Sudha Ganesh Chella and Anuradha Jaishankar
Mathematics has a rich history of being considered the most difficult subject in school. So much so that many people consider it a “badge of honour” to say that they were bad in mathematics when in school. These difficulties were generally attributed to a lack of intelligence or hard work.
However, in the past few decades, there has been a lot of research into understanding the reasons behind these difficulties. Three major types of difficulties have been recognized; those related to the nature of mathematics as a discipline, those related to the way it is being taught and others related to the learner herself. It has also been recognized that all three are related.
Some learners have certain learning difficulties possibly related to genetic or brain structures. The underlying causes for many of these conditions are still not fully known. In most cases there is no effect on general mental functions.
The most commonly encountered conditions are dyslexia and dyscalculia. Dyslexia relates to difficulties in reading and writing and dyscalculia to difficulties with mathematical concepts and ways of thinking.
We would like to clarify here that the term “mathematical ways of thinking” implies far more than the concepts and skills that we learn in mathematics in school. It involves a wide range of cognitive skills for understanding and transacting any body of knowledge.
Though dyscalculia may not affect language learning in a significant way, the reverse is not true. This is because, ultimately even mathematics has to be understood and expressed through the medium of language. The other learning difficulties namely dysgraphia (issues in handwriting), dyssemia (difficulty in spatial orientation), dyspraxia (difficulty in motor coordination), dyslalia (issues in articulation), and dysphasia (difficulty with language) also have a significant impact on a child’s overall learning ability.
In this article, we will try and describe some of the difficulties such students face in learning mathematics under three broad headings – Basic developmental deficits, Perceptual difficulties and Cognitive deficits.
Basic developmental deficits
Children with physical and motor developmental delays face gross and fine motor issues. When a child has difficulty in stringing beads or in jumping, she misses the early math learning experiences that happen at home during the initial years of 1 to 3.
Sensory integration issues
Lack of synchronicity in functioning of various senses leads to sensory integration issues and also impairs brain-body connections. Such a child will have issues in eye-hand coordination and poor perceptual number sense. These result in delay in learning pre-number concepts like more/less, big/small, colours, etc.
A child picks up many of the pre-number concepts such as one/many, long/short at home during the early years. Delay in speech impacts the early expressive language of math. They don’t get to speak and practice words like more, less, one, two, etc.
A child finds it difficult to stay on task either due to attention deficit hyperactive disorder (ADHD) or attention deficit disorder (ADD). In either case, lack of attention affects concentration and thus impairs learning in all aspects.
Good memory is essential for learning, retention and retrieval of concepts, facts and skills. Children may have difficulties in both short-term memory (remembering a number during carry over addition, copying a number from the board) and long-term memory (recalling a formula or a multiplication fact). Difficulty in recalling math facts like tables, labels, procedures such as long division, multiplication, etc., are some of the difficulties faced by children with poor memory.
Though it sounds like an easy task, counting in various contexts requires specific cognitive skills. If the concepts of “one to one correspondence” is not internalized, she grows up to have difficulties in counting from memory, counting the sides of an object like cube, counting objects with increasing criteria (number of square pieces with green on top and blue at the bottom), counting objects in motion, counting while moving, etc. It later poses difficulties in skip counting, computation of numbers, handling money and time, etc.
A child with difficulty in letter-sound association can find it hard to correspond a numeral to its quantity. This manifests as lack of number sense, inability to compare quantities and understand basic operations, reading a word problem and writing statements.
A child with poor language skills will not be able to comprehend commonly used words in a math context (balance, appreciate, etc.), math specific vocabulary (perimeter, hypotenuse) and word problems.
A good spatial orientation ability helps children perceive sides (front, back, left, right) and directions. Clarity on direction and position is important to understand topics like place value, basic operations, graph and geometry. Lack of this skill makes it difficult to learn place value, ascending and descending order, understand the characteristics of a shape irrespective of its orientation, addition and subtraction with regrouping, signs, etc.
Time has always been a difficult concept for young children. If the child is unable to perceive the idea of time, she does a poor planning of time (always in a hurry or too slow), struggles to follow the units of time like minutes, hours, days of the week, months of the year, concepts like before and after.
Lack of closure
The idea of part-whole relationship is an important concept to comprehend topics such as shapes, graphs, geometry, mensuration, etc. The child who has lack of closure, sees the parts of a whole as independent entities and misses the connection between them. All diagrammatic representations become a challenge for him.
