- Memory and Learning Math
- Factors that can handicap learning math
- Math Skill Assessment
- Our Math Intervention Approach
- The Principles behind the math teach at Lexicon
Lexicon Reading Center is guided by internationally regarded research and understandings of Specific Learning Difficulties.
How is dyscalculia, a specific learning difficulty for learning math, defined?
The British Dyslexia Association has adopted the Dyscalculia definition used by the UK Department for Education in 2001:
‘Dyscalculia is a condition that affects the ability to acquire arithmetical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number facts and procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence.
A more recent definition, from the American Psychiatric Association (2013) of Developmental Dyscalculia (DD) is:
A specific learning disorder that is characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculations.
These difficulties must be quantifiably below what is expected for an individual’s chronological age, and must not be caused by poor educational or daily activities or by intellectual impairments.
Typical symptoms of dyscalculia/mathematical learning difficulties
A learner may present with all of these characteristics, but there should be concern if many are evident.
- Has a poor sense of number, for example, cannot ‘see’ that four items are 4.
- Has difficulty when counting backwards.
- Has difficulty counting in quantities other than 1, for example, in 2s, 5s or 10s, especially when starting with a number other than zero, such as 7.
- Finds estimation very difficult, including with money.
- Has difficulty in remembering ‘basic’ facts, despite many hours of practice/rote learning.
- Has no strategies to compensate for lack of recall of these facts, other than to use counting.
- Has difficulty in understanding place value and the role of zero in the Arabic/Hindu number system.
- Has no sense of whether any answers that are obtained are right or nearly right. This is linked to poor estimation skills.
- Tends to be slower to perform calculations. Pressure to work more quickly is likely to create anxiety.
- Forgets mathematical procedures, especially as they become more complex, for example ‘long’ division.
- Addition is often the default operation. The other operations are usually very poorly executed (or avoided altogether).
- Avoids tasks that are perceived as difficult and likely to result in a wrong answer. Withdraws from maths.
- Has great difficulty with mental arithmetic.
- Difficulty with understanding time.
- Finds it hard to see patterns and inter-relationships in numbers.
- High levels of mathematics anxiety.
Because mathematics is very developmental, any insecurity or uncertainty in early topics will impact on later topics, hence to need to take intervention back to basics. Any early learning that is incorrect, for example, thinking that 6 x 7 = 67, is very resistant to correction.
Memory and Learning Math
Factors that can handicap learning math
There are a number of factors that can be behind the math learning difficulties exhibited by a child.
Math Skill Assessment
Our Math Intervention Approach
Starting at the student’s current level as determined by the thorough assessment above, we work to develop math skills using a multi-dimensional approach :
The Principles behind the math teach at Lexicon
The programme is about teaching mathematics concepts to learners and building understanding. .A child who is failing in math should not be denied conceptual teaching.
- The focus is on the learner and so the factors that influence the ability to learn are recognised and addressed in lessons. These include poor short-term memory, weak (and inaccurate) mathematical memory, speed of processing, working memory, language, vocabulary and affective issues such as anxiety.
- Research into maths learning difficulties, teaching and into dyscalculia has guided these principles as has experience of training teachers in some 30 countries worldwide and 24 years of teaching experience with students with learning difficulties.
- There is an attention to detail, for example, topics are carefully and exhaustively analysed to identify what might confuse or be a barrier to the learning process.
- Intervention uses core facts, reducing demands on long-term mathematical memory. Students are shown how to extend these to access other facts by constructing and deconstructing numbers.
- Strategies to access facts and procedures are used to reduce the sense of helplessness that many students experience in math when their memory fails them.
- Listening to, responding to and encouraging feedback from learners is a part of the instruction process.
- Meta-cognition is taught and encouraged. Different cognitive styles are acknowledged.
- Learners are encouraged to analyse and think before acting.
- Helping the student to understand math is a key factor in developing concepts and supporting long-term memory. Fallible memory skills are recognised and circumvented as much as is possible.
- The programme includes frequent reviews.
- Estimation, operation sense and number sense are used to develop concepts and confidence.
- Generalising and pattern recognition are guided to encourage accurate learning and reduce the load on long term memory..
- Diagnostic teaching and the recognition of error patterns are key elements.
- Anxiety and motivation are addressed by ensuring experiences of meaningful success and by managing failure.
Frequently Asked Questions:
1. What makes a good math learner?
The structure of mathematical abilities from Krutetskii:
Krutetskii (1976), presented a broad outline of the structure of mathematical abilities during school age, that is, the following abilities are needed to be successful at math
- The ability for logical thought in the sphere of quantitative and spatial relationships, number and letter symbols; the ability to think in mathematical symbols.
- The ability for rapid and broad generalisation of mathematical objects, relations and operations.
- Flexibility of mental processes in mathematical activity
- Striving for clarity, simplicity, economy and rationality of solutions.
- The ability for rapid and free reconstruction of the direction of a mental process, switching from a direct to a reverse train of thought.
- Mathematical memory (generalised memory for mathematical relationships), and for methods of problem solving and principles of approach.
These components are closely interrelated, influencing one another and forming in their aggregate a single integral syndrome of mathematical giftedness.
2. What are the cognitive functions that affect learning math?
This question is answered in part by Krutetskii (FAQ 1)
A child also needs a good short term memory and a good working memory. These abilities are especially critical for mental arithmetic.
3. What is mathematics memory?
It is the ability to retrieve from long term memory, usually quite rapidly, mathematical information, for example, basic facts and procedures.
