Decoding Dyscalculia: Unlocking Algebra with Algebra Tiles

Summary

Algebra is inherently abstract and often taught at a symbolic level from the outset. For many students, especially those with dyscalculia or other mathematical learning difficulties, this can create significant barriers to understanding. Without first establishing strong, concrete foundations, these students may struggle to understand algebraic concepts and to apply them meaningfully. This is why Decoding Dyscalculia: Unlocking Algebra with Algebra Tiles is so important!

Manipulatives such as algebra tiles offer a powerful bridge to overcome these barriers. By physically representing integers, variables, expressions and equations, they help students build robust internal representations of algebraic concepts and relationships. Once confident with these concrete representations, students can gradually transition to visual depictions and, eventually, to abstract reasoning via a carefully scaffolded fading process.

However, algebra tiles alone are not a shortcut to deeper understanding. Success depends on the groundwork laid beforehand: explicit teaching of key vocabulary and conventions, and sustained practice using tiles to model core concepts before progressing to simplification, solving, or factorisation. In this article and accompanying video, I share how I introduce algebra tiles to students with dyscalculia and other mathematical learning difficulties, unlocking deeper understanding and supporting greater success in mathematics.

What Are Algebra Tiles?

Algebra tiles are manipulatives shaped like squares and rectangles:

A small square represents the number one

A rectangle represents the variable x

A large square represents x squared

Algebra tiles are based on the area model of multiplication, where the dimensions of each tile represent factors, and the area is the product. Red tiles (or another distinct colour) are used to represent negative values, while a different colour rectangle (e.g., green) may stand in place for  tiles or the product of  and .

For students who struggle with abstract symbols, algebra tiles:

• Ground algebra in spatial reasoning
• Make multiplication visual and tactile
• Reinforce the concept that,  x multiplied by x = x squared, by representing it as a square

Virtual equivalents of algebra tiles are freely available, offering an alternative to physical manipulatives when they are unavailable, encouraging greater autonomy for students. They are also ideal for online learning.

Before Introducing Algebra Tiles

Jumping straight into algebra tiles risks turning them into something else that students do mechanically, without genuine insight or understanding. To unlock their full potential, we must first invest time in laying a strong conceptual foundation. Only then can students truly benefit from the deeper mathematical thinking these manipulatives are designed to support. Time must be spent building mathematical vocabulary, understanding algebraic conventions and reinforcing the area model of multiplication used to name tiles.

Build Vocabulary

Mathematics has its own language. Keywords like “integer”, “expression” or “term” are rarely encountered outside the classroom or carry different meanings in everyday contexts. To help students make sense of lessons, build lasting understanding, express when they need support and establish a common vocabulary, algebraic vocabulary must be explicitly taught and regularly reviewed.

Understand Algebraic Conventions

Algebra has specific conventions, such as interpreting  or  as multiplication. These rules may be easy for some students to understand and remember. However, students with specific learning difficulties in mathematics may require explicit instruction and reinforcement. Algebra tiles offer a hands-on way to demonstrate and internalise these rules.

Reinforce Pre-Skills

Before using algebra tiles, students need a solid grasp of the area model. Specifically:

•        Area of a square: A = s², where s is the length of one side

•        Area of a rectangle: A = lw, where l is the length and w is the width

These concepts should be taught visually and tactiley, helping students connect spatial understanding to algebraic reasoning.

Introducing Algebra Tiles

Once a solid foundation has been established, algebra tiles can be introduced. Before progressing to tasks such as simplifying expressions, solving equations or expanding brackets, it is essential to draw students’ attention to the key features of tiles and model their use to represent core concepts in a repetitive, scaffolded manner. This approach helps students build confidence and conceptual understanding, ensuring they engage with algebra thoughtfully, rather than simply reproducing procedures they have learnt by rote.

Focus on Key Features

Students may not automatically connect the shape and area of tiles to algebraic values. Guide them to notice:

A small square =  1 (like a 1cm square in your mathematics book)

A rectangle = x  (like a beach towel that is 1m wide with an unknown length)

A large square = x squared (like a square garden with equal, unknown sides)

Relating tiles to real-world examples helps learners, especially those with dyscalculia or mathematical learning difficulties, internalise algebraic logic.

Repetition, Modelling and Scaffolding

Confidence in algebra tiles results from repeated, supported opportunities to model integers, variables, expressions and equations. Explicitly model each step, scaffold tasks carefully, and fade support gradually. While this takes time, it deepens understanding and develops autonomy later when higher-order concepts and problem-solving are introduced.

Encourage Visual and Mental Representations of Concrete Models

Once students are confident with tiles, help them to transition to visual and mental models.

• Encourage drawing tile representations
• Prompt with questions like: “If you were using algebra tiles, what would that look like?”

Some students may need to continue using visual aids during problem-solving and should be supported in doing so for as long as necessary.

Play Games to Reduce Anxiety

Many students who struggle with maths experience mathematics anxiety. Maths anxiety often stems from how the content is presented rather than the maths itself. A games-based approach can reduce stress and free up valuable working memory space. Games may be no longer than a few minutes and should reinforce the skill the student has been learning. This builds confidence, fosters a growth mindset, and helps students see themselves as capable mathematicians.

Conclusion

Rushing into algebra tiles risks turning them into something else students do in mathematics, mechanically, without genuine insight or understanding. To unlock the full potential of algebra tiles, we must first invest time in laying a strong conceptual foundation. As endurance swimmer Lewis Pugh said, “When you get the basics right, everything else falls into place.” This principle is especially critical for learners with dyscalculia or other mathematical learning difficulties, where gaps in number sense, spatial reasoning, or symbolic understanding can make algebraic concepts feel inaccessible or overwhelming.

For these learners, algebra tiles should not be introduced as a shortcut to solving equations, but as a carefully scaffolded bridge between concrete understanding and abstract reasoning. Before progressing to tasks such as simplifying expressions, solving equations, or expanding brackets, it is essential to draw students’ attention to the key features of the tiles and model their use in a repetitive, structured way. This approach supports cognitive processing, reinforces visual-spatial connections, and allows learners to build confidence through predictable routines. With the right groundwork, algebra tiles can become a powerful tool for deepening understanding, not just a procedural prop.

Tools and Resources

• Maths Bot Algebra Tiles
• Media 4 Maths Library
• NCETM Algebra Tiles
• Polypad Algebra Tiles
• White Rose Maths Algebra Tiles

Decoding Dyscalculia September 2025 – https://dyscalculianetwork.com/decoding-dyscalculia-doubling/

This post was written by Dr Fiona Campbell – https://dyscalculianetwork.com/assessor-tutor/dr-fiona-campbell/