| name | questions-and-assessments |
| description | Create Wolfram Language QuestionObject and AssessmentFunction expressions. Use this skill whenever the user wants to build a quiz question, assessment, multiple-choice item, true/false question, short-answer grader, numeric question, fill-in-the-blank, or any kind of interactive question for a Wolfram notebook or course. Also trigger when the user asks about scoring, partial credit, explanation feedback, comparison methods (AlgebraicValue, CalculusResult, CodeEquivalence, etc.), QuestionGenerator, or QuestionInterface types. Trigger even if they just say "make a question about X" or "how do I grade answers in WL".
|
Questions and Assessment in Wolfram Language
This skill guides you through constructing correct, idiomatic QuestionObject and
AssessmentFunction expressions — the core building blocks of the Wolfram Language assessment
framework (System context, experimental).
QuestionObject should only be used when you want to create an interactive question interface for use in a Wolfram Notebook.
AssessmentFunction is purely computational. It is used to determine if answers match an answer key.
Core Structure
QuestionObject[prompt, AssessmentFunction[key]]
QuestionObject[prompt, AssessmentFunction[key, method]]
QuestionObject[prompt, AssessmentFunction[key, <|settings...|>]]
QuestionObject[assess] (no explicit prompt) derives a prompt automatically from the key.
AssessmentFunction Key Syntax
The key specifies correct and incorrect answers. Each entry can be:
| Form | Meaning |
|---|
ans | correct answer (score 1) |
ans -> score | answer with explicit score (positive = correct) |
ans -> True / ans -> False | correct / incorrect shorthand |
ans -> <|"Score"->s, "Explanation"->"...", "AnswerCorrect"->True|> | full answer spec |
Single correct answer from a list — give one entry a positive score; everything else becomes incorrect automatically:
AssessmentFunction[{1, 2, 7 -> 1, 9, 10}]
(* Only 7 is correct *)
All answers correct — omit scores entirely:
AssessmentFunction[{Pi, 3.14159}] (* both accepted *)
Explicit True/False scores:
AssessmentFunction[{755 -> True, 714 -> False, 868 -> False}]
Full answer specification with per-answer feedback:
AssessmentFunction[{
"Paris" -> <|"Score" -> 1, "Explanation" -> "Correct! Paris is the capital of France."|>,
"Lyon" -> <|"Score" -> 0, "Explanation" -> "Lyon is France's second largest city, not the capital."|>,
"Nice" -> <|"Score" -> 0, "Explanation" -> "Nice is a city in the French Riviera."|>
}]
Interface Types
The interface is usually inferred automatically from the key, but can be set explicitly with
QuestionInterface[type, <|properties|>].
| Interface | Auto-inferred when… | Notes |
|---|
"MultipleChoice" | list key, exactly one correct | Radio buttons |
"ChooseMultiple" | list key, multiple correct + "SeparatelyScoreElements" | Checkboxes |
"TrueFalse" | key has True/False entries | Two-option radio |
"ShortAnswer" | string comparison method or single string key | Text input |
"NumericRange" | "Number" or "Quantity" method + Tolerance | Slider |
"SelectCompletion" | explicit only | Fill-in-the-blank from choices |
"ClickTheAnswer" | explicit only | Click to select answer |
"HotSpot" | explicit only | Click on image |
Explicit interface example:
QuestionObject[
QuestionInterface["ShortAnswer", <|"Prompt" -> "Name a prime between 10 and 20"|>],
AssessmentFunction[{11, 13, 17, 19}, "Number"]
]
Comparison Methods
Specify in AssessmentFunction[key, "method"] or inside the settings Association.
For open-ended answers like "ShortAnswer", the ComparisonMethod determines how the submitted answer is compared to the key. Choosing the right method is crucial for correct assessment.
