Australia’s national testing results tell a worrying story. Last year’s NAPLAN results revealed that around 500,000 students did not meet standard expectation levels in literacy and numeracy.
Meanwhile, our performance in international tests like PISA has steadily declined since 2003. While Australia still ranks in the OECD’s top ten for maths, this is largely due to global drops rather than local improvements.
Compared to top-performing countries like Singapore, Australian students are now performing two to three years behind.
Only a small percentage of students are currently exceeding expectations in mathematics—around 10% in Year 3, 12.5% in Year 5, and 13.5% in Year 7.
The figures highlight an urgent need for reform, particularly as the achievement gap between high and low socioeconomic areas, and between major cities and regional or remote communities, continues to widen.
Despite numerous policy cycles and interventions, traditional methods have failed to lift performance at scale. But what exactly needs to change? And how do we help schools achieve excellence in mathematics teaching and learning?
Beyond Broken Systems: The Case for Educational Innovation
Despite well-intentioned efforts, many educational reforms have followed repetitive patterns even as student performance continues to decline.
Traditional approaches often provide teachers superficial solutions or swing between extremes—either focusing too heavily on explicit instruction with mechanical teaching methods or emphasising investigative learning without ensuring students grasp fundamental concepts.
The disconnect between practice and effective mathematics learning not only limits teachers’ professional development by simplifying content and methodologies, but also prevents students from experiencing rich, meaningful mathematical engagement.
To put it simply, schooling is failing our children, and they would be advantaged by educational innovation rather than clinging to failing systems.
Linear Abacus, offers a different path forward: a pedagogy that honours the richness of mathematical thinking while making it accessible, tangible, and deeply engaging. At the heart of our pedagogy lies a powerful insight: sense making is prototypical problem solving.
Our solution ensures teachers and students engage meaningfully with mathematics, developing lifelong learning skills through proven methodologies that bridge theoretical understanding with practical application.
Our approach was co-founded by Dr. Andrew Waywood, a pedagogical theoretician who developed a new semiotic framework for mathematics education, and Genovieve Grouios, an educational practitioner and reformer.
Together, we built a model that bridges high-level theory with practical, everyday teaching. We recognised that neither theoretical understanding nor practical reform alone would suffice—effective solutions require both.
Linear Abacus is dedicated to transforming how mathematics is taught and learned, preparing students not just for tests but for thoughtful participation in a world increasingly organised through mathematical structures. Our belief is that the greatest gift to give a learner is understanding.
Our mission is to empower every child with the mathematical thinking needed for tomorrow’s world by making Linear Abacus® central to education, demonstrating how physical actions reveal how numbers model the structure of thought itself.
This will create learners who understand mathematics, preparing students not just for tests, but for thoughtful participation in a world increasingly organised through mathematical structures.
From Concept to Classroom: Turning Theory into Transformation
Linear Abacus has found that the deep issue in schools is the lack of cohesion in the curriculum and without an explicit understanding of curriculum there is no meaningful explicit teaching of maths.
Unless you know why you are teaching it and how it holds together you have no basis for explicit teaching sequences.
The Linear Abacus is an induction into the symbolic competence that will be the foundation of future work.
Our model for learning isn’t hypothetical. It’s already being implemented and changing classrooms across Australia. Since 2023, schools across Victoria and Western Australia have implemented our range of programs with remarkable outcomes in NAPLAN 2024:
● Woodville Primary School (Year 3): Achieved results 14% higher than similar schools, with an 11% improvement from the previous year.
● Fitzroy Primary School: Year 3 scores jumped 14% compared to last year and were 11% above similar schools; Year 5 results doubled.
● St Albans Heights Primary School: Recorded a 16% improvement in one year and now exceeds the performance of schools with comparable student populations.
What makes these achievements particularly noteworthy is their occurrence within a relatively short implementation timeframe, often in schools facing significant socioeconomic challenges.
Consistent gains across diverse school settings show that the Linear Abacus approach breaks traditional barriers and offers a scalable path to educational equity.
Spotlight on St Albans Heights Primary: A Case Study in Transformation
St Albans Heights Primary School presents a compelling case study of how the Linear Abacus approach can transform mathematics education in complex, low-SES settings.
With 96% of students coming from language backgrounds other than English, the school faced persistent challenges—especially in teaching word problems that require both numeracy and language comprehension.
