Early exposure to numbers and counting is just as important as exposure to letters, words and reading. Here are some simple strategies to help children come to grips with the four pillars of maths. Try thinking of mathematics in the same way as you would about as building a house. You have your foundations (concrete stage, fundamental skills), walls (semi-concrete stage) and roof (abstract stage).
Maths is a complex subject, so if the foundations aren’t solid, the rest of the house will be full of cracks. Often, children with severe maths challenges get stuck on the concrete level and simply can’t move to the next stage.
Essentially, maths is comprised of four pillars or components, namely:
- Learning and recalling facts (bonds and tables)
- Learning and using procedures (operations)
- Understanding concepts (including vocabulary and topics such as the measurement, time, working with money, etc.)
- Problem solving (word sums).
The following points break down some of the challenges that have been identified in children who struggle with maths, as well as some ways in which teachers can address these challenges within each of the four components.
#1 Learning (and recalling) the facts:
A child:
- does not have a strong sense of numbers and does not understand that there are basic patterns in numbers, i.e., 2+3 = 5 and 3+2 =5, or struggles to learn skip-counting and place value.
- is inconsistent, remembering some maths facts while forgetting others (memory and attention play a big role).
- has difficulty remembering multiplication, division, and/or other facts while solving problems (working memory).
Supporting the primary school child
- It is important to learn to recognise and read number names and symbols. Abstract number symbols must be linked to the number names for the child to see. It might be necessary to show the actual object before showing the picture of the object for smaller children to correlate, otherwise counting becomes rote, which can cause difficulty in understanding what is required.
- Have real objects or counters available. Don’t expect children to count or calculate in their heads if they aren’t there yet. Encourage children to use number grids, number lines, times-table grids (crutches), but always go back to the real object if this is more helpful.
Supporting the high school student
- Make use of tips and tricks like mnemonics and raps, 11, 22, 33, 44 etc. (search YouTube for ideas).
- Use the commutative property in addition and multiplication.
- Use a strategic approach and start with what you know; for example: “I don’t know 7 x 6, but I do know that 7 x 5 = 35, so one more 7 makes 42; or I know that 7 x 7 = 49, so one less 7 makes 42.”
- Be aware of the impact of attention and memory.
- Don’t do maths s homework late at night.
- Encourage self-checking with a calculator.
#2 Learning maths procedures / operations:
A child:
- struggles with the methodology, struggles to remember the steps in a sum, i.e., long division or multiplication.
- struggles to remember the rules, i.e., rules for working with fractions; rules for solving equations and formulae, e.g., area is length x breadth; how to round off numbers.
Supporting the primary school child
- Break multi-step problems (including equations with several computations, word problems, etc.) into smaller parts; each step counts one mark; if you skip a step, you lose marks.
- Have a rule book and write rules down for reference purposes.
- Encourage students to practise using a calculator.
Use mnemonics to help students remember steps to maths algorithms. For example, Daddy, Mama, Sister, Brother can be used for the long division algorithm (Divide, Multiply, Subtract, Bring - down).
The same ideas can also apply for high school students.
#3 Understanding concepts:
A child:
- has difficulty in understanding sequencing and how numbers relate to each other.
- struggles to use number lines and to create a visual image of number positions (before, after, between), linked to using mental pictures to represent maths s concepts,
- struggles to understand and learn vocabulary such as, zero, more than, less than, fewer than, place holder, divide, sum of, perimeter etc.
- has problems transferring concepts learned in the maths classroom to real-life situations such as telling the time and being able to use money, graphs and measurement. Do they know the difference between g. or kg., m. or km., s. or mins?
- Not able to guestimate e.g., How many marbles are in the jar? Can they estimate or do they want to try and count?
Supporting the primary school child
- Use real objects to explain concepts, e.g. pizza can be used to demonstrate ratio and fractions.
- Guide students in visualising patterns.
Supporting the high school child
- To visualise the problem, the shape, the pattern, etc., draw, or write it out using symbols.
