Cambridge International Education Thinking Skills AS & A Level

SECTION 1 — PROBLEM‑SOLVING SKILLS

Below, each syllabus skill is turned into:

• Definition

• Example

• Short supporting line from the syllabus (quoted)

1.1 Organise Information

Understand information in various forms

Definition: Ability to interpret information presented as text, tables, charts, or diagrams.
Example: A bus timetable (table) + a route map (diagram) + a paragraph describing delays (text) → you combine all to choose the best bus.
Syllabus line: “Understand information presented as text, tables and diagrams.”

Extract relevant information

Definition: Selecting only the information needed to solve the problem.
Example: A word problem mentions ages, names, and prices, but the question asks only for total cost → ignore ages and names.
Syllabus line: “Extract the information that is relevant to the problem to be solved.”

Extract data from related data sets

Definition: Combining information from multiple sources to solve a problem.
Example: One table shows hourly pay; another shows hours worked → combine to calculate weekly pay.
Syllabus line: “Extract data from related data sets that can be combined…”

1.2 Understand logical relationships

Simple models

Definition: A rule or system showing how inputs produce outputs.
Example: Taxi fare = $3 + $1.50 per km.
Syllabus line: “Simple models may be described as instructions for calculations…”

Necessary and sufficient conditions

Necessary: Must be true for something to happen.
Example: Having a ticket is necessary to board a plane.

Sufficient: Guarantees the result by itself.
Example: Scoring 100% is sufficient to pass an exam.
Syllabus line: “Identify necessary and sufficient conditions.”

Deduce information from processed data

Definition: Using summaries (averages, totals, graphs) to infer properties of original data.
Example: If average score is 95% with low variation, most students scored high.
Syllabus line: “Deduce some information about the original data.”

SECTION 2 — PROCESS INFORMATION

2.1 Perform operations

Use information appropriately

Definition: Choosing and performing the correct calculations or steps.
Example: Multiply price × quantity to find total cost.
Syllabus line: “Use one or more items of information appropriately…”

Apply a model

Definition: Substitute real values into a given rule or formula.
Example: Cost = 3 + 1.5×10 = 18.
Syllabus line: “Apply a model to a given situation.”

2.2 Identify cases that satisfy criteria

Search through possible solutions

Definition: Checking all options to find those that meet every condition.
Example: From a list of students, choose those over 16 and with perfect attendance.
Syllabus line: “Search through all possible solutions… to identify those which satisfy given criteria.”

Identify unmet criteria

Definition: Spotting which rule a proposed solution breaks.
Example: A schedule fits all lessons but violates “no lessons after 5 pm.”
Syllabus line: “Identify criteria that have not been met…”

2.3 Make appropriate deductions

Definition: Drawing new conclusions from given information.
Example: If A > B and B > C, then A > C.
Syllabus line: “Draw conclusions based on the information available.”

SECTION 3 — ANALYSE DATA

3.1 Transform data

Recognise alternative representations

Definition: Seeing that different formats show the same data.
Example: A bar chart and a pie chart showing the same proportions.
Syllabus line: “Recognise alternative representations of a set of information.”

Identify features of a model from representations

Definition: Interpreting graphs/tables to understand model behaviour.
Example: Gradient of a distance–time graph = speed.
Syllabus line: “Interpret the gradient appropriately in the context of the model.”

3.2 Explain trends

Suggest explanations for trends

Definition: Giving plausible reasons for patterns or changes.
Example: Sales rise in December → holiday shopping.
Syllabus line: “Suggest possible explanations for trends…”

Fit a model to information

Definition: Adjusting a formula so it matches data.
Example: Taxi prices → deduce fixed fee + per‑km rate.
Syllabus line: “Deduce the values for… parameters so that the model fits…”

SECTION 4 — CONSIDER WIDER PROBLEMS

4.1 Impact of a change

Definition: Considering how a scenario change affects your solution.
Example: Road closure increases travel time → adjust schedule.
Syllabus line: “Consider the implications of a change…”

4.2 Develop a model

Identify features to include

Definition: Deciding which real‑world factors must be represented.
Example: Rush‑hour traffic in a travel‑time model.
Syllabus line: “Identify features… which need to be included.”

Adjust a model

Definition: Modifying the model to better match reality.
Example: Add peak‑time surcharge to fare model.
Syllabus line: “Adjust a model to incorporate additional features.”

SECTION 5 — EVALUATE & USE EVIDENCE

5.1 Evaluate evidence

Credibility

Definition: How believable evidence is.
Example: A peer‑reviewed study is more credible than an anonymous blog.
Syllabus line: “Assess credibility of evidence – reliability, plausibility…”

Reliability

Definition: Trustworthiness of the source.
Example: A trained observer is more reliable than a distant witness.

Plausibility

Definition: Whether the claim itself seems likely.
Example: “People need sleep” is plausible; “humans don’t need sleep” is not.

Corroboration & consistency

Corroboration: Two sources support each other.
Consistency: They do not contradict.
Example: Two surveys showing similar results.

