Dr Fiona Campbell on teaching algebra to students who have specific learning differences.
Algebra is a core part of the secondary school mathematics curriculum. However, many students, especially those with specific learning differences such as dyscalculia, dyslexia or ADHD, find it abstract, hard to learn, and irrelevant to everyday life. Additionally, some students struggle with algebra due to significant challenges in retaining information in their working memory and transferring it to their long-term memory. Misconceptions about algebra can also hinder students’ learning process. A negative mindset undermines their willingness and motivation to learn, not just in algebra, but in all areas of mathematics. As educators, we must work to change this mindset. We must transform algebra from a subject students dread to a challenge they eagerly engage with. We can achieve this by building strong mathematical foundations in our students, by supporting their learning needs, and by making manipulatives a must-have in every classroom. In doing so we will help students develop critical thinking and abstract reasoning.
Spotting dyscalculia
Number sense is an intuitive understanding of numbers and their relationships. Students with strong number sense can easily grasp algebraic concepts, while others may struggle with even basic equations. A lack of number sense together with misconceptions about algebra can hinder learning. It may also be indicative of dyscalculia—a condition affecting around 5-8% of students. Teachers must be equipped to identify signs of dyscalculia (see Figure 1) and provide appropriate support, especially since these students are 100 times less likely to be diagnosed compared to their peers with dyslexia.
Teach basic arithmetic fluency for deep conceptual understanding
Success in algebra depends on fluency in basic arithmetic operations. Students who lack fluency may rely on developmentally immature strategies such as counting in ones on their fingers, which is both time-consuming and error-prone. Teaching arithmetic for deep conceptual understanding, rather than rote memorisation, enables students to reason through problems effectively. Students should be taught strategies such as using doubles or near-doubles for addition, and learning key multiplication tables such as the 2x, 5x and 10x tables to serve as anchors for other facts. Mastery of basic arithmetic is essential for building confidence in algebra.
Working memory
Working memory is the ability to hold and manipulate information simultaneously and plays a crucial role in algebra. Students with specific learning differences often experience co-occurring impacts on their working memory, causing them to lose their place in problems, forget procedural steps, or fail to recall necessary information. To support these students, educators can break information into smaller “chunks,” repeat instructions, and allow the use of external memory aids such as calculators and number lines. Scaffolding tasks and providing repeated opportunities for practice can also help students manage their working memory more effectively.
Transfer of information to long-term memory
Students with specific learning differences may find it hard to transfer information from their working memory to their long-term memory. To help these students retain algebraic concepts, educators should link new information to what students already know, provide meaningful real-life examples of algebra, and make learning multisensory. For instance, using a washing line as a number line to solve equations not only presents information in multiple sensory channels, but does so in a way that fosters logical reasoning skills and deepens understanding
Transition from concrete to abstract thinking
Algebra is inherently abstract and often taught almost entirely at an abstract level. However, many students will struggle to understand it without first building strong concrete foundations and being allowed to transition to abstract reasoning via a gradual fading process. Manipulatives such as algebra tiles and balance scales, along with virtual equivalents, can help students form strong internal representations of algebraic concepts. Once comfortable with concrete representations, students can progress to visual depictions followed by more abstract forms of algebraic reasoning.
Algebraic vocabulary
Understanding algebraic vocabulary is crucial for success in algebra. Terms such as “simplify,” “solve,” and “expand” must be explicitly taught and regularly revisited. Interactive teaching methods, such as games and low-stakes exercises, can help reinforce vocabulary in an engaging way.
Understanding algebraic conventions
Algebra has specific conventions that students must grasp, such as the order of operations (BIDMAS) and how to handle variables and coefficients. These conventions can be difficult for students to remember, but explicit teaching and reinforcement through interactive lessons can help students internalise these rules.
Word problems in algebra lessons
Word problems can be particularly challenging for students, especially for students with underlying literacy difficulties. To support them, teachers should break down problems into manageable steps, highlight important information, and encourage students to sketch the problem. Starting the problem-solving process, even if the student does not know the final answer, fosters resilience and critical thinking.