While Math was probably one of my better subjects in High School, I was far from the best in my class. I chose a college in part based on the availability of Applied Mathematics and/or Computer Science as a major. I expected that my High School courses would have prepared me well for college math, but unfortunately that was not the case. While I knew the math I had studied well, my approach to learning math did not work at the college level. The first test in my first math course Freshman year was a “multiple guess” test. The professor added 10 points to our score for each correct answer, and subtracted 5 points from our score for each incorrect answer. My score was a -15. That’s right, negative. I did not feel particularly encouraged.
That first test, and a few that followed it, served as a wake up call. I heard it… but it took me another couple of years to learn how to pay just as much attention to concepts as to procedures. On hindsight I should also have given more weight in my college decision-making process to the reputation of my professors as teachers, instead of the reputation of the university as a whole. I persevered nonetheless and earned my B.Sc. in Applied Mathematics, with a minor in Computer Science, in the late 1970’s.
After college I worked for three years, including one as a teacher, then enrolled in graduate school. My two years of graduate work studying Finance, Marketing, and more Statistics were a wonderful experience. I had many wonderful teachers who explained complex and quantitative topics clearly and with passion. The approaches, teamwork, patience, and perseverance I had learned in college and on the job were invaluable in helping to make graduate school a successful and fun experience.
Since then I have evolved into more of a generalist (one who knows less and less about more and more) than anything else. My wife and I moved to Maine and started new chapters in our lives in the early 1990’s. I missed teaching, so I signed up as a Substitute Teacher at several local High Schools, began teaching computer courses via our town’s Community Services programs, and started tutoring math students after school – in addition to my computer and marketing consulting work.
I have now been tutoring math students for 25 years, and occasionally teaching math classes when needed as a substitute. Along the way, I became a parent – which has added another perspective to my ramblings. This blog is intended to document, revisit, and hopefully improve upon many of the approaches that seem to have helped students the most over these years. Some of the postings are explanations that have evolved over many tutoring sessions. Others are musings about how math “should be” taught… some from personal experience, and some hoping I will follow my own advice “next time”.
Despite being a perpetual “work in progress”, I hope this blog can:
- offer helpful approaches to topics that are frequent stumbling blocks for students.
- encourage both students and teachers to approach math conceptually as well as procedurally.
- let folks who find math challenging at times know that they are not alone, that many people who are “good at math” still experience the same challenges.
- encourage people to be patient with themselves as they seek to master new concepts and skills. Patience and perseverance are two critical attributes when seeking to master any concept or skill.
- encourage people to ask questions (of me or others) and engage in dialog with others (either written or verbal) about quantitative topics. I often learn a great deal more about a topic by writing or talking about it than I do by just reading about it… thus this blog!