Science Problem Solving Strategies | Advanced Science Tutorials

Science problem solving strategies help students when the question does not look like the example they memorised. Strong problem solvers do not immediately search for a formula or keyword. They decide what is being asked, extract the relevant information, represent the system, choose a model, build a solution path, execute carefully, explain why the steps are valid and check whether the answer makes scientific sense.

This Advanced Science Tutorials guide is written for parents and students in Sengkang, Punggol and across Singapore who search for Science problem solving, problem solving strategies in Science, how to solve Science questions, STEM problem solving, how to solve unfamiliar Science problems, Physics problem solving, Chemistry problem solving and scientific problem solving skills. It develops a general problem-solving operating system from Primary Science through PSLE and Secondary G1, G2 and G3.

Stanford’s Center for Teaching and Learning summarises expert STEM problem solving as a four-part process: Plan, Execute, Explain and Reflect. The Plan stage receives particular emphasis because experts first work out what is being asked and build a symbolic solution map before plugging in numbers; the Execute stage follows the plan; the Explain stage justifies the steps; the Reflect stage extracts lessons for future problems. See Stanford CTL: Problem Solving in STEM. Harvard’s Bok Center similarly treats problem solving as a skill that develops through repeated guided practice. See Harvard Bok Center: Problem Solving in STEM.

The Science problem-solving operating system

Read: identify the command and target.
Represent: draw, list, table, diagram or equation the system.
Recall: activate the relevant scientific model.
Plan: map the steps before calculating or writing.
Execute: carry out the plan with units and evidence visible.
Explain: justify the scientific relationship.
Check: test unit, magnitude, direction and consistency.
Reflect: record what decision was difficult and how to recognise it next time.

Primary 1 and Primary 2: teach “What do we know? What are we finding?”

Younger learners can build problem-solving readiness with comparison, sorting, prediction and simple measurement. Ask them to say what information is given, what needs to be found and what could be tried first. This reduces the habit of guessing from the most visually obvious clue.

The goal is not to accelerate formal Physics calculations. It is to build a calm first move when a problem feels unfamiliar.

Primary 3 and Primary 4: represent before answering

Primary Science problems often become easier when the student draws the system, labels the changed condition or writes a short cause-and-effect chain. Students should learn that representation is part of solving, not evidence that they are weak.

A simple diagram can reduce working-memory load and prevent the student from repeatedly rereading the entire question.

Primary 5 and Primary 6: unfamiliar context becomes normal

Older Primary and PSLE questions frequently change objects, diagrams or experiment setups while testing familiar concepts. The learner should strip away the story and ask what scientific relationship remains. Is this a heat-transfer problem, a food-web problem, a fair-test problem, a force problem or a data-interpretation problem?

The Science Exam Techniques owner covers paper execution; this article focuses on the deeper problem-solving process.

Secondary G1, G2 and G3: plan becomes more important

As calculations, models and practical data become more complex, jumping straight into arithmetic becomes more expensive. Secondary students should increasingly write a symbolic or verbal solution map before substituting values. This is especially useful in Physics and Chemistry but also applies to Biology systems and experimental questions.

The problem solver should be able to answer, “Why is this the next step?” not merely “Which formula contains these numbers?”

Read the command

Problem-solving move. The command word defines the job: state, describe, explain, calculate, predict, infer, suggest or evaluate.

Common failure. Students solve the topic but not the task.

Better method. Translate the command into an operation before using content.

Question to ask. What would a complete response have to do?

Practice task. Rewrite the question in your own words.

The deeper test is whether this move helps on a new problem where the surface context changes. Students should practise the same operation across Biology, Chemistry, Physics, Earth Science and experimental questions so that problem solving becomes a transferable capability rather than a chapter-specific trick.

Identify the target

Problem-solving move. The target is the quantity, explanation or decision the problem asks for.

Common failure. Students start manipulating given information without naming the goal.

Better method. Write the target at the top of the working.

Question to ask. What exactly must the final answer contain?

Practice task. State target in words and unit.

List the givens

Problem-solving move. Given information should be extracted from prose, table, diagram or graph.

Common failure. Students repeatedly reread the stem and miss values or conditions.

Better method. Create a compact list of known quantities or facts.

Question to ask. Which givens are numerical, qualitative or conditional?

Practice task. Build a given/unknown table.

Separate relevant from irrelevant

Problem-solving move. Not every detail in a Science problem is needed.

Common failure. Students assume every number must enter the calculation.

Better method. Ask what each piece of information contributes to the target.

Question to ask. Would the answer change if this detail disappeared?

Practice task. Cross out one irrelevant detail in practice.

Identify hidden information

Problem-solving move. Some values or relationships are implied rather than stated directly.

Common failure. Students wait for every quantity to be written explicitly.

Better method. Use definitions, graph slopes or conservation rules to derive missing information.

Question to ask. What can be inferred from the setup?

Practice task. Find one hidden quantity before solving.

Draw the system

Problem-solving move. A diagram externalises components and relationships.

Common failure. Students try to hold the entire system mentally.

Better method. Sketch only features relevant to the problem.

Question to ask. What must be connected or positioned?

Practice task. Draw a simple labelled system.

Choose the boundary

Problem-solving move. System boundaries decide what is included in analysis.

Common failure. Students accidentally change what they are tracking.

Better method. Define the object, organism, circuit or chemical system.

Question to ask. What can enter or leave the system?

