Creating Exercises

Interactive elements do something textbooks cannot: they require the student to produce an answer before revealing whether they're right. That act of retrieval — trying before seeing — is one of the most effective learning techniques we know.

Choosing a Question Type

• multichoice: Checking whether a student can identify a correct answer among plausible alternatives
• wordbank: Vocabulary, labelling diagrams, or recall of specific terms in context
• mathresponse: Practising procedures where the student must calculate or derive an answer
• notepad: Open-ended reflection, written explanations, or working space

Writing Good Multiple Choice Questions

The question (called the stem) should present one clear problem. The correct answer should be unambiguously right. The distractors — the wrong answers — should be plausible, not absurd.

Effective distractors are common mistakes, not random errors. A distractor that no one would choose teaches nothing.

multichoice{
    What is the derivative of $f(x) = x^3$?
}[
    choice{ $3x^2$ }(correct: true)
    choice{ $x^2$ }
    choice{ $3x^3$ }
    choice{ $\frac{x^4}{4}$ }
](shuffle: true)

The distractors above reflect common errors: forgetting the coefficient, forgetting to reduce the power, and confusing differentiation with integration.

Wordbanks for Vocabulary and Context

A wordbank forces students to retrieve the correct term in context, which is harder and more effective than simply recognising it in a list.

Keep blank slots to the point: one or two per sentence. Overloading a sentence with blanks makes it hard to reason about.

Include one or two distractors — words that are plausible but wrong — to prevent guessing by elimination.

wordbank{
    A function is !blank() if every element of the range is mapped to
    by at least one element of the domain.
}[
    word{ surjective }(blank: 1)
    word{ injective }
    word{ bijective }
]

mathresponse for Procedural Practice

Use mathresponse immediately after a worked example, with a question that is structurally identical. Increase difficulty gradually across a sequence of questions.

The algebraic mode is the most forgiving — it accepts any equivalent form. Use this unless you have a specific reason to require exact format.

Always write a hint. Students who are stuck are more likely to disengage than to solve a problem they've been sitting on for five minutes. A good hint points to the method, not the answer.

mathresponse{
    Find the derivative of $g(x) = 4x^3 - x + 2$.
}(
    answer: 12x^2 - 1
    mode: algebraic
    hint: Differentiate each term using the power rule. Constants vanish.
)

Sequencing Questions

A single isolated question is less valuable than a sequence. Structure questions to build:

• Recall — can the student remember the relevant concept?
• Procedure — can they apply the method in a familiar form?
• Transfer — can they apply it in a slightly different context?

The quiz container is useful when you want to walk students through a sequence one question at a time, with navigation controls.

quiz{
    multichoice{
        Which rule is used to differentiate $f(x) = \sin(x^2)$?
    }[
        choice{ Product rule }
        choice{ Chain rule }(correct: true)
        choice{ Quotient rule }
        choice{ Power rule }
    ]

    mathresponse{
        Use the chain rule to differentiate $f(x) = \sin(x^2)$.
    }(
        answer: 2x * cos(x^2)
        mode: algebraic
        hint: Let $u = x^2$. Then $f = \sin(u)$. Apply chain rule: $f' = \cos(u) \cdot u'$.
    )
}

Open-Ended Questions with Notepad

Not all learning goals can be assessed automatically. Use notepad for questions that ask students to explain their reasoning, reflect on a concept, or work through a multi-step problem in their own words.

notepad{
    In your own words, explain why the derivative of a constant is zero.
    What does the graph of a constant function tell you?
}(
    placeholder: Write your explanation here...
    rows: 5
)