>From the article (posted by Jerry Becker at the head of this thread) "When math makes sense - - Teachers combine math with construction, cooking classes" - see : > ************************** <snip> > The difference in the students is evident. They're > walking tall and rightfully proud of what they've > built. Burrows said that every teacher looks for that > light that comes on when a student really understands > and he's seeing a lot more lights these days. > > "I had the lowest grade in the pre-test, it was a 22 > and now I've got a 77. That's much better," said Angel > Coleman. "I still don't like math, but I can understand > it." > <snip> > I guess that's the heart of the matter, it is, in fact, the whole ballgame right there:
i) The students are walking tall and rightfully proud of what they've built (via cooking or construction);
ii) For the teacher, the "light that comes on (in the student's face) when he/she really understands"... and
iii) A previously failing student now understanding math...
(There are several other meaningful examples quoted in the article, but the above will do to make my point).
As might be anticipated, the 'usual suspects' (those on the side of traditional math teaching) are predictably dismissive.
Who are these 'usual suspects'? Professor Wayne Bishop; Greg Goodknight; Robert Hansen [RH]. Haim is currently absent from this Forum - though (one suspects) that, had he been present, he would have issued his usual trenchant call to "PUT THE EDUCATION MAFIA IN JAIL!".
The 'usual suspects' on the other side have of course not been automatically dismissive of the thesis of the article (as have been the usual suspects supporting the traditional teaching methods) - but I believe (from the postings I've read) that the 'non-dismissers' too have not adequately understood and therefore have not adequately emphasised the crucial facts in the above-quoted instances:
a) students were taking pride in their achievement (based on an improved understanding of math that they had previously feared and loathed);
b) there was actual, real, measurable improvement in performance by students; and that
c) at least one teacher saw cases of "the light that comes on when a student really understands something".
The above indicates, to me, that there IS a strong case for revisiting the 'conventional processes' we have of teaching math.
It has been my case for umpteen years that the fear and loathing of math that afflicts the great majority of students leaving school is in fact unnatural, and indicates that there is something very wrong in the way math is conventionally taught.
The 'Transitions Learning Center' at Frontier Middle School has investigated and discovered that significant improvement is possible.
However, I suspect, from what I've read at the article, that they've not adequately understood how to develop effective 'learning systems' that can be applied to each level of learning, for all students. I believe that such effective learning systems should be installed and implemented at the very start of the 'math learning process' (and also, I believe, of all learning of all disciplines) - and then such effective learning systems should be developed for all levels.
The Montessori system has developed and applied useful ] learning tools' for math and other disciplines at the elementary levels. I suspect (from the fact that most students leaving school still fear/loathe math) that such effective learning tools and systems are not in place for levels beyond the primary.
In one of his posts at this thread, RH has claimed: "Now all we need to do is reestablish an oath of teaching whereby the policy makers, schools and teachers provide honest and reasonable guidance to their students and their prospects".
Yes indeed, that is precisely one of the things that has to be done in all of education. As I've often claimed, it is ESSENTIAL to get hold of all the ideas that ALL stakeholders in the teaching system(s) may have about how they would want the systems improved. The stakeholders comprise of: students; teachers; parents; administrators; teaching experts; politicians; others interested in education. Currently, there is little (beyond rather ineffective 'parent-teacher meetings') in the way of formal process to ensure that ideas about the functioning education system are gathered and something appropriate is done with those ideas. Such a process of gathering and integrating ideas from stakeholders has to be an ongoing exercise, built into the very system.
In other posts (in other threads), RH has claimed that the Montessori system is highly ineffective. This is an idea (which in my opinion is profoundly mistaken) that has to be gathered into the proposed improved education system and evaluated. [As noted, we do need practical means to gather, evaluate and utilise ALL useful ideas that may be available to improve our educational systems - RH has provided his ideas, as has Haim ("PUT THE EDUCATION MAFIA IN JAIL!"). Such ideas do need to be gathered and evaluated for possible integration into the proposed education systems as they are improved].
As ideas are gathered from stakeholders, it is also ESSENTIAL to 'integrate' useful ideas into an 'action plan' to improve the system: this is readily done by constructing models showing just how the things suggested to be done (or the current practices) may "CONTRIBUTE TO" the 'Mission' of improving the system. Simultaneously, we should also investigate just how other things (/existing practices) may "HINDER" or "PREVENT" accomplishment of the 'improvement Mission'. As this modeling becomes part of 'the system', the improvement is automatic.
At this point RH will no doubt come out with the (IMHO) irrelevant observation that he had covered the walls of all the halls and all the corridors of some office where he worked with PERT Charts [based on the "PRECEDENCE" relationship], and found no benefit whatsoever. I note that I entirely agree with RH that PERT Charts are largely useless for the purposes of helping us accomplish any Mission: I am NOT recommending (nor have I ever recommended) that anyone constructs any PERT Charts at all! (However, in the spirit of taking in all ideas brought up by stakeholders, this idea of RH's should also be gathered and, if appropriate, utilised: it WILL be utilised - because there is no need whatsoever for people involved in trying to improve the educational systems to construct a single PERT Chart!!)
Brief information about the system processes and the modeling tools that are useful to improve any system (e.g., the educational system) may be found at the attachments to my post heading the thread "Democracy - how to achieve it" - see http://mathforum.org/kb/thread.jspa?threadID=2419536 . More information (and the needed modeling software) can be made available on request.
(I am NOT claiming that all students will become Einsteins or highly-skilled in math. I AM claiming that it is not natural for the great majority of students leaving school to fear/loathe math - and we need to design our educational systems to remove this unnatural fear and loathing).