Before implementing Linear Abacus, teachers grappled with fragmented planning, a lack of culturally relevant resources, and limited time for meaningful assessment and moderation.
Students struggled to connect language with mathematical operations, making key concepts difficult to grasp. The introduction of our comprehensive programs, namely the Additive Thinking Unit, catalysed remarkable change across multiple dimensions:
● NAPLAN numeracy scores improved by 16% in just one year, exceeding performance of similar schools
● Post-assessment growth ranged from 6 months to 2 years in core concepts like addition and subtraction
● Students demonstrated clearer reasoning, stronger problem-solving skills, and confidence in explaining their thinking
The transformation wasn’t just academic, it was cultural. Teachers reported a renewed sense of purpose, more effective planning and learner journey mapping, and meaningful professional collaboration and conversations about mathematics pedagogy.
As one teacher shared: “Our planners now have clear purpose and direction, allowing us to anticipate student needs and challenges.”
Teachers at St Albans Heights have deepened their understanding of mathematics and reconnected with their passion for teaching—not just because of improved outcomes, but because our approach invites them to think deeply about mathematical concepts and their application, just as it does for students.
The structure and support provided have freed them from endless planning and resourcing, giving back valuable time for reflection, assessment, and professional dialogue.
Most importantly, the program has proven particularly effective for students from non-English speaking backgrounds. The Linear Abacus offered a visual and tactile anchor for students navigating maths in a second language, making abstract ideas accessible and enabling deeper understanding.
Another teacher revealed that, “Students who previously struggled with the language of mathematics now had a concrete reference point to connect words with mathematical operations.”
This case demonstrates the power of embodied, language-inclusive maths education—and what’s possible when schools are equipped with the right tools, training, and support.
The Linear Abacus®: The Swiss Army Knife of Mathematical Tools
At the core of our solution is the Linear Abacus®—a single, versatile tool that replaces the cluttered array of mathematical manipulatives found in most classrooms.
Designed to support learning from early numeracy through to algebraic thinking, it allows students to explore key concepts such as place value, number operations, fractions, decimals, percentages, measurement, and statistics — all within one comprehensive tool.
The consistent visual model enhances conceptual clarity, helping students build connections across mathematical ideas as they progress, while the familiarity with a single tool reduces cognitive overload and supports deeper learning.
Its accessible and intuitive design brings abstract concepts to life for diverse learners, and unlike single-use resources, this tool encourages creativity, flexible, cross-topic thinking and real-world problem-solving.
Together with the Linear Abacus®, we offer a suite of complementary programs that strengthen mathematical thinking at every stage:
● The Induction to Foundational Numeracy Program: An innovative, sequenced approach that represents a paradigm shift in primary-secondary mathematics transition.
● The Additive Thinking Unit: Teaching children to interpret word problems and connect them meaningfully with calculations, models, and real-world applications.
● The Games Book: Encouraging mental reasoning and mathematical creativity through engaging activities.
We’re also committed to bridging geographic and socioeconomic divides through initiatives like our Western Australia Wheatbelt Tour. We deliver expert-led training directly to rural communities—ensuring that educational opportunity isn’t dictated by postcode.
Partnering with Numero, we provide rural educators with active, hands-on learning experiences that drive sustainable impact and close the city-rural divide.
The Path Forward
The Linear Abacus approach directly addresses the most common barriers holding students back—particularly in disadvantaged schools.
It provides high-quality, accessible resources regardless of funding levels, supports diverse learning styles, and bridges language gaps with concrete, visual models.
The flexibility of our resources allows teachers to tailor learning to individual needs, support diverse learning styles, and deliver timely interventions when students fall behind.
If we are serious about closing Australia’s widening maths achievement gap, we must prioritise what works. Educational tools like the Linear Abacus can help bridge the achievement gap between students from different socioeconomic backgrounds. To scale this impact, we recommend:
- Targeted funding to expand access to proven tools and programs in disadvantaged schools
- Teacher development that equips educators with the skills and support to deliver these tools effectively
- Collaborative networks to foster communities of practice and share what works across schools and systems
- Evidence-based policy that reflects real-world classroom data, not just theory or ideology
With continued commitment to innovation and equity, we can ensure every Australian student has the opportunity to develop the mathematical thinking needed for tomorrow’s world.
