Street Math, Making Sense, Confidence and Problem #1
On the weekly math sheet, Problem #1 is usually an arithmetic problem,
so that no one gets left out. Some 8th graders haven't had algebra or
geometry. But also, there are students even in later grades who can
use some refreshing in arithmetic. For some there are gaps in what
they can reliably get right. Then there are some who can execute all
the rules flawlessly but don't really have a clear concept of why
those rules yield correct answers.
This is true not only in College Bound. The Math Instinct, a book by
Keith Devlin, "NPR's math guy," provides insight and data on how
people do math. In Chapter 10 there's a captivating account of the
distinction between street math and classrooom math. Using systematic
observations of kid street vendors in Brazil and adult shoppers in
Nunes et al.
show how the same people who get stuff right, working in their head,
in the real world, can screw it up when sitting down with paper and
pencil in a testing setting, where they somehow forget their
understanding and try to apply rules they don't understand.
Street math can be a start, but it will only take you so
far. Translation: find the student's genuine conceptual
understandings, clarify, solidify, enhance, and use them as bridges
into the world of formal manipulation of numbers, operators and other
symbols. Doing this is not easy, but it's well to keep it in mind. The
goal is for the formal statements and processes of mathematics to be
seen not as arbitrary commands to memorize and obey,
enforced by teachers (and us!), but rather as handy summaries of what
the student already understands. When rules make sense, they become
more acceptable, easier to remember, and even reconstructable when you
Students also need to believe that they can do it. I have heard
students say "I hate math." That's a cover for "I'm bad at math." To
them let us say, "No, you just feel bad when you don't do it well. And
not doing it well probably means you haven't been taught to understand
it. So now we're going to fix both of those things." The solution
sheets should help with this. If not, complain to me!
There are those - and I mean grownups - who say that we should teach
less math because it's too hard. That's insulting to kids and probably
false. There is actually research indicating that "convincing students
that they could make themselves smarter by hard work [leads] them to
work harder and get higher grades." (See
The Myth of 'I'm Bad at Math'
in The Atlantic, October 2013.) Recently a professor (not of math)
called for a halt in requiring HS algebra (see
Is Algebra Necessary?, New York Times, July 28,
2012), saying it's irrelevant -- while ignoring all the
application-oriented material in many high school math texts. Google
yields 192,000 hits with the exact phrase "STEM jobs." US Immigration
lists 36 STEM fields. Algebra is not only a grand human achievement;
it's also a pathway.