Teach the Brain Forums

To add this, I've been looking at studies on Working Memory, and more particularly the distinctions between what is called Verbal Memory and Visual-Spatial Memory.
Where essentially, Verbal Memory deals with the Facts.
Whilst Visual-Spatial Memory provides a terms of reference to Facts.
For example, if I say the word; Dog?
Do you simply see and hear the word ?
Or did you attach an image to it?
If so, was the dog standing, sitting or something else, as it flashed into your mind? What colour was the dog, and what breed?
Yet, if you didn't attach any visual spatial image to the word.
What would occur as you read the word?
Other than sounding out the word in your mind.
In turn, I would suggest that this is equally relevant to Maths, where the words Addition and Subtraction, equally have visual associations.
Where the visual element constructs a cognition of the concept attached to these words.
Without this visual working memory association, information recieved cannot be transferred and applied to different contexts.
So in relation to Maths, it needs to be not simply learnt, but understood.

geodob Wrote:In turn, I would suggest that this is equally relevant to Maths, where the words Addition and Subtraction, equally have visual associations.
Where the visual element constructs a cognition of the concept attached to these words.
Without this visual working memory association, information recieved cannot be transferred and applied to different contexts.
So in relation to Maths, it needs to be not simply learnt, but understood.

I think you are right about imagery and maths. I remember seeing a report about teaching multiplication. It framed the problems in the following ways,

Equivalent groups - There are 3 cars with 4 persons in each car. How many persons are in the cars?

Rate - Each token costs 8 cents. How much does it cost for three tokens?

Multiplicative comparison - There are 5 times as many cats as dogs. There are 3 dogs. How many cats are there?

Rectangular array - There are 4 rows of students. Each row has 6 persons. How many persons are there?

Cartesian product - There are 6 girls and 4 boys in the class. What number of boy-girl combinations are there?

As I recall they recorded the percent correct for each type of problem. They did not do a cognitive analysis of the problems but as you have indicated the visual imagery associated with each type of problem is quite different. The arithmetic for each of the problems has the same level of difficulty.
The image increases in complexity from the first to the last problem type. As would be expected the percent correct decreased with the complexity. The difference in score is not due to the arithmetic.

I think you may be able to explain this in terms of what you wrote.

I was inspired to write this after reading about framing problems in different ways.
I am teaching the division algorithm now. The first day I gave them a division problem in number sentence fashion: 72 d. by 9 (I don't have the ability to show the division sign, so I'm using d.) Here is the series of questions I had for them:
1. copy the number sentence
2. Write it in words (that made them think)
3. Write a story problem using this number sentence.
4. Write this using the division "house" 9)72
5. Write this in words (many wrote "nine divided by seventy two")
6. Write down the process of putting this problem on the calculator (many wrote nine d. 72 =)
7 Put this into an array of rows and columns
8. Write the multiplication fact that you would use to find this answer.

If I had just taught them the algorithm without going through all of this, they woud have learned the steps, but not what it meant. It's kind of like learning how to read, but not having comprehension.
Hopefully, as they become more adept at learning the algorithm, they will also increase their ability to apply this function.
One of my more capable students was very frustrated by not being able to remember all the steps (divide, multiply, subtract, bring down). I told him to remember what the guest neuroscientist said about learning is making new pathways, and repeating those pathways more and more ( this neuroscientist works with primates at the U of Washington). The more my student practiced, the better he would get. Lo and behold, the next day he was faster. Learning about pathways gave him reassurance that his brain was still functioning.

geodob Wrote:To add this, I've been looking at studies on Working Memory, and more particularly the distinctions between what is called Verbal Memory and Visual-Spatial Memory.
...
For example, if I say the word; Dog?
Do you simply see and hear the word ?
Or did you attach an image to it?
If so, was the dog standing, sitting or something else, as it flashed into your mind? What colour was the dog, and what breed?
...
where the words Addition and Subtraction, equally have visual associations.
Where the visual element constructs a cognition of the concept attached to these words.
Without this visual working memory association, information recieved cannot be transferred and applied to different contexts.
So in relation to Maths, it needs to be not simply learnt, but understood.

