Carrol
On 6/1/2011 2:22 PM, Chuck Grimes wrote:
>
> [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
>
> ---------
>
> 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. ''
>
> http://www.mathunion.org/icmi/icme-12-news/details/?tx_ttnews%5Btt_news%5D=87&tx_ttnews%5BbackPid%5D=795&cHash=a193001384
>
>
> 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
>
>
>
>
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