John Kenelly is Alumuni Professor of Mathematical Sciences at Clemson University. He has chaired the College Board’s Mathematical Sciences Advisory Committee and directed reading of Advanced Placement Examinations for the Educational Testing Service.
What’s your response to the suggestion that what we really need to do is get back to basics in math education?
Understanding the way information works is today’s basic.
If the teacher is just teaching kids to manipulate the numbers, and not generating any understanding of the numbers, then the teacher is preparing the student for a life that doesn’t exist anymore. I’m not speaking of just their professional careers; I’m speaking of their day to day activity.
Mathematics instruction must move from learning manipulation to learning information design and interpretation. Students have to learn to design the kind of mathematics they want to use and then to interpret the results.
How can teachers help students develop these skills?
Do more hands-on mathematics. Do more small group interaction, far less “Johnny-see-Johnny-do” kind of material. Let Johnny figure out what there is to do, or let him work with a couple of other students, and discuss what it is they need to do. Then you get the interpretation, which is, “What do you do after you’ve gotten it?”
What you want to do is allow the student to discuss a concept, to present it to the class. Look at the way they’ve taught music students for all these years. They say “OK, it’s time to interpret the music, and you go ahead and interpret the music in a performance, or a presentation.”
I would have a lot of students getting up and making presentations about the math problems they’ve done. When I was taking college physics I did 16 lab activities which taught me very little. But there were 8 lab activities where I had to present, and I learned a great deal from them, because you can’t get up and explain something without having a great deal of understanding of it.
What type of equipment do you think today’s students should have?
I would say a portable, affordable microcomputer – we desperately need devices that students can carry with them that are “information crunchers.” Call them information appliances, or whatever you like. Something they can write with, process information with, wherever they are.
This is especially true in terms of equity considerations because the well-to-do kids are probably going home to computing facilities. The less than well-to-do kids are probably not going home to computing facilities. If we don’t address that, then we further reinforce the economic divide in our society.
The very thought that a grocery store cashier has more technology in their workspace than our teachers and students do is absurd. What’s more important, educating our kids or checking out groceries?
What is the role of mathematics teaching in preparing students for today’s careers?
Mathematics and science try to explain the universe. You look at something that’s taking place and you say, “How can I explain this mathematically?” You look at how you’re going to combine various objects and you say, “How can I represent this mathematically so I can address it more effectively?”
I find that people that are good math students are very successful in banking and industry because they have learned how to focus on what we call the driving functions – the street term is “what’s the skinny?” What are the basic elements that are making this behave the way it does? You express that mathematically and that gives you focus on the heart of the problem.
The high paying jobs are for the people who are able to design the spreadsheets. That’s why I say that understanding the way information behaves is today’s basic.