Practice task. Redraw with an alternative boundary and compare.

Use a table

Problem-solving move. Tables organise matched conditions and values.

Common failure. Students compare mismatched rows.

Better method. Place variables and cases in aligned columns.

Question to ask. Which entries belong in one valid comparison?

Practice task. Create a compact comparison table.

Use a graph

Problem-solving move. Graphs can reveal relationships not obvious in prose.

Common failure. Students calculate before inspecting trend or axes.

Better method. Read axes, units and shape first.

Question to ask. What relationship does the graph already show?

Practice task. Sketch expected trend before exact reading.

Use a concept map

Problem-solving move. Concept maps reveal relationships among ideas.

Common failure. Students retrieve isolated terms without structure.

Better method. Link terms with labelled relations.

Question to ask. Which path leads from cause to effect?

Practice task. Build a five-node concept map.

Name the concept

Problem-solving move. Naming the underlying concept narrows the solution space.

Common failure. Students chase surface nouns.

Better method. Ask whether the problem is fundamentally about forces, energy, particles, systems, cycles, evidence or another model.

Question to ask. Which chapter idea explains the relationship?

Practice task. Rename the question using the concept only.

Choose the model

Problem-solving move. The model should fit the question and conditions.

Common failure. Students use the most familiar model automatically.

Better method. Select the representation that preserves the needed relationship.

Question to ask. What assumptions does this model require?

Practice task. Compare two candidate models.

Recall the principle

Problem-solving move. The principle is the scientific rule or relationship that drives the solution.

Common failure. Students search memory for phrases instead of mechanisms.

Better method. State the rule in words before using symbols.

Question to ask. Why should the outcome follow?

Practice task. Write principle in one sentence.

Predict direction

Problem-solving move. A qualitative prediction gives a pre-calculation check.

Common failure. Students compute without knowing whether answer should rise or fall.

Better method. Predict increase, decrease, no change or direction first.

Question to ask. If X increases, what should Y do?

Practice task. Make directional prediction.

Estimate scale

Problem-solving move. A rough magnitude estimate catches absurd answers.

Common failure. Students accept calculator outputs blindly.

Better method. Use familiar benchmarks and powers of ten.

Question to ask. Should answer be closer to 0.1, 10 or 10000?

Practice task. Estimate before exact arithmetic.

Plan steps

Problem-solving move. A plan maps intermediate quantities or reasoning steps.

Common failure. Students discover the route while calculating and become lost.

Better method. Write the sequence symbolically or in short phrases.

Question to ask. What must be found before the target?

Practice task. Create a three-step solution map.

Work backwards

Problem-solving move. Backward planning starts from the target and asks what would be needed to find it.

Common failure. Students begin with the first number in the stem.

Better method. Trace dependencies from target to known quantities.

Question to ask. What formula or evidence would give the target?

Practice task. Build a backwards dependency tree.

Work forwards

Problem-solving move. Forward planning starts from available information and asks what can be derived.

Common failure. Students generate many intermediate values without purpose.

Better method. Use only derivations likely to connect to target.

Question to ask. Which knowns combine naturally?

Practice task. Compare forward and backward routes.

Decompose the problem

Problem-solving move. Complex problems can be split into smaller linked decisions.

Common failure. Students search for one giant formula or one perfect sentence.

Better method. Solve subproblems and reconnect them.

Question to ask. What is the first independently solvable piece?

Practice task. Number the subproblems.

Solve symbolically first

Problem-solving move. Symbolic planning reduces arithmetic distraction.

Common failure. Students plug numbers too early.

Better method. Rearrange and connect equations before substitution.

Question to ask. What relationship remains if numbers disappear?

Practice task. Solve in symbols then insert values.

Track units

Problem-solving move. Units provide semantic and dimensional checks.

Common failure. Students drop units until the end.

Better method. Carry units through conversions and calculations.

Question to ask. What unit must the target have?

Practice task. Cancel units explicitly.

Convert units early

Problem-solving move. Compatible units prevent hidden factors of ten.

Common failure. Students mix cm, m, min and s.

Better method. Convert all inputs to the intended unit system before substitution.

Question to ask. Which conversions are required?

Practice task. Build a unit-conversion line.

Use significant figures sensibly

Problem-solving move. Final precision should match data and instructions.

Common failure. Students copy every calculator digit.

Better method. Keep working precision then round final answer appropriately.

Question to ask. Which input limits precision?

Practice task. Compare overprecise and sensible answers.

Check algebra

Problem-solving move. Rearrangement errors can reverse or scale results.

Common failure. Students assume formula choice guarantees correct calculation.

Better method. Solve symbolically and verify by re-substitution.

Question to ask. Does the rearranged formula reproduce the original?

Practice task. Reverse-check one rearrangement.

Check calculator entry

Problem-solving move. Brackets, exponents and negative signs can change results.

Common failure. Students trust the displayed number.

Better method. Compare typed expression with written line.

Question to ask. Were all grouped operations entered correctly?

Practice task. Use one deliberate calculator audit.

Use conservation

Problem-solving move. Conservation rules can simplify many problems.

Common failure. Students think matter or energy disappears.

Better method. Account for what enters, leaves and changes form.

Question to ask. Where did the conserved quantity go?

Practice task. Create before/after accounting.

Use proportionality

Problem-solving move. Ratios can solve problems without full formula memorisation.

Common failure. Students treat every trend as proportional.

Better method. Check constant ratio and conditions.