Your response is very interesting. I am often asked how situations like the one you describe can be put into a more explicit brain context. With your permission I would like to describe how I would deconstruct your statements (or construct from my elements) the situation that you describe.

You describe an external stimulus of a “dog”. This may be spoken, visual, or induced by saying “Think of a dog.” Any way this is done it is coming into the person from the outside world. It enters through the vertical channels of the nervous system.

At some point in the processing of the information the signals becomes isolated from the outside analogue world and become a part of the brain neural processing system. At this point everything becomes conjecture as there is no scientific model of this part of the process. The brain is, in my estimation, a massively powerful multitasking, multiprocessing, multimodal, state oriented computational system that operates on chemical and electrical principles in a topological network of neurons of many types. These signals are what makes up the brain and the fields of neuroscience and various forms of brain scanning and monitoring.

Now comes something that is our own scheme that has been very useful to us. We assume that the brain signals form some type of logical patterns. As such they are only logic, probably related in some way to axiomatic logic. I believe the logic is more complex but that axiomatic logic is a subset of the brains logic. A part of the logic is the associative nature of the brains cortex.

Logic on its own is bland. There must be some interpretation placed on this pattern of logic in order to have meaning. This is where the mind comes in. At this point the psychologists and other cognitive variants step in. It is at this interpreted level that educators and other real world people are forced to live and act.

The problems arise when a logical pattern can have more than one interpretation. There are many practical examples of multiple interpretations and there is even some brain scan data to support the idea.

We have now placed the Brain, the Mind, and the World in our BMW complex. Your “dog” stimulus is in the world. The memory types are in the brain, and your attributes for the dog come from the associative processing of the brain.

The facts are at the interpreted level(s) and are generated by the interpretations set up by the brain.

This may all be wrong, however, it sure helps us handle problems like this and most importantly I find it very practical in dealing with social and educational questions.

OECD Wrote:Do you encounter math difficulties in your students? And if so how do you cope with these challenges? Are there any formal measures within your school infrastructure to help identify and deal with math difficulties.
Please pose any questions you might have now to our OECD science expert in math difficulties.

I want to apply brain science in my classroom. I read about emotions and learning and I was wondering how I could make mathematics emotional in the classroom. I read an interview with Antonio R. Damasio in which he described the complexity of the field. Fortunately I could find myself in the “physical and social environment” so I know I belong there. Does anyone have examples or advice?

Bea Esser, I can refer you to an article on my website that addresses making mathematics emotional in the classroom. Generally, the piece is about making math fun instead of trying present it as something hard; the fact that it's on the college level is what makes it interesting.

As a teacher educator devoted to the use of play in communication and learning, I have found that playfulness goes a long way in reducing learning fears and resistances that often block positive feelings about math.

For more information about play and learning read my position paper that I presented to the OECD at the Emotions, Learning, and Education Symposium last fall.

Best,
Jeffrey Peyton
Puppetools

In regard to Maths and cultural differences, I've just been having a look at the history of Chinese Maths. Which evolved quite differently.
In traditional Chinese maths, to write the number 647 would require 5 symbols.
e.g.: A symbol for 6, followed by a symbol representing 'times 100'. Then a symbol for 4, followed by a symbol for 'times 10'. Then a single symbol for 7.
This evolved to a simplified model where to write the number 777 utilises 3 different symbols., representing either 700, 70 or 7. An entirely different approach. Also to carry out calculations, a separate Bamboo Rod system was utilised.
So it appears that their is some cultural differentiation.
Geoff.

papertalker Wrote:Bea Esser, I can refer you to an article on my website that addresses making mathematics emotional in the classroom.
Best,
Jeffrey Peyton
Puppetools

The article on your website was very interesting. I believe that curricula have been designed by mathematicians with the intent to create mathematicians. As the article implies there is another way to teach mathematics to those who will use mathematics and not create it.

