(Well, maybe it is; I don't know. If you come across other sites being built along these lines, could you let us know? I'd love to see how other people handle the information architecture challenges we're facing here at ktm.)

Yesterday I came up with the image that Kitchen Table Math is an 'office.'

It's a new office, one that hasn't existed before.

It's an office for parents, teachers, therapists, and, I hope, eventually students, too.

So far, that image is working for me.

As a parent, I need colleagues.

And I don't have them.

I do have parent-colleagues for the standard issues of child-rearing: behavior, discipline, friends, moral values, chores, summer camp, siblings, allowances--all of that good stuff.

I also have parent-colleagues, to a limited degree, when it comes to education. I can talk to other parents about the various doings and goings-on in our schools.

But I don't really have parent-colleagues with whom I can discuss supporting and supplementing and, in some instances, replacing my son's curriculum and teaching.

collaborating with teachers

Schools simply aren't set up to promote teacher-teacher collaboration or teacher-parent collaboration. Every minute of a teacher's day is spent in the classroom, teaching.

We need release time! We do!

This year Christopher's 5th grade teacher, Mrs. D'Arcy, spent a huge amount of time just sitting me down and telling me how she teaches math.

She could do this because she's young (no kids yet), lives close to the school, and just so happened to have a classroom on the first floor close to where I was running my Singapore Math class in the after-school program.

So we'd run into each other, and she'd give me advice.

I believe strongly that we need formal mechanisms to create, promote, and sustain parent-teacher collaboration (and not the public-diplomacy-masked-as-collaboration event-oids that TRAILBLAZERS advises. Uggh.)

So, at the moment, I'm thinking that's what ktm is, and will become.

It's an office for parents, teachers, therapist, kids and all other interested parties.

So today, thanks to Carolyn's heavy lifting, we're one step closer to that reality.

comments...

(And, thanks to Carolyn's heroic Creation Of Many Topic Threads last night, I have been able to enter this post in the Cognitive Science category! After I'm done with this, I think I'll go enter it under educational research, too!)


HOW THE MIND WORKS

by Steven Pinker (Linguistics department, MIT)
W.W. Norton & Company, Copyright 1997
page 341

The...way to get to mathematical competence is similar to the way to get to Carnegie Hall: practice. Mathematical concepts come from snapping together old concepts in a useful new arrangement. But those old concepts are assemblies of still older concepts. Each subassembly hangs together by the mental rivets called chunking and automaticity: with copious practice, concepts adhere into larger concepts, and sequences of steps are compiled into a single step. Just as bicycles are assembled out of frames and wheels, not tubes and spokes, and recipes say how to make sauces, not how to grasp spoons and open jars, mathematics is learned by fitting together overlearned routines. Calculus teachers lament that students find the subject difficult not because derivatives and integrals are abstruse concepts--they're just rate and accumulation--but because you can't do calculus unless algebraic operations are second nature, and most students enter the course without having learned the algebra properly and need to concentrate every drop of mental energy on that. Mathematics is ruthlessly cumulative, all the way back to counting to ten.

Evolutionary psychology has implications for pedagogy which are particularly clear in the teaching of mathematics. American children are among the worst performers in the industrialized world on tests of mathematical achievement. They are not born dunces; the problem is that the educational establishment is ignorant of evolution. The ascendant philosophy of mathematical education in the United States is constructivism, a mixture of Piaget's psychology with counterculture and postmodernist ideology. Children must actively construct mathematical knowledge for themselves in a social enterprise driven by disagreements about the meanings of concepts. The teacher provides the materials and the social milieu but does not lecture or guide the discussion. Drill and practice, the routes to automaticity, are called "mechanistic" and seen as detrimental to understanding. As one pedagogue lucidly explained, "A zone of potential construction of a specific mathematical concept is determined by the modifications of the concept children might make in, or as a result of, interactive communications in the mathematical learning environment." The result, another declared, is that "it is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve."

As Geary points out, constructivism has merit when it comes to the intuitions of small numbers and simple arithmetic that arise naturally in all children. But it ignores the difference between our factory-installed equipment and the accessories that civilization bolts on afterward. Setting our mental modules to work on material they were not designed for is hard. Children do not spontaneously see a string of beads a elements in a set, or points on a line as numbers. If you give them a bunch of blocks and tell them to do something together, they will exercise their intuitive psychology for all they're worth, but not necessarily their intuitive sense of number. (The better curricula explicitly point out connections across ways of knowing. Children might be told to do every arithmetic problem three different ways: by counting, by drawing diagrams, and by moving segments along a number line.) And without practice that compiles a halting sequence of steps into a mental reflex, a learner will always be building mathematical structures out of the tiniest nuts and bolts, like the watchmaker who never made subassemblies and had to start from scratch every time he put down a watch to answer the phone.

Mathematics is deeply satisfying, but it is a reward for hard work that is not itself always pleasurable. Without the esteem for hard-won mathematical skills that is common in other cultures, the mastery is unlikely to blossom. Sadly, the same story is being played out in American reading instruction. In the dominant technique, called "whole language," the insight that language is a naturally developing human instinct has been garbled into the evolutionary improbable claim that reading is a naturally developing human instinct. Old-fashioned practice at connecting letters to sounds is replaced by immersion in a text-rich social environment, and the children don't learn to read. Without an understanding of what the mind was designed to do in the environment in which we evolved, the unnatural activity called formal education is unlikely to succeed.


Steven Pinker



see also:
TheLanguageOfNumbersIsNotLanguage
Children's Mathematical Development: Research and Practical Applications
DavidKleinAtAEI

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