Context in Math: Do Students See It?

I am frequently asked (yesterday, for example) whether students have changed during my time working with developmental students.  People often assume that I will say ‘yes, their math skills are even worse’ … I don’t say this, because I do not believe it’s true.  Certainly, there have been changes — areas of ignorance and zones of bad ideas have shifted, but not in a fundamental way and not in a significantly increasing way.  My answer is this:

Students have changed, especially in the past 10 years, in terms of their academic and social skills.  More effort is needed — in all of my classes, not just the lowest — on these soft skills.

Among these soft skills is an awareness of surroundings and knowledge of context.  Last week, I noticed a comment over at the Chronicle’s page (http://chronicle.com/article/So-Many-Hands-to-Hold-in-the/134454/?cid=cc&utm_source=cc&utm_medium=en):

I have a grandson who at 22 cannot literally read a real map!  He cannot navigate himself to and from a doctor’s appointment or an auto parts store without the directions capability of his smart phone.  Technology is a wonderful thing; however, it does have a down side.  In the grandson’s instance, he does not pick out reference points as to where to turn or to retrace his steps, ie, being aware of his surroundings.

If you look for this comment, be sure to load older comments (this one is from about Sept 19).  Context is critical in mathematics, like most other academic areas; one can not know context if one is unaware of surroundings. 

In math classes, this means that students are even more likely to apply a strategy or concept when it does not apply (context) … students are more resistant to analysis of special cases (surroundings).  The student magic and silver bullet used to be ‘know all the formulas’; now, the silver bullet is ‘know the one formula. 

For those of us who like to teach math ‘in context’, I wonder if the nature of our students makes this approach less desirable.  If students have trouble identifying context accurately, and we teach from context, they may not see the intended context. [In many cases, I think students see our ‘context’ as just a longer word problem that is more interesting.]

For all of us, I wonder if our students see their mathematical surroundings in the intended manner.  Learning is constrained by perception; incomplete perception can not lead to quality learning of mathematics.

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