the average reader. However, if the target audience includes other doctoral candidates and researchers in the field then it may be a very well written article...to that I cannot speak.

As a requirement of this blog post I must find a point the author makes and elaborate and voice my opinion. I was able to decipher a few key take aways from the article that I feel synthesize well with other readings regarding CAS and the umbrella subject of incorporating technology in the classroom.

In the article, Drijvers discusses the instrumental approach to using computer algebra and arrives at the same conclusion presented by Conrad Wolfram in his Ted talk, "By freeing the students from the algebraic calculations, computer algebra would offer opportunities to concentrate on concept development and on problem-solving strategies" (Drijvers, 80).  However, Drijvers also discusses the dangers with incorporating technology into the classroom, "Because the CAS already contains all the algebra, the computer algebra tool might somewhat abstract and formal top-down character, and might turn out to be inflexible with respect to informal notation and syntax" and goes on to add "Furthermore, the CAS might be a black box for students, as it carries out complex procedures in a way that is not transparent to them" (Drijvers, 80).

I believe Drijvers hits the nail on the head here. By handing a student a calculator with CAS built in, you risk the possibility of requiring minimal cognitive effort to complete a task.  Often this "minimal cognitive effort" comes in the form of using the "Black Box" Drijvers mentions above, where students are only concerned with arriving at the final solution, regardless of the method or procedure used. Further synthesizing, the judicious use of technology in the classroom is required by secondary mathematics teachers to ensure the incorporation of CAS does not lead to the "black box approach" for students.