Project-Based Learning Meets Mental Math: A New Classroom Model

For decades, mathematics education has been organised around a simple premise: teach the skill, practise the skill, test the skill. It is efficient, it is measurable, and — for a growing number of educators and researchers — it is increasingly inadequate. Children who can pass a page of long multiplication problems often cannot estimate the change they should receive at a shop. The skill exists in isolation, disconnected from the contexts where it actually matters.

Project-based learning (PBL) offers a compelling alternative. And when combined with strong computational fluency — including the kind that abacus and mental maths training develops — it produces something genuinely powerful.

What Project-Based Learning Is

Project-based learning is a pedagogical model in which students acquire knowledge and skills through sustained inquiry into complex, real-world questions or challenges. Defined by the Buck Institute for Education (now PBLWorks), a rigorous PBL project has several key features: a driving question, student voice and choice, sustained inquiry, reflection, and a public product or presentation.

PBL is not new — Dewey advocated for experiential learning in the early 20th century — but it has grown significantly in adoption over the last decade. The International Baccalaureate curriculum, the Finnish national curriculum, and increasingly the CBSE curriculum in India have incorporated project and inquiry-based elements. In the UAE, the Ministry of Education's focus on 21st-century skills has driven school investment in PBL professional development for teachers.

The appeal is straightforward: when students work on problems that feel real, they are more motivated, retain knowledge better, and transfer skills more effectively to new contexts (Thomas, 2000; Krajcik & Shin, 2014).

The Traditional Critique: Maths in Isolation

The most persistent criticism of traditional maths teaching is that it produces students who know how to compute but not when or why. Research by Jo Boaler (Stanford, 2016) found that students taught through rote procedures consistently struggled to apply mathematical knowledge to unfamiliar problems, even when they had technically "learned" the relevant method.

Mental maths training — particularly at the abacus level — faces a version of this critique too. A child who can sum five three-digit numbers in four seconds has a remarkable skill. But can they deploy it when the numbers are hidden in a real-world problem? Can they recognise when rapid calculation is the right tool, and when estimation or written method is better?

PBL answers this. It forces mathematics out of the abstract and into the applied.

How Mental Maths Becomes a Tool, Not Just a Subject

In a PBL classroom, mathematics is not a subject period — it is a resource students reach for when the project demands it. A student with strong mental calculation skills has a powerful resource available at all times: a fast, reliable internal calculator that requires no device, no paper, and no time to set up.

This changes the experience of mental maths from "the thing we do in warm-up" to "the thing that makes me faster than everyone else at this project." For abacus-trained students at Level 5 and above, the mental abacus becomes genuinely useful in project contexts — not as a party trick, but as a practical edge in tasks involving budgeting, measurement, statistics, and planning.

Three PBL Projects That Incorporate Mental Maths

Project 1: Designing a School Shop Budget

Driving question: How do we set prices in our school tuck shop so it makes enough money to fund a new piece of playground equipment?

Year group: Years 4–6 (ages 8–11)

Students must work with unit costs, selling prices, margins, and running totals. Mental maths skills apply directly: calculating profit per item, estimating total income from daily sales, adjusting prices and re-estimating in real time.

For abacus-trained students, this is a natural habitat. Adding three- or four-digit revenue figures mentally, comparing two price scenarios without a calculator — these are exactly the skills Level 5–7 abacus students have practised. The project gives those skills a purpose.

Mathematics embedded: multiplication, percentages (upper KS2), addition of multi-digit numbers, data recording.

Project 2: Planning a Class Trip

Driving question: What is the most cost-effective destination for our class trip, and how should we divide the budget fairly?

Year group: Years 3–5 (ages 7–10)

Students research transport options, entrance fees, and meal costs. They must compare total costs across multiple destinations, handle per-person calculations, and present a costed proposal to the class (and ideally to a teacher or parent panel).

Mental maths surfaces at every stage: quick per-person cost division, running budget checks, comparing two options in a discussion without reaching for a calculator. The student who can mentally calculate "that's £14.50 per person if there are 28 of us" commands the room.

