Times tables are a fundamental aspect of mathematics that can greatly affect a person’s ability to solve daily math problems. However, individuals with dyslexia and/or dyscalculia often struggle with learning and recalling times tables, which puts them at a disadvantage compared to their peers who have a greater fluency in this area. In the second part of this two part blog post, we will investigate some strategies that can support these learners in their times table learning journey.
The 3-step CAP approach
The examples above have used a 3 stage approach to develop a conceptual understanding in learners. Recently school’s have been adopting this approach, known as ‘Singapore maths’. Ironically, Singapore maths arose in the 1980s when the government in Singapore, concerned about their low standards of maths compared to those in western schools, identified the best methods of western maths teaching and develop this 3 stage programme, also known as the CAP programme.
Concrete stage – In this children first use concrete, physical manipulatives such as counters, lego bricks or numicon. This may involve putting physical objects into cups to share them out and develop the concepts of grouping.
Pictorial stage – In this children learn to represent the physical objects with pictorial representations. These might be pictures of people and sweets early on, for examples questions such as the ones above, but students learn to develop their representations into images such as a tally chart
Abstract stage – Once students have a firm grasp of the pictorial stage to illustrate number, they will move onto the formal notation of using number symbols.
Completing the times table grid
Once students have used the methods above to have a firm grasp of the mathematical concepts that underpin times tables, they will be in a position to start to learn them. A useful approach to do this is showing them how to complete a times table grid. For this use a 11 x 11 grid with numbers 1 – 10 along the top row and also descending along the left hand column. The first step students need to do is complete the 2 times table, working along the row. They can do this by step counting in twos. The next row to complete is the 4 times table, which is simply double the two times table.
Completing the 10 times table is usually easy for students to achieve (just add a zero) and also halving the result means that students can usually complete the five times table without too much support.
A trick for completing the 3 times table is counting the joints on a finger (1 finger has 3 joints, 2 fingers have 6 joints). Again, students should be able to count in steps of 3 to complete this, then double it to complete the 6 times table.
The 7 times table requires students to block out the 3 and 4 times table (a strip of paper the correct size could cover these rows) so that the 2 and 5 times table can only be seen. By adding the results of these, the 7 times table can be completed.
Students often find the 8 times table to hardest to do. Some prefer to double the 4 times table, others prefer to use the 7 then add another 1 (5×7 is 35 plus 5 = 40).
Students usually enjoy completing the 9 times table, working along the row once they realise the digits add up to nine.
Using a times table grid
Once students are able to complete and develop a times table grid, they can also be shown how to read it to quickly find answers to multiplication problems. Using a grid students can solve multiplication problems such as 8 x 5 by finding the 8 along the top row, 5 on the left hand column and working down / across until the lines meet (at 40). Reinforcing previous teaching they can find 5 x 8 and realise the number is the same. Division is possible, such as 40 divided by 8 = ? and the student can find the 40 in the 8 column in the table and read across to find that it is the 5 row.
Summary
Understanding is the key to application. Without understanding the basic numeracy and concepts that underpin times tables, students will have will have difficulty in calculating and apply them. Part of this understanding involves developing students flexibility of number as this is a fundamental building block towards application. Language is also important, not only mathematical terminology, but also linking this to every day language such as ‘twice as much’, ‘double the amount’, ‘half of that’. Likewise application of mathematical problems to real world examples, such as ‘a recipe is written for 4 people but you are cooking for 12 people. How much more ingredients do you need?’ The CAP approach of starting with concrete examples under pins later learning, which can be applied to visual problems before the number symbols are introduced. Also, student’s familiarity to the times table square, completing it and using it reinforces learning as well as builds their confidence in this important aspect of mathematical understanding.
Learning times tables – part 2
Times tables are a fundamental aspect of mathematics that can greatly affect a person’s ability to solve daily math problems. However, individuals with dyslexia and/or dyscalculia often struggle with learning and recalling times tables, which puts them at a disadvantage compared to their peers who have a greater fluency in this area. In the second part of this two part blog post, we will investigate some strategies that can support these learners in their times table learning journey.
The 3-step CAP approach
The examples above have used a 3 stage approach to develop a conceptual understanding in learners. Recently school’s have been adopting this approach, known as ‘Singapore maths’. Ironically, Singapore maths arose in the 1980s when the government in Singapore, concerned about their low standards of maths compared to those in western schools, identified the best methods of western maths teaching and develop this 3 stage programme, also known as the CAP programme.
Completing the times table grid
Once students have used the methods above to have a firm grasp of the mathematical concepts that underpin times tables, they will be in a position to start to learn them. A useful approach to do this is showing them how to complete a times table grid. For this use a 11 x 11 grid with numbers 1 – 10 along the top row and also descending along the left hand column. The first step students need to do is complete the 2 times table, working along the row. They can do this by step counting in twos. The next row to complete is the 4 times table, which is simply double the two times table.
Completing the 10 times table is usually easy for students to achieve (just add a zero) and also halving the result means that students can usually complete the five times table without too much support.
A trick for completing the 3 times table is counting the joints on a finger (1 finger has 3 joints, 2 fingers have 6 joints). Again, students should be able to count in steps of 3 to complete this, then double it to complete the 6 times table.
The 7 times table requires students to block out the 3 and 4 times table (a strip of paper the correct size could cover these rows) so that the 2 and 5 times table can only be seen. By adding the results of these, the 7 times table can be completed.
Students often find the 8 times table to hardest to do. Some prefer to double the 4 times table, others prefer to use the 7 then add another 1 (5×7 is 35 plus 5 = 40).
Students usually enjoy completing the 9 times table, working along the row once they realise the digits add up to nine.
Using a times table grid
Once students are able to complete and develop a times table grid, they can also be shown how to read it to quickly find answers to multiplication problems. Using a grid students can solve multiplication problems such as 8 x 5 by finding the 8 along the top row, 5 on the left hand column and working down / across until the lines meet (at 40). Reinforcing previous teaching they can find 5 x 8 and realise the number is the same. Division is possible, such as 40 divided by 8 = ? and the student can find the 40 in the 8 column in the table and read across to find that it is the 5 row.
Summary
Understanding is the key to application. Without understanding the basic numeracy and concepts that underpin times tables, students will have will have difficulty in calculating and apply them. Part of this understanding involves developing students flexibility of number as this is a fundamental building block towards application. Language is also important, not only mathematical terminology, but also linking this to every day language such as ‘twice as much’, ‘double the amount’, ‘half of that’. Likewise application of mathematical problems to real world examples, such as ‘a recipe is written for 4 people but you are cooking for 12 people. How much more ingredients do you need?’ The CAP approach of starting with concrete examples under pins later learning, which can be applied to visual problems before the number symbols are introduced. Also, student’s familiarity to the times table square, completing it and using it reinforces learning as well as builds their confidence in this important aspect of mathematical understanding.
Click here to read more about gamifying maths teaching: https://www.dyslexiauk.co.uk/gamifying-maths-learning-dyscalculia-and-maths-anxiety-part-1/
View the common signs of dyscalculia here: WHAT ARE THE SIGNS OF DYSCALCULIA?
To discuss your concerns with a dyslexia assessor, please click here
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