Higher Order Thinking and Problem-Solving
Higher order thinking means you cannot simply recall a fact - you must analyse a situation, evaluate options, or create a strategy. The core concepts are: identifying the real goal (what is actually being asked), recognising constraints (time, rules, resources), breaking a complex problem into smaller steps, and checking whether a solution actually satisfies every condition.
A reliable technique is the working-backwards method. When a question describes a final state and asks for a starting value, undo the operations in reverse order. If a number is doubled then increased by 6 to reach 20, reverse it: subtract 6 to get 14, then halve to get 7.
Common traps: (1) Answering the wrong question - a problem may ask how many are left, but the tempting answer is how many were removed. (2) Ignoring a constraint - for example, a seating puzzle where one condition says two people cannot sit together. (3) Stopping at the first plausible answer without verifying it against all conditions. (4) Over-complicating - many problems have a simple structure hidden under wordy context.
Rule of thumb: after finding an answer, re-read the question and test your answer against every stated condition. If it fails even one, it is wrong. Also ask whether the answer is reasonable in the real-world context described.
Worked example: A jug holds 3 litres. It is filled, then half is poured out, then 500 mL is added. How much is in the jug? Start: 3000 mL. Half poured out leaves 1500 mL. Add 500 mL gives 2000 mL (2 litres). Checking: 3000 − 1500 + 500 = 2000. ✓