| Method | Best for | Distance |
|---|
"Number" | numeric answers | Norm[#1-#2]& |
"Quantity" | answers with units (Quantity[...]) | Norm[#1-#2]& |
"String" | text, case-insensitive option | EditDistance |
"Expression" | exact WL expressions | exact match |
"HeldExpression" | expressions that must not evaluate | exact match |
"AlgebraicValue" | equation solving — multiple algebraically equivalent forms | exact match |
"ArithmeticResult" | arithmetic computation answers | exact match |
"PolynomialResult" | polynomial answers | exact match |
"CalculusResult" | derivatives, integrals | exact match |
"CodeEquivalence" | WL code that should behave the same | behavioral |
"Date" | DateObject answers | DateDifference |
"GeoPosition" | geographic locations | GeoDistance |
"Vector" | vector answers | Norm[#1-#2]& |
"Color" | color values | ColorDistance |
With Tolerance (for numeric-distance methods):
AssessmentFunction[9.8, <|"ComparisonMethod" -> "Number"|>, Tolerance -> 0.05]
Multiple algebraically equivalent correct answers:
AssessmentFunction[
{-Sqrt[(1+b)/a], Sqrt[(1+b)/a]},
"AlgebraicValue"
]
Partial Credit and Multiple-Select (ChooseMultiple)
Use "ListAssessment" -> "SeparatelyScoreElements" to score each selected item independently:
QuestionObject[
"Select all prime numbers:",
AssessmentFunction[
{2 -> 1, 3 -> 1, 4 -> 0, 5 -> 1, 6 -> 0},
<|"ListAssessment" -> "SeparatelyScoreElements"|>
]
]
Other ListAssessment values:
"WholeList" (default) — the entire submitted list is assessed as one answer"AllElementsOrdered" — list elements must match in order"AllElementsOrderless" — list elements can be in any order
Explanation and LLM Feedback
Per-answer static explanation (best for discrete choice questions):
"Paris" -> <|"Score" -> 1, "Explanation" -> "Correct!"|>
Dynamic ExplanationFunction — receives an Association with keys
"GivenAnswer", "AnswerCorrect", "TargetAnswer", "Score", etc.:
AssessmentFunction[
correctAnswer,
<|"ExplanationFunction" -> Function[a,
If[a["AnswerCorrect"],
"Great work!",
"The correct answer is " <> ToString[a["TargetAnswer"]] <> ". Try again!"
]
]|>
]
LLM-generated feedback using the Wolfram Prompt Repository:
AssessmentFunction[
{"their" -> 1, "they're", "there"},
<|"ExplanationFunction" -> LLMResourceFunction["QuestionAssessmentExplanation"]|>
]
Custom Comparator
When built-in methods don't fit, supply your own comparison function:
(* Accept any string that contains "Newton" *)
AssessmentFunction[
Automatic,
<|"Comparator" -> Function[{answer, _}, StringContainsQ[answer, "Newton", IgnoreCase -> True]]|>
]
"Selector" alternative — useful when you want to pick the nearest key:
<|"Selector" -> Composition[First, Nearest]|>
QuestionGenerator
Randomized questions — wrap in a function that returns a QuestionObject:
QuestionGenerator[Function[{},
Module[{a = RandomInteger[{2, 9}], b = RandomInteger[{2, 9}]},
QuestionObject[
"What is " <> ToString[a] <> " × " <> ToString[b] <> "?",
AssessmentFunction[a*b, "Number"]
]
]
]]
AssessmentResultObject
Applying an AssessmentFunction directly returns an AssessmentResultObject:
af = AssessmentFunction[{755 -> 1, 714 -> 0, 868 -> 0}];
result = af[755]
result["Score"] (* 1 *)
result["AnswerCorrect"] (* True *)
result["Explanation"] (* None, unless set *)
result["MaxScore"] (* 1 *)
result[All] (* full Association of all properties *)
Common Patterns and Pitfalls
SelectCompletion answers must be lists:
(* Wrong *)
AssessmentFunction["red" -> 1]
(* Right — wrap in a list *)
AssessmentFunction[{{"red"} -> 1}]
ChooseMultiple needs SeparatelyScoreElements to show checkboxes:
Without it, the interface defaults to MultipleChoice even with multiple correct answers.
AlgebraicValue requires Hold internally — you write the expressions normally; WL wraps them automatically. Don't Hold them yourself.
Tolerance only applies to distance-based methods ("Number", "Quantity", "Vector", "GeoPosition", "Date", "Color"). It has no effect on "Expression" or "AlgebraicValue".
Quick Decision Guide
| User wants… | Use |
|---|
| Pick one from a list | AssessmentFunction[{a->1, b->0, c->0}] |
| Pick many from a list | AssessmentFunction[{a->1,b->0,c->1}, <|"ListAssessment"->"SeparatelyScoreElements"|>] |
| True or false | AssessmentFunction[{True->1, False->0}] |
| Numeric answer ±tolerance | AssessmentFunction[val, <|"ComparisonMethod"->"Number"|>, Tolerance->δ] |
| Algebra / solving equations | AssessmentFunction[{ans1, ans2}, "AlgebraicValue"] |
| Calculus answer | AssessmentFunction[ans, "CalculusResult"] |
| Code that should work the same | AssessmentFunction[codeExpr, "CodeEquivalence"] |
| Free text | AssessmentFunction[ans, "String"] or custom "Comparator" |
| Physical quantity with units | AssessmentFunction[Quantity[...], "Quantity"] |
| Randomized question | QuestionGenerator[Function[{}, ...]] |