Question to ask. Does doubling one quantity double the other?

Practice task. Solve one by ratio reasoning.

Use rate reasoning

Problem-solving move. Rates compare change per unit time or other denominator.

Common failure. Students compare totals from different intervals.

Better method. Normalize to a common denominator.

Question to ask. Per what?

Practice task. Calculate and compare rates.

Use limiting cases

Problem-solving move. Extreme cases can test whether a model or formula makes sense.

Common failure. Students accept equations that predict impossible behaviour at zero or infinity.

Better method. Ask what happens when a variable becomes very small or large.

Question to ask. Does the relationship behave sensibly?

Practice task. Test one formula at a limit.

Use symmetry

Problem-solving move. Symmetry can simplify systems when conditions are equivalent.

Common failure. Students assume symmetry where none exists or miss it when present.

Better method. Identify mirrored or repeated conditions.

Question to ask. What should be equal by symmetry?

Practice task. Use a symmetric force or circuit example.

Use invariants

Problem-solving move. An invariant is something that remains unchanged while other parts vary.

Common failure. Students focus only on changing features.

Better method. Look for conserved mass, total charge, fixed geometry or constant conditions.

Question to ask. What stays the same across cases?

Practice task. Identify invariant before comparison.

Use constraints

Problem-solving move. Constraints eliminate impossible solutions.

Common failure. Students evaluate every option equally.

Better method. Apply conservation, sign, range, geometry or biological feasibility.

Question to ask. What must be true?

Practice task. Cross out impossible outcomes.

Use dimensional analysis

Problem-solving move. Dimensions can reject wrong equations or conversions.

Common failure. Students see unit cancellation as decoration.

Better method. Check whether both sides of a relationship have compatible dimensions.

Question to ask. Does this equation produce the right kind of quantity?

Practice task. Test candidate formulae.

Use order of magnitude

Problem-solving move. Magnitude reasoning detects factor-of-ten errors.

Common failure. Students accept values because calculator produced them.

Better method. Compare with physical scale or known benchmarks.

Question to ask. Is the result plausible for this system?

Practice task. Locate a deliberate ×1000 error.

Use boundary cases

Problem-solving move. Boundary cases test behaviour at edges of allowed range.

Common failure. Students solve only middle values.

Better method. Check zero, maximum, minimum or threshold cases where meaningful.

Question to ask. What happens at the boundary?

Practice task. Test a graph or formula at an endpoint.

Use counterexamples

Problem-solving move. Counterexamples reveal overgeneralised rules.

Common failure. Students accept a rule after one success.

Better method. Search for a case where the proposed rule should fail.

Question to ask. Can you find one valid exception?

Practice task. Create a counterexample.

Generate alternatives

Problem-solving move. Multiple hypotheses prevent tunnel vision.

Common failure. Students commit to the first explanation.

Better method. List at least two plausible mechanisms before deciding.

Question to ask. What else could produce this evidence?

Practice task. Compare alternatives.

Rank alternatives

Problem-solving move. Explanations should be compared by fit with evidence and assumptions.

Common failure. Students choose the most familiar explanation.

Better method. Ask which explains more evidence with fewer unsupported assumptions.

Question to ask. Which prediction differs between models?

Practice task. Rank three explanations.

Design a discriminating test

Problem-solving move. A good test separates competing explanations.

Common failure. Students collect more of the same evidence.

Better method. Find an observation that the models predict differently.

Question to ask. What result would favour A over B?

Practice task. Design a conceptual test.

Use evidence hierarchy

Problem-solving move. Evidence type should match the question.

Common failure. Students demand one universal ‘best’ evidence source.

Better method. Experiments, field observations, models and historical data serve different purposes.

Question to ask. What evidence is possible and relevant?

Practice task. Choose an appropriate design.

Read the data before explaining

Problem-solving move. Data should constrain the explanation.

Common failure. Students write expected theory even when results differ.

Better method. Describe pattern first.

Question to ask. What does the evidence actually show?

Practice task. Write results sentence before discussion.

Separate observation and inference

Problem-solving move. Direct evidence and interpretation should be distinct.

Common failure. Students present inferred causes as measured facts.

Better method. Mark which sentence is observed and which is inferred.

Question to ask. Could another observer verify this directly?

Practice task. Split one answer into two layers.

State assumptions

Problem-solving move. Assumptions make the solution conditions explicit.

Common failure. Students hide assumptions inside equations.

Better method. Write assumptions such as negligible air resistance or constant temperature where relevant.

Question to ask. Would the answer change if assumption fails?

Practice task. Annotate a solution with assumptions.

Recognise approximation

Problem-solving move. Approximations trade detail for tractability.

Common failure. Students treat approximate models as exact or reject them entirely.

Better method. Ask whether omitted effects are small enough for purpose.

Question to ask. What error does the approximation introduce?

Practice task. Compare exact and approximate reasoning conceptually.

Choose a representation

Problem-solving move. Different representations support different steps.

Common failure. Students stay in prose when a graph or diagram would clarify.

Better method. Switch representation deliberately.

Question to ask. Would a table, diagram or equation reduce complexity?

Practice task. Solve same problem using two representations.

Translate representations

Problem-solving move. Expert solving often moves among prose, diagram, equation and graph.

Common failure. Students understand each separately but cannot connect them.

Better method. Translate one into another.

Question to ask. What feature is preserved?

Practice task. Convert a graph into verbal mechanism.

