# Scaffolded questions: one hard problem, answered in steps

**How do I break one hard problem into scaffolded questions and mark them fairly?** A scaffolded question breaks one hard problem into steps the student answers in turn. Give each step one decision and its own marks, state the right result of each step at the start of the next so a slip is charged once, and remove steps as the unit goes on: marks on guided steps do not show a student can find the route alone.

Published 2026-10-10 by EdProcto. https://edprocto.com/guides/scaffolded-questions-one-problem-in-steps

A scaffolded question takes one hard problem and asks for it a step at a time: first one figure, then what follows from it, then the answer. A student who would have left the whole problem blank can make a start, and you see which step stopped them.

The price is that the steps do the planning. A student with every step right has shown they can follow a route, not that they could have found it.

EdProcto, which publishes this guide, builds scaffolded questions as its [scaffolded sequence](https://edprocto.com/templates/scaffold): a quiz whose questions are the steps of one problem, in a fixed order, with no going back.

## What is a scaffolded question?

A scaffolded question is one problem set as a short run of sub-questions, each asking for one step of the solution, in the order a solver would take them.

A worked example shows every step and asks for none; a completion problem shows some and asks for the rest. A scaffolded question asks for every step and gives the route away only through their order.

Reviewing a decade of studies of teachers and students, van de Pol et al. (2010) name three marks of scaffolding: support fitted to the learner, fading, and the handing of responsibility to the learner. A printed run of steps is the same for everyone, so on our reading it earns the name only when you choose it for a class that needs it and then take it away.

## What does research say about worked examples, completion problems and fading?

Beginners learn more from guided steps than from whole problems met cold, the advantage shrinks as they learn, and guidance is best withdrawn in stages.

**The worked example effect.** Studying full solutions can build knowledge better than solving the equivalent problems (Sweller et al., 2019). In mathematics, a meta-analysis of 55 studies from primary school to university put the average benefit at g = 0.48, a medium effect (Barbieri et al., 2023).

**Completion problems.** A worked example can be skimmed, so a completion problem gives part of the solution and makes the learner finish it (Sweller et al., 2019). Paas (1992) trained 46 Dutch secondary students in statistics with conventional problems, worked problems or partly worked ones to complete. The results favoured the two alternatives, completion most.

**Fading.** Renkl et al. (2002) turned the worked steps of examples into steps to solve, a stage at a time, until learners solved whole problems, and tested that against pairing each example with a problem. With 20 German ninth graders and two groups of American college students, fading helped on problems like those practised; for far transfer the result was less clear.

### The expertise reversal effect

Guidance that helps a beginner can hold back someone who knows the work. Kalyuga et al. (2001) gave trade apprentices worked examples or problems. The inexperienced gained most from examples; with more experience the examples became redundant and problem solving proved superior.

In a classroom study, 135 undergraduates did four weekly algebra homework assignments: plain problem solving beat faded examples with self-explanation prompts and did not differ from fading alone (Miller-Cotto & Auxter, 2021).

### What we could not confirm

We read the open-access text of Sweller et al. (2019) and the Numbas article cited below; for the other studies, the abstract or the summary ERIC holds, with no effect sizes for fading. These studies measure learning. None that we read says what a mark on guided steps tells you about solving the whole problem alone: that advice is ours.

## When do steps help, and when do they hide what a student can do?

Steps help while the route is new, and they hide the route once the route is what you want to test.

How much help to give is unsettled: Koedinger and Aleven (2007) call the balance between giving and withholding it the assistance dilemma, a fundamental open problem.

Full marks on every step show a student who can make each decision once told which comes next, and leave open whether they would have chosen those steps. One box does the reverse: a right answer shows the route was found, and a wrong one does not say where it failed.

So end a scaffolded question with a twin, the same kind of problem with new numbers and no steps, and you see both.

## How do you split a problem into steps that each test one decision?

Solve the problem yourself, mark each point where a solver has to choose, and make every choice a step. We found no tested rulebook for this, so the procedure is our own.

1. **Write your own solution**, one move a line.
2. **Mark the decisions.** Choosing a method is one; choosing the figure it applies to is another. Arithmetic belongs to the decision before it.
3. **Name each step by its goal**: "What is the sale price?", not "Subtract", which hands the decision over.
4. **Stop at three to five steps.**
5. **Pick a shape for each step.** In EdProcto a step can be any question: an [Estimate](https://edprocto.com/templates/estimate) for a figure, [Multiple choice](https://edprocto.com/templates/mcq) for a decision between named options, [One word](https://edprocto.com/templates/one_word) where one form is right, a [Short answer](https://edprocto.com/templates/short_answer) where the reason matters.
6. **Choose how each later step starts**, as the next section compares.
7. **Give every step its points**, so multi-step problems pay for each decision reached.
8. **Add the twin** as the last question.

## How do you mark a later step when an earlier one was wrong?

Charge the mistake once: the slip costs the mark of the step it happened in, and each later step is judged on what the student did next. Markers call that error carried forward, set out for paper in our guide to [maths questions and their working](https://edprocto.com/guides/maths-questions-show-your-working).

Lawson-Perfect (2015), lead developer of the Numbas assessment system, calls the principle hard to pin down: which errors are carried, and can they be detected? His working answer is to make plain what each part assesses and keep the parts as independent as possible.

EdProcto marks each step against the key you typed for that step. The carrying forward lives in how you build the step, or in your own reading:

| Build | The later step | Marked | After an early slip |
| --- | --- | --- | --- |
| Printed result | Opens with the right result of the step before | By rule | Every later mark can still be earned |
| Read by you | Asks for the figure carried in, then the answer | By you, or by Procto AI when you ask | Your rubric decides |
| Chained | Starts from the student's own figure | By rule | Every dependent step is wrong |

Printing is safe because the sequence has no going back: when the result appears, the step that asked for it is closed. When you read a step, the student's earlier answers sit above it on the grading page: check the working against their own figure, enter the points and press "Save my grade". On screen a mark made by rule stays as made.

