Lesson 2 — Multiple-Choice Strategies for Math

Reading time: about 7 minutes.

The structure of a TExES item

A typical multiple-choice item on the TExES Math 7–12 (235) has one correct answer and three distractors. The distractors are not random; they are written by item-writers to capture predictable errors — sign mistakes, off-by-one indexing, applying the wrong formula, or stopping the calculation one step early. Knowing this changes how you read the choices.

1. Read the stem before you look at the choices

This sounds obvious. It isn't, in practice, when you are tired and three hours into the exam. Reading the stem first means you have already done some of the math (or formed an estimate) before the choices have a chance to bias you. If you glance at the choices first, the most plausibly-shaped distractor will pull your reasoning toward it. McMillan's (2007) review of testwiseness research repeatedly identifies the “stem-then-choices” order as the single most-cited difference between strong and weak test takers.

2. Eliminate before you choose

For each item, work through the four choices and try to rule out at least one. The categories that lend themselves to fast elimination on math items:

• Wrong sign. If the answer should be negative and a choice is positive, rule it out.
• Wrong order of magnitude. If you estimate the answer should be near 100 and a choice is 0.1 or 10,000, rule it out.
• Wrong units. If the question asks for square inches and a choice carries linear units, rule it out.
• Plausibility under domain constraints. A probability greater than 1, an angle outside [0°, 360°), a domain element where the function is undefined — these rule themselves out.

Geiger's (1997) study of answer-changing on multiple-choice tests found that students who eliminated systematically before selecting were not only more accurate on the first attempt; they also produced better outcomes when they did revise an answer, because the revision was bounded by their eliminations.

3. Work backward from the choices when stuck

If a question asks you to solve an equation and you cannot see how to start, plug each remaining choice back into the equation and check. This is slower than solving forward but always works for closed-form answers. It is especially powerful on system-of-equations and root-finding items.

This strategy also works on word problems whose final quantity is one of the four choices — set up the relationship, then test which choice satisfies it.

4. Estimate before you compute

Before you do the full calculation, ask: what should the answer look like? If you compute and end up far from your estimate, you have either (a) made an arithmetic error, or (b) set up the problem incorrectly. Either way, the discrepancy is a signal worth investigating before you select.

This is the cheapest insurance you can buy on a math test. A 5-second order-of-magnitude estimate catches most decimal-point and unit errors before they cost you a point.

5. Read “which is NOT” questions twice

Negation in stems is the single most common source of careless errors on multiple-choice math items. When the stem asks “which of the following is not a solution?”, you have to evaluate every choice individually and pick the one that fails — the opposite of what your hand-trained reflex wants to do. Underline the negation word with your finger or your eraser. Read it twice.

6. Trust your first instinct, but verify

The folk wisdom “always go with your first answer” is partially right and partially wrong. Geiger (1997), reviewing a long line of empirical studies, found that students who change answers improve their score more often than they hurt it — but only when the change is driven by a specific reason (a re-read of the stem, an elimination they missed, a recomputation). Changing an answer because of a vague second-guess is what hurts performance.

The practical rule: if you have a specific reason to revise, revise. If you have only a feeling, leave the original.

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