[Edited slightly from original posting.] Date: Wed, 11 Oct 2000 11:31:31 -0500 (CDT) From: Mike Sullivan To: SIUTEACH-L SIU.EDU Subject: Math Education This post is more or less motived by the "Report by Commission on Mathematics & Science Teaching," sent out over this list by John McIntyre . As I teach and do research in math, most of my comments will focus on math. Elementary School: Mathematics needs to be taught by math specialists. I have taught math for prospective elementary school teachers. Most do not like math and are not very good at it. Some cannot even do arithmetic. The classroom teacher should not be asked to cover math anymore than he/she would be asked to teach music or Spanish. I do not think science should be taught in K-3. The children do not yet have the ability to think critically, so all science education can be is propaganda. (Isn't science cool? Let's fix the environment!) Propaganda, even for a good cause, has no place in education. If they learn to swallow "good" propaganda now, what will they fall for in the future? Similarly for history. Early education should focus on skills: math, reading, music, art, sport, dance, a second language, and social skills. These develop basic mental functions. They build a foundation. By the sixth or seven grade students need to begin to see the axiomatic foundations of arithmetic. They need to know why, for example, ab=0 => a=0 or b=0. (None of my calculus students knew this.) I dream of the day we start teaching set theory again (non-axiomatically). Note: SIUC has an option for elementary school majors to specialize in math. But our program is bad. We really have no upper level courses that make sense for an elementary school teacher. Certification: The certification categories in Illinois make no sense. A K-8/9 (8 or 9 depending of which document you read) certification standard is too broad. (Now the state wants us to include trigonometry in the math for elementary education majors sequence!) There should be K-4, 4-6, 6-9, and 9-12, certification standards. A 3rd grade teacher should not have to learn trig and an 8th grade teacher does not need to come up with cleaver ways to explain fractions (one would hope!). Prospective teachers should study what they need in depth rather than merely touch on many topics. High School: A good high school education costs money and the public had better figure this out. High school math and science teachers need to have majors in their fields. Math education majors need to take hard courses both in math and in related fields like physics and economics. They cannot do so now because they have to take a lot of courses in the COE that really could be consolidated. The COE's will object that it is only following state requirements. But COE's lobby the state to impose these requirements. In terms of content: Axioms! Proofs! Sets! Graphs! Please! I want to be able to talk to my freshmen! Students should know why the formulas and methods they use work. Make them derive the quadratic formula. Make them prove the properties of logs. They should understand why a graph looks the way it does. There is no magic in math. Everything we do makes sense and should make sense to the college bound students. (60% of high school students go to college! Why is a mystery. Maybe colleges are acting like businesses and are just trying to get money from "customers" who really do not need their product.) People who are good at math can get high paying jobs in industry. In order to keep such people in the high schools we need to pay them more than other teachers. College faculty are paid according supply and demand. I make more than an English professor but less than a business professor. It is not really fair. But if we did what high schools do, it would be difficult to impossible to hire quality faculty in many fields. Would that be fair to the students? High school teachers need to be treated much better, especially in the first couple of years. First year teachers should get a reduction in their teaching load and have no extracurricular duties. All school administrators should teach at least one course a year. It should be illegal to hire academic teachers on the basis of what sports they can coach. (Let the PE teachers coach sports!) Universities: When universities, like SIUC, gut academic admission standards, and accept clearly unprepared students, we undermine the efforts of good high school teachers. A high school science teacher I know told two poorly performing students that they had better study harder if they wanted to go to college. The students laughed and said that anyone can get into college. _________ Mike Sullivan Assoc. Prof. Math Dept (4408) SIUC 62901 msulliva@math.siu.edu