Identification of characteristics of different shapes
The ability to identify and discriminate each shape/size is a prerequisite to learn geometry. When a child is unable to internalize the characteristics of a figure properly, he will have issues in identifying shapes and angles based on inter-class and intraclass differences.
If a child is unable to sort and group things based on specific criteria, she faces difficulties in understanding properties of numbers and their relations (odd and even numbers, factors, multiples), identifying shapes, mensuration (area, perimeter), etc.
A child who struggles to match oral instructions with visual content finds it hard to follow instructions and copy from the board. This can severely affect classroom learning.
There are cognitive deficits which affect learning in a general way – Information gathering, information processing and information output.
Information gathering – lack of systematic information gathering, inability to filter the relevant from the irrelevant, poor attention and improper perception.
Information processing – comprehension, problem definition, sequencing, comparing, hypothetical thinking, extrapolation, estimation, logical thinking, analysis and synthesis.
Information output – Improper geometry work, illogical answers due to impulsivity, not writing the units, statements, incomplete work, lack of details, inability to communicate effectively.
Educating children with learning difficulties
Educating children with learning difficulties in integrated classes can be a challenging experience for the teachers. These students will need to be taught differently and require time to comprehend, assimilate and internalize concepts. Revisiting the concepts regularly helps them.
But teachers need to remember that these learning difficulties get amplified when such children are stressed or under pressure to perform. Unconventional assessments are better tools to understand such students’ conceptual clarity and performance.
Children with dyscalculia may not have all the issues listed above. Also, dyscalculia can occur in isolation. It may or may not happen along with dyslexia, ADHD, etc.
Grow with math program
Diksa Learning Centre has been running a program, “Grow With Math”, for the last three years, combining our understanding of learning difficulties with multi-sensory ways of learning math. Some of the highlights of the program are
- Mirroring primary math concepts through simple manipulatives, personal life experiences and role play (see box for how you can do this in your classroom).
- Visualization of numbers, number properties and number relations.
- Structured, sequential and interactive sessions with a spiral curriculum.
- “Math Chat” time which encourages students to share their math experiences in daily life and develop their language ability.
- Multi-sensory learning through visual, auditory and kinaesthetic activities.
- Creatively designed activity sheets.
- Activities and activity sheets that aim at developing logical reasoning and inculcating mathematical thinking in students.
- Peer interaction and peer learning.
- Projects involving life skills math.
The program has helped children overcome their math phobia and instilled willingness to learn and experience mathematics. Regular exposure to real life math situations helps them see the connection between learning and experience. Students are willing to talk ‘math’ in the classroom. They are keen to try new and different methods. They are able to ‘mathematize’ simple problems. Overall, there is a tremendous increase in motivation and understanding in the students.
Using simple manipulatives – place value concept can be mirrored with ice cream sticks. A set of 10 sticks bundled using a rubber band will mirror the idea of tens. So 32 can be represented with 3 bundles and 2 sticks, whereas 23 can be represented with 2 bundles and 3 sticks. It also visually shows the student that 32 is bigger than 23. It does not require a rule to be memorized.
Personal life experiences – Our life is full of events which mirror the four arithmetic operations – addition, subtraction, division and multiplication. On your birthday, getting two gifts from your school friends and three gifts from your relatives, mirrors the idea of addition. You have a total of five gifts and can be written as 2+3=5.
Role Play – Imagine an activity when one student is asked to take 12 crayons and distribute them equally to four students.
At the end of above exercise, he will realize that he has no crayons with him and also that each student has got three crayons.
This mirrors the idea of division and can be written as 12÷4=3.
Sudha is a post graduate in child development and family relations and a BEd in special education. She founded Diksa, a centre for children with learning difficulties in the year 2000. Sudha was recently honoured by the Rotary Club of Madras North with the Rotnorth Aasan Award for her contribution to the field. She was also honoured by CHILD – Centre for Holistic Integrated Learning and Development for her outstanding service and dedication towards individuals with learning difficulties. She can be reached at [email protected].
Anuradha Jaishankar is a Special Educator working with Diksa for the last 12 years, teaching children with dyslexia. She is an Engineer and a Post Graduate in Childcare and Education. She specializes in teaching math to children with learning difficulties and life skill math to young adults. She has completed standard levels 1 and 2 of Instrumental Enrichment program from ICELP, Jerusalem. She has participated in several International Conferences on learning difficulties and primary math workshop conducted by the University of Cambridge. She plays a key role in conducting the “Grow with Math” program of Diksa. She also trains teachers on effective teaching of primary math. She can be reached at [email protected].