Do you understand?
March 7th, 2006 by SplineGuy
I’ll confess that I am not much of a pedagogical expert when it comes to how I teach mathematics and yet I have made many assumptions about the effectiveness of certain methods as I present daily lectures to “eager” minds. In light of that, I thought I’d pass on a couple of interesting articles from Keith Devlin discussing the issue of understanding versus procedure when it comes to mathematics education.
Math back in forefront, but debate lingers on how to teach it
In each case, Devlin makes the case that full understanding of mathematical concepts comes only after practice of the procedures, and much of it. While I agree that the sort of understanding to which he is referring, such as a full appreciation of the concept of derivative or even what is meaning of dividing fractions, finally arrives when we have mastered the procedures involved. I cannot make an argument based on research in the area but, in reference to my own experience, the mastery of procedures is most often a result of a commitment to the practice of the procedures and for a majority of “non-math enthusiasts” that commitment is lacking. In my experience, some explanation of the underlying concepts is necessary when it comes to making the point that mathematics is USEFUL. Some understanding of the concepts leads to a motivation for learning, for practicing, and thus for mastery.
There are several good points that Devlin makes and if you have the time, I encourage you to read those articles (if such things interest you). If you do by chance read them, please make comments here for myself and others to read. Or, post them to your blog and link back here. Thank you.
I found your site to be very interesting. I am searcing for questions and answers. I teach math at the present time and am applying for a math coach position. I am looking for the ultimate answer of what makes me stand out or why am I right for the job. You may ask why am I asking a stranger, well, good question. I know what is in my heart, but it does not seem to want to travel to my mouth. So, I am turning to outside help. What makes a good math teacher stand out? How would you go about helping a teacher that did not want your help?
Debra