Math — What is so good about THAT??

I was thinking that I could post a “What we see … What they see” item on math.  After all, we see many good things but our students see very little worth their time.  Then I thought some more about the ‘we see many good things’ part, and realized that this is not as obvious as we might think.

You’ve probably heard the phrases ‘intended curriculum’ and ‘received curriculum’ (or similar phrases).  When we advocate for a mathematics curriculum we are suggesting that the intended curriculum has sufficient value for students.  In mathematics, I think we confuse daily topics with the curriculum more than most disciplines do.  Instead of saying that a course deals with properties and relationships involving symbolic expressions of certain types, we say that the course covers factoring – rational expressions – radical expressions – and quadratic functions.  One problem is that these are internal code words that mean almost nothing outside of mathematics; the bigger problem is that these statements do not communicate any mathematics (in most cases).

Here is another concept about curriculum:  A course should have a basic story to tell.  Think about asking students who have completed a math course with a good grade:  “What was that course about?”  or “What are some good things to come from that course?”  Given that we do so much of our work in a symbolic world without a strong narrative, students will have great difficulty answering these types of questions compared to non-math courses.

So, if we want students to see the ‘good stuff’ about mathematics, we better increase our use of narrative forms.  This is not easy for us, since mathematics encourages brevity and non-repetitiveness.  However, this lack of narrative is one reason students find math ‘different’ … and ‘difficult’.

Which brings up a related point:  Can a person reason using only symbols?

We have a reputation for focusing on procedures and answers.  We often justify what we do by saying that we are building the reasoning skills of students by requiring that solutions involve a specified level of detail in symbolic form.  Instead of thinking about the reasoning, many students respond by mimicking our solution steps — which is not what we want (for most of us).

My favorite course to teach avoids some of the problems I’m talking about.  The Math – Applications for Living describes the content in phrases that many students can understand — quantities, geometry (a tougher one), finance, etc.  We also employ more narrative in the course (which frustrates some students, but usually helps overall).  We talk about good steps and solutions, but we talk more about how to figure something out — reasoning.  It’s not that we ‘cover Polya’ or anything like that, but students know that we are learning how to solve problems.

I think the curricular problems in math are causally related to the calculus-fixation that still drives much of our work:  It’s like everything prior to Calculus I is considered remediation, so we don’t do any real problem solving before then.  In the old days, this remediation approach was stated explicitly at the larger universities; I have not heard this recently, but our courses before calculus have not changed very much overall.

Developmental mathematics is changing.  We are developing courses that tell a story, we emphasize reasoning, and use narrative more than previously done.  It’s time for courses after the developmental level to look at these issues; it’s time for US to look at these issues and what they mean for our courses and students.

What would you want students to say was “good about that math class”?

 Join Dev Math Revival on Facebook:

No Comments

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a comment

You must be logged in to post a comment.