In line with Howard Gardner’s theory of multiple intelligences, it is possible that there are multiple memories, so that a child may have a strong memory for musical information and a weak memory for mathematical information.
Some children learn to enhance their mathematical memory by using linking strategies and patterns. Some children do not do this themselves and have to be guided and instructed to achieve these strategies.
4. How does slow process speed results in math difficulties?
Partly this is the culture of math, especially with mental arithmetic or retrieving a basic fact, The child is expected to answer quickly. Unfortunately, this will make some children anxious and anxiety tends to exacerbate the problem.
Secondly, when performing metal arithmetic the limited capacity means that there should be minimum demand for accessing the facts, and procedures, needed to answer the question. If this takes time, it increases demand on WM and can lead to failure to answer,
5. What is the difference between short term memory and working memory while learning math?
First, consider a common characteristic. Neither of these memories store information. If it is lost from memory there is no way of retrieving it. It has to be provided again. This is a critical understanding for the classroom.
Stm holds information for a short time. It is about recalling the information for a short time. An example would be to remember a phone number while you key it into the phone. Capacities vary and tend to get better as a child gets older. This is not always so. For a child or young adult with a stm capacity of 3 items, information that requires 4 items to be recalled will be an impossible task. That communication will be ineffective and frustrating for both child and teacher.
WM works on information. A classic example is mental arithmetic. The child uses WM to compute an answer and stm to remember the question as WM is working on it. If a computation has 5 steps and the child’s WM has a capacity of 4, the child will fail.
Thus these have serious implications for performing maths.
6. Why does your math assessment involve cognitive assessment?
Partly to get a comprehensive picture of the child’s cognitive abilities and partly to set a guideline base for expectations of performance. (Note the APA definition of dyscalculia).
7. My child relies heavily on counting while studying math. How can this be overcome?
Over reliance on counting in ones is a very great handicap in developing mathematical skills. Among other influences, it handicaps generalizing and recognition of numerical patterns.
This reliance is comfortable for the child. Since it will require much effort to overcome it, the child may need much encouragement and motivation to attempt the task. In early math it works, making it even harder to encourage the child to move on.
Thus intervention will have to motivating, primarily by generating success and showing the child that the new approach is more efficacious. Patterns, with materials and visuals will be essential. This will be a key intervention for developing math skills and concepts and one where specialist intervention is essential.
8. How is your math intervention program different from regular math tutoring?
In its use of visual and manipulative materials to support conceptual development. It also acknowledges learning factors such as stm, WM, the need for consistency appropriate pacing of the work and weak recall of facts. The approach is tailored to the individual.
There are so many factors that can create failure in math, that a preventive approach, based on a pragmatic awareness of these factors is hugely beneficial
9. How often you assess progress? How do you monitor progress?
Our teaching is diagnostic, so there is ongoing informal monitoring of progress. This is backed up by using worksheets diagnostically and finally by more formal testing at longer intervals, that is, termly.
How can I make my child less anxious about math?
By reducing the pressures and expectations and giving the child experiences of meaningful success. Expectations are frequently misunderstood and often applied in ways that almost guarantee failure for too many children. Expectations have to be ‘unanxious’ and constantly adjusted as the child develops. They have to be set to stretch the child without setting , in the child’s eyes, unreachable targets.
Discuss the way math is perceived by the child, the family and society. Show how there is much math in everyday life and that the child already can do many things, Focus on praising the work rather than the child. That way failures are not personalized. Encourage lots of estimating as a way of developing number sense.
How can I help my child learn the basic facts?
Teach them strategies that link the facts (and teach more math as well). For example, show how 5 + 5 = 10, which is easier to recall, can be extended to 5 + 6, 6 + 5, 4 + 6
If rote learning hasn’t worked then find an alternative.
What games will help my child understand numbers?
Numbershark and Nessy have good programmes.
Can I help my child to do math quickly?
This is a very big challenge and the quick answer is ‘Probably not’. General intervention programmes may well lead to this outcome as a side benefit. Practice to make work quicker might be counter-productive in terms of anxiety.
Why can’t my child tell the time?
Time has many challenges and, for the child, inconsistencies. Instead of base ten, they now have to work in base 12 and 60, the analogue clock face is a circular, not straight, number line, children have to count backwards (25 minutes to 8, 24 minutes to 8…..). Early experiences of failure will not help. Digital clocks may help a child to ‘tell’ the time but may not help them understand the concept of time.
Steve Chinn, PhD AMBDA FRSA
Steve Chinn founded Mark College, a specialist school in the UK for dyslexic students, in 1986 after being Head of a specialist school in the USA. The College gained several awards, including Beacon School status from the UK government. This award, in addition to recognising excellence, funded the College to train teachers to use Assistive Technology and how to teach students with math learning difficulties/dyscalculia. The College was a pioneer in both of these areas.
Dr Chinn has studied and researched math learning difficulties for over 30 years. The 4th edition of his seminal book, ‘Mathematics for Dyslexics and Dyscalculics’ and the 3rd edition of his award winning book, ‘The Trouble with Maths’ were published in 2016. He has written many papers and has contributed chapters to many books. He was editor of ‘The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties’ (2015).
He has lectured and trained teachers in thirty countries. He Chairs the British Dyslexia Association’s dyscalculia committee.
Dr Chinn is a consultant for Lexicon and lectures at their workshops and conferences. He advises Lexicon on teaching math to students with dyscalculia and math learning difficulties.