Handle unfamiliar contexts

Problem-solving move. Surface novelty should not hide familiar structure.

Common failure. Students think unfamiliar object means unfamiliar Science.

Better method. Rename objects generically and identify deep relationship.

Question to ask. What would this problem be called without the story?

Practice task. Strip context from a PSLE-style question.

Handle extra information

Problem-solving move. Some problems include nonessential details.

Common failure. Students use every number and fact.

Better method. Test relevance against the plan.

Question to ask. Does this information connect to any step?

Practice task. Remove irrelevant data.

Handle missing information

Problem-solving move. Some problems require inference from definitions, graphs or earlier parts.

Common failure. Students wait for explicit numbers.

Better method. Derive missing quantities when justified.

Question to ask. What can be calculated or inferred first?

Practice task. Find one hidden value.

Handle ambiguous wording

Problem-solving move. If a problem genuinely lacks necessary clarity, interpretation should be explicit.

Common failure. Students guess silently.

Better method. State the reasonable interpretation or seek clarification in learning contexts.

Question to ask. Which assumption resolves ambiguity?

Practice task. Rewrite the question more precisely.

Explain each step

Problem-solving move. Explanations reveal whether the method is understood.

Common failure. Students produce correct arithmetic with no rationale.

Better method. Add a short why beside major steps.

Question to ask. Why is this operation scientifically valid?

Practice task. Teach the solution aloud.

Justify formula choice

Problem-solving move. Formula selection should follow the model.

Common failure. Students choose by matching symbols or keywords.

Better method. State the scientific relationship before equation.

Question to ask. What physical law connects these quantities?

Practice task. Explain formula choice in words.

Justify evidence choice

Problem-solving move. Evidence should be relevant and sufficient for the claim.

Common failure. Students cite any true fact.

Better method. Explain why the selected data discriminate among explanations.

Question to ask. How does this evidence change confidence?

Practice task. Remove irrelevant evidence.

Check sign

Problem-solving move. Signs can encode direction or change.

Common failure. Students discard negative signs as errors.

Better method. Interpret sign physically.

Question to ask. What does negative mean in this coordinate or change?

Practice task. Explain sign before final answer.

Check direction

Problem-solving move. Vector or flow direction matters in many problems.

Common failure. Students report magnitude only.

Better method. State direction relative to defined frame.

Question to ask. Which way does the force, current, heat or flow act?

Practice task. Add direction to final answer.

Check units

Problem-solving move. Final units must match target quantity.

Common failure. Students attach a plausible-looking unit without verifying.

Better method. Derive units from working.

Question to ask. Do the dimensions match?

Practice task. Use unit mismatch to find an error.

Check magnitude

Problem-solving move. Physical plausibility is a strong final filter.

Common failure. Students stop at arithmetic completion.

Better method. Compare with known scales or limiting values.

Question to ask. Could this happen in the real system?

Practice task. Flag implausible results.

Check boundary

Problem-solving move. The answer should satisfy stated constraints.

Common failure. Students produce probabilities above 100% or efficiencies above 100%.

Better method. Compare with physical and mathematical bounds.

Question to ask. What values are impossible?

Practice task. Use bound checks.

Check trend

Problem-solving move. The exact result should agree with qualitative prediction unless the model reveals something unexpected.

Common failure. Students forget their earlier prediction.

Better method. Compare calculated direction with predicted direction.

Question to ask. If they differ, which step needs review?

Practice task. Reconcile prediction and calculation.

Check graph

Problem-solving move. Graphical interpretation can verify calculation or mechanism.

Common failure. Students use numerical and visual evidence separately.

Better method. Locate the result on the graph or sketch expected shape.

Question to ask. Does the graph support the answer?

Practice task. Cross-check one calculation graphically.

Check with alternative method

Problem-solving move. Independent methods can catch hidden mistakes.

Common failure. Students repeat the same route and reproduce the same error.

Better method. Use ratio, graph, equation or estimate as second route.

Question to ask. Do both approaches agree?

Practice task. Solve one problem two ways.

Reflect on the first hard step

Problem-solving move. Reflection should identify where cognitive work was concentrated.

Common failure. Students write ‘the problem was hard’.

Better method. Name the first decision that required help.

Question to ask. What clue would help recognise this next time?

Practice task. Write one future cue.

Build a problem type library

Problem-solving move. A personal library should store deep structures, not copied questions.

Common failure. Students sort only by chapter.

Better method. Tag by reasoning pattern: conservation, proportion, system, graph, fair test, multi-step calculation.

Question to ask. What problems share the same structure?

Practice task. Group mixed questions by deep type.

Use worked examples

Problem-solving move. Worked examples can reveal expert planning if studied actively.

Common failure. Students copy every line.

Better method. Cover the next step and predict it.

Question to ask. Why did the solver choose this step?

Practice task. Complete partially worked solutions.

Use faded examples

Problem-solving move. Faded examples gradually remove steps as competence grows.

Common failure. Students jump from full example to independent work too quickly.

Better method. Remove one step at a time.

Question to ask. Which step can the learner now generate?

Practice task. Use progressive completion.

Self-explanation

Problem-solving move. Explaining solved steps improves transfer.

Common failure. Students read solutions silently.

Better method. State why each step follows.

Question to ask. Could another method work?

Practice task. Annotate worked solution.

Error analysis

Problem-solving move. Wrong solutions can be powerful learning material.

