Well, summer officially ended on Thursday as we went back to
school. This year I have my normal load
of honors pre-calculus classes along with one section of algebra 1. All the classes are off to a good start, but
the first “real” discussions won’t happen until Monday, so we’ll see how things
go. Yes, this includes the algebra 1
classes. While I’m not running my
section in as independent and discovery-driven a way as we do with the honors
pre-calc kids, I am still infusing a lot of discussion into a relatively small
amount of lecturing. In particular, the
emphasis is going to be on the applications as opposed to being on the
mechanics of algebra. That doesn’t mean
that we’re not going to work on the mechanics, because we are. Obviously, it’s a little difficult to do a
basic algebra problem without the mechanics.
However, I thought of/realized something over the summer about the
mechanics of high school mathematics that seems to have struck a chord with
everyone to whom I have mentioned it.

Grammar is important in English class. No one disagrees with this. Grammar is important and it needs to be
emphasized. However, proper grammar is
not the point of English class. The
point of English class is to improve the communication skills of the students, in
terms of their ability to both take in and interpret information and to share
information with others. Proper grammar
is a point of focus and an important aspect of attaining this goal, but it is
not the actual goal.

Now, let’s look at a typical algebra 1 class. Are the mechanics of algebra important? Absolutely.
We really can’t do much without them.
However, the mechanics of algebra are the “grammar” of the subject. The point of algebra 1 (or of any high school
math class, in my opinion) is to improve the problem-solving skills of the
students. Solid mechanics can certainly
help the students reach this goal. But
if all the students can do is push the symbols around while having no idea
about how to use the mechanics to solve a problem, then we haven’t really done
much in terms of realizing the actual objective. For that matter, the mechanics of algebra are
not the only means available to the students to solve a problem. Geometry and statistics play a vital role in
helping the students become well-rounded problem solvers. Sadly, I experienced several conversations in
different settings over the summer where a person solving a problem got to the
correct answer without algebra and described the process they used as “not
really involving any math” precisely because there was little to no algebra
involved. Some used well-drawn pictures
and a healthy dose of geometry, some used data tables and graphs, but since
there was a lack of creating an equation and pushing the symbols around, the
conclusion was that there wasn’t really any math going on.

AUGH!

So, in addition to incorporating a healthy amount of
discussion into my algebra 1 class, my goal for the year is to get the students
in all of my classes to see everything they are doing as they attempt to solve
an exercise as “doing math”. I want the
kids to realize that drawing a picture, creating a table, making and testing a
conjecture, making a quick calculation, and yes, writing and solving an
equation are all “doing math”. All are valuable
tools to have at their disposal in order to reach the goal of improving their
problem-solving skills.

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