[WS:] Oh, c'mon, Chuck, stop behaving like a cornered dog biting anything that moves. They sound like typical liberal do gooders - wasting their money but basically not an enemy.
wojtek
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Context. Go back and listen to Doug's show or look up The Joyce Foundation. The latter does sound at first glance like a do-gooder wasting money. But the money wasn't wasted because it was used to lobby the Illinois legislature to write and pass a bill where:
``Performance [is] included as a factor when making hiring, layoff, and dismissal decisions...''
This is just code for laying off teachers by using student test results and making the curriculum teaching to the test. It's softcore wording, compared to Moe's, but no less obnoxious.
Moe's idea that you could teach math with a computer instead of a teacher really pissed me off. This so-called expert knows nothing about mathematics and nothing about teaching it at any level. He is a neocon ideologue. Like Doug said, bad cop v. good cop.
I've spent a lot of time thinking and doing background reading on teaching math. I discovered hopefully, a much more enlightened approach by people who seem to know their mathematics and a lot about the modern developments in the field. Their basic mission is how to bring modern developments into the classroom. It's called the International Commission for Mathematics Instruction, or ICMI. The organization was founded in 1908, which is highly significant. It was about then in Europe that a lot of modern mathematics were getting developed and yet were not getting taught.
The ICMI produces reports and studies which can be found by wiki. From their Bulletin 54, 2004:
``Concerns about students' learning compel attention to teachers, and to what the work of teaching demands, and what teachers know and can do. A second reason is that no effort to improve students' opportunities to learn mathematics can succeed without parallel attention to their teachers' opportunities for learning. The professional formation of teachers is a crucial element in the effort to build an effective system of mathematics education. Third, teacher education is a vast enterprise, and although research on mathematics teacher education is relatively new, it is also rapidly expanding.''
Translation. Most school mathematics below upper division courses in mathematics and physical science are from the 19thC and don't represent modern developments. This is a big problem. ICMI has been working on this problem since well, since 1908. Here's quick scan of a recent call for papers item 1 of 7:
``Issues related to early algebra, like what is its nature; children's capabilities in thinking algebraically and dealing with symbols; early algebra's contribution to children's later understanding of middle/ secondary school algebra; challenges involved in doing "early algebra" in the classroom: what works, what does not. ''
I bought a used book set called, The Fundamentals of Mathematics, ed. Behnke et al, MIT press, 1974. The original German edition came out in 1962. I used it as a broad reference for occasional study. It's very good for that.
One day I got to wondering where this three volumn set come from? It represents a huge amount of work. From the copyright page:
``...The publication was sponsored by the German section of the International Commission for Mathematics Instruction...''
Now, go back and think about elementary, secondary, and community college teachers. I bet virtually none of these teachers were ever exposed to the level of mathematics the ICMI has in mind.
My math teacher buddy A, who teachs 8th grade math and algebra sure hasn't been exposed to this material. The developments provide a lot of motivation and a broader understanding. Now this material impacts the whole k12 curriculum right back to the beginning of learning arithmetic and various little hurdles all children encounter and that I distinctly remember.
You'll need an example. It comes from ancient greek math, but has had lots of importance ever since. It's called the Euclidean Algorithm. Here's the wiki:
http://en.wikipedia.org/wiki/Euclidean_algorithm
It maybe hard to see its importance in teaching elementary school. You have to go back and remember you first learned simple division with a remainder. Then you were introduced to fractions and wrote the whole number first and the fraction after. Later you learned the decimal notation and carried out the division to some decimal and rounded.
Behind all these elementary division tasks lays the development of modern number theory and the development of the real numbers of Cantor and Dedekind. Here's the wiki on Dedekind:
http://en.wikipedia.org/wiki/Richard_Dedekind
Beyond the material importance, is another story. It's about the relationship between teaching a subject and seeing places to make contributions. The Dedekind Cut was first a simple teaching tool, an illustration device. Dedekind wasn't alone. Most of the famous mathematicians of the late 19th and early 20thC were teachers. The state of mathematics during the period was just a vast collection of apparently unrelated material. It had to be organized in some fashion so it could be taught.
The most famous of these organizers was Felix Klein and his Erlangen Program. Here's his wiki:
http://en.wikipedia.org/wiki/Felix_Klein
See? The Erlangen program was motivated by the needs of teaching the `new' geometries. There is a way to introduce these ideas directly into the current elementary geometry level. It's called Incidence Geometry. I owe this insight to W. Prenowitz, M. Jordan, The Basic Concepts of Geometry, Xerox pub, 1965. They wrote the book to introduce high school teachers of geometry to modern geometry. It's a great little book. They don't recommend the material for students. I think they are mistaken. You can use the incidence models. The mistake most texts make is they introduce the ideas in set theoretic form (a bunch of symbols). If you use the diagram form, the ideas are much more accessible.
By studying these models in diagram form and their axiom sets, you can see what Klein saw. Well I think you can. This gets way too complicated to explain.
Anyway, from an advanced perspective this obcession with test scores is just stupid, and viciously stupid. As you wrote: ``This whole brouhaha about improving school performance, testing an related bullshit has nothing to do with education and everything to do with money.''
The real education issue is teaching kids how to think in mathematics. Sure learn to do your sums. But that barely touches the surface.
CG