It is interesting that they appear to be so successful at the college level, however, they are dealing with students who have successfully gone through the part of the education system where we are losing so many students. The question is whether the philosophy and ideas used at Williams College can be brought to the elementary classroom. The problem I have now is trying to understand what they are doing at Williams. Does anyone have references for this?

OECD Wrote:Do you encounter math difficulties in your students? And if so how do you cope with these challenges? Are there any formal measures within your school infrastructure to help identify and deal with math difficulties.
Please pose any questions you might have now to our OECD science expert in math difficulties.

I want to make a point first. If you have not yet read the FAQ
http://www.oecd.org/faq/0,2583,en_2649_1..._1,00.html
I recommend it.

The first question in the FAQ asks in part, “Is brain research too reductionist ...” and a part of the answer is:
“Brain research can be used to gain additional information or perspectives on questions of importance for education.”

I have been hoping that during some dialogue I would have an opportunity to discuss the following. The opportunity has not arisen so I will present it now.

As the FAQ states, at this time the important thing is new ways of thinking. Years ago I was doing some work related to traffic flow. New instrumentation was collecting data faster than people could figure out how to use it. One of the problems was the breakdown in traffic flow. The data showed that there were clearly two different modes of traffic flow. The problem was that the breakpoint between the regions was apparently random.

I had read in a British Journal ( I think something like Journal of Ergonometrics ) that they had studied the affects of mental work load on drivers. They had found that as they increased the work load the alpha rhythm of the brain would change.

I thought that this might be the reason that there is a sudden break in the way that traffic flows. If the processing load gets too high then drivers would change the way their brains process information and this would cause a transition in traffic flow mode. I made a model that said that the information to be processed depended on the speed of the vehicle and the density of the traffic.

This is logical. If there is no traffic on the road we drive as fast as we want. If there is a lot of traffic we slow down. Since mathematics is not numbers but logic I should be able to show this mathematically. I converted the logic to a model and sure enough the breakpoints fell right on the curve.

This shows one of the ways we take brain science and use it in practice now. Brain science gave me a new way to think about the problem. There was no treatise “ On Alpha Rhythm and Disruption of Traffic Flow”, nor has there been one since. But I was able to gain great insight into human behaviour. It was amazing that this to me was like the transition from deterministic physics to statistical physics where the statistical function of a population of drivers described their collective behaviour.

There are many similar opportunities that are available for educators now. This field is like microcomputers twenty-five years ago. The opportunities lie in thought experiments. Check the educational backgrounds of Dell and Gates. My guess is that everyone on this list is too educated to succeed as they have. (That does not mean that other ways to succeed don't require extensive education, because they do. What it means is that everyone fits into the goals the OECD has set for this project!)

Perhaps you might like to share your model with us, unless you have a problem with copyright?

I have a Personal Information Management (PIM) system that I use for my own purposes. The following is extracted from a file on brain and education matters.

I use the following Creative Commons license to assure people of their rights and to be sure that their rights continue.

Attribution-NonCommercial-ShareAlike 2.0
For any reuse or distribution, you must make clear to others the license terms of this work.
Any of these conditions can be waived if you get permission from the copyright holder.
Your fair use and other rights are in no way affected by the above.


Highway Traffic and Brain Operation

This undertaking is provided for the following reasons.
1.it shows a way that results from brain research can be applied to the analysis of real world problems.
2.this example shows how the brain can change its mode of operation and how this can be reflected in observable group behavior.


The Brain Research
Many decades ago, in the early sixties, I was involved in some studies of highway operations and I read an article in, as I recall, a British journal on ergonometrics. The article was describing a study in which the researchers were trying to determine the effects of cognitive processing load on driver behavior. The driver was given various cognitive tasks to do while driving under various conditions. For example, the driver would be asked to repeat a list of words or do simple counting tasks.

One or the observable that the researchers monitored was the driver's alpha rhythm during the experiment. It was found that if the processing load was high the frequency of the drivers alpha rhythm would drop.

The Traffic Flow Research

At that time I also saw some data from some freeway operations research sites that were plotted as volume-density plots. These data showed explicitly that traffic flow on the highways had at least two and maybe three distinct modes of operation. I felt that the two sets of research may be related.

