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More emphasis needs to be placed on developing rapid, effortless, and errorless recall of basic math facts. What this suggests is that there are huge differences in the amount of instruction individual children need to become fluent at retrieving answers to basic math facts.

Special Education students constitute a targeted group but in fact a much larger population of math-troubled, resistant learners falls outside the Special Ed sphere.

Further, this lack of fluency interferes with the development of higher-order mathematical thinking and problem-solving. Let’s look beyond fluency

In my own experience as a parent of two LD boys, I have seen Special Ed kids fall victim to the Special Ed protocols and lable. The emotional distress and stigma contribute to student resistance, motivation, block. This gets in the way of emotional 'can-do' self-image in many subjects, not just math. The focus on remediation in special ed classrooms rarely attempts to find pathways that support a special learner's learning strengths. The culture segregates on the basis of differences and has not learned to tolerate differences. If you are different, you don't fit. Period.

Given these factors, we should zoom out and look at the learning culture as a whole. The culture is a major part of the problem. The culture provides positive reinforcement only to the elite of learners lucky enough to have learning dispositions perfectly suited to the culture: thus the select trophy students. The cultural expectations of all students to keep up not only with the elite pack but with the expectation of ‘the time constraints imposed by the culture are damaging. Teachers do not have time to vary the instruction; they are pressured to cover the material, and the communication is limited—does not lend a voice of nurturance and individuality to kids who naturally thrive on more physical, emotional relatedness—relatedness that builds interest, motivation, confidence, and meaning.

The question of fluency is obviously one of literacy: Education is notorious for its failure to teach foreign languages to children. Three years of a language in high school still results in little grasp or ownership. Foreign Language classes, despite the use of ‘immersion’ techniques, rely on memorization and testing to teach the language. If you agree that math literacy is also akin to learning a language and becoming fluent, the way native speakers build fluency in early childhood, then you would also agree that the conventional approach to teaching fluency is devoid of immersion, engagement, fun, excitement, selective as opposed to instructive activity on the part of the student. What is the culture doing to promote an engaged, immersive experience? The conventional classroom is a culture devoid of nature, and so tools must be found to make the learning of anything an experience that means something enough for the student to develop a sense of self, ownership, control and mastery. Otherwise, students are just like parrots in a cage—parroting but not articulating.

Building Problem Solving and Reasoning
Students with math difficulty find mathematical problem solving, particularly word problems, challenging for a variety of reasons as discussed by Babbitt & Miller (1996) in their review of literature. These challenges included misreading the problem, having difficulty detecting relevant versus irrelevant information, misidentifying the appropriate mathematical operation, making calculation errors, missing steps needed to carry out the problem, and having trouble organizing the information in the problem (Babbit & Miller, 1996). These challenges can be classified as problems with declarative, procedural, and conceptual knowledge. Students need all three types of knowledge to be able to solve problems. Problem solving requires students to know their basic mathematical facts, to execute the strategies and procedures needed to solve the problem, and to understand conceptually how to apply those facts and procedures. Without this conceptual understanding, there is no guarantee that the students will be able to apply this knowledge in meaningful ways when confronted with problem situations.

Experiences, expereinces! Math use and problem-solving has to matter individually to the student. Like group activity in writing and composing sentences and constructing a written argument, learning math language patterns can be a social, shared experience in which everyone participates. Sitting at a computer alone or using video will not do the trick. Either the culture commits itself to a strong, human, interpersonal presence in the student’s life, that gives the student room to grow into the language of math, with being compared to his peers, or we simply won’t reach everybody. Also, using words to put math problems in front of students is also counterproductive for many students whose relationship with words presents challenges. Experiencing a problem is different from reading it.

To enable students to become successful problem solvers, they must develop a working and dynamic relationship between declarative, procedural, and conceptual knowledge. MEANING. A computer program can’t create personal investment. However, in principle, a computer game, a very sophisticated, subtle embedding of math challenges in a game could provide a consistent flow of experience that would enable the student to develop a math knowledge-base and the faculties to engage and use it.


