Critical Thinking
Critical Thinking in CCSLC Mathematics asks you to judge a piece of reasoning, not merely produce a number. You are shown a claim, a graph, a small data set or a proposed calculation, and asked whether it is sound, what it assumes, and what would overturn it. The mathematics involved - averages, percentages, rates, simple probability - is deliberately plain, so the reasoning is what is being assessed.
Questions to ask of any claim
- What is the base? An increase from 4 to 6 is 50%, but it is only two items.
- Who or what was measured, how many, and how were they chosen? Twelve shoppers in one town support no regional conclusion.
- Which average is being used? Mean, median and mode answer different questions.
- Is the comparison fair - same period, same units, same starting conditions?
- Does the evidence show cause, or only that two things moved together?
Testing rather than accepting
A general statement falls to a single counterexample: "all prime numbers are odd" fails at 2. An argument with a hidden assumption fails when that assumption is false - a fuel calculation that assumes constant speed, or a budget that assumes every month has exactly four weeks. Reading graphs critically means checking axis labels, whether the vertical axis starts at zero, and whether a picture's area exaggerates a difference the data does not support.
Worked example
Ten employees earn a monthly wage: nine receive EC$1,800 and the manager receives EC$24,000. A notice states "average wage EC$4,020". Mean = (9 × 1,800 + 24,000) ÷ 10 = (16,200 + 24,000) ÷ 10 = EC$4,020, so the arithmetic is correct. The claim is still misleading: nine of the ten earn EC$1,800, and the median is EC$1,800. One extreme value has pulled the mean upward, so the median describes a typical worker better. The critical response is to accept the calculation, reject the implied conclusion, and name the reason.
Traps that cost marks
- Rejecting a correct calculation because you dislike the conclusion, or accepting a wrong one because it suits you.
- Confusing correlation with cause.
- Treating "average" as automatically meaning the middle value.
- Ignoring units when comparing rates.
- Giving a bare "yes" or "no" with no stated reason.