Every wrong answer means something
· 3 min read
On most tests, a wrong answer counts the same as any other wrong answer. In Algebra Readiness, each wrong answer choice is written to say something about how the student is thinking.
Wrong answers, written on purpose
Every wrong answer choice in Algebra Readiness is tagged to a misconception from a controlled catalog. Some of the misconceptions it describes will be familiar to any math teacher:
- Larger denominator means larger fraction: judging 1/8 greater than 1/3 because 8 is greater than 3.
- Multiplication always makes it bigger: expecting 5 × 2/3 to be more than 5.
- Reading the equals sign as “write the answer here”: treating = as an instruction to compute, rather than a statement that both sides name the same number.
- Ordering negative numbers by size, ignoring the sign: calling −7 greater than −3.
- Additive rather than multiplicative comparison: extending a ratio table from 2:3 to 3:4 instead of to 4:6.
Not just multiple choice
Typed and graphed answers work the same way. Numeric and graphing questions carry a set of common wrong answers, each tagged to a misconception, so a typed answer or a drawn graph that matches one of them, such as a point plotted with its coordinates reversed, points to the specific idea behind the mistake.
Why a catalog
The misconceptions come from one catalog rather than being written fresh for each question. That means the same misconception carries the same name wherever it appears, across standards and grades, so a pattern across several questions points to one idea rather than several unrelated slips.
An example
Take a question like this: which is greater, one third or one eighth? A student who picks one eighth isn’t just wrong. That choice is tagged to a specific idea: judging a fraction by the size of its denominator, because 8 is greater than 3. The right answer is one third, because thirds are larger pieces than eighths. Each wrong choice in a question is tagged to the idea it reveals, so the answer a student picks says something about how they reached it.
What a tag is, and isn’t
A tag describes the idea behind one answer, not a judgment about the student. A student can hold a misconception in one context and not another, and the same student can make a careless slip on a question they understand. That’s why the catalog names misconceptions consistently across questions: an idea that appears again and again, across several questions, is easier to tell apart from a one-off slip.