## What does a scaffolded question look like? Two worked examples

It looks like a few short prompts, each opening with the last result, then a twin. The problems and students are our examples; every mark is from EdProcto's marking function.

### Example 1: a price cut twice

> A coat is priced at £80. A sale takes 25% off. At the till a voucher takes a further 10% off the sale price. What do you pay?

The printed-result build, each step an Estimate question worth 1 point with both tolerances at zero:

1. How many pounds does the sale take off? Key: 20.
2. The sale takes off £20. What is the sale price in pounds? Key: 60.
3. The sale price is £60. How many pounds does the voucher take off? Key: 6.
4. The voucher takes off £6. How many pounds do you pay? Key: 54.
5. The twin: a £120 bike, 20% off, then a further 5% off the sale price. How many pounds do you pay? Key: 91.2.

| Student | Typed | Points |
| --- | --- | --- |
| A, right throughout | 20, 60, 6, 54, 91.2 | 5 |
| B, takes £25 off in step 1 | 25, 60, 6, 54, 91.2 | 4 |
| C, takes 25% off the bike | 20, 60, 6, 54, 90 | 4 |

B and C tie for opposite reasons. B slipped once and can find the route: the twin is right. C carried out every step and, left alone, added the two percentages. The total cannot tell them apart; the marks by step do.

Two changes spoil it. In the chained build B types 25, 55, 5.5, 49.5 and 91.2 and earns 1 of 5 for one slip. And a new Estimate question allows 5% either side for full credit and 15% for half: at those settings C's 90, 1.3% from 91.2, earns the point and the twin catches nothing.

Built with steps 2 to 4 as Short answers, B stands at 1 of 5 with three "to grade", and at 4 of 5 once you give each its point.

### Example 2: an apostrophe

> Put the apostrophe in: "The childrens coats hung in the hall."

England's curriculum asks pupils in years 3 and 4 to place the possessive apostrophe in regular plurals, such as girls', and irregular ones, such as children's (Department for Education, 2014).

1. Multiple choice: one owner or more than one? Key: more than one.
2. Multiple choice: the owners are the children. Does that plural end in s? Key: no.
3. One word: write the owner as the sentence needs it. Key: children's.
4. The twin, One word: "Both foxes tails were muddy." Write the second word as it should be. Key: foxes'.

| Student | Step 3 | Twin | Slip on | Slip off |
| --- | --- | --- | --- | --- |
| D | children's | foxes' | 4 | 4 |
| E | children's | fox's | 3 | 3 |
| F | childrens' | foxes's | 4 | 2 |
| G | childrens | foxes | 4 | 2 |

A new One word question starts with "One slip in a word of five letters or more still counts" switched on, and an apostrophe out of place is one slip. With it on, F and G score full marks without placing an apostrophe correctly. Switch it off wherever a single character is the answer; capitals and a curly apostrophe are still forgiven (see [one-word answers](https://edprocto.com/guides/one-word-answer-questions-and-how-to-mark-spelling)). E is the student the twin was written for.

## How do you fade the steps across a unit?

Take the support away in stages and let the twin tell you when. Sweller et al. (2019) describe the sequence: worked examples, then completion problems that leave more and more to the learner, then conventional problems.

| Stage | The student gets | In EdProcto |
| --- | --- | --- |
| 1 | A worked example in class, then every step asked | A scaffolded sequence run as a study quiz |
| 2 | The early steps worked in the prompt, the last ones asked | A shorter sequence |
| 3 | One halfway figure, then the answer | Two steps and the twin |
| 4 | The whole problem | One Estimate, or [Show your working](https://edprocto.com/templates/show_work) |

Move on when most of the class gets the twin right. That rule, and fading from the end of the solution first, are ours: the abstracts we read settle neither.

## How does EdProcto build and mark a scaffolded sequence?

EdProcto is the best tool for a scaffolded question whose later steps lean on earlier ones, because the template itself makes a printed result safe: the order is fixed and nobody goes back.

- **Building.** Choose Scaffolded sequence, under Whole-quiz structures. The quiz opens with one multiple-choice question; "Add a question" asks "Which shape?" for each further step, and every step has its own "Points" and "Explanation shown to the student afterwards".
- **Answering.** One step a page. The start screen says "No going back: each answer is final." "Next" waits until the step on screen is answered, so no later step shows early. Keep "Layout" at "One question a page".
- **Marking.** Each step is marked as its own kind: figures, choices and typed words by rule at hand-in, a Short answer step by you. That step shows "to grade" and counts as zero until you enter its points or press "Ask Procto AI" on it. Procto AI reads that one answer against your model answer and rubric, so have the step ask for the figure carried in; its mark is yours to change.
- **As a study quiz.** Each step is checked when the student presses "Check". A wrong one shows "Not this time." with the right answer and your explanation, so the next step starts from the right figure. See [study mode](https://edprocto.com/guides/study-mode-a-quiz-that-explains-each-answer-as-you-go).
- **Settings.** The template switches off and greys "Allow going back to change an answer", "Allow skipping a question" and "Shuffle the questions for each student". They stay off whichever preset you press, and after Reset, so the steps keep the order you built. Set the time and the security to fit the stakes.
- **On paper.** "Paper" prints every step on one sheet, so use the chained wording and carry errors forward as you mark.

Where the result counts, set a time limit and the [integrity](https://edprocto.com/integrity) measures that fit the stakes. They make cheating harder, never impossