geodob Wrote:Hi Glen Penn
I was equally excited to read about your longitudinal project into working memory. Also that you are looking at it in terms of poor maths abilities, Dyscalculia. Where it has major implications in Procedural Dyscalculia.
Yet equally implied in the more publicly known Maths Anxiety/ Phobia.
Where anxiety causes a reduction in Digit Span.

geodob Wrote:Though I have also developed a hypothesis that working memory may be a major factor in Non Verbal Learning disorders, within the Autistic Spectrum?
Whilst this is highly speculative, the difficulties seem to be occurring in the working memory?

geodob Wrote:I was also very interested to read that you are considering interventions?
Not too long ago, I recieved an instructional manual to develop Speed Reading skills, where it appears to me that it basically helps one to learn new Working Memory skills?

geodob Wrote:But Glen, what this really highlighted to me, is that Working Memory is not a 'fixed thing' that we are born with?
But rather it is a 'stage' where a spectrum of skills are brought together?
Where the crucial factor, is that these skills need to be developed?
What Speed Reading identifies, is that they are able to be 'further developed/ refined'. That they are not 'fixed'!

geodob Wrote:In terms of Dyscalculia, I am currently conducting informal trials of exercises I am developing, to enable the development of visual-spatial mental imaging skills, which is a major factor in Dyscalculia.
Where my main reason for noting this, is that these visual spatial exercises that I have them doing. Are singularly Working Memory exercises, where they are designed to help them to develop visual-spatial working memory skills?
Where a few people that have tried them so far, have reported some success?

geodob Wrote:But Glen, the really major issue that this is all suggesting, is that Working Memory is not 'something that we are born with'?
But rather, that Working Memory is a 'Blank Space', that we need to develop a whole spectrum of skills, to fully use?
The crucial issue being that we need to Develop all of the Skills to use it?
Afterall, this is the place that we 'Think'?
It is also the place that we interpret our Sensory Information?

But it is also a convergence point of different sensory interaction accompanied by retrieved long term memories?

geodob Wrote:Glen, I particularly noted your consideration of using interventions?
Where as an extension of this, I would suggest that the spectrum of skills that our Working Memory utilises.
Should in fact be taught by schools?
We need to actually learn how to use our Working Memory?

Maybe my basic point, is that education needs to shift its focus from learning 'what to think'?
To a model which helps Students learn 'How To Think'?
To fully learn, develop and utilise the spectrum of potential skills of this thing called a brain.
Where the interventions that you are considering, may in fact be incorporated into the standard curriculum?
Perhaps one day, Working Memory will become a Subject/skill that is taught within Schools?
With Literacy and Numeracy understood as Applied Working Memory?

geodob Wrote:Forgive my carrying on, but I'm really excited to be able to discuss this issue of Working Memory with someone!
I would also mention that I'm an administrator of a dyscalculia website, with over 250 Members. Where if we can be of any assistance, let us know.
Geoff.

Karldw Wrote:This is one of the most interesting articles I have read. It is like a poem or an allegory about the United States today. It can be read at multiple levels but I do not think that the author intended this. I believe that his intent was that we would read at the denotational level and understand his contentions about math curricula and education administration which he sees as conflicts of power between many interest groups.

The irony of this article is that the author appears to have little interest or belief in brain based concepts such as “theory of math education known generally as discovery learning” or “innate ability to understand math”. In spite of his perceived lack of utility in brain science it is precisely brain science that permits the understanding of the article.

The United States at this time has become a religious, morally driven state. This is described in cognitive science terms by cognitive scientist George Lakoff in his book “Moral Politics” and his more recent book “Don't think of an elephant”. What amazed me about the article is how well the article fit the theory of Lakoff, which is to me a validation of brain science. This will be developed further later. First I will indicate the levels of interpretive reading that I see in the article.

The obvious one is to read this as an article about the state of mathematics education in the U.S. The second is to look at the state of discourse that presently exists in the U.S. The third is see how this article fits the United Statesian psychology as defined by Lakoff. The fourth is how this article fits into the political landscape of the U.S. The fifth is to use the above to analyze the arguments. Now you see why I like the article so much. There is so much to it that for me the mathematics gets lost.

