Additional Math Pages & Resources

Tuesday, July 19, 2011

Math Curriculum, Part II

Yesterday I talked about math curriculum in Mongolia, where math teachers operate in a very complex environment. They have struggled with several character sets and alphabets, under communist or other political systems, using traditional, Russian or Western education methods.

Mongolia's math challenges are daunting, but every country faces some degree of political upheaval, economic upset, language and population shifts due to immigration, changing expectations about their schools, etc.

What we share with Mongolia is an expectation that science points us in the right direction to improve education. Or to use the lingo:

Evidence-based practice refers to preferential use of interventions for which systematic empirical research has provided evidence of statistically-significant effectiveness in solving specific problems

I'm going to color the following paragraphs to represent two divergent points of view:

Traditional education, although based on the experience of generations of teachers, lacks "scientific evidence". Please notice that a lack of scientific evidence SHOULD NOT IMPLY traditional methods are less than ideal or contrary to an ideal, just that so far there is no research.

Many education policymakers believe it's vital to identify which approaches work best so those practices can be promoted (and others abandoned or suppressed). Lack of major progress in education may be the result of random, disconnected and non-cumulative practices employed by individual teachers in local school districts, each re-inventing the wheel and failing to learn "what works" based on scientific evidence

Opponents argue that scientific evidence is a misnomer. Knowing that a technique works in engineering or chemistry is not the same as knowing a teaching method works with students. Centralizing control of education in the hands of government, scientists or "experts" is not the answer.

Evidence-based practitioners reply that teachers should happily choose from scientifically-proven options; that their only goal is to eliminate unsound or ineffective practices in favor of those showing better outcomes. One simple solution is to approve only methods or materials about which scientifically-valid studies have been published. Educators will be encouraged (or compelled) to select from this subset of methodologies.

Traditionalists point out that we lack of complete, reliable and useful data. We can't adopt Technique A before evaluating research design, quality of implementation, the backgrounds of the researchers, the volume of data available to the public. etc. Not all evidence is equal. No all techniques lend themselves equally to scientific investigation. Here are some categories into which our teaching options may be sorted (by scientists):
  1. evidence-based: randomized study design to compare new methods with existing methods, results are independently replicated, blind evaluation of outcomes, and written documentation of the methods.
  2. evidence-supported: non-randomized study compares methods, results are independently replicated, blind evaluation of outcomes, and written documentation of the methods.
  3. evidence-informed: case studies on similar but not identical populations outside the target group, without independent replication; documentation does exist, and there is no evidence of harm or potential for harm. 
  4. belief-based (traditional): little or no published research, based on composite populations; uses religious or ideological principles, or claims to be based on accepted theory without providing a scientific rationale; there may or may not be documentation, and there is no evidence of actual or potential harm
  5. potentially harmful: negative mental or physical effects have been recorded, or by referring to documentation an expert may conclude there is potential for harm
Do you see the the blind alley we're in?

There's never enough science to satisfy science! Ideally we could have scientifically-based research determine the ideal process to compare traditional and scientifically-valid methods. Instead, by design or default (perhaps with no consideration of economics, interest, or practical value), the scientific approach places traditional education methods just above "potentially harmful".

This situation reminds me of Woody Allen's movie, SLEEPER:

Doctor A: For breakfast he requested "wheat germ, organic honey and tiger's milk."
Doctor B: [chuckling] Oh, yes. Those charmed substances thought to contain life-preserving properties.
Doctor A: [in amazement] You mean there was no deep fat? No steak or cream pies or... hot fudge?
Doctor B: Those were thought to be unhealthy... precisely the opposite of what we now know to be true.
Doctor A: Incredible!

Steak, rare, with chocolate ice cream

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