Common failure. Students only study correct methods.

Better method. Find the first wrong step and explain its consequence.

Question to ask. What misconception produced the error?

Practice task. Debug a flawed solution.

Compare solutions

Problem-solving move. Multiple correct methods reveal flexibility.

Common failure. Students think one method is universally best.

Better method. Compare efficiency, assumptions and clarity.

Question to ask. Which method generalises better?

Practice task. Solve with two approaches.

Timed problem solving

Problem-solving move. Time pressure should be added after method is stable.

Common failure. Students practise only slowly then panic in exams.

Better method. Use modest timed sets and analyse where time is spent.

Question to ask. Which stage—reading, planning, calculation or writing—is slow?

Practice task. Track time by stage.

Stuck strategy

Problem-solving move. Being stuck should trigger a sequence, not random guessing.

Common failure. Students reread or try formulas blindly.

Better method. Return to target, givens, representation and principle.

Question to ask. What is the smallest subproblem you can solve?

Practice task. Use a written stuck checklist.

Ask a better question

Problem-solving move. Changing the internal question can unlock the solution.

Common failure. Students ask ‘What formula do I use?’ too early.

Better method. Ask ‘What is changing?’, ‘What is conserved?’, ‘What evidence matters?’

Question to ask. Which relationship is controlling this system?

Practice task. Rewrite self-talk.

Use partial progress

Problem-solving move. A complete solution need not appear all at once.

Common failure. Students do nothing until they see the entire route.

Better method. Write a diagram, known value or principle to create momentum.

Question to ask. What valid step can you take now?

Practice task. Score progress by reasoning, not answer only.

Know when to stop

Problem-solving move. Some solutions become less reliable with unnecessary extra work.

Common failure. Students keep adding explanation or recalculating correct results.

Better method. Stop when target is answered and checks pass.

Question to ask. Has the problem been completely but minimally solved?

Practice task. Edit overlong solutions.

Communicate final answer

Problem-solving move. The final response should make the scientific meaning visible.

Common failure. Students end with a bare number or vague phrase.

Better method. State value, unit, direction or relationship as required.

Question to ask. What does the answer mean for the system?

Practice task. Write a full final sentence.

Transfer to Biology

Problem-solving move. Biology problems often involve systems, data, mechanisms and populations.

Common failure. Students think problem solving is only mathematical.

Better method. Use causal chains and evidence comparison.

Question to ask. What structure-function relationship controls the result?

Practice task. Solve an unfamiliar biological system question.

Transfer to Chemistry

Problem-solving move. Chemistry problems mix particle models, equations, quantities and practical data.

Common failure. Students use calculations without particle meaning.

Better method. Connect symbolic steps to substances and conservation.

Question to ask. What particles or moles does the equation represent?

Practice task. Solve a changed-substance problem.

Transfer to Physics

Problem-solving move. Physics problems frequently require representation, equations and unit checks.

Common failure. Students plug numbers into memorised formulas.

Better method. Draw system and predict direction first.

Question to ask. Which interaction creates the relationship?

Practice task. Solve a new-context force or energy question.

Transfer to Earth Science

Problem-solving move. Earth problems often require scale, systems and time-series evidence.

Common failure. Students demand controlled experiments for inaccessible systems.

Better method. Use observational data, models and physical constraints.

Question to ask. What scale and evidence source apply?

Practice task. Interpret an Earth-system dataset.

Transfer to experiments

Problem-solving move. Experimental problems require variable, measurement and evaluation reasoning.

Common failure. Students focus on equipment names.

Better method. Reconstruct question, variables, evidence and limitations.

Question to ask. Which design feature protects the conclusion?

Practice task. Debug a flawed experiment.

Transfer to news claims

Problem-solving move. Real-world Science problems require source and evidence evaluation.

Common failure. Students separate school reasoning from media claims.

Better method. Apply causation, uncertainty and model limits.

Question to ask. What evidence type supports the headline?

Practice task. Evaluate one science-news claim.

Reflect and retest

Problem-solving move. A solved problem becomes learning only when the key decision can be repeated later.

Common failure. Students review the solution immediately and assume mastery.

Better method. Schedule a new structurally similar problem after delay.

Question to ask. Can you solve without remembering the surface answer?

Practice task. Retest after several days.

A twelve-week Science problem-solving programme

Week 1: target, givens and relevance.
Week 2: diagrams, tables and representations.
Week 3: concept and model selection.
Week 4: planning forward and backward.
Week 5: proportional, rate and conservation reasoning.
Week 6: units, dimensions and magnitude.
Week 7: causal mechanisms and alternatives.
Week 8: graphs, data and experiment problems.
Week 9: multi-step quantitative problems.
Week 10: unfamiliar contexts and extra information.
Week 11: checking, reflection and error analysis.
Week 12: mixed timed transfer across Science branches.

When tuition may help with Science problem solving

Extra support can help when a learner knows the chapter content but freezes on unfamiliar questions, chooses formulae by keywords or cannot plan multi-step answers. A tutor should model the planning process aloud, then fade the prompts until the learner creates the representation and plan independently.

For current Primary 3–6 and PSLE programme information, use Primary Science Tuition Sengkang. Secondary problem-solving coverage here is educational transition material.

Frequently asked questions

What is the best first step in a Science problem?

Identify exactly what is being asked and represent the known information before choosing a formula or writing an explanation.

Why do I know the topic but still cannot solve the question?

