Triveni Goswami Vernal
(Registered Special Educator CRR No. A64010)
In the previous blogs, I have written about Subitizing (the ability to visualize or see the number of items in a small group instantaneously, without having to count them one by one) and the critical role it plays in Dyscalculia and Math Learning Difficulties. I have also written about the use of Dot Cards, Cluster Cards and Cuisenaire Rods in Subitizing.
In today’s blog, I will be writing about the mathematical operations of Addition and Subtraction and the use of various visual tools, like Dot Cards, Cluster Cards and Cuisenaire Rods (resources shared at the end of the blog) for the same.
Rochelle Kenyon, has listed several strategies for teaching a student with math learning disabilities, (https://www.washington.edu/doit/what-are-strategies-teaching-student-math-related-learning-disability),
• “Avoid memory overload. Assign manageable amounts of work as skills are learned.
• Build retention by providing review within a day or two of the initial learning of difficult skills.
• Provide supervised practice to prevent students from practicing misconceptions and “misrules.”
• Make new learning meaningful by relating practice of subskills to the performance of the whole task.
• Reduce processing demands by preteaching component skills of algorithms and strategies.
• Help students to visualize math problems by drawing.
• Use visual and auditory examples.
• Use real-life situations that make problems functional and applicable to everyday life.
• Do math problems on graph paper to keep the numbers in line.
• Use uncluttered worksheets to avoid too much visual information.
• Practice with age-appropriate games as motivational materials.
• Have students track their progress.
• Challenge critical thinking about real problems with problem solving.
• Use manipulatives and technology such as tape recorders or calculators.”
For individuals with Dyscalculia and Math Learning Disabilities (MLDs), visual representation of the strategies used, for the various mathematical operations, is of great significance and the key to their learning process.
Special Educator, Consultant and Coach, Rebecca Lord, lists out the various ways in which Addition and Subtraction can be taught using manipulatives such as Dot Cards, Counters, etc (Decoding Math, https://www.lordmath.com/online-learning/).
Addition and Subtraction:
1) Explanation: First, explain what Addition and Subtraction means, to the child. Not just verbally, but combine gestures with specific terms used. For example, Addition can be described as “putting things together”, and one can also gesturally show the sign of addition (cross the arms to form a plus sign). In comparison, for Subtraction, one can describe it as ‘taking away” and gesturally show the movement of the arm away, to indicate “take away”.
2) Use Dot cards and Counters: You can show a Dot card of a particular number and ask the child to represent the same through counters. Then, keep adding a counter or two, to arrive at a new number. For example, for Addition, if you take the Dot Card of 4 and represent it with 4 counters and then ask the child to “add” or “put together” 2, the child should be able to not only represent 6 through counters, but also add a Dot card of 2 to the Dot card of 4, to make 6. Similarly, for Subtraction, for example, if you take a Dot card for 5, and ask the child to represent the number through counters and then ask, to take away 2, the child should be able to physically remove two counters from the total 5, as well as cover the 2 dots from the 5, to be left with 3.
3) Make a template:
Make a template, to represent an equation of a numeral, sign of addition/subtraction, numeral, equal to, and the resultant number (for eg., 3 + 2 = 5). Leave all of them blank.
For Addition, when you show them the dot cards, ask them to place the numerals in writing on the template and also include the symbols for Addition and Equal, so that they can visually represent the equation. Once they are able to put 3+2=5, you also do the other number bond, 2+3= 5. You can use the same template, to visually represent the equation of Subtraction.
4) Once the child is familiar with both Addition and Subtraction, two templates can be used simultaneously, one above the other, to show how the processes of Addition and Subtraction, can visually represent the Decomposition of the number. For example, 2+3=5 and 5-2=3
5) Once the child is familiar with Addition and Subtraction, the child can be taught Doubles. Show the same Dot cards twice. For example, Double 4 makes 8. Later, show them one dot card and ask them what the Double of that number will be? Doubles, is Repeated Addition,
Thus, we see the possibilities are endless. There are several tools available, but the strategies adopted, to make math learning, visually fun and engaging, is very important and should be especially considered while working with individuals with Dyscalculia and other Math Learning Difficulties.
Author Triveni Goswami Vernal
The author has a Professional Development Certificate in Dyscalculia (Decoding Math: Foundation course), Lord Math Education, Sep-Oct, 2023 and is also Certified in Dyslexia Teacher Training, Learning Disorders, OG Phonics, Ripples Centre for Enhanced Learning, 2019.
Artwork by artist Kabir Vernal