When Are we Going to USE this?

I think all students receive the same email when they register for a math class; this email says “The BEST way to irritate your instructor is to ask ‘When are WE going to USE this?’ at the first sign of confusion. Not only does this irritate your instructor, but this will distract the instructor from your lack of understanding.”

Of course, my introduction above is a weak attempt at humor (a dangerous choice on my part!!).

Seriously, the issue is this: Do students NEED to see the application of everything that we tell them to learn? Are some concepts okay to learn, even if there are no applications that the student values?

Underneath this issue is the curricular issue: What is the purpose of this course? For developmental mathematics, we are in a “preparing for” business. Our students need to take further mathematics (of various kinds), science classes, and technology classes; we also prepare students for college in general. These future situations are a justification for the mathematics they learn … is it reasonable for us to expect students to appreciate the applications while they are learning the mathematics?

In a recent post (https://www.devmathrevival.net/?p=282 ) I emphasized mathematics as a practical science. For a recent conference in Michigan, I gave a talk on general education (http://jackrotman.devmathrevival.net/General%20Education%20Mathematics%20in%20Michigan%20May%202011.pdf) in which I highlighted the ‘usefulness’ of mathematics we require students to take. It’s pretty common for people to conclude that I think developmental mathematics should be applied and in-context, in almost all topics we teach.

However, that is not my judgment about what is appropriate. The traditional developmental mathematics courses are predominantly procedures; we do ‘applications’, but 90% of these applications are puzzles (you have to know the answer in order to write the problem). This is not enough practicality to show students that mathematics is powerful and practical. We need more applications meaningful to students, and we need content which will benefit our students.

At the same time, it is obvious to me that we would make a mistake to limit the mathematics we teach to those ideas for which we have applications that students would understand at that time. A math course is not employment preparation (only), nor is it solving problems (only) … just like it is not beautiful mathematics (only). We need a balance. Students will need to learn material with no clear applicability to them in other classes, and learning in the face of ‘not useful right NOW’ is a critical survival skill.

We can also use learning research to provide guidance. My own reading of theory and research indicates that context, and applications that students value, plays a positive role for motivation when done in moderation; an emphasis on context complicates the learning process, and may make the important seem invisible. [For some references, see http://jackrotman.devmathrevival.net/sabbatical2006/9%20Situated%20Learning.pdf.]

I hope you will think about the purposes of our math courses, and reach your own conclusion about the appropriate role of applications that students will understand to support the learning of mathematics. I am sure that we can design our courses so that students can learn powerful mathematics that WILL be useful to them, and that we can incorporate applications along the way.

Developmental Mathematics Revival!

Bringing a new vitality to college mathematics 2011 to 2019