The fundamental problem in the U.S. is Habermasian discourse is unknown. People do not have discourse they talk at each other and past each other. This introduces some interesting artifacts; language and complexity of issues.

For complexity Garelick identifies the many different factions of the U.S. arena.
“The math wars revolve around a four-part problem: A disputed theory of education that informs NCTM's standards; state boards of education that base their standards of learning for mathematics on the NCTM standards; textbooks written to incorporate these standards; and teachers and others in the education establishment who are indoctrinated in the disputed education theory and who may not possess enough knowledge of mathematics to overcome the first three factors.”

He also indicates that the federal government is involved and that the NSF funded texts for the NCTM's standards and the states have their governments and state departments of education and ..... Now there is a mess of complexity no one can deal with.

Garelick is skilled in political discourse as he is a government employee and was on a special assignment working in a Democratic senator’s office. He has apparently learned that if conventional language is inadequate then you invent your own words. “I will use the term 'educationist' to refer to those who promote the contested theory of math education known generally as discovery learning.”

There we are – complexity and language. This has a purposeful effect in U.S. discourse. The reader is now desperate for a hero on a white horse who has an answer. And here he comes!

This sounds ludicrous, but before you write it off lets look at it. The U.S. has taken its democracy concepts to an extreme. Kenneth J. Arrow wrote a book “Social Choice and Individual Values” in which he shows that there is no democracy unless you are limited to only two choices. In the book he says “Theorem 1 is, in a sense, the logical foundation of the Anglo-American two-party system.” When you live in a bi-polar society in which there is right-wrong, black-white, Republican-Democrat, liberal-conservative, then you start to see everything this way. You either have the wrong way or the way mathematicians see it.

The conservative psychological position is defined in chapter 1 of “Don't think of an elephant”.

“The strict father model begins with a set of assumptions:
The world is a dangerous place, and it always will be, because there is evil out there in the world. The world is also difficult because it is competitive. There will always be winners and losers. There is an absolute right and an absolute wrong. Children are born bad, in the sense that they just want to do what feels good, not what is right. Therefore, they have to be made good.

What is needed in this kind of a world is a strong, strict father who can:

• Protect the family in the dangerous world,
• Support the family in the difficult world, and
• Teach his children right from wrong.

What is required of the child is obedience, because the strict father is a moral authority who knows right from wrong.”

It is amazing to me how this psychology fits the Garelick article where he makes statements like the following.

“Hell hath no fury like a mathematician whose child has been scorned by an education system that refuses to know better.”

“I use 'educationist' to refer to those who promote the contested theory of math education known generally as discovery learning.

“... textbooks like Mary Dolciani’s 'Structure and Method' series for algebra and geometry continue to be used by math teachers who understand mathematics and how it is to be taught.”

“new-math era was one of the only times that mathematicians were given an opportunity to make proper math education available to the masses.”

“so constructivism taken to extremes can result in students’ not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering—and taking ownership of—the wrong answer.”

This has described some of the second and third levels of interpretations of the article - the state of discourse that presently exists in the U.S. and how this article fits the United Statesian psychology as defined by Lakoff. The fourth is how this article fits into the political landscape of the U.S.
The article was published in Education Next which is a publication of the Hoover Institution. Information about some of the people associated with the Hoover Institution was taken from Hoover Institution documents and is given below.

“Chester E. Finn Jr co-authored with William J. Bennett and John Cribb; and What Do Our 17-Year-Olds Know”

“John E. Chubb is a founding partner, executive vice president, and chief education officer of Edison Schools [Paul Allen, Microsoft Billionaire is a partner in this for-profit schools venture, as is Chester Finn]”

“Hoover Board of Overseers includes:
Donald H. Rumsfeld · Chicago, Illinois
William H. Draper III · San Francisco, California
General William Draper's son and heir, William H. Draper III, was co-chairman for finance (chief of fundraising) of the Bush-for-President national campaign organization in 1980.”

You can see from the above that within the Hoover Institution are very conservative persons who have reasons to oppose established public education. The conservative right has worked for years through think tanks such as the Hoover Institution to direct the thinking of the population. I believe that there may be ulterior motives for the publication of this article. There may be more to this than the denotational expression.

All that remains of the levels of interpretation is to go to the denotational level and analyze the arguments. If people are interested I will respond.