You may have a selection or representation problem rather than a content problem. Practise identifying the deep relationship in unfamiliar contexts.

Should I plug numbers into formulas immediately?

Usually no. Plan symbolically and make units compatible first. This reduces arithmetic distraction and makes the scientific relationship clearer.

What do I do when I am stuck?

Return to target, givens, diagram, concept and smallest solvable subproblem. Avoid random formula searching.

How can I check a Science calculation?

Check unit, order of magnitude, sign, physical bounds and whether the result agrees with your qualitative prediction.

Can problem solving be improved by practice?

Yes, especially when practice includes planning, explanation, error analysis and transfer rather than only repeating similar final answers.

Final operating rule

Do not begin a difficult Science problem by asking, “Which formula do I use?” Begin with: What is being asked? What do I know? What system am I analysing? Which scientific model applies? What must be found first? Then execute, explain, check and reflect. The solution becomes transferable when the student can recognise the same structure inside a different-looking problem.

Read the command — problem-solving clinic 1

Start with a fresh problem where read the command is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students solve the topic but not the task.. Ask how that failure changes the solution path. Then apply the better method: Translate the command into an operation before using content. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What would a complete response have to do? Run the practice task: Rewrite the question in your own words. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Finish with delayed transfer to another Science branch. Parents can ask what the first solvable step is; tutors can compare different valid routes. The final target is a learner who can start unfamiliar problems calmly without waiting for a template.

Identify the target — problem-solving clinic 1

Start with a fresh problem where identify the target is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students start manipulating given information without naming the goal.. Ask how that failure changes the solution path. Then apply the better method: Write the target at the top of the working. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What exactly must the final answer contain? Run the practice task: State target in words and unit. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

List the givens — problem-solving clinic 1

Start with a fresh problem where list the givens is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students repeatedly reread the stem and miss values or conditions.. Ask how that failure changes the solution path. Then apply the better method: Create a compact list of known quantities or facts. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which givens are numerical, qualitative or conditional? Run the practice task: Build a given/unknown table. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Separate relevant from irrelevant — problem-solving clinic 1

Start with a fresh problem where separate relevant from irrelevant is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students assume every number must enter the calculation.. Ask how that failure changes the solution path. Then apply the better method: Ask what each piece of information contributes to the target. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Would the answer change if this detail disappeared? Run the practice task: Cross out one irrelevant detail in practice. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Identify hidden information — problem-solving clinic 1

Start with a fresh problem where identify hidden information is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students wait for every quantity to be written explicitly.. Ask how that failure changes the solution path. Then apply the better method: Use definitions, graph slopes or conservation rules to derive missing information. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What can be inferred from the setup? Run the practice task: Find one hidden quantity before solving. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Draw the system — problem-solving clinic 1

Start with a fresh problem where draw the system is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students try to hold the entire system mentally.. Ask how that failure changes the solution path. Then apply the better method: Sketch only features relevant to the problem. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What must be connected or positioned? Run the practice task: Draw a simple labelled system. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Choose the boundary — problem-solving clinic 1

Start with a fresh problem where choose the boundary is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students accidentally change what they are tracking.. Ask how that failure changes the solution path. Then apply the better method: Define the object, organism, circuit or chemical system. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What can enter or leave the system? Run the practice task: Redraw with an alternative boundary and compare. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use a table — problem-solving clinic 1

Start with a fresh problem where use a table is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students compare mismatched rows.. Ask how that failure changes the solution path. Then apply the better method: Place variables and cases in aligned columns. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which entries belong in one valid comparison? Run the practice task: Create a compact comparison table. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use a graph — problem-solving clinic 1

Start with a fresh problem where use a graph is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students calculate before inspecting trend or axes.. Ask how that failure changes the solution path. Then apply the better method: Read axes, units and shape first. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What relationship does the graph already show? Run the practice task: Sketch expected trend before exact reading. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use a concept map — problem-solving clinic 1

Start with a fresh problem where use a concept map is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students retrieve isolated terms without structure.. Ask how that failure changes the solution path. Then apply the better method: Link terms with labelled relations. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which path leads from cause to effect? Run the practice task: Build a five-node concept map. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Name the concept — problem-solving clinic 1

Start with a fresh problem where name the concept is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students chase surface nouns.. Ask how that failure changes the solution path. Then apply the better method: Ask whether the problem is fundamentally about forces, energy, particles, systems, cycles, evidence or another model. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which chapter idea explains the relationship? Run the practice task: Rename the question using the concept only. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Choose the model — problem-solving clinic 1

Start with a fresh problem where choose the model is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students use the most familiar model automatically.. Ask how that failure changes the solution path. Then apply the better method: Select the representation that preserves the needed relationship. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What assumptions does this model require? Run the practice task: Compare two candidate models. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Recall the principle — problem-solving clinic 1

Start with a fresh problem where recall the principle is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students search memory for phrases instead of mechanisms.. Ask how that failure changes the solution path. Then apply the better method: State the rule in words before using symbols. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Why should the outcome follow? Run the practice task: Write principle in one sentence. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Predict direction — problem-solving clinic 1

Start with a fresh problem where predict direction is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students compute without knowing whether answer should rise or fall.. Ask how that failure changes the solution path. Then apply the better method: Predict increase, decrease, no change or direction first. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: If X increases, what should Y do? Run the practice task: Make directional prediction. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Estimate scale — problem-solving clinic 1