This video and accompanying lesson plans can be retrieved from the Wisconsin Center for Education Research Web site, http://www.wcer.wisc.edu/TEAM/index.html. The above use of video may come close to the game model, but it’s not quite as immersive

One major goal of educators of students with math difficulty should be to conduct ongoing research to determine the best use of existing technology for enhancing mathematical learning. Further, educators and researchers should work closely with developers and publishers of new hardware and software and conduct high-quality research targeted at identifying effective practices that accompany the use of new products. In this paper we have attempted to identify important areas in need of research and development and to examine a variety of technologies that can enhance the mathematical learning of all students, but especially those students with math difficulty. Hopefully, we have identified areas of need that will serve as a guidepost for future research and development activities.

It is my belief, as a promoter of play in learning, that two important factors need to be addressed: teachers need to be trained in the art of communication--brain-based communication--to create experiences that defuse anxiety and involve groups socially and collectively. The shadow of fear must be removed with lightness, freedom to screw up, adult modeling that intentionally 'screws up,' and the creation of experiences that bond students instead of pitting them against each other. This sort of teaching goes much further than the flat ‘interactivity’ that develops between a body and a monitor, and serves to create a social foundation for using and speaking ‘math’ as a native language. Sadly, elementary schools are too busy not experimenting with this sort of ‘instruction’ (for lack of a better term), consumed by the lockstep of testing. Here is one attempt on the college level to change the nature of instruction.
http://puppetools.com/library/pdf/williams1.pdf

Thanks very much for this Jeff. You have made some extremely interesting and powerful comments. I would love to hear reactions on this...

All the best,
Christina

Where Are You Geoff Come In From The Cold

Our children are born exactly as they are,

we can not effect the way they are when they are born,

we can not afect the way they are when they arrive at the school door.


But we can affect the way they are from that day on, as an individual arriving late to the educational table i feel you have all been locked in a time warp since the death of Maria Montissori, my abacus is for her and every child, she well realised the problems children have in learning, spending her whole life developing her simple ideas ni order to make learning easy.

the only thing that stands between a child and a good education easily achieved are teachers.


i am writing something i will insert here happy chewing

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.

I have to admit to not being fully au fait with Dyscalculia, as the original body fo work was designed to merely examine the developmental trajectory of maths in conjunction with the developmental trajectory of working memory, of typically developing children. However as with all things research based, this has widened somewhat to break down the curriculum components of "number", "measures, shape and space", "problem solving" and "addition and subtraction" and also differences been high acheivers and low acheivers memory skills. As yet this is still very much a work in progress!!

I have read quite a bit on anxiety and math performance in the past (my memory is shocking!) and individual difference in anxiety/maths.
With dyscalculia being a specific problem, I have not "diagnosed" any of my participants, but plan to consider the data of the low acheivers to see where the problem lies. It's entirely feasible that it is merely anxiety/confidence. Or it could be that combined with poor memory function.
Also the majority of articles I have read with regard to amths difficulties, tend to be with adults or children over the age of seven. Hence the "exploratory" nature of my work so far.

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?

Again my knowledge of this would be very limited, but it sounds really interesting. It might also imply ionterventions could lessen the effect of the disorder.

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?

from my reading, I have come across many tasks that claim to improve short term memory skills, and in fact do appear to do so. My issue with many of these skills, is that there is very little evidence that maps onto the theoretical frameworks that underpin WM. Yes, there are several notions of WM (just to confuse the issue).

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'!

If you read any work by Prof Susan Gathercole, Dr Sue Pickering, and their colleagues it's possible to see that under their theoretical background, WM "develops". Certain aspects of WM appear not to "come into focus" until a child reaches approximate age of 7. Then between 11 - 15 (ish) a child develops adult-like WM capacity/spans. Further to this there is literature to support cognitive decline effects in old age, and cognitive failures in drug users....all suggesting that WM can be manipulated and is subject to external effects.. (forgive me as I am dashing off in a mo to go out testing for my research and trying to answer everything hurriedly).

