The Mathematics Learning System shows how learning can move. The Next-Step Decision Guide asks which move is justified now.
A learner does not need every BTT system activated at once. They need the right next move.
That is the job of the Mathematics Next-Step Decision Guide: read the current state, identify the correct public route, define what improvement should look like, watch the evidence, and reroute if the first interpretation proves wrong.
The Decision Guide does not replace the BTT Mathematics Learning System. The Learning System describes the full learner route. The Decision Guide is the shorter decision board above it.
It also does not replace the BTT Mathematics System Map, which declares routing boundaries, or the Starting Mathematics Support, which declares how the system starts.
Read state → choose route → define success → observe change → reroute or release.
The Decision Guide asks five questions
- What state is the learner in now?
- Which public route has the right job?
- What should improve if this route is correct?
- What evidence would force us to reroute?
- When can support reduce or stop?
If these five questions are answered clearly, BTT can usually avoid two costly errors: activating too much intervention and staying on the wrong route for too long.
Step 01 — Read the current state
The first task is not to decide what to teach. It is to describe what is happening.
The learner may be in one of several broad states:
- a prerequisite is missing or unstable;
- the representation is not carrying meaning;
- a procedure works only when the form is familiar;
- retrieval is unreliable after delay;
- transfer breaks when wording or context changes;
- task language is interfering;
- the Mathematics is known but examination execution is weak;
- support is carrying too much of the route;
- or the learner is stable and ready for stretch.
The public state route is Find My Mathematics State | What Should I Fix First?.
If the learner’s marks or behaviour have started to slip and the visible error may not be the true cause, use When Mathematics Slips | Find the First Useful Break.
Step rule: do not route from the mark alone.
Step 02 — Decide whether the state is sufficiently clear
Some states are obvious enough to act on. Others are not.
If a learner repeatedly mishandles negative signs across algebra, coordinate geometry and substitution, the probable repair point may already be reasonably clear. If a learner fails one long examination question, several explanations may still be plausible.
The Decision Guide therefore asks:
Do we have enough evidence to choose an intervention, or do we still need to discriminate between competing explanations?
If the answer is no, route to How Mathematics Diagnosis Works | Finding the Earliest Weak Link.
Step rule: when uncertainty is high, increase evidence resolution before intervention volume.
Step 03 — Choose the correct public route
Once the state is clear enough, the Decision Guide chooses the route whose job matches the problem.
| Observed state | Activate this route | Do not confuse it with |
|---|---|---|
| Broad state unclear | Find My Mathematics State | Deep diagnosis |
| Visible failure, cause unclear | Mathematics Diagnosis | More worksheets by default |
| Likely weak link known | How Mathematics Help Works | Full reteaching by default |
| Attempt needs a useful response | Mathematical Feedback | Right/wrong reporting only |
| Understanding exists but reliability is weak | Mathematical Practice | Diagnosis |
| Familiar questions work, changed forms fail | Mathematical Transfer | More blocked repetition |
| Repair needs testing | BTT Mathematical Lab | Assuming understanding from one corrected example |
| Knowledge survives untimed, marks do not | Mathematics Examination Craft | Relearning known content |
| Support may be ready to reduce | Independent Mathematics | Keeping yesterday’s scaffolds indefinitely |
| Learner is stable and ready to move | Mathematics Journey or stage route | Inventing a repair problem |
The complete routing declaration is kept in the BTT Mathematics System Map.
Step 04 — Define the success signal before acting
A route becomes much stronger when BTT decides in advance what improvement should look like.
Examples:
| Working hypothesis | Expected success signal |
|---|---|
| Signed-number weakness causes algebra errors | Embedded sign handling improves inside algebra, not only in isolated drills |
| Graph–equation connection is weak | Learner can translate in both directions on a changed example |
| Support dependence is the main problem | Same task succeeds with less prompting after fading |
| Retention is weak | Method can be retrieved after delay without rebuilding from notes |
| Method selection is weak | Mixed practice improves even when chapter labels disappear |
| Examination execution is weak | Timed performance approaches untimed capability without reteaching the content |
This changes teaching from “try something and hope” into a testable intervention.
Step rule: every important repair should make a prediction.
Step 05 — Choose the smallest intervention that could produce the signal
The Decision Guide resists overreaction.
If one discriminating question can restore a missing relationship, a full lesson may be unnecessary. If one prerequisite is causing several downstream errors, repairing the prerequisite may be more efficient than revising every affected chapter.
BTT’s intervention route is the How Mathematics Help Works, whose public ladder is:
WAIT → ASK → REFRAME → CUE → HINT → MODEL → TEACH → GUIDED PRACTICE → INDEPENDENT ATTEMPT → VERIFY → FADE.
The Decision Guide does not demand the smallest possible intervention regardless of need. It demands the smallest justified intervention.
Step rule: do enough to restore productive movement, then hand the problem back.
Step 06 — Watch the learner, not just the answer
A correct answer can still be produced through a fragile route. A wrong answer can contain useful progress.
The Decision Guide therefore watches for changes in behaviour:
- The learner starts with less prompting.
- The first step becomes more mathematically relevant.
- Representations are chosen more usefully.
- Repeated error types decline.
- The learner detects mistakes earlier.
- Questions become more specific when help is requested.
- Changed forms cause less disruption.
- Support can reduce without the route collapsing.
These are leading indicators of a changing mathematical state.
Step 07 — Reroute when the prediction fails
A failed repair is not wasted work. It is new evidence.
