Saturday, August 30, 2008

Not Adding Up


Anonymous said...

There is still a lot of confusion over the pedagogy and the textbook's approach (especially Core Plus) Spokane does look like a perfect storm.

"Reform is heavy on problem solving, estimation, calculators, computers, group work and constructivist approaches (where children figure out things for themselves). It's typically light on basic arithmetic, practice and direct teaching."

Core Plus uses what has been coined as a "structured approach" to teaching mathematics that dates back to the late 50's.

I looked for constructivism in wikipedia and some author has really wacked it up at the beginning with structuralized, psychology jargon.

"Constructivism values developmentally-appropriate facilitator-supported learning that is initiated and directed by the learner." - A. Misnomer.

Vygotsky focused centrally on the role of culture, particularly language, as a mediating factor.

One should argue that there are at least two competing theories of constructivism - Luria and Leontev were more "Western" or cognitive in their writing.

Kirschner and Mayer make an attempt to ground the Western model back to reality - by describing a continuum of faded guidance.

Vygotsky's model was a competing theory that emphasized how meaning is shared and made between groups of people, sometimes called social constructivism. The most basic unit would be a dialog between a teacher and student. ZPD still remains one of the most important contributions to the theory of learning today.

There is another flavor of constructivism which is motivational and concerns students leaving their own imprint in the classroom. All too often this gets confused with discovery or inquiry based learning, but it is not the same thing and most of the multiple intelligences crowd fits in here somewhere. Most classrooms have examples of student work.

Western education doctors are still too attached to their anglophilic and xenophobic ideas to consider other non-English speaking cultures can be successfully taught math and science, and in English mind you...

An ELL student that substantially outperforms an English proficient student in mathematics does not fit into the developmental spectrum and cannot be explained satisfactorily by Westernized cognitive constructivists, like JD, SF, JP, etc..

Vygotsky would say well of course, in 1920s-style Russia, where we have hundreds of languages being spoken and very limited resources for educating our people, we must go about educating everyone to be a global power. That is the revolutionary aspect of education and it was the same for Paulo Freire.

Interesting that both philosophers were administrators, grounded in reality with very similiar tasks.

Anonymous said...

I disagree that "reform is heavy on problem solving, estimation, technology, group work, and constructivist approaches.

1. What is the constructivist approach? I believe the author intended to mean "discovery or inquiry-based learning." This is not the same as "learn by doing" or "hands-on learning".

2. What about problem-solving? It would be better perhaps to differentiate the types of problems that children are being asked to do? I would add clarity by saying that there are good problems, bad problems, and poorly worded problems (meaning we're not sure what the authors intended students to do. The DOE's exemplary textbooks have too many problems of the second and third category. They expect teachers to supplement their textbooks with drills and skills practice.

3. The textbook authors should probably not attempt to defend their logic of using non-standard algorithms, but actually call them what they are exercises in regrouping.

4. The same should be said for a book like Core Plus that purports to teach algebra. It can be used pretty successfully with a group of sophomores who have passed algebra, instead of taking geometry. But having said that, why would anyone want to, since it shouldn't/doesn't satisfy the general university requirement. Again one has only to look at the numbers of college freshmen enrolled in remedial math (half!)

3. Rather than estimation, I would say reform math teaches algorithms that are only suitable for whole numbers and therefore students spend a great deal of time truncating and hence their answers are only estimates. Secondly, since exponents are not taught explicitly (they must be supplemented) students cannot do serious estimation as we know it (finding orders of magnitude).

Students are being asked to estimate in the wrong places. Estimate when accuracy is required and compute when estimation is required.

4. Technology is an interesting question because of what it promises. But we fail to grasp its limitations. I don't feel the authors put enough effort into understanding how technology interfaces with student learning. As an example, take graphing calculators - when I ask students to draw the graph, I don't mean a sketch of the calculator display which by the way is non-standard. I mean a 'traditional' sketch with axes labeled and so forth. The sketch I frequently get from 11th and 12th graders raised on reform math is usually quadrant I and it looks like they tried to sketch it from a TI-83/84.

Also, I don't see how a teacher is maximizing their time staying tethered to a television display with a graphing calculator and troubleshooting students. Its absurd.

5. Group work would seem to be the only redeeming value of a class as ludicrous as what I am imagining. At least my fellow students and I would have the pleasure of knowing we all had to sit through a class as boring as this.

6. Finally, reform math doesn't go beyond simple arithmetic. Practicing non-standard algorithms seems rather convoluted. I'm trying to decide how to describe it, but its not standard (that's for sure). As for direct teaching, yes, the teacher to great extent has to do some form of intervention but that does not imply good teaching.

Classes with reform textbooks like EDM or Core Plus spend more time processing and interpreting what the problem is asking, than they actually spend on finding a successful approach for problem-solving and then finally doing computation. The fact that students are doing computation with non-standard algorithms only makes the work more demanding for teachers, who must now decide on which answers are acceptable.

College Preparatory Math (UC Davis) does not use a structured approach. It is the 'exemplary curriculum that fits closest to the Singapore model.

What should be done is a blind test, so that neither publishers, investigators, teachers, and students know which curriculum or textbook they are using in the classroom.