Many people, both within education as well as the general public, may feel somewhat bewildered by the controversy surrounding mathematics education. Some may be bombarded by contradictory messages and overblown rhetoric in hotly-contested textbook adoption. Others may simply be curious how something that may appear to be so cut-and-dried could be the topic of such emotion.

But the common denominator is a concern for our children. Are they getting the mathematical preparation they deserve, so that they can be successful in this technological age? Our goal is to provide you with balanced, research-based information about mathematics teaching and learning. Read for yourself and make your own decision. But keep an open mind; our children live in a very different world than the one we grew up in.

The remainder of this section is presented in a "Q & A" format, where questions you may have are posed, short answers are given, and links to resources on this and other sites are provided giving more complete information. If you have other questions that you would like addressed, please contact us at [email protected].

Q: What is all the controversy about?

Some people feel that mathematics should be taught as it has always been taught, as a collection of facts and methods to be memorize. Others feel that new approaches are needed that emphasize understanding and higher-order thinking. Read more about the differences in philosophy in the article "Reform vs. the Basics." <MathematicallySane.com/analysis/reformvsbasics.asp>

Q: What does the research say?

Evidence suggests that students taught with "reform" methods often make impressive gains in achievement. For example:

• A recent study by the Educational Testing Service shows improvements with students who receive mathematics instruction emphasizing higher-order thinking; see "Teaching Really Does Matter." <MathematicallySane.com/evidence/teachingmatters.asp>
• Urban school systems adopting the "reform" methods have shown improvements; see "The Philadelphia Story." <MathematicallySane.com/evidence/philadelphia.asp>
• Several subgroups within the Third International Mathematics and Science Study showed impressive gains.
  • "TIMSS-R Results In Ontario" <MathematicallySane.com/evidence/ontario.asp>
  • "The Michigan Invitational Group" <MathematicallySane.com/evidence/mig.asp>
• But we should be realistic about what can actually be provem by research; see "Relationships between Research and the NCTM Standards." <my.nctm.org/eresources/article_summary.asp?article_id=68>

Additional references can be found in the "Evidence" <MathematicallySane.com/evidence.asp> section of this site.

Q: Do the "reform" textbooks really work?

Beginning in the early 1990s, the National Science Foundation funded a number of projects to develop textbooks reflecting new trends and priorities in mathematics education. A complete list of these texts can be found at "The NSF-Sponsored Curricula." <MathematicallySane.com/links/nsfprojects.asp>

In contrast to misinformation spread in some quarters, these are among the most thoroughly tested curricula that have ever been developed in this country; see "Mathematics Curricula and Guinea Pigs." <my.nctm.org/eresources/article_summary.asp?article_id=361>

And studies of their effectiveness show a pattern of improvements compared to traditional curricula; see "Results from the NSF-Sponsored Curriculum Projects." <MathematicallySane.com/evidence/nsfevidence.asp>

Q: Isn't the main problem that our students aren't learning their basics they way they used to?

Actually, the world our children live in is quite different from when we were children. For example, long division is used by some critics as a litmus test of "rigor", yet hardly anyone actually uses it in any practical setting; see "Standards, Division, and Constructivism." <MathematicallySane.com/analysis/mathstandards.asp>

Furthermore, "The Good Old Days Never Were." <MathematicallySane.com/analysis/goodolddays.asp> That is, the perceived problems with the "basics" are nothing new.

Indeed, student performance on the basics has steadily increased since 1973; see "National Assessment Shows Encouraging Trends in Mathematics." <nces.ed.gov/pressrelease/rel2000/8_24_00.asp>

Q: What about calculators? Aren't they keeping children from learning?

Actually, research on calculator use shows that they may have great benefits for student learning. See "The Role of Calculators in Math Education." <education.ti.com/t3/resources/therole.html>

Q: Hasn't California, where reform began, pretty much abandoned these changes?

The California board of education initiated a major shift in direction, based on recommendations by a small but vocal group of parents and mathematicians who acquired political clout. Many teachers have felt disenfranchised by the unilateral decisions made in this process. For more information on the politics behind these changes, see "The Politics of California School Mathematics." <www.pdkintl.org/kappan/kbec0003.htm> For more information on the different persepctives, see "What Are the "Math Wars" in California All About?" <MathematicallySane.com/analysis/mathwars.asp>

Q: Isn't this "backlash" spreading to other states?

Yes. This same group of parents and mathematicians is active in other schools or districts that are trying to implement "reform" methods or curricula. For information on how to respond to their tactics of intimidation, see "Standing Up to the Critics." <MathematicallySane.com/analysis/standingup.asp>

Q: Where can I find out more about these critics?

They maintain a website, http://mathematicallycorrect.com. As you read what they have to say, you might ask yourself, Where is the evidence that supports their viewpoints? How much of what they have to say is based on scare tactics and misinformation? Do they present both sides of the issues? We ask that you rationally weigh the evidence, not react based on mere emotion.

Q: Where can I find out more about Mathematically Sane?

MathematicallySane.com is dedicated to getting out more balanced information about mathematics education reform. For more information, see our "Mission Statement." <MathematicallySane.com/mission.asp>

Q: How can I react productively if controversy erupts in my school or district?

Perhaps the most important point is to be proactive and work to form alliances with like-minded people before problems begin. It is important to talk to different populations in useful, informative terms. For more ideas, see "Surviving the Math Wars." <MathematicallySane.com/analysis/survival.asp>