The "traditional" math sequence

Well first there is algebra in 9th grade. But then take the entire sequence geometry --> algebra I --> algebra II --> precalc --> calc I --> calc II etc. (Maybe if you are advanced enough you get to do Calc III or linear algebra in the last term of high school or maybe the opening semester of college.) Why necessarily in that order? Is it necessary to have fully mastered all the theorems of geometry before moving on to algebra I?

Furthermore, there is a perspective lost in the entire sequence, because generally, a lot of fields from number theory to graph theory are not even considered until college, except as shallow "enrichment" activities. Are kids capable of doing hardcore number theory in eighth grade? Well take the International Math Olympiad (for young students) or your average state math competition. You can get straight As on your calculus exams and totally get creamed at these competitions by a bunch of ninth graders from a school with a more dedicated math team.

Formal linear algebra is mind-expanding, but it occurs to me it doesn't require college-level understanding to master its basic concepts (like transformations). Arguably, you /really/ understand what differentiation and integration is all about when you learn to map from one polynomial space to another. The most important thing about solving math is abstraction, and a rather powerful abstraction is the ability to rotate entire shapes by a simple entity called a matrix; ever had that annoying geometry problem where you had to tediously map all the points of some crazy polygon after it was rotated an arbitrary angle? Well now, what a perfect time to bring up a concept that would systematically map every point to its new point after the rotation...

Here is the place to use a calculator. Take a polygon with 20 points (or some inconvenient number). Students would then have to design a matrix that carried out said transformation. Perhaps an arbitrary transformation whose formula wouldn't generally be memorised (like with standard rotations). The calculator is the "reward": simply input all the points, the appropriate transformation and then report the results of the magic. Here, the calculator ensures that students actually understand how to use the abstraction being learnt (rather than say manually applying an algorithm to each point). On the other hand, it is not being used as a crutch for bad understanding.

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There has been much said about "holistic" educations. Many ostensibly "holistic" curricula are not holistic curricula at all. One of my disenchanted teachers put it -- you can't just toss a bunch of department heads together into biweekly meetings and call the result "holistic". (Now mind you, this teacher was from a top Singaporean school and he had been "released" from duty by being too vocal about certain teaching practices.) There is so much reteaching of math concepts from applied subject to applied subject. And oh, all the forgetting! Imagine what could be done if all the inefficiency was removed...

See, I don't actually disagree with the actual idea of integrated math. Integrated math should be a vehicle for exploring important life concepts (like, ooh, equilibrium! optimisation under constraints! recursion! etc.) taught tightly with useful, complex, mind-expanding applications. You could pack a lot of learning into a year. It shouldn't be about using matrices as some sort of organisational table for keeping scores of random soccer matches.

Holistic Teaching

My current, and last, class to obtain a Reading Specialist endorsement is Teaching Reading to Special Needs Students.

Here is the publisher's description of the book as provided on Amazon.com:

When the first edition of Readers and Writers with a Difference appeared in 1988, it shattered the myth that whole language instruction was too unstructured and inexplicit to help remedial and learning disabled students. By providing specific assessment and instructional strategies, it was one of the first texts to show that struggling readers and writers could, indeed, benefit from holistic methods-not just in the resource room, but in the regular classroom as well. [Great, just what we need, more whole language for those students who didn't learn with whole language the first time around.]

Today, as more and more students with learning problems are entering mainstream classroom settings, the models presented by Rhodes and Dudley-Marling are more cogent than ever. But the framework upon which whole language theory rests has greatly evolved since the first edition was published and has also come under increasing attack. This second edition renews the case for whole language theory, taking into account the various developments in language arts over the past eight years. Included are new and expanded sections on literacy theory, instruction and assessment, and literacy as social practice; and a reconsideration of how teachers, administrators, and parents might work and learn collaboratively.

I cannot emphasize enough how frustrating I have found my reading endorsement classes. I can't wait to finish this last one and be done (hopefully) choking down the unsupported garbage that passes for reading pedagogy. There is real research showing real results using Direct Instruction and its ilk, that is not only ignored, but denigrated, by progressivists. I'm tired of "learning" all this useless tripe, and I'm totally fed up with it. I still want to earn a Master's degree in some area of education, but I'm not going to continue with my current university. The Educational Research class I took was the last straw (some day I'll post about it). If anyone knows a good, research based Master's program online, please let me know about it.

Teacher YOU Training Institute
k9sasha on holistic teaching