- Make the problem relevant Use daily situations such as reading recipes, timetables, calendars, etc.
- Work out the percentage discount on sale items.
#4 Maths problem-solving
A child:
- has difficulty reasoning through a problem or using strategies effectively during problem solving.
- has difficulty using mental pictures (such as patterns or shapes) to represent maths concepts or has difficulty ‘seeing’ the maths problem in his/her mind.
- doesn’t know how to get started on word problems, or how to break problems down. This could be linked to poor reading-comprehension skills.
Language processes could also create problems with the understanding of specific terminology, for example, children often think that the word ‘calculate’ means that it is an addition sum.
Supporting the primary school child
- Have real objects or draw pictures to represent what is going on in a word problem.
- Propose a number sentence, e.g., 6 + 4 and have the children come up with a story problem for that number sentence.
- If they are having difficulty, keep the story the same but make the numbers smaller, until they understand the problem being asked.
- Provide students with a general strategy that can be used in many problem-solving situations, e.g., Who? What? Where? How?
If students struggle to understand word or story problems, here are further solutions and strategies for teachers to help to address the issue:
1) Break down the problem
Start by breaking down the word problem into smaller, more manageable parts. Highlight the important information and help students identify the key elements, such as the question being asked, the known quantities, and the operations involved. Encourage them to underline or circle the relevant information to enhance their focus.
2) Provide visual representations
Visual aids can greatly support students’ understanding of word problems. Use diagrams, charts, or drawings to help them visualise the problem. For example, if the problem involves dividing apples among children, draw apples and circles representing each child to illustrate the situation. Visual representations make abstract concepts more concrete and accessible.
3) Teach problem-solving strategies
Introduce students to various problem-solving strategies, such as guess and check, drawing a picture, making a chart or table, using objects or manipulatives, or creating an equation. Teach them when and how to apply each strategy based on the context of the problem. Provide opportunities for students to practise these strategies with different types of word problems.
4) Scaffold learning
Gradually scaffold students’ learning by starting with simpler word problems and gradually increasing the complexity. Begin with problems that involve single-step operations and then progress to multi-step problems. Provide support and guidance as needed, and gradually reduce assistance as students gain confidence and understanding.
5) Use real-life examples
Connect word problems to real-life scenarios that are relatable to students. Use examples from their everyday lives, such as sharing toys, buying snacks, or planning activities. Relating maths to real-life situations helps students see the practical relevance of word problems and enhances their engagement and understanding.
6) Encourage verbal reasoning
Engage students in discussions about word problems. Encourage them to explain their thinking process and reasoning behind their answers. This verbal reasoning helps them organise their thoughts, clarify their understanding, and identify any misconceptions. It also promotes communication and collaboration among peers.
7) Provide guided practice
Offer guided practice opportunities where students can work on word problems in small groups or pairs. This allows for peer support and collaboration. As students work together, they can discuss different strategies, share their thinking, and help one another to solve problems. Encourage students to explain their reasoning to their partners, fostering a deeper understanding.
8) Offer multiple approaches
Recognise that there may be different valid approaches to solving word problems. Encourage students to explore alternative strategies and compare their solutions. This promotes critical thinking and flexibility in problem-solving, allowing students to discover different pathways to reach the correct answer.
9) Incorporate technology
Integrate technology tools and resources into your teaching practice to support students’ understanding of word problems. There are various educational apps, online platforms, and interactive tools that provide interactive problem-solving activities and step-by-step guidance.
10) Provide feedback and reinforcement
Offer constructive feedback focusing on a child’s problem-solving strategies rather than just the final answer. Encourage them to reflect on their approach, identify errors, and make necessary corrections. Celebrate their efforts and reinforce their progress to build confidence and motivation.
Remember, understanding word problems takes time and practice. By implementing these strategies, providing support, and creating a positive learning environment, teachers can help students overcome their struggles and develop the skills necessary to tackle word problems effectively.