If the predicted improvement does not appear, the Decision Guide should not automatically increase the same intervention.
Instead ask:
- Was the supposed prerequisite actually stable?
- Is the failure in representation rather than procedure?
- Are two weak links interacting?
- Did the learner succeed only because support remained visible?
- Is retention the real problem?
- Is task language blocking access to known Mathematics?
- Is the difficulty only appearing under examination conditions?
If necessary, return to Mathematics Diagnosis.
Step rule: the evidence can overrule the route.
Step 08 — Separate practice, transfer and performance
These three states are often collapsed into one idea of “more practice”, but they measure different things.
| Layer | Question being tested | Route |
|---|---|---|
| Practice | Can the learner make the Mathematics more reliable? | How Mathematical Practice Works |
| Transfer | Does the relationship survive changed surface and method selection? | How Mathematical Transfer Works |
| Performance | Can available capability become marks under bounded conditions? | Mathematics Examination Craft |
A learner can pass one layer and fail another. The Decision Guide routes accordingly.
Step 09 — Know when to validate
Some repairs are low-cost and obvious enough that formal validation can be brief. Others affect many downstream topics or influence larger teaching decisions.
Use the BTT Mathematical Lab when the system needs stronger evidence that a diagnosis-to-repair path actually worked.
Observe → Probe → Repair → Validate → Release.
Validation is especially useful when:
- one proposed weak link appears to explain several downstream errors;
- a learner has had repeated interventions without durable change;
- support dependence may be hiding the true state;
- or BTT is deciding whether the learner is ready to move forward.
Step 10 — Release when the capability is owned
The Decision Guide does not measure success by how long the learner remains inside BTT’s intervention systems.
Release becomes appropriate when the learner can increasingly:
- retrieve the Mathematics after delay;
- handle a changed question;
- select methods without chapter cues;
- detect and recover from errors;
- verify results;
- perform under required conditions;
- and work with less external support than before.
The return route is How Independent Mathematics Works | When the Learner Can Carry the Route.
Step rule: support is not successful because it can continue. It is successful when some of it can stop.
The 60-second Step Tower
| Question | If yes | If no |
|---|---|---|
| Do we know what state this is? | Choose route | Find My Mathematics State |
| Do we know where the first useful break is? | Choose intervention | Diagnose |
| Can the learner move with a small prompt? | Return task | Escalate HELP carefully |
| Is the familiar form now stable? | Test transfer | Practise for the missing capability |
| Does the repair survive changed work? | Perform or release | Reroute / diagnose |
| Can support now reduce? | Release more control | Keep only justified support |
Parent Step Tower
Parents need a simpler board.
- Bring the evidence. A recent marked paper or piece of working is more useful than “my child is weak”.
- Ask what kind of problem this is. Knowledge, transfer, retention, execution or support?
- Ask what the first useful repair is. Avoid rebuilding everything automatically.
- Ask what should improve. The intervention should have a success signal.
- Ask when support can reduce. Independence is part of the plan.
The parent-facing route remains Parents’ Guide to Mathematics | What Should I Do Next?.
Learner Step Tower
The learner can internalise the same control logic:
- What is the question asking?
- What part do I understand?
- Where exactly did I stop trusting the route?
- What representation would make the structure clearer?
- What is the smallest hint I actually need?
- How will I check the answer?
- Can I do a changed version without the hint?
When the learner can run more of these checks independently, the Decision Guide is moving inside the learner rather than staying outside as a tutor function.
Tutor Step Tower
For the tutor, the compact operating discipline is:
Observe → classify → choose route → intervene minimally → return task → watch prediction → reroute or release.
In a three-student tutorial, the three learners can occupy three different states. One may need a prerequisite repair, one may need mixed transfer practice, and one may be ready for examination performance work.
The Decision Guide makes that difference explicit without changing the identity of the class.
Stage routing remains with stage guides
The Decision Guide does not own curriculum content.
| Need | Route |
|---|---|
| Primary worked learning estate | Primary Mathematics Learning Hub |
| Primary → JC overview | Singapore Mathematics Curriculum Overview |
| Secondary G1 / G2 / G3 | How SEC Mathematics Works |
| Additional Mathematics | Additional Mathematics Directory |
| JC Mathematics | JC Mathematics |
| Stage-to-stage capability progression | The Mathematics Journey |
The Decision Guide routes into these routes only when the learner’s state says stage-specific content is the next useful move.
How this guide differs from the other system pages
| Page | Job |
|---|---|
| BTT in the eduKate Ecosystem | Declares BTT’s Mathematics-specialist role |
| Mathematics Learning System | Explains the full learner route |
| System Map | Declares public routes and boundaries |
| Starting Mathematics Support | Explains how Mathematics support starts |
| Mathematics Next-Step Decision Guide | Chooses the next active route and checks whether to continue, reroute or release |
The decision principle
The purpose of a control system is not to create more control for its own sake.
It is to make the next decision clearer, detect when the route is wrong, and reduce external control as the learner becomes more capable.
The right route is the smallest route that explains the evidence, changes the Mathematics in the predicted direction, and leaves the learner with more control than before.
BTT Step Tower principle: read the state before choosing the tool, define success before intervening, let evidence override the first route, keep specialist routes distinct, separate practice from transfer and performance, validate important repairs, and release control whenever the learner can safely carry more.
Runtime routes: System Map · Find My Mathematics State · complete Mathematics directory.
Runtime routes: System Map · Find My Mathematics State · complete Mathematics directory.