Evaluating Problem-Solving Strategies

When you face a problem, there is rarely only one way to solve it. Evaluating problem-solving strategies means looking at two or more ways of reaching a solution and deciding, with evidence, which one actually works better. This goes a step further than simply describing a method: it asks you to weigh strategies against each other using specific criteria, a skill closely related to Analyzing Solution Effectiveness.

Evaluating a strategy is different from simply using it. When you use a strategy, you follow its steps to reach an answer. When you evaluate a strategy, you step back and ask whether that answer was reached in the best possible way. Two people can solve the exact same problem correctly and still use methods of very different quality: one might take twelve steps and several minutes, while the other reaches the same correct answer in three steps and under a minute. Evaluation is the process of noticing that difference and explaining why it matters.

This kind of thinking is not limited to one subject. You compare strategies when you decide whether to skim a passage or read it closely before answering a comprehension question, and you compare strategies when you decide whether to guess and check or set up an equation to solve a word problem. In every case, the goal is the same: identify which approach is stronger for the problem in front of you, not which approach is stronger in general.

To compare strategies fairly, you need consistent criteria rather than a vague impression that one method "felt easier." Four criteria are especially useful.

Accuracy asks how often a strategy leads to a correct result. You can measure this directly with an accuracy rate, \( \dfrac{c}{n} \times 100 \), where \(c\) stands for the number of correct results and \(n\) stands for the number of attempts. A strategy that is correct 9 times out of 10 attempts is more reliable than one that is correct only 6 times out of 10.

Efficiency asks how much time, effort, or number of steps a strategy requires. A method that reaches the same correct answer in fewer steps is more efficient, even if both methods are equally accurate.

Appropriateness asks whether a strategy fits the specific problem. A strategy built for estimating a rough answer quickly is not appropriate when a problem demands an exact result.

Transferability asks whether a strategy still works when the problem changes slightly. A strategy that only works for one very specific case is weaker than one that adapts to related problems.

Consider this problem: a rectangular garden has a perimeter of 30 metres, and its length is twice its width. What is the width?

Strategy A: Guess and check. You pick a width, calculate the matching length and perimeter, and adjust your guess until the perimeter equals 30. Trying a width of 4 gives a length of 8 and a perimeter of \(2(4+8)=24\), which is too small. Trying a width of 6 gives a perimeter of \(2(6+12)=36\), which is too large. After a few more adjustments, you narrow in on a width of 5.

Strategy B: Set up an equation. Let the width equal \(w\), so the length equals \(2w\). The perimeter equation becomes \(2(w+2w)=30\), which simplifies to \(6w=30\), giving \(w=5\) in one calculation.

Both strategies land on the correct width of 5 metres, so accuracy is equal. Efficiency is not equal: Strategy A required several rounds of guessing and adjusting, while Strategy B reached the answer in a single, direct calculation. For this problem, the algebraic method is the more efficient strategy, even though guess and check remains useful for problems where setting up an equation is harder to do quickly.

Organizing your comparison into a simple table makes the differences easier to see and easier to explain to someone else.

A strong evaluation does more than declare a winner: it explains the reasoning behind that choice using the criteria above. Instead of writing "the algebraic method is better," a stronger justification names the specific criterion and the evidence: "the algebraic method is more efficient here because it reaches the answer in one calculation instead of several rounds of guessing, even though both methods produced the same correct result." This kind of justification also acknowledges limits, noting when the weaker strategy might still be the better choice, such as when the relationship between quantities in a problem is not yet clear enough to write an equation.

Accuracy Rate: The proportion of correct results a strategy produces out of the total number of attempts.

Efficiency: The amount of time, effort, or number of steps a strategy requires to reach a solution.

Appropriateness: How well a strategy fits the specific demands and constraints of a given problem.

Transferability: The extent to which a strategy remains effective when applied to a related but different problem.

Justification: A reasoned explanation, supported by evidence, for why one strategy is judged stronger than another.

Related lessons

• Strategy Impact Assessment