Tying The Two Together

The implication that I wanted to make was that the apparent change in traffic flow mode was due to the human drivers information overload and therefore the manner in which they processed information in their brains changed. This appears to be a reasonable hypothesis but the idea needs to provide a model with observable measures for the logical assertion that under informational load the brain changes its operating mode and this is reflected in traffic behavior.

The EEG rhythms are classified based on their frequency ranges as: alpha - 8-13 Hz, beta - 13-30 Hz, gamma - higher than 30 Hz, delta- 2-4 Hz, theta - 4-8 Hz. I am not sure whether the researchers were seeing a drop in the alpha rhythm, a shift to another rhythm, or a combination of effects. My application of the research results is not predicated on the fact that the experiment was measuring the alpha rhythm only. For the argument that I am making that is irrelevant. All I care is that there is a sudden change in brain wave patterns, it is repeatable, it is caused by information overload, and it reflects a change in how the brain is operating. Since the report is in a respectable journal and the researchers are with respectable organizations I have no reason to doubt that what they communicate is true.

It is easy to make an error of assuming homogeneity of both flow modes, i. e., that the population of cars and drivers on the highway is not the same at all times. That is the subtle phenomenon. The drivers did not change. The drivers minds changed. We still have the same population of drivers, ----but, their minds are now processing in a different manner and this affects the system that we are trying to analyze. It appears that this is a fundamental property of the human being. I happens to all people and essentially under the same conditions. If I do not accept the fact that the population of drivers has changed then I am free to continue on with my assumption of a homogeneous population.

Joining Two Worlds

The above has set up a plausible explanation of why traffic flow may reflect results from research on brain processing. If this is true then how can we demonstrate it? Theories are only as good as their correlation with empirical results. The first thing to do is suggest a link between observable traffic parameters and the concept of information overload changing the brains processing mode an inducing a change in the observable parameters.

I developed a model of how traffic generates information for the brain to process. It is a simple model but in a gross manner rather pleasing. Simplicity always seems to be natures way.

To develop the model use a little empathy. As Einstein did, you sit on some of these particle or reference frames and do a thought experiment. In this case it is not to hard to imagine being a driver. As you sit in the drivers seat the more cars that are around you the more you have to pay attention to, i.e., the information load increases with the traffic density.

Assume that you are pretty much alone on the highway. You have to watch the road alignment, the signs, the exits, and other such fixed objects. The faster you go the faster you have to think about this information, i.e., the information load increases with speed.

And there is our model. The information the brain has to process (I) is

I = Cu × u + Ck × k
where
Cu is the rate at which information increases with speed
Ck is the rate at which information increases with traffic density
u is the free-flow speed, i.e. the speed when there are no constraints placed on a driver by other vehicles on the road - miles per hour
k is the (average) density of vehicles - vehicles per mile

Very simple - unless you have no sensitivity to brain operation and multi-modal systems. We now have the concepts and a model linking the worlds. What we need is a simple clear data presentation that would indicate whether or not this might be true.

Below is a graph that was prevalent in traffic theory. It is the volume-density curve in which the volume of traffic (vehicles per hour) is plotted against the traffic density (vehicles per mile). Density is one of our model parameters, but how do we see the other parameter, speed.
(the graph has been converted to text to accommodate the list)


Vol..............|
veh/hr........|.........X <--- linear flow mode
..................|,,,,,,X................... X........X
..................|...... X.......................... X X................................random congestion flow.
..................|......X........................ .........X............X
..................|.....X......................... ................X,,,X
.................X----------------------------------------------------------------
.................................................. ........................ density veh/mi

The slope of the curve is veh/hr ÷ veh/mi which results in mi/hr, or speed. Thus the volume-density curve is a good presentation for checking our theory. The first part of the plot is a straight line that says that on this highway traffic travels with a certain speed. As the traffic increases people maintain their speed until there is so much traffic that they can no longer stand it - and they change their way of life.
A problem that had occurred in real data was that the breakpoint of the plot appeared to be random when data from different days and times were compared. The slope of the first segment would remain the same. What changed was the point at which the flow would ?breakdown?.

