Teaching mathematics – the ill-defined problem
Let me start with a few questions that probably most parents and
students are thinking about:
Is mathematics hard?
Does it require special skills?
Are there kids that will never be comfortable with mathematical
reasoning?
Do all kids need intermediate and advanced math curricula?
What is the best way to teach math?
First, let me be honest about my background.
I love math. I took math courses at all levels, including post-graduate
research. My masters and PhD dissertations were about mathematics. I’m a member
of the Mathematical Association of America
(MAA).
Second, let me be honest about my training.
My math courses were very traditional and tough. Homework was very time
consuming.
Can mathematics be taught in a very entertaining and efficient way?
Probably, yes. Khan Academy is one of the best examples I know. Computer
science is a great vehicle for teaching math. Computer graphics is one of the
most exciting applications of advanced matrix algebra, calculus and
trigonometry. Most programming text books are very heavily invested in mathematical algorithms.
In my opinion, learning math beyond basics is a process that requires a
lot of dedication. It is similar to learning how to play musical instruments. It
takes years of dedicated work. I’m not aware of any shortcut methods.
The good news is that, in time, it gets easier. My kids spend a lot of
time working on their math exercises (and musical instruments). Initially, our
progress was slow. After a couple of year, they started to rapidly improve.
Currently, they are able to do a lot of work independently. Their progress is
very impressive. They have learned how to use mathematical software to help
them with graphing functions and checking the correctness of solutions. I think
that they enjoy math, which could be the greatest success in this journey. My
son recently decided that he will be posting YouTube vides on calculus problems.
After completing an intermediate algebra book we started working on
calculus about 6 months ago. Our approach is simple. We discuss each topic and
solve all example problems and end-of-chapter exercises.
Obviously, college level text books are not perfect for a 12 year old
kid. Particularly, some of the textual problems require a lot of background in
science and English comprehension.
In general, the progress shown by my boys is quite impressive. Devoting
a couple of hours on solving mathematical exercises is extremely beneficial. This
approach leads to, a slow, but measurable problem solving skill development. I’m
not sure if non-traditional, edutainment based techniques would allow problem
solving development at this rate.
Let me use the music analogy again. Years of dedicated practice, often
mundane and tedious exercises, develops young musicians into mature artist capable
of understanding and performing great classical symphonies. Improving original
music can also be achieved after devoting significant about of time into
practice.
Is there any other way to achieve our educational goals …?
Finally, how do we asses the learning outcomes? I’m aware about
significant research in this field. What counts for me is a couple of things.
Enjoyment. This was my big hope.
I keep telling my kids to start loving and enjoying math. Once you develop your
skills, you will start enjoying the logic, problem solving, your ability to
understand new concepts, etc. It appears that our very traditional approach to
learning worked. Now, my kids come to me almost every day showing how quickly
they understood another chapter.
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