Issue 20: The power of games to help students who struggle with maths | Sarah Wedderburn

Games divert attention away from the tyranny of the right answer, creating a more open field for ideas of all qualities.

In this article, we examine the role of games in specialist maths tuition and diagnostic maths assessment, looking at examples and exploring their advantages.

Number Patterns

Research has shown the importance of the automatic recognition of the number patterns – the patterns on a dice.

For children with a poor sense of number, there are definite benefits from working with patterned visual number images:

• The images prevent a ‘one after another’ view of numbers.
• Each number pattern has a distinctive identity.
• The images develop a view of numbers as internally patterned constructs, wholes that can be built up, broken down and built up again.

To begin a student’s recognition of number patterns, I start working in a concrete mode using individual Lego blocks or Smarties, counting them out one by one and laying them into the pattern that we find on the dice. The student can then check with the dice to see that their pattern matches the one shown there. We can then reinforce their knowledge by playing Number Pattern Bingo.

Number Pattern Bingo

Each student has a number pattern bingo board, and the winner is the first person to fill their board.

The questions are placed in a pile, and turns are taken to pick up a card. Before they answer the question on the card, I ask them:

• To read the question aloud.
• Give me an alternative word that we could use for the minus symbol.
• Will your answer be larger or smaller?
• Why?
• Do you know the answer, or how shall we work it out?

So, this game provides more learning than just the over-learning/revisiting of number pattern recognition. It also gives us the chance to develop the student’s analysis of the question, expand their vocabulary of mathematical symbols, build their confidence, ensure they can work out the answer to simple questions and, importantly, have fun. It is an example of why games are a more powerful learning tool than worksheets.

We also use the game to develop specific maths vocabulary and knowledge:

The 100 Square Game

The 100 square is an important tool as it is a visual representation of our number system. However, it is also very abstract (moving your finger down a row does not mean that you have added on ten; it means you’ve moved your finger down a row!).

As with all concepts, we would introduce the 100 square in a concrete mode, building up the student’s knowledge from a number line. As their understanding of numbers, place value and numerical sequences expands, we find that our number lines become so long that they continually fall off the desk and onto the floor. So, we ask, how can we work with these lines on our table all at the same time? We move them around to make the numbers flow correctly but place the lines one above the other – in effect making a 100 square.

This game then encourages both physical interaction and manipulation of the 100 square.

The 100 square game is played as a race to 100. As you will see, my 100 square board begins with 1 at the bottom left-hand corner, not at the top. This is because numbers get larger as they go up the board, like building a house up from its foundations. If, however, your school uses a 100 square with 1 at the top left corner, then the same game can be played with a descending number board.

The question cards are turned, and the numbers found on the board are marked, either with fingers, Lego or highlighter pens, allowing for the questions to be easily answered. This game involves concrete interaction with the 100 square as well as revision of odd and even numbers. Players move by the scores given on the cards, gaining a real understanding of how the 100 square works.

The 100 square is a resource that we introduce to young students and often stop using before students with maths difficulties have gained a real understanding that will allow them to manipulate it usefully. So, we use the same baseboard with higher concepts and vocabulary to provide our older students with a second bite at the cherry – often leading to many light-bulb moments!

As with the original game, this is played as a race to 100 using the 100 square as the game board. This time, the questions cover odd & even, squared and cubed numbers, multiples and primes, cubes, products and factors. This is complex vocabulary, and yet the game mode reduces stress. We allow our students as much time as they need to answer the questions as well as pencil and paper to calculate their answers. They gain confidence as they work out their answers and often have the boost of winning!

Which Operation

Many of my students enjoy completing worksheets with similar questions once they know how to calculate the specific operation. Their difficulties arise when they have to decide which operation to apply to solve the problem. To help with this, we play a game ‘Which Operation’.

Each player has their own gameboard, and the winner is the first to cover each operation with an appropriate question.

The questions are piled up, and players take it in turn to choose a card. Each player is then prompted to:

• Read the question.
• Repeat it in your own words.
• If possible, draw a simple diagram of the problem.
• Provide an estimate of the answer – will it be bigger or smaller, by lots or only a little?
• Decide which operation they would use to answer the question.

The game can be played in whatever way that is most beneficial for the student, but, generally, I do not ask for a numerical answer – just which operation. In this way, I am decreasing stress and enabling the student to fully enjoy the game while maintaining the focus on the numerical operations.

As you will have seen from Number Pattern Bingo, 100 Square and Which Operation, the games cover more than just one aspect of maths. These games also help develop vocabulary, teach how to analyze a problem and, more importantly for my students who struggle, make maths fun.

The role of games in diagnostic maths assessment

There are different types of tests available to help identify maths difficulties and dyscalculia: screeners, standardized tests, and diagnostic tests. Each one has a role to play, and they work alongside each other to create a testing protocol.

