math and chess
17 Feb 2010
Dyscalculia Children Cases Documented – Article 1
Canada certified math teacher
Ho Math and Chess Learning Centre
January 2, 2010
After starting to pay attention to dyscalculia children, I noticed there are some general symptoms emerged from those children.
There are many different views on how dyscalculia shall be defined. A neuroscientist might define it from the scanning result of a child’s brain, a psychologist might define it from the result of psychometric test, and a math educator might define it as a result of a math ability test. As a math educator, my interest is to observe and to find out why a dyscalculia child has fallen through crack and what I can do about it? My observations are:
1. It could happen when children are very young even as young as 5 years old, at this stage many parents will draw their own conclusions to be just because their children are young.
2. Dyscalculia could also persist to older grades like grade 7 and after this, the symptoms start to appear unnoticeable to parents since they are allowed to use calculators but could be detected by very experienced math tutors by watching and examining their calculation steps. A decisive sign is they never seem to be able to keep math at A regardless how much efforts math tutor has put in.
3. It may have something to do with their general intelligence level although some parents only complain about their children’s math marks.
4. Dyscalculia children may be very talkative but when asked math questions, all the sudden, they become different persons - they are very quiet. When asked the reasons why they gave some answers, they normally could not say anything. There were confused about their own answers and simply could not make a reason themselves why they gave an answer – no reason given.
5. They seem to have poor memory and are not able to get answers using taught knowledge. For example, if 5 + 5 = 10, they know it but when asked 5 + 6 or 5+ 7 is what then they might get confused.
6. Their response time to get answers is normally longer then non-dyscalculia children.
7. They cannot do mental math, instead, they use fingers to physically count each number to get answers. All calculations are done with the idea they can physically see or touch to get answer. They do not know how to transfer the computational procedure to their brains.
The following documents my experience with children who have learning difficulties in learning arithmetic.
Case 1. Boy A, grade 4.
On the second day (January 3, 2009) of class, I tested him both in writing and orally and found out he seems to have dyscalculia and his parent apparently is not aware of it. His father mentioned that he also had English reading problem and after getting special help from school, he is now better. Father mentioned that his school did not teach him math. Boy A could do 7 + 5 = 12 but when asked orally about what was 5 + 7, he did not know or would give some illogical answers. Many dyscalculia children do not seem to understand commutative law. After using objects to explain, he understood but gave wrong answers when the same question was asked again later. He could not do 11- 2 or any borrowing at all at grade 4. He could not do what is 5 plus 10 or sometimes he could do but he could not do it again if the numbers changed to 10 + 7. He has no sense of how a ten can be added to 5 and he could not see the pattern when a single digit is added to 10.
I am going to give him some special worksheets so he has a chance to actually write out each questions to reinforce his memory and these questions are also specially designed so that he should be able to “see” patterns between each question.
January 4, 2009
I invited Boy A to come for a further review since I wanted to know if he has some memory problem and a simple test shows that his memory is average. I asked him how he did his calculation and he told me that he was taught to count the number of dots when doing addition. For example, 3 + 2 he would count 3 dots and then 2 dots to get 5 and then he carried on to use this method to do all addition and subtractions. He uses fingers to do additions or subtractions and sometimes he feels he does not have enough fingers to do calculations. This could be a source of his problems that is a way of teaching concept was then carried on by him as a procedure of doing all calculations, a big mistake. Boy A never learned the technique of comparing computation patterns and school work did not provide him with enough practices to hone his skills and also he did not have the innate to get number sense by himself.
I start to suspect the teaching method of addition and subtraction at schools might be problematic for some children.
For example, when adding 5 + 3, students were taught to draw 5 dots and then 3 dots so a child would count each dot sequentially to get the answer 8. If a child starts to use this method (by drawing dots or use fingers) for all his additions then it would be a problem when this child is doing additions by counting each dot sequentially, the child will never get the fluency of addition. In most math teachings, dots, fingers, beans are often used as manipulative for this kind of sequential forward counting or backward counting for teaching addition or subtraction; children will have problem with subtraction since they did not get the idea of part1 + part 1 = total. So when doing the reverse of addition (subtraction), it will be difficult for them.
They were taught to count, skip counting using dots etc, but were not taught on how to add by relationships, logic, and comparisons etc. techniques.
They need to be taught on how to use “techniques” to do addition and subtraction, not by counting. There is something wrong with our school math education at the beginning level.
I guided him by using comparisons between adding numbers and taught how he could use different techniques to do computation instead of relying on counting fingers.