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?

I'd be interested in the exercises that you are using.

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?

I'd disagree that it's a blank space based on the literature that I have read and the evidence that pertains the the theories I work within, however I do think that that notion is a little inline with the work of Jones and Macken in Cardiff university.
I do agree that it is a convergent point for other information, in particular I would say semantic knowldege and understanding. There's some evidence to support a "buffer" in WM that links WM to long term memory and semantic and episodic memory.

I firmly believe that we do need to develop all the skills within WM for successful scholastic attainment. I am not sure if it IS the same place that we process things like sensory information, I'm sure I ahve read that different parts of the brain are activated with things like touch and taste and smell....but if you mean sensory in the idea of visual and spatial awareness and understanding then I suppose yes, it is probably the same place.

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?

I agree. I have many unsubstantiated "opinions" on this matter and hope to make some headway into turning these opinions into theory. Then into practice. I think psychologists can inform education if we can understand how children think, how their brains work, how their memory works. It would make a whole lot of sense to me if "memory training" was implemented in schools. Espeically with regard to maths and things like language learning, it would probably be really useful.

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.

It's nice to talk to you also. I'd definitely be interested in the Dyscalculia website and a colleague has recently joined our department who did her thesis solely on dyscalculia so I am hoping to join forces with ehr at some point and see where that research takes us.

Please forgive my typos, I have one arm in my coat sleeve now as I dash out.....thanks

glen

Glen,
I just came across this, which seems to me to represent how our working memory 'chunks' information:

Count every "f" in the following text:

FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC
STUDY COMBINED WITH THE EXPERIENCE OF YEARS.....
--------------------------

How many did you spot? If three (3) check again.... There are actually six (6). The brain seems to not be concerned with the word "OF"?
Geoff.

Just saw this. Whoever wrote it should get over himself. BG

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.

Dear Sir

i'm Joanna Katsavria i'm working in the Ministry of Education in Greece. Also i'm studing Political sciences in the university and i'm researcher in the field of gifted education..

You cann't imagine how much relief i felt when i red ur message about the education policy. Last year i was trying to create a communicational bridge between the Greek Politicians the Greek Professors and the teacher community, i spend so many time for that but i had no results. The Politicians told me that it's not possible to create programs about gifted children because they don't have the money, the professors told me that they don't want to talk with the Politicians and the teachers told me that it's not fair to create special program for gifted. I want you to inform me about your project please. I want to see your option about that issue.

Yours

Joanna

I have to admit, I'm a little tired and I know that I didn't truly absorb all the wonderful, thought-provoking ideas that have been presented -but I did catch the concern about kids and problem solving. I work with students with learning disabilities in all grades and for the last year and a half have taught math for our middle school students with LD and ADD/ADHD. One of my primary concerns is concept building and problem solving. So many of my students, particularly the ones with math struggles, have been turned off of math because they know they are bad at it and they see the same things all the time. The only relevance for them is that math shows how dumb they are. It took me a year to get a few to see that math is more than calculation and that (especially if you have memory problems) calculators can be support, but there is not any real support for real problem solving. You can only rely on yourself and how well you know how to make meaning.

One of the programs we use in our math classes is Solve It! which is a problem solving remediation/instruction module:
"Solve It! (Montague, 2003) is a curriculum designed to help middle and secondary school students who have difficulty solving mathematical problems. Solve It! teaches students the necessary cognitive and metacognitive processes and strategies that good problem solvers use. "
I had a class with Marjorie (Montague) once and she was great. If I've linked this correctly, you should be able to access an article(?) by her that talks about problem solving as well as this curriculum: http://www.k8accesscenter.org/training_r...olving.asp. Maybe this will help - and I'm interested to hear others' thoughts on this approach and struggle as well.....