Carraher et al discuss in this article how
children with a formal school education differ from children without a formal
school education, in the ways that they solve problems. To illustrate the scenario, we are taken to
the rural streets of Recife, a city in Brazil with a population of 1.5 million
people. Most of the citizens either work
in the informal sector, or have a family member that works in it to support the
family income. This informal
(non-school-based) way of problem-solving is driven by “four pressing needs. .
.finding a home, acquiring work papers, getting a job, and providing for
immediate survival.” (p.240) When I
consider what drives me in my everyday activities, I suppose that I’m not far
off from what drives a citizen of Recife. We all are looking for a job, a home, and a
means of survival.
I found it interesting when Carraher
mentioned that it is not uncommon for children who are 8 or 9 years of age to
help with the transactions of their parents’ line of work. I have a student in my class who is 10 years
old and often helps at the family restaurant working the till. We currently are just finishing up our unit
on fractions in our class, and recently this student was having difficulty
converting ¾ into a decimal. When I put
the questions in terms of money, he was able to solve the problem.
A study was performed where children who
worked on the streets were tested in two different scenarios. One scenario involved solving problems that
related to their line of work and were all oral. The other scenario involved solving problems
in a more formal school-based setting.
Some of these formal questions were given context, while others weren’t. There seemed to be a direct correlation
between problems that were solve with context versus without context. The children found having context much easier
to solve. Interestingly, we tend to
teach algorithms by themselves before we teach how they can be applied to word
problems. These children show that the
opposite can be achieved as well. It
should be noted that if the children had to solve larger multiplication questions,
their chunking strategies may not have been as effective.
Your points about context after mechanism is interesting, and I wonder if this is because so many teachers use the textbook to support mathematics instruction in the classroom. I would go so far as to suggest that there could be a correlation between teachers with low mathematical training and a positive promotion of mechanism-before-context, or even textbook use (here's a free MA thesis for anyone who wants one).
ReplyDeleteNow, when they talk about chunking, is that the same chunking as the one discussed in psychology involving clustering of multiple pieces of information? Let's discuss this on Wednesday.
Your mention of the student in your class matches quite well with this article! I think many students have difficulty grasping the symbolic notation that we use in written mathematics, for the natural quality of quantity. As soon as symbolic notation is represented, somehow it seems more like a "math problem" and students revert to solving the problem the way they have seen it done before. Perhaps this was the situation for your student? Although he knew how to work the problem in his context, somehow the "real context" seemed disjoint from the abstract symbolic one.
ReplyDeleteMost of the mathematics that we teach is based off of world observations, and those observations were translated into a symbolic language. The term "real world math" and "real world problems" have always bothered me. It somehow makes mathematics seem like a non-human endeavor and disjointed from our lives unless it has been placed in a day-to-day context.