In 2-hour of work, he already showed improvements in his speed and accuracies to get answers right, his rapid improvement is encouraging. I assign some homework, which reinforces pattern and also counting of adding up to 10 and also doubling. All these are aiming to get him away from using fingers but to use more of his brains to figure out answers him self.
January 9, 2010
Boy A has improved. He is able to do one digit addition rather quickly and without counting every numbers to get the total.
His improvement is remarkable. When compared to a girl whom I taught but did not show significantly improvement the reasons were:
1. Her parents not only wanted to see improvements in her basics such as addition, subtraction but also insisted that we should help her on her then current schoolwork and hoped she could get “good” marks. This approach put lots of pressure on her and she simply did very little practice on her basics.
2. Her parents’ emphasis seemed to be on marks but not to give her time to be fluent with basics.
3. The girl “tells” her parents what she wants to do, not the other around, she is the queen and parents are just servants.
January 27, 2010
Boy A still progresses but has slowed a bit since for twice I a row, he did not do any homework I assigned to him. He told me he was too busy. He is now able to do reverse calculation so he is still significant better then he was when he first attended Ho Math and Chess math class. I phoned his father to tell him that Boy A needs to continue to do work at home, his father asked me how he is doing and I honestly told him how I felt he has made progress. I feel strange that he did not give me any feedback how he has felt about his own son’s status so far.
January 30, 2010
Boy A has not been doing his homework; I am disappointed so he was asked to do his homework in my class. His progress has staled but is still much better than where he was when joined my class.
February 14, 2010
I am somewhat disappointed about Boy A’s progress since today I discovered that has done some pages very wrong when carrying over 1 to hundred’s place. This errors can be very easily checked and stopped at home only if his parents could spare a bit time to check on his work but despite my request the cooperation was not forthcoming. The teaching has been dampened by Boy A’s showing of interests in taking a bit challenge at all when some of my invented new worksheets were showed to him.
I feel like to close this case with the following observations:
1. A child needs to be helped with parent’s active involvement at home or at least monitoring.
2. The child has to learn to take an active role in learning, it does not help if a child shows no interest in understanding concept teaching but only wants to know how to work out the procedure and be done with homework.
Case 2. Boy J, kindergarten
January 20, 2010
This boy is very interesting because all he wants is to play chess but he does not think while playing, only interested in pushing “wood”. He gets mad and even threw pieces around if he loses games. He eyes look at other side way when I tried to explain to him on how to do worksheet, he would not even allow himself to have a chance to listen other than asking for candy or play chess. This is a very tough case to handle. He does math by physically count each object so 5 + 2, he will count 5 fingers and then plus 2 fingers or he will draw 5 circles and then 2 circles to get answer.
I asked his mom what interests him, maze is what his mom told me, so I created a chess maze for him but to make a move he needs to calculate some simple math to move around, he will not even listen to me on how the maze should be played. I had to give it up and asked his mom to try it at home. He refused to do it by scribbling random lines on the entire maze I printed for him so the maze is basically defaced and announced uselessness to work on.
I then created some number mixed with dots to mimic his way of doing finger math but trying to get him away from using fingers or drawing dots so his calculation will be slowly transferred to his brain without physically using fingers or dots. I await his response when I give to him in the next class.
Chess teacher has to constantly remind him to sit nicely and pay attention.
Boy J’s mom told me that when Boy J was young his grandma always let him to have his way and this even caused conflicts between mom and grandma on how to educate Boy J.
Boy J is difficult for me to say if he has dyscalculia or not since he is just beginning to learn math, one thing I can see is he does not want to do it, and he only wants to do some tasks, which he does not have to use a lot of thinking. This is evident in his way of playing chess since other than trying to follow chess rules, he is not interesting in any “cause-consequence” effect.
January 30, 2010
Mom did not stay with Boy J and he did not want to do any math work so mom asked him to be sent to the chess class. I asked mom to supervise Boy J to do the new set of math worksheets at home.
February 14, 2010
Boy J’s mom is taking an active role in helping her boy at home and she also make sure that he would finish all his assigned homework, he continue to make progress and does not count on his fingers to get answers when doing 1-digit to 1-digit addition, but still having trouble to sit straight in his seat to do work other than playing chess. I have given him more worksheets especially designed for him to continue to encourage him to work on math worksheets.
Perhaps when he gets a bit more mature then he would overcome his own weakness by not being able to sit at his own seat and does work. Now his mom has to sit beside him to get him to do work, and this is not a long-term solution of course. He is able to sit down when he plays chess but is not able to sit down when he does math.