questions-and-assessments

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[{}, ...]]