Representativeness

Definition: Whether a sample reflects the population.
Example: Surveying only teenagers does not represent all adults.
Syllabus line: “Representativeness could be affected if the sample shares a characteristic…”

Assess presentation of data

Definition: Checking for misleading graphs/tables.
Example: A truncated y‑axis exaggerates differences.

5.2 Use evidence

Assess explanation

Definition: Judging whether an explanation fits all evidence.
Example: An explanation that ignores half the data is weak.

Assess inference

Definition: Checking whether a conclusion logically follows.
Example: “Some students cheat → all students cheat” is invalid.

Suggest explanation

Definition: Proposing a plausible cause.
Example: Sales drop → new competitor entered market.

Suggest inference

Definition: Drawing a reasonable conclusion from evidence.
Example: 90% satisfaction → product is well‑received.

Form a judgement

Definition: Combining multiple sources to reach a conclusion.
Example: Reading several studies before judging a policy.

SECTION 6 — ANALYSE REASONING

6.1 Structure of arguments

Recognise an argument

Definition: Identifying when reasons support a conclusion.
Example: “Ban cars because they cause pollution.”

Key elements

• Main conclusion — the main claim

  • Example: “Therefore, we should raise wages.”

• Intermediate conclusion — supports another conclusion

• Reason — supports a conclusion

• Counter‑assertion — opposing claim

• Counter‑argument — reasoned objection

• Example — specific case supporting a claim

• Evidence — data/statistics/expert opinion

Syllabus line: “Key elements: main conclusion, intermediate conclusion, reason…”

Unstated assumption

Definition: A hidden step required for the argument to work.
Example: “Close the park because it’s dangerous” assumes closing it reduces danger.

SECTION 7 — EVALUATE REASONING (FLAWS)

Each flaw includes definition + example.

• Equivocation: Switching meaning of a word.
  Example: “Feathers are light → feathers can’t be dark.”

• Conflation: Treating different concepts as identical.
  Example: Legal = moral.

• Circular argument: Conclusion used as a reason.
  Example: “He’s honest because he tells the truth.”

• Begging the question: Assuming what must be proved.
  Example: “Games are harmful because they’re bad.”

• Invalid deduction: Incorrect logic.
  Example: “Ground is wet → it must have rained.”

• Causal flaw: Assuming correlation = causation.
  Example: Ice cream sales cause drowning.

• Rash generalisation: Too little evidence.
  Example: “Two rude teens → all teens rude.”

• Sweeping generalisation: Ignoring exceptions.
  Example: “Exercise is good → everyone must run daily.”

• False dichotomy: Only two options given.
  Example: “Support this law or hate safety.”

• Confusing necessary/sufficient:
  Example: “Degree required → degree guarantees job.”

• Slippery slope: Claiming inevitable disaster.
  Example: “Phones in class → no learning at all.”

• Ad hominem: Attacking person.
  Example: “Don’t trust her argument; she failed school.”

• Tu quoque: “You do it too.”
  Example: “You litter, so you can’t criticise me.”

• Straw man: Misrepresenting opponent.
  Example: “Regulate social media → ban free speech.”

SECTION 8 — WEAKNESSES IN REASONING

• Support too weak: Evidence supports only part of conclusion.

• Inconsistency: Contradictory statements.

• Reliance on weak assumption: Unsupported claim used as reason.

• Irrelevant appeal: Celebrity endorsement, popularity, emotion.

• Weak analogy: Few relevant similarities.

• Failure to respond to counter: Ignoring obvious objections.

SECTION 9 — CONSTRUCT REASONING

• Articulate a conclusion

• Provide reasons

• Develop strands

• Use intermediate conclusions

• Strengthen with:

  • counter‑argument + response

  • examples

  • evidence

  • analogy

  • hypothetical reasoning

SECTION 10 — COMMAND WORDS

SECTION 11 — ASSESSMENT OBJECTIVES

• AO1: Understand information and relationships

• AO2: Evaluate/process information to draw conclusions

• AO3: Suggest explanations, construct arguments, devise methods

SECTION 12 — FORMULAS & METHODS

12.1 Distance–Rate–Time

• Distance=Rate×Time

• Rate=DistanceTime

• Time=DistanceRate

Example:
Speed = 50 km/h, time = 3 h → distance = 150 km.

12.2 Area

Rectangle

A=length×width
Example: 5 × 3 = 15.

Square

A=side2
Example: side 4 → 16.

Triangle

A=12×base×height
Example: ½ × 8 × 4 = 16.

12.3 Perimeter

Rectangle

P=2(length+width)

Square

P=4×side

Triangle

P=a+b+c

12.4 Algebra — expressions & equations

• Expression: No equals sign

  • “Three more than twice x” → 2x+3

• Equation: Has equals sign

  • “Twice x plus 3 equals 11” → 2x+3=11

12.5 Substitution method

1. Rearrange one equation

2. Substitute into the other

3. Solve

4. Substitute back

Example:

x+y=10,2x−y=4

→ y=10−x
→ substitute → solve → find both values.