Page 83 - A Mind For Numbers: How to Excel at Math and Science

“I decided to go back to school again for an engineering degree. Mathematics—especially
calculus—is far more important when studying engineering than it is when training as a hands-on
technician. At this point, my lack of foundation of mathematics from the earliest years of grade
school started to catch up with me.
“By this time I was married, a new father, and working full-time. Now the challenge I faced was
no longer just basic cognition, but time management. I had only a few hours each day to learn
advanced concepts at a far deeper level than I ever had to before. It was only after a few hard
knocks (I earned a D in my differential equations class—ouch!) that I started to approach learning
in a more strategic way.
“Each semester, I get a copy of the syllabi from my professors and begin reading the textbooks
at least two to three weeks before the courses begin. I try to stay at least a chapter ahead of the
class, although by the middle of the semester this is often impossible. Practice in problem solving
—building chunks—is key. Over my learning career, I gradually developed the following rules,
which have allowed me to satisfactorily complete my courses. My objective is a good career that
will support my family—these techniques are helping me get there.”

Paul’s Techniques for Limited Study Time

1. Read (but don’t yet solve) assigned homework and practice exams/quizzes. With
this initial step I prime my mental pump for learning new concepts—new chunks.

2. Review lecture notes (attend every lecture as much as possible). One hour of lecture
is worth two hours reading the book. I learn far more efficiently if I am faithful in
attending lectures and taking detailed notes—not just staring at my watch and waiting
for it to be over. I review my notes the following day while the subjects are still fresh in
my mind. I’ve also found that thirty minutes with a professor asking questions is easily
worth three hours reading the book.
3. Rework example problems presented in lecture notes. It never helped me to
practice problems given by either the instructor or the textbook that didn’t have
solutions to provide feedback. With the example problems I already had a step-by-
step solution available if necessary. Reworking helps solidify chunks. I use different-
colored pens when I study: blue, green, red—not just black. I found that it helps me
focus on reading my notes better; things pop out more, instead of blending together
into a confusing collage of inexplicable mathematical chaos on the page.

4. Work assigned homework and practice exam/quiz questions. This builds “muscle
memory” chunks for the mind in solving certain types of problems.