Applied Reasoning Across Subjects

Introduction

Here's something that might surprise you: the critical thinking skills you've been learning in this course don't just apply to one type of question. They apply to every subject you'll encounter in the FSCE 11+ exam — and in secondary school beyond it.

The FSCE exam is specifically designed to test whether you can transfer your thinking skills from one situation to another. This means the same skills you use to evaluate an argument in English can help you solve a problem in maths, and the same pattern-spotting you use in maths can help you with comprehension in English.

In this lesson, you'll see how critical thinking works across English comprehension, maths problem solving, and creative writing — and you'll practise applying the same thinking skills to very different question types.

The Big Idea: Transferable Thinking

graph TD
    A["CRITICAL THINKING SKILLS"] --> B["English Comprehension"]
    A --> C["Maths Problem Solving"]
    A --> D["Creative Writing"]
    A --> E["Science & General Knowledge"]
    B --> F["Evaluating arguments, spotting bias, identifying facts vs opinions"]
    C --> G["Breaking down problems, finding patterns, logical deduction"]
    D --> H["Structuring ideas, using evidence, making connections"]
    E --> I["Drawing conclusions from data, questioning assumptions"]
    style A fill:#e3f2fd
    style B fill:#e8f5e9
    style C fill:#fff3e0
    style D fill:#fce4ec
    style E fill:#f3e5f5

Worked Examples

Worked Example 1: The Same Skill in Three Subjects

The skill: Identifying what's relevant and what's not

In English Comprehension: "Read this passage and answer the question: Why did the character decide to leave?"

A strong reader ignores the descriptions of the weather, the character's breakfast, and the colour of their clothes. They focus on the sentences that explain the character's motivation — the relevant information.

In Maths: "A train leaves London at 9:15 travelling at 60mph. The train has 8 carriages and can carry 400 passengers. How far has it travelled by 10:45?"

A strong problem solver ignores the number of carriages and passengers (irrelevant to distance). They focus on the speed (60mph) and the time (1 hour 30 minutes) — the relevant information. Distance = 60 x 1.5 = 90 miles.

In Creative Writing: "Write a story about a character who faces a difficult choice."

A strong writer doesn't include every detail about the character's life. They focus on the details that are relevant to the choice — the character's feelings, the options available, and the consequences.

The skill is the same: separating what matters from what doesn't.

Worked Example 2: Pattern-Spotting Across Subjects

In Maths: "What comes next? 2, 6, 18, 54, ___" Each number is multiplied by 3. Answer: 162.

In English: "Read these three paragraphs from the story. What pattern do you notice in how the character reacts to bad news?"

Paragraph 1: Character receives bad news, gets angry, then calms down. Paragraph 2: Character receives worse news, gets angrier, then calms down. Paragraph 3: Character receives the worst news...

Pattern: Each time, the character reacts more strongly but still calms down. A critical thinker might predict that in Paragraph 3, the character either follows the pattern (getting even angrier but calming down) or breaks the pattern (this time, they don't calm down — which creates a dramatic turning point).

In General Reasoning: "In a class election, the same candidate has won for the past three years. Does this mean they will win this year?"

A critical thinker recognises the pattern but also knows that past patterns don't guarantee future results. They consider what might change this year (new candidates, different voters, changed circumstances).

Worked Example 3: Evaluating Evidence Across Subjects

In English Comprehension: "The author argues that homework should be abolished. How convincing is their argument?"

You evaluate: What evidence do they give? (Research study — strong. Personal anecdote — weak.) Is it balanced? (No counter-argument presented.) Conclusion: Partly convincing but one-sided.

In Maths/Data: "The table shows that students who eat breakfast score higher on tests. Does this prove that eating breakfast improves test scores?"

You evaluate: The data shows a correlation but doesn't prove causation. Maybe students who eat breakfast also get more sleep, or have more supportive home environments. The data is interesting but doesn't prove the claim.

In Science: "An advert claims: 'Our vitamin supplement is clinically proven to boost energy by 50%.' How reliable is this claim?"

You evaluate: Who conducted the study? (The company selling the product — source bias.) What does "clinically proven" mean? (Vague — what was the study design?) What does "boost energy by 50%" mean? (50% compared to what?) The claim is weak without more information.

The skill is the same: questioning whether the evidence supports the conclusion.

Worked Example 4: Logical Deduction in Different Contexts

In Reasoning: "All the cakes on the top shelf contain nuts. The chocolate cake is on the top shelf. Is the chocolate cake safe for someone with a nut allergy?"

Deduction: No, because all top-shelf cakes contain nuts, and the chocolate cake is on the top shelf, so it contains nuts.

In Comprehension: "The story tells us that Mrs Henderson never goes out on Sundays. The mysterious visitor came on a Sunday. Could Mrs Henderson have been the mysterious visitor?"

Deduction: No, because Mrs Henderson never goes out on Sundays, and the visitor came on a Sunday. If Mrs Henderson was at home (as she always is on Sundays), she couldn't have been the visitor.

In Maths: "A number is greater than 50, is even, and is a multiple of 7. What is the smallest number that fits all three conditions?"

Deduction: Multiples of 7 greater than 50: 56, 63, 70, 77... Even multiples: 56, 70, 84... Smallest: 56.

Worked Example 5: Before and After

Question (cross-curricular): "A graph shows that schools which spend more on technology have higher exam results. The government concludes that buying more technology will improve exam results in all schools. Evaluate this conclusion."