By Jay Mathews
Thursday, January 8, 2009
Dear Extra Credit:
Referring to your Oct. 30 column ["In the Real World, Advanced Math Doesn't Always Add Up"], you might not use the specific tools of mathematics every day, but where else in your academic career do you learn how to solve the general problems that are part of life? It's not all in the numbers. Mathematics teaches tools and techniques that carry over into solving non-quantitative problems. Math students learn to read and understand problems and break them into identifiable parts. They can organize and use their experience and skills as tools to address their problems. They develop concentration and persistence and find the satisfaction of being accurate and correct. Surely these lessons learned via mathematics are important to all of us and worth the emphasis in our schools.
Dear Extra Credit:
When I was in public school in Minnesota in 1988, in addition to having to walk through three feet of snow, we got our first exposure to algebra in the sixth grade. I remember thinking it was simple, but I could not find any value in it. I was probably too young to appreciate its many applications. In light of this, I see no reason to find something other than algebra to teach eighth-graders who struggle with math. How long do we need to keep teaching them basic arithmetic, which is algebra's only prerequisite?
Dear Extra Credit:
What is particularly vexing to me is the way math is used to keep people out of college or graduate programs when such advanced math has nothing to do with the course of study or profession. I took algebra, geometry, trigonometry and pre-calculus in high school. It was my desire to major in political science and then go to law school. I did both, and have been a practicing lawyer for 30 years.
I certainly do not consider it a bad thing to have taken any of the above math classes. Knowledge is always enriching. I do object to using knowledge and proficiency in such subjects as a requirement for endeavors that do not incorporate these studies. Nothing I ever did in law school ever turned upon the use of sines and cosines.
Dear Extra Credit:
I am a PhD economist who also has a bachelor of science degree in mathematics and who has published papers in mathematics and economics academic journals. You probably think I am going to extol the virtues of higher math for the masses. Not quite. What I do think is needed is a change of emphasis. The focus should be on math you can use. If you have that sound foundation out of secondary school, and your abilities and inclinations lead you to higher math in college, you are not going to have any trouble advancing your level of learning as needed.
What should be the focus of mathematics in high school? Not calculus (although I think the fundamental concepts should be introduced), but rather two basic subjects. The first is algebra, emphasizing how to use it in practical, everyday applications. The second is probability and statistics, emphasizing multivariate regression analysis and its limitations.
The reason that most people don't use algebra after high school is that nobody taught them how. I use algebra not just professionally but in everyday problems in finances and around the house. That's what should be emphasized in high school: how practical problems can be formulated and solved as simple algebra problems. Kids will appreciate math more as a powerful practical tool than as a bunch of abstractions.
No college-bound student should graduate from high school without a full year's course in probability and statistics, with emphasis on multivariate regression analysis, subjects often not taught in high school today. These mathematical tools are heavily relied upon today in the physical and social sciences, so students are likely to find these tools central to whatever field of study they pursue.
Moreover, all of us are bombarded in the popular press with information based on results obtained with these tools. As a professional economist, I can tell you with great confidence that far too much of what gets published misrepresents or overstates its meaning and significance and, at worst, isn't worth the paper it's printed on. The next generation will need a statistical literacy that is sorely lacking today to think critically about important claims presented to them.
I came back to this topic for one more column because of the torrent of messages I received. It inspired more comment than all but three or four subjects Extra Credit has examined, and I think there is a good reason for that. These fine observations and suggestions are all tied to our uncertainty about the connection between what we do in school and what we do the rest of our lives. Will the writing I do in AP English Lit help me get a good job strategizing new concepts for Google? Will IB Biology come in handy if I want to go into hospital administration? Does trigonometry make any sense for someone hoping to be an immigration lawyer? If I want to go to a trade school right away and learn how to repair antipollution devices, does a philosophy course make sense? The research strongly indicates that preparation for college and preparation for the job market right out of high school should follow the same track, particularly with thinking and presentation skills. We need to look harder at what that means for high schools and whether we are steering young people toward dead ends, without knowing it.
Please send your questions, along with your name, e-mail or postal address and telephone number to Extra Credit, The Washington Post, 526 King St., Suite 515, Alexandria, Va. 22314. Or e-mail firstname.lastname@example.org.