Applying the New Model

To test the theory I took a set of days and estimated the point at which the regression line of the random data and the low level flow line would intersect. The coordinates of this point are in the first two columns of the table below.

Volume.............V/D
..........Density
82 ........45...........1.82
100.......51..........1.96
95.........50..........1.90
98.........40..........2.4
99.........46..........2.15
96.........51..........1.88
101.......41..........2.46

The average of the V/D values is 2.08 and the maximum deviation from this mean is about 15%. This gave we the confidence to assume that drivers are bimodal. There is much more to consider, however, this is a very promising first cut. If this is true then there are many studies of behaviors of human populations in which the time variant nature of the mind should be considered.

In the free flow mode the the speed is constant therefore Cu × u is a constant. Using this fact the equation for the maximum information rate is
(I - Cu × u) / Ck = k
All of the left hand side is a constant therefore the breakpoint should occur at a constant value of density (k). In the data the average is 46.29 and the maximum deviation is about 10% which implies that the prediction is better than 90% accurate which I take as rather good for such a crude model.

Thanks Karldw for sharing your most interesting hypothesis and study on traffic. It is currently a BIG question on how today's multimedia society of new millenium learners brains deal with many diverse inputs and all at once (kids doing homework, listening to music, engaging in a chatroom etc. all at the same time).
I found an article that may be of interested to the readers of this math thread:
Education Next, Spring 05 edition: "An A-Maze-ing Approach To Math"

OECD Wrote:Thanks Karldw for sharing your most interesting hypothesis and study on traffic. It is currently a BIG question on how today's multimedia society of new millenium learners brains deal with many diverse inputs and all at once (kids doing homework, listening to music, engaging in a chatroom etc. all at the same time).
I found an article that may be of interested to the readers of this math thread:
Education Next, Spring 05 edition: "An A-Maze-ing Approach To Math"

I think that this is a great article. It can be found at

http://www.educationnext.org/20052/28.html

I hope many others will read this and comment. I have much to say ( as usual) but must collect my thoughts.

OECD Wrote:I found an article that may be of interested to the readers of this math thread:
Education Next, Spring 05 edition: "An A-Maze-ing Approach To Math"

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.

January 21, 2006

Hi Fourth Grade Teacher....
Is this the subject that you were looking for......?
Best,
Rob

thank you for digging this out. Looks like I have a lot of reading to catch up on.

Hi 4th grade teacher,
Welcome back.
I was happy to see that you are reading a book on the important issue of Sense of Number. This remains a major factor in the 8% of people with Dyscalculia.
Maths acquisition can only develop from the base of a Sense of Number.
Without it, maths rely purely on rote memory.
Numbers do not have quantity?
For example; the number 4 is identified by counting out 1,2,3,4.
In the same way as D is found in the alphabet, A,B,C,D.
Where the order of placement of D in the alphabet, has a similiar rationale?
Without a sense of number, 4 + 4 makes as much sense as D + D.
Geoff.

I thought it interesting that there was mention that in Michigan the “benchmarks” can be lowered for students struggling in math. In Washington it has been made emphatically clear that benchmarks will not be lowered for students struggling with learning math, but that we must find a way to raise the student’s achievement to meet the same standards as all other learners. As you can imagine this causes a great deal of anxiety among teachers and places a great deal of stress on students. (Not, I must add, healthy stress that helps the student focus and learn, but negative stress often leading to frustrations and eventual “shut down” by the child.)
It would seem to me that with all we have learned about the brain’s different rates of development there would be a move away from judging a child’s success based on age specific standardized testing (that is, “you will know all of this at age 10, and this at 14, etc”) and a move towards a system that recognizes individual development and readiness, then uses that as the criteria for success.

Hi Kepeow
I must quote your words:
"It would seem to me that with all we have learned about the brain’s different rates of development there would be a move away from judging a child’s success based on age specific standardized testing (that is, “you will know all of this at age 10, and this at 14, etc” and a move towards a system that recognizes individual development and readiness, then uses that as the criteria for success."