Mathematics embedded: division, addition of money, rounding, basic ratio and proportion.

Project 3: Analysing Sports Statistics

Driving question: Which athlete in our class would perform best at the school Olympics, and how do we measure that fairly?

Year group: Years 5–7 (ages 9–12)

Students collect performance data across multiple events (sprint times, jump distances, ball throws), calculate averages, identify trends, and present findings with recommendations. Speed in calculation allows students to iterate quickly — testing different weighting schemes, re-ranking as new data comes in.

Flash Anzan-trained students — working at Level 7–8 in abacus programmes — can process running totals and comparative sums at a rate that makes data analysis feel fluid rather than laborious. This is a significant advantage in a project where the interesting work is the interpretation, not the arithmetic.

Mathematics embedded: averages, data handling, graphing, percentage change.

How Anzan Students Use Their Skills Differently

There is a qualitative shift in how students with strong mental computation engage in PBL versus those without it. It is not simply that they calculate faster — it is that they engage with the mathematics more freely.

A student who finds arithmetic effortful tends to avoid it. They approximate, they reach for a calculator, they delegate the calculation to a partner. A student with Anzan-level fluency leans into the numerical work because it does not feel like work. They are more willing to re-estimate, to test a hypothesis numerically, to challenge an assumption with a quick calculation.

This is what mathematics educators sometimes call number confidence — a dispositional quality that PBL rewards and that deliberate mental maths training builds.

The Role of the Teacher in PBL + Mental Maths

In a traditional lesson, the teacher is the primary source of mathematical knowledge. In PBL, the teacher's role shifts to facilitator: asking questions that push thinking forward, connecting project work to mathematical vocabulary and written recording, and ensuring that the mathematical content embedded in the project is made explicit enough to be retained.

For mental maths, this means the teacher's most important moves are:

Narrating the skill: "Notice that Aisha just calculated that in her head — that's called mental estimation, and it's a maths skill."
Challenging dependence on calculators: "Before you reach for that, can you estimate the answer first?"
Celebrating speed and accuracy together: not just "right answer" but "right answer, quickly, from memory."

Research on PBL and Computational Fluency

The evidence base for PBL is strong on engagement and knowledge transfer; the intersection with computational fluency specifically is an emerging research area. What is established:

Boaler (2002) found that students in project-based mathematics classrooms significantly outperformed those in traditional classrooms on applied problem-solving tasks, while performing similarly on standard tests.
A 2019 study (Han et al.) found that PBL in primary mathematics improved both conceptual understanding and procedural fluency when the project was well-designed and the teacher actively connected project tasks to skill development.
Abacus research consistently shows that the transfer of mental calculation skills to novel contexts is stronger when practice includes open-ended application tasks — exactly what PBL provides.

The implication: PBL and structured mental maths training are not competing models. They are complementary. PBL provides the context; structured abacus training provides the fluency.

Digital Tools That Support PBL and Mental Maths Integration

Several digital tools bridge the gap between project work and computational skill:

Data collection tools (Google Sheets, Microsoft Forms) that generate datasets for student analysis
Digital abacus platforms with classroom dashboards, so teachers can track which students have the fluency foundations to engage confidently with project maths
Screencast and presentation tools for final project presentations that embed student-generated calculations

AnzanPro's platform provides the computational fluency layer: structured, assessed, level-appropriate mental maths practice that runs alongside (not instead of) whatever curriculum model the school uses. For a school adopting PBL, AnzanPro ensures that students arrive at each project with the number confidence to engage fully — rather than being held back by arithmetic that should be automatic.

The combination of project-based learning and strong mental mathematics is not an experiment — it is an evidence-informed direction that a growing number of schools globally are pursuing. If you are a school leader, curriculum designer, or teacher exploring how to bring computational fluency into a project-based model, AnzanPro's education team would be glad to talk through the options. Visit anzanpro.com to connect with the team or explore how a school partnership could work for your context.