The Technology Atlas

The useful classification is by function. A number line and an AI tutor are very different implementations, but both can be evaluated by the same questions: what mathematical function is being supported, what capability is being exposed or hidden, what evidence supports the use, when should support fade, and what can the learner still do when the tool is removed?

Room	Primary function
Representation Technology	Make quantities, structures and relationships perceptible through manipulatives, models, notation, diagrams and multiple representations.
Dynamic Mathematics Technology	Change parameters and observe invariants, graphs, constructions and mathematical behaviour dynamically.
Practice & Memory Technology	Control examples, retrieval, spacing, interleaving, cumulative practice and fluency.
Diagnostic & Feedback Technology	Turn working, errors, response patterns and formative assessment into evidence for the next teaching decision.
Adaptive Learning & Intelligent Tutoring	Estimate learner state and change sequence, scaffolding, questions or feedback accordingly.
AI in Mathematics Education	Use conversational and generative systems for explanation, questioning, tutoring, authoring and feedback without replacing the learner’s cognitive work.
Mathematical Computing Technology	Use calculators, graphing calculators, CAS, spreadsheets, coding and numerical systems to compute, visualise and model.
Assessment & Examination Technology	Design, deliver, mark, analyse and interpret mathematical assessment while respecting examination constraints.
Accessibility & Inclusive Mathematics	Reduce barriers to mathematical notation, representation, input, output and interaction without changing the mathematical target unnecessarily.
Teacher Technology & Orchestration	Help teachers author, sequence, monitor, compare evidence, plan interventions and maintain human oversight.
Choosing Mathematics Technology	Select a tool by function, evidence and learner state; define its success condition, dependency risk and removal rule before use.

The complete technology continuum

Concrete → Represent → Visualise → Explore → Practise → Retrieve → Feedback → Diagnose → Adapt → Compute → Simulate → Tutor → Assess → Verify independence.

Digital tools occupy only part of this continuum. A bar model, worked example, graphing calculator, dynamic geometry environment, adaptive system and AI tutor all belong to the same larger question: which function should be augmented now, and which human capability must eventually remain?

Singapore already separates these functions

Singapore’s Student Learning Space provides a useful live example. Its Adaptive Learning System recommends learning modes, resources and practice based on readiness; Feedback Assistant – Mathematics analyses working and can provide line-by-line hints and feedback; AI-enabled tools support dialogue and authoring; teacher-facing assessment tools support monitoring and intervention. These are related technologies, but they solve different problems.

The BTT technology test

1. Name the function. What mathematical or teaching function is being changed?
2. Name the learner state. What evidence says this learner needs that function augmented now?
3. Name what the technology exposes. Does it make structure, error, variation, feedback or state more visible?
4. Name what it hides. Does it automate a decision the learner eventually needs to own?
5. Name the evidence strength. Is support theoretical, observational, experimental, meta-analytic or still emerging?
6. Name the dependency risk. Could performance improve while independent capability stays unchanged?
7. Name the fade rule. When and how should prompts, automation or visual support be reduced?
8. Name the independence test. What should the learner be able to do after the technology is removed?

A technology has not succeeded merely because the learner gets the answer with it. Ask what human capability remains without it.

Evidence rules

Research on educational technology repeatedly warns against treating the device itself as the intervention. The Education Endowment Foundation frames digital technology around improving processes such as assessment, feedback and practice. Meta-analytic evidence in mathematics suggests positive average effects for technology-enhanced instruction and dynamic mathematics software, but outcomes depend on didactical function, implementation, teacher preparation and transfer. Current AI evidence is more uneven: tutoring and adaptive systems are promising, while general-purpose generative AI can improve task performance without guaranteeing learning.

AI RUNTIME CONTRACT · BTT-MATH-TECH-V1

TECHNOLOGY object	Function; mathematical object; stage; learner state; target; evidence; prerequisite; exposes; hides; cognitive cost; dependency risk; teacher oversight; assessment legality; success signal; fade rule; independence test; recompile condition.
Selection rule	Choose the smallest technology that changes the needed learning function. Do not select by novelty, brand or popularity.
Diagnostic rule	Do not use technology to compensate for a weak link before deciding whether that weak link should instead be repaired.
Human-capability rule	Separate assisted performance from unassisted capability. Verify the latter deliberately.
AI rule	AI WITH → AI LESS → AI WITHOUT. Scaffolding should reduce as learner control grows.
Exam rule	Check current SEAB rules before assuming a calculator, CAS, AI system or other aid is permitted in a national examination.
Recompile rule	If transfer, independence or retention fails, reconsider the technology, teaching sequence or original diagnosis.

Evidence anchors

• Singapore SLS · AI-enabled Features
• SLS and EdTech Masterplan 2030
• EEF · Using Digital Technology to Improve Learning
• IES / What Works Clearinghouse · Mathematical Problem Solving
• OECD Digital Education Outlook 2026
• CAST UDL Guidelines 3.0