Start with a fresh problem where estimate scale is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students accept calculator outputs blindly.. Ask how that failure changes the solution path. Then apply the better method: Use familiar benchmarks and powers of ten. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Should answer be closer to 0.1, 10 or 10000? Run the practice task: Estimate before exact arithmetic. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Plan steps — problem-solving clinic 1

Start with a fresh problem where plan steps is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students discover the route while calculating and become lost.. Ask how that failure changes the solution path. Then apply the better method: Write the sequence symbolically or in short phrases. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What must be found before the target? Run the practice task: Create a three-step solution map. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Work backwards — problem-solving clinic 1

Start with a fresh problem where work backwards is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students begin with the first number in the stem.. Ask how that failure changes the solution path. Then apply the better method: Trace dependencies from target to known quantities. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What formula or evidence would give the target? Run the practice task: Build a backwards dependency tree. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Work forwards — problem-solving clinic 1

Start with a fresh problem where work forwards is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students generate many intermediate values without purpose.. Ask how that failure changes the solution path. Then apply the better method: Use only derivations likely to connect to target. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which knowns combine naturally? Run the practice task: Compare forward and backward routes. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Decompose the problem — problem-solving clinic 1

Start with a fresh problem where decompose the problem is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students search for one giant formula or one perfect sentence.. Ask how that failure changes the solution path. Then apply the better method: Solve subproblems and reconnect them. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What is the first independently solvable piece? Run the practice task: Number the subproblems. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Solve symbolically first — problem-solving clinic 1

Start with a fresh problem where solve symbolically first is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students plug numbers too early.. Ask how that failure changes the solution path. Then apply the better method: Rearrange and connect equations before substitution. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What relationship remains if numbers disappear? Run the practice task: Solve in symbols then insert values. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Track units — problem-solving clinic 1

Start with a fresh problem where track units is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students drop units until the end.. Ask how that failure changes the solution path. Then apply the better method: Carry units through conversions and calculations. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What unit must the target have? Run the practice task: Cancel units explicitly. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Convert units early — problem-solving clinic 1

Start with a fresh problem where convert units early is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students mix cm, m, min and s.. Ask how that failure changes the solution path. Then apply the better method: Convert all inputs to the intended unit system before substitution. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which conversions are required? Run the practice task: Build a unit-conversion line. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use significant figures sensibly — problem-solving clinic 1

Start with a fresh problem where use significant figures sensibly is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students copy every calculator digit.. Ask how that failure changes the solution path. Then apply the better method: Keep working precision then round final answer appropriately. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which input limits precision? Run the practice task: Compare overprecise and sensible answers. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Check algebra — problem-solving clinic 1

Start with a fresh problem where check algebra is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students assume formula choice guarantees correct calculation.. Ask how that failure changes the solution path. Then apply the better method: Solve symbolically and verify by re-substitution. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Does the rearranged formula reproduce the original? Run the practice task: Reverse-check one rearrangement. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Check calculator entry — problem-solving clinic 1

Start with a fresh problem where check calculator entry is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students trust the displayed number.. Ask how that failure changes the solution path. Then apply the better method: Compare typed expression with written line. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Were all grouped operations entered correctly? Run the practice task: Use one deliberate calculator audit. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use conservation — problem-solving clinic 1

Start with a fresh problem where use conservation is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students think matter or energy disappears.. Ask how that failure changes the solution path. Then apply the better method: Account for what enters, leaves and changes form. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Where did the conserved quantity go? Run the practice task: Create before/after accounting. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use proportionality — problem-solving clinic 1

Start with a fresh problem where use proportionality is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students treat every trend as proportional.. Ask how that failure changes the solution path. Then apply the better method: Check constant ratio and conditions. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Does doubling one quantity double the other? Run the practice task: Solve one by ratio reasoning. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use rate reasoning — problem-solving clinic 1

Start with a fresh problem where use rate reasoning is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students compare totals from different intervals.. Ask how that failure changes the solution path. Then apply the better method: Normalize to a common denominator. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Per what? Run the practice task: Calculate and compare rates. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use limiting cases — problem-solving clinic 1

Start with a fresh problem where use limiting cases is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students accept equations that predict impossible behaviour at zero or infinity.. Ask how that failure changes the solution path. Then apply the better method: Ask what happens when a variable becomes very small or large. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Does the relationship behave sensibly? Run the practice task: Test one formula at a limit. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use symmetry — problem-solving clinic 1

Start with a fresh problem where use symmetry is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students assume symmetry where none exists or miss it when present.. Ask how that failure changes the solution path. Then apply the better method: Identify mirrored or repeated conditions. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What should be equal by symmetry? Run the practice task: Use a symmetric force or circuit example. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use invariants — problem-solving clinic 1

Start with a fresh problem where use invariants is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students focus only on changing features.. Ask how that failure changes the solution path. Then apply the better method: Look for conserved mass, total charge, fixed geometry or constant conditions. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What stays the same across cases? Run the practice task: Identify invariant before comparison. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use constraints — problem-solving clinic 1

Start with a fresh problem where use constraints is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students evaluate every option equally.. Ask how that failure changes the solution path. Then apply the better method: Apply conservation, sign, range, geometry or biological feasibility. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What must be true? Run the practice task: Cross out impossible outcomes. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use dimensional analysis — problem-solving clinic 1

