A kit to transform mathematics learning

The Problem

1. No real-world connection: students rarely see why concepts matter.
2. Poor interdisciplinary integration: math is siloed, cut off from the sciences it fuels.
3. Overly formal and unplayful: play is treated as the opposite of learning, increasing the fear of the subject

Constructivism as a solution

• Inspired by Piaget, Vygotsky, and Papert, constructivist learning emphasises understanding through doing.
• Students build their own knowledge via active exploration, collaboration, and carefully designed tasks that connect to their lives.
• Two teaching methodologies suggested:
  • "BIG" (Beyond the Information Given): information given before interaction with tools, focused on reflection and connecting information to experience
  • “WIG” (Without the Information Given): interaction with the tools comes first then reflection after, focused on discovery through experience
• Types of learning tools:
  • Construction Kits: building blocks that students can use to construct more complex structures; Lego is a classic example, but programming commands are also a form of construction kits.
  • Phenomenaria: simulations for presenting phenomena that can be observed and manipulated. Identified instances of phenomenaria include simulating a phenomenon in physics using lab apparatus, modeling environments using the visual programming language using Scratch

The key was crafting tools that supported this approach without creating a steep learning curve for teachers or students.

The Opportunity

By combining low-cost sensors, modular kits, and curriculum-aligned activities, we can:

• Turn abstract math into a lived experience, a “Mathsland” in the classroom.
• Help students connect physical phenomena to mathematical concepts
• Reduce fear and increase enjoyment of mathematics.
• Give teachers ready-to-use tools that don’t require programming skills but open doors to creative, hands-on learning.

Choosing the right design methods

I drew from three complementary methodologies:

1. Double Diamond – to keep the process structured: discover → define → develop → deliver. This ensured I started wide, exploring many possibilities before focusing in on the most promising.
2. Research through Design – because I needed to learn by making. Each prototype was both an experiment and a research tool.
3. Participatory Action Research – to keep the work rooted in teachers’ real-world constraints, even when Covid-19 prevented full co-design workshops. Teacher interviews and case studies from the literature became stand-ins for live collaboration.

This blend allowed me to remain research-led while staying design-flexible, moving between theory and classroom reality.

Identifying what works (and what doesn’t)

Through literature, existing classroom projects, and teacher interviews, I tested the viability of different technological approaches against key criteria:

• Ease of use: can a teacher with no programming background get this running?
• Modularity: can it be easily repurposed for different levels and activities?
• Engagement: does it encourage active, collaborative problem-solving?
• Constructivist fit: does it allow for learning through discovery?

From this filter, three technology categories emerged:

Programmables

Tools like Arduino boards or Crickets blocks allow building and coding from scratch.

• Strength: High creative potential, proven in constructivist projects.
• Limitation: Requires significant teacher training in programming, which often isn’t feasible.

Sensor Data Kits

Tools with built-in sensors for collecting and graphing real-world data (e.g., Arduino Science Journal).

• Strength: Minimal setup, direct link between action and data visualisation.
• Limitation: Less open-ended than full programmables unless paired with other tools.

Tangible User Interfaces (TUIs)

Physical objects that manipulate digital information (e.g., FlyStick).

• Strength: High engagement, strong conceptual grounding through embodiment.
• Limitation: Often expensive or complex to reproduce.

Interdiscplinary Integration

Physics motion became the perfect interdisciplinary anchor to physicalise mathematics:

• It's universally understood by students (everyone moves)
• Directly measurable by sensors (acceleration, angular velocity, proximity)
• Naturally links to functions and geometry in mathematics
• Proven in prior studies to improve graph interpretation and functional thinking

By framing the activities around five types of motion (rectilinear, curvilinear, circular, rotational, and oscillatory) I could give each student group a tangible, relatable starting point.

Designing for classroom adoption

To design the ideal tools, there were some design constraints and characteristics

• Modular foam-board “tangible kits” so teachers and students could assemble them with scissors and glue guns
• Velcro attachments for quick reconfiguration during activities
• Pre-programmed Arduino boards named by group, so connecting was as easy as “find your device and start”
• Activities that encouraged discovery first, discussion after — aligning with constructivist WIG principles

By the end of the design phase, I had a clear pathway from theory to practice: modular tangible kits + Arduino sensors + motion-based tasks = hands-on, discoverable mathematics.

The tangible kit

Core Technology

• Arduino Nano 33 BLE Sense — chosen for its small form factor, built-in sensors (acceleration, angular velocity, proximity, light, temperature, etc.), and Bluetooth Low Energy for wireless connection.
• A small power bank — to power the Arduino board easily and safely

Physical Design

• Central unit: foam-board box holding both the Arduino and a power bank, with the board mounted securely on top for sensor accuracy.
• Velcro attachment points: allowed students to reconfigure the kit depending on their assigned motion type.
• Interchangeable parts: springs, wheels, spinners, magnets, and cardboard arms that could be attached to create oscillations, rotations, or linear paths.

Approach

• The prototypes needed to feel finished to reduce students' fear of experimenting with them fully. I used sleek, robust design and colouring to achieve this.
• Foam board and wide Velcro hit the sweet spot between low fidelity (safe to tinker with) and functional robustness.
• Relied on design (rather than instructions) to signal functionality: e.g. velcro on different sides of central units, cushioned foam container with narrow sides to afford throwing.

The Digital kit

• Arduino Science Journal app — gave students instant visual feedback as live graphs, without needing to program anything.
• 3D Geometry Interface — link Arduino sensor data directly to a virtual environment so movements not only produced graphs, but also manipulated a 3D visual object (e.g., a ball moving in sync with acceleration data). I built the interface with JavaScript, P5 and HTML/CSS

Why the 3D Interface

• To encourage playful experimentation
• To test intuitive understanding of complex mathematics topics
• Graphs are powerful for mathematically inclined students, but visual-spatial learners benefit from seeing the same concept in a simulated “world.”
• It created a feedback loop: move it physically, see it change digitally, then check the graph to understand why.

• Creating a continuous thread between the Arduino board, Science Journal App and tangible kit by using the same visual identity.
• The option to select from a variety of 3D shapes and transform them through physical interaction with the tangible kit
• Students can rotate, stretch or move the chosen shape on three axis using different sets of data (proximity, acceleration, tilting, and light intensity)

What happened in the room

• Exploration and creativity: Students improvised wildly different setups. One group taped the Arduino kit to a fidget spinner to explore rotation. Another attached it to a swinging pendulum for oscillation. The kits became tools for invention, not just instruction.
• Excitement in the data: When graphs spiked or curved in real time, students shouted things like “Whoa, that’s it!” They began adjusting their motions just to see how the graphs would change.
• Collaboration: Groups naturally split roles – one holding the kit, one monitoring the app, another taking notes, and others suggesting ideas. Even quieter students found entry points.
• Surprises: Students reported unexpected data quirks, such as extra spikes in acceleration when releasing a pendulum. Instead of seeing this as “wrong,” they tried to explain it, leading to richer discussions.

Teacher's perspective

The teacher noted a different energy compared to typical lessons:

• Students were more engaged and collaborative.
• Conversations went beyond “what’s the right answer?” into why the graph looked the way it did.
• Seeing graphs emerge from movement helped students connect mathematical abstractions to lived reality in a way standard lessons rarely achieve.
• Students dealt with higher levels of math and pointed out advanced mathematical and technical observations

the code → The thesis →