As a specialist teacher, I find diagnostic tests to be the most useful for analyzing a student’s mathematical profile. Maths can appear difficult because, unlike most other school subjects, there is a right or a wrong answer, and the possibility of failure is high. Continued failure can lead to a withdrawal of confidence, and students may feel it is safer not to answer a question rather than take the risk of giving an incorrect answer. This can mean that written standardized scores do not provide an accurate picture of a student’s knowledge and mathematical ability. An assessment that shows true ability will:

Most importantly, the Diagnostic Assessment allows me to listen to my students’ explanations, and from this, I can tell which concepts are understood as the student can explain them clearly to me. (We should bear in mind that research from Kinga Morsanyi has shown that 81% of children with dyscalculia have some kind of comorbid conditions, and 11.5% have speech and language difficulties [5 times more likely than in children without dyscalculia]).

Snakes and Ladders Multiplication

An example of a diagnostic test that I might use at the start of a Key Stage Two assessment would be Snakes and Ladders multiplication.

We use two 12-sided dice and a multiply/divide dice.

It’s a game, and it’s competitive – both of which will relax my students and encourage them to interact with me and with the mathematical calculations.

From the game, I can tell:

• Which multiplication tables are secure
• Does the student understand the difference between the two operations (easily seen if they groan when they throw the dividing dice)?
• Are they more comfortable multiplying than dividing – look at their body language - shoulder slump, hesitations, avoidance strategies?
• Do they understand how to divide if there is a remainder? In this test, we ignore the remainder. So, if we throw 7 divided by 3, the answer would be 2, and we would ignore the remainder of 1.
• How good is their mental addition (we ask them to add on their score mentally rather than counting in ones through the board)?
• What strategies do they use for mental addition? How efficient are these strategies?

I can examine all these areas in a single, fun, interactive game, the whole time listening to my student and noting their vocabulary.

Greater than, equal to, or less than a half fraction game

Another example would be ‘Greater than, equal to, or less than a half fraction game’.

Here, we use a set of cards with amusing clipart to dissipate any tension.

The greater than a half, equal to a half and less than a half cards are placed as column headings. The rest of the cards are placed in a pile. As each card is turned, the student is asked to read the fraction - can they pronounce it confidently with ease and then place it under the correct column? Why have you placed it in this column? It is this ability to ask questions that is the great strength of qualitative assessment, and it is the students’ explanations that demonstrate how strong and secure their understanding of fractions is.

In conclusion, games encourage interaction with learning with minimal anxiety. They involve constant over-learning and revision of multiple concepts in the same activity, as well as language growth. They encourage the development of learning strategies that can be applied across all mathematical areas. Most importantly, games allow me to listen to my student’s explanations so I can reinforce their strategies and correct any misconceptions.

Games are the super-power of maths teaching - they make our lessons interactive and fun, and they help me develop a positive relationship with my students and start them on the road to maths recovery.

References

• Tay, C. (2018, February 22). A good start: The pedagogical challenge of engaging prior knowledge for all pupils. Impact: Journal of the Chartered College of Teaching. [my.chartered.college]
• Unicorn Maths. (n.d.). Games. (The games mentioned in the article are all available at a small charge as downloads from the Unicornmaths website. [unicornmaths.com]
• Reeve, R., Reynolds, F., Humberstone, J., & Butterworth, B. (2012). Stability and change in markers of core numerical competencies. Journal of Experimental Psychology: General, 141(4), 649–666. [doi.org]
• Morsanyi, K., van Bers, B. M. C. W., O'Connor, P. A., & McCormack, T. (2018). Developmental Dyscalculia is Characterized by Order Processing Deficits: Evidence from Numerical and Non-Numerical Ordering Tasks. Developmental Neuropsychology, 43(7), 607-620. [pubmed.ncbi.nlm.nih.gov]

Sarah Wedderburn

Sarah Wedderburn founded Unicornmaths in 2003 based on the principle ‘Make numbers real and make them fun’. She believes that effective maths remediation needs to encourage students to touch and move concrete resources so that they develop a full understanding and strong visual images before moving on to abstract reasoning.

Students with learning difficulties require continual over-learning and Sarah uses games to make this revisiting engaging and interactive.

Sarah runs dyscalculia courses for teachers, presents webinars and speaks at conferences. She is the author of the Diagnostic Assessment of Numeracy Skills (DANS), a qualitative maths assessment that uses activities and games to discover what a student really knows, rather than what they can present on paper. The DANS Map clearly shows which numerical concepts are fully understood, and which need reinforcing.

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DANS - the Diagnostic Assessment of Numeracy Skills

Sarah is the author of the DANS – the Diagnostic Assessment of Numeracy Skills and DANS Solution One and Two. All of which are available from SEN Books.

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Extracts from Dystinct Magazine