Start with a fresh problem where use dimensional analysis is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students see unit cancellation as decoration.. Ask how that failure changes the solution path. Then apply the better method: Check whether both sides of a relationship have compatible dimensions. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Does this equation produce the right kind of quantity? Run the practice task: Test candidate formulae. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use order of magnitude — problem-solving clinic 1

Start with a fresh problem where use order of magnitude is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students accept values because calculator produced them.. Ask how that failure changes the solution path. Then apply the better method: Compare with physical scale or known benchmarks. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Is the result plausible for this system? Run the practice task: Locate a deliberate ×1000 error. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use boundary cases — problem-solving clinic 1

Start with a fresh problem where use boundary cases is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students solve only middle values.. Ask how that failure changes the solution path. Then apply the better method: Check zero, maximum, minimum or threshold cases where meaningful. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What happens at the boundary? Run the practice task: Test a graph or formula at an endpoint. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use counterexamples — problem-solving clinic 1

Start with a fresh problem where use counterexamples is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students accept a rule after one success.. Ask how that failure changes the solution path. Then apply the better method: Search for a case where the proposed rule should fail. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Can you find one valid exception? Run the practice task: Create a counterexample. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Generate alternatives — problem-solving clinic 1

Start with a fresh problem where generate alternatives is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students commit to the first explanation.. Ask how that failure changes the solution path. Then apply the better method: List at least two plausible mechanisms before deciding. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What else could produce this evidence? Run the practice task: Compare alternatives. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Rank alternatives — problem-solving clinic 1

Start with a fresh problem where rank alternatives is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students choose the most familiar explanation.. Ask how that failure changes the solution path. Then apply the better method: Ask which explains more evidence with fewer unsupported assumptions. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Which prediction differs between models? Run the practice task: Rank three explanations. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Design a discriminating test — problem-solving clinic 1

Start with a fresh problem where design a discriminating test is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students collect more of the same evidence.. Ask how that failure changes the solution path. Then apply the better method: Find an observation that the models predict differently. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What result would favour A over B? Run the practice task: Design a conceptual test. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Use evidence hierarchy — problem-solving clinic 1

Start with a fresh problem where use evidence hierarchy is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students demand one universal ‘best’ evidence source.. Ask how that failure changes the solution path. Then apply the better method: Experiments, field observations, models and historical data serve different purposes. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What evidence is possible and relevant? Run the practice task: Choose an appropriate design. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Read the data before explaining — problem-solving clinic 1

Start with a fresh problem where read the data before explaining is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students write expected theory even when results differ.. Ask how that failure changes the solution path. Then apply the better method: Describe pattern first. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What does the evidence actually show? Run the practice task: Write results sentence before discussion. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Separate observation and inference — problem-solving clinic 1

Start with a fresh problem where separate observation and inference is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students present inferred causes as measured facts.. Ask how that failure changes the solution path. Then apply the better method: Mark which sentence is observed and which is inferred. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Could another observer verify this directly? Run the practice task: Split one answer into two layers. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

State assumptions — problem-solving clinic 1

Start with a fresh problem where state assumptions is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students hide assumptions inside equations.. Ask how that failure changes the solution path. Then apply the better method: Write assumptions such as negligible air resistance or constant temperature where relevant. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Would the answer change if assumption fails? Run the practice task: Annotate a solution with assumptions. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Recognise approximation — problem-solving clinic 1

Start with a fresh problem where recognise approximation is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students treat approximate models as exact or reject them entirely.. Ask how that failure changes the solution path. Then apply the better method: Ask whether omitted effects are small enough for purpose. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: What error does the approximation introduce? Run the practice task: Compare exact and approximate reasoning conceptually. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Choose a representation — problem-solving clinic 1

Start with a fresh problem where choose a representation is useful but not announced. Ask the learner to make a first attempt, then identify whether the move was used spontaneously. If not, ask what clue in the problem should have triggered it.

Surface the common failure: Students stay in prose when a graph or diagram would clarify.. Ask how that failure changes the solution path. Then apply the better method: Switch representation deliberately. The learner should rebuild the plan rather than merely correct the final answer.

Now ask: Would a table, diagram or equation reduce complexity? Run the practice task: Solve same problem using two representations. Require explanation of why the move works. A correct answer without a reusable decision rule is not yet robust problem solving.

Read the command — problem-solving clinic 2

Identify the target — problem-solving clinic 2

List the givens — problem-solving clinic 2

Separate relevant from irrelevant — problem-solving clinic 2

Identify hidden information — problem-solving clinic 2

Draw the system — problem-solving clinic 2

Choose the boundary — problem-solving clinic 2

Use a table — problem-solving clinic 2

Use a graph — problem-solving clinic 2

Use a concept map — problem-solving clinic 2

Name the concept — problem-solving clinic 2

Choose the model — problem-solving clinic 2

Recall the principle — problem-solving clinic 2

Predict direction — problem-solving clinic 2

Estimate scale — problem-solving clinic 2

Plan steps — problem-solving clinic 2

Work backwards — problem-solving clinic 2

Work forwards — problem-solving clinic 2

Decompose the problem — problem-solving clinic 2

Solve symbolically first — problem-solving clinic 2

Track units — problem-solving clinic 2

Convert units early — problem-solving clinic 2

Use significant figures sensibly — problem-solving clinic 2

Check algebra — problem-solving clinic 2

Check calculator entry — problem-solving clinic 2

Use conservation — problem-solving clinic 2

Use proportionality — problem-solving clinic 2

Use rate reasoning — problem-solving clinic 2