You have said it all!
If after all of the words that have been written on this forum, your statement was used as a summary, I would be very happy.
In a simple concise statement,you have said it all!
A model for Education for the new Millenium!
A model of education "that recognises individual development and readiness, then uses that as the criteria for success."

Under such a model, no Student would be made to feel a Failure, but simply be aware of their current state of development and awareness.
On their life-long pathway of learning.
Learning as a journey with different arrival times at points along the path for each of us.
Just because I stop and look around along the way to the next point on the path. Do I need to be classed as a failure, and made to feel that I shouldn't bother continuing on the path of learning?
Not a Slow Learner, just a Slow Walker.

The major issue with not recognising "individual development and readiness".
Is that an individual's level of development and readiness can even be considered as a failure?
This is absurd! It is not a race to the finish line?
It is a lifelong journey of learning.
Where the vital element is to maintain one's confidence and motivation to continue on the journey of learning!
The word failure should removed from the education system, and replaced with a recognition of individual development and readiness.

Anyway kepeow, I liked the way that you put it!
Geoff.

I'm really excited by the discussion in this thread and have got a lot of reading to catch up on.
I'm a postgrad psychologist conducting a longitudual research project into working memory (temporary storage and processing) and mathematical abilities. I'm closely linking the maths abilities to the UK National Curriculum.

I'm considering using interventions with the children with poor mathematical abilities and poor memory skills to see if attention training will help imrove both the maths and memory skills. I'm hoping to do this sometime in the coming year (after I have finished my final phase of data collection).

I know of many colleagues working in a similar area and I have lots of information regarding how working memory is implicated in scholastic acheivement especially maths, but really not a whole lot regarding possible interventions, or diagnostic measures (aside from the Dyscalculia Screening tool) in psychological literature.

Thanks for your post. This work sounds most interesting! I am sure that our forum members would very much appreciate learning about your research.

Best wishes,
Christina

A related topic is now getting a great deal of press here in the United States, that is the difference between male and female brains and learning. You can read an article on this topic in Newsweek at:

http://www.msnbc.msn.com/id/10965522/sit...k/from/ET/

The article speeks to the implications of both how we teach and how we measure learning.
This relates to math in that we (I mean here in Washington State) are placing a great deal of emphasis on written responses to math questions, leaving those with less developed verbal skills to stuggle not only with math concepts but how to express their answer.

glen_penn Wrote:I'm really excited by the discussion in this thread and have got a lot of reading to catch up on.
I'm a postgrad psychologist conducting a longitudual research project into working memory (temporary storage and processing) and mathematical abilities. I'm closely linking the maths abilities to the UK National Curriculum.

I'm considering using interventions with the children with poor mathematical abilities and poor memory skills to see if attention training will help imrove both the maths and memory skills. I'm hoping to do this sometime in the coming year (after I have finished my final phase of data collection).

I know of many colleagues working in a similar area and I have lots of information regarding how working memory is implicated in scholastic acheivement especially maths, but really not a whole lot regarding possible interventions, or diagnostic measures (aside from the Dyscalculia Screening tool) in psychological literature.

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.

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?
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?
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'!
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?
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?

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?

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.

Geoff good news for me, i have just obtained financial help for the production and initial distribution of abacus one, a friend of mine who has just won the lottery has already assisted and i have also managed to get a group of none teacher head of departments from my favourite bank HSBC to review a trial to be carried out under a newly trained reception class teacher, working in a failing london infant school,after the half term.
have i said or done anything wrong in my correspondance with you,
you have not advised my of your comments on the stuff i sent you.

i can now pack and post 100 abacus to you if you will supervise a small trial with your local children.

no offence intended

john

Good Morning 2-4-06

I would be very very interesting in your comments regarding any phase of the enclosed executive summary on math retrieved from the internet 2-3-06.
Thank you.
Rob
URL: http://www.citeducation.org/mathmatrix/T..._early.pdf