Fraction Error Classifier
Detect the add-the-denominators misconception in a fraction-addition response.
Description
A fraction-addition classifier compares a supplied answer with the correct rational sum and one specific error pattern.
A fraction-addition classifier compares a supplied answer with the correct rational sum and one specific error pattern. Equivalent unsimplified correct answers are accepted.1
Detect the add-the-denominators misconception in a fraction-addition response.
When to use Fraction Error Classifier
Use this tool to detect the add-the-denominators misconception in a fraction-addition response.
Prepare the lesson timeline, roster, observations or assessment labels requested. Use consistent units and exact identifiers, then choose comparison criteria appropriate to the activity.
How to use Fraction Error Classifier and understand its results
- Prepare the lesson timeline, roster, observations or assessment labels requested. Use consistent units and exact identifiers, then choose comparison criteria appropriate to the activity.
- Enter firstNumerator, firstDenominator, secondNumerator, secondDenominator, studentNumerator, studentDenominator using the field table and calculation rules, then run the tool.
- Read expectedNumerator, expectedDenominator, errorClass. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| firstNumerator | First numerator | number | Required |
| firstDenominator | First denominator | number | Required |
| secondNumerator | Second numerator | number | Required |
| secondDenominator | Second denominator | number | Required |
| studentNumerator | Student numerator | number | Required |
| studentDenominator | Student denominator | number | Required |
Enter safe-integer numerators and positive safe-integer denominators. Reduce the expected sum, first check equivalence, then label added-denominators only for equal original denominators and literal summed numerator/denominator. Otherwise return other.
sum=(n1d2+n2d1)/(d1d2), reduced by GCD; classify through cross multiplication Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| expectedNumerator | Expected numerator | number |
| expectedDenominator | Expected denominator | number |
| errorClass | Error class | string |
{
"input": {
"firstNumerator": 1,
"firstDenominator": 4,
"secondNumerator": 2,
"secondDenominator": 4,
"studentNumerator": 3,
"studentDenominator": 8
},
"output": {
"expectedNumerator": 3,
"expectedDenominator": 4,
"errorClass": "added-denominators"
}
}Limitations and assumptions
Other misconceptions and proportional variants of the incorrect form are not identified. Products of large safe integers can exceed exact arithmetic range; use modest values.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use MCQ Distractor Audit: Audit MCQ distractors for duplicates and caller-defined minimum length. For a complementary task, use Completion Problem Transition: Gate a completion-problem fade by observed student success.
References
-
Fraction Error Classifier — tool.io
Similar or alternative tools
- MCQ Distractor Audit
Audit MCQ distractors for duplicates and caller-defined minimum length.
- Completion Problem Transition
Gate a completion-problem fade by observed student success.