Saturday, April 5, 2008

Applications and Misapplications
of Cognitive Psychology
to Mathmeatics Education

Very cool paper:
Applications and Misapplications of Cognitive Psychology to Mathematics Education

Recommendations for Instruction

We need to be more tentative in our recommendations for instructional methods than in our recommendations for research. Nevertheless, there is already considerable empirical support for the superiority, relative to mainstream classroom methods, of a number of procedures (like the learning-from-examples and learning-by-doing methods already mentioned) that are ready for classroom testing on a large scale.

The use with children of experimental methods, that is, methods that have not been finally assessed and found effective, might seem difficult to justify. Yet the traditional methods we use in the classroom every day have exactly this characteristic--they are highly experimental in that we know very little about their educational efficacy in comparison with alternative methods. There is widespread cynicism among students and even among practiced teachers about the effectiveness of lecturing or repetitive drill (which we would distinguish from carefully designed practice), yet these methods are in widespread use. Equally troublesome, new "theories" of education are introduced into schools every day (without labeling them as experiments) on the basis of their philosophical or common-sense plausibility but without genuine empirical support. We should make a larger place for responsible experimentation that draws on the available knowledge--it deserves at least as large a place as we now provide for faddish, unsystematic and unassessed informal "experiments" or educational "reforms." We would advocate the creation of a "FEA" on analogy to the FDA which would require well designed clinical trials for every educational "drug" that is introduced into the market place.


Anonymous said...

I have a rant for you. The state is making math more difficult than it needs to be. Math is a simple, but not easy, discipline to understand. Why must the state try to implement two sets of standards for high school math? This complicates an already confusing situation. Math 1, 2, 3 standards and Alg1, Geom, and Alg 2 standards make little sense to me. In reading the standards, I also do not see how they can test students fairly and reliably given two different sets of standards. I saw that you are on a state board of education committee and was hoping you could shed some light on the popular thinking in regards to the two sets of standards. Tsquared

dan dempsey said...


You are indeed a thoughtful individual. The plan as I understand it is to produce a set of high school standards by course. It remains to be seen as to whether there will be separate standards for integrated.

If you look at integrated books from Asian countries they have a much greater similarity to our traditional sequence of Alg, Geom, Alg II than to the bizarre NSF sponsored reform curricula.

It is also interesting to note when Dr Bergeson initially attempted to fly this idea of three texts maximum, what she really hoped for was one curriculum that would enable the children to transfer with ease throughout the state.

The idea of a more traditional approach and an NSF style reform integrated approach does seem contradictory.

Even more bizarre is the idea that the state could not support more than three texts with adequate coaching. Now research is telling us that we have done such little research of substance we have no idea what works -- How will the wisdom of the state know what to tell us???

Obviously that is of little importance when expansion of bureaucracy is the goal.

I am slowly beginning to figure out these hucksters.

I much prefer the:

1... tell 'em whatcha gunna teach 'em
2... teach 'em
3... test 'em on whatcha taught 'em

All the standards need to do is tell me what I am going to teach.

Then hopefully end of course testing can test on what I was supposed to teach.

Success of course has a lot to do with the level of preparation of the incoming students.

For many the transition from current competence to the preparation for Authentic Algebra or actually taking and successfully completing an Authentic Algebra course will be the equivalent of a turtle ramping up for breaking the sound barrier and doing so.

It would be exceptionally fine if teachers were able to use an adequate text book for the task.

note: Lecturing should not be confused with teaching. I am a direct instruction fan when students are directed to do something and do it. I mean do it correctly because they have learned from examples and instruction.

Certainly extending beyond is a great idea but could we please have some focus.

One thing we do know is that for most kids the spiral curricula without an emphasis on mastering anything are disasters.

So why are districts that select spiral curricula like Seattle, Issaquah, and Bethel for 2007-2008 thinking they are qualified to tell anyone about best math practices when they are so incompetent they can not select an adequate textbook?

Just wondering.


As I look over the NMAP and all the accompanying press releases of the day. I can not help but notice that there is very little actually known about what makes for an effective math teacher.

Or even what practices actually work in a math classroom.

Given that; what are these $2+ million dollars annually expended on math coaching for teachers actually doing in the SPS?

It is becoming more apparent by the day that by abandoning schooling based on Core-Knowledge in favor of process oriented education, we have been snookered.

I love the title of Don Orlich's book:

School Reform: The Great American Brain Robbery

I believe things are getting better I see stock futures in Math Clowns are now falling after an extremely bullish market for Math Clowns over most of the last decade. This school year the Vancover WA SD is actually requiring that math coaches know some math and be certificated for math. What a refreshing change over the previous requirement to whistle the Politically Correct tune of "Oh How I love best practices -- whatever they might be".

Think about it the NSF spent $100 million to develop 13 programs that have no evidence of success, we have little research into what actually works in the math classroom although the indications are that:
Good examples and carefully designed practice are beneficial.

This should not be confused with droning lectures and poorly designed practice.

Again who decided what practices are best and how did they decide it?

They may well be determined by political alignment with the PC line. For that is what education has been about for it certainly has not been about results.

PISA 474 and falling.

UW still pushing the stuff that has not worked for the last decade. Brought to you by the College of Education co-conspirators with NSF, SPS and Bellevue in the great collapse of non-Asian minority math skills.

Spring 2007 WASL Math grade 10 achievement gap for Black Students in Bellevue 55% in Seattle 52%

Bellevue White students passed at 73% while Blacks passed at 18% -- and Eric McDowell, Mike Riley, Rosalind Wise, Carla Santorno and Uri Triesman think that Fidelity of Implementation is a great idea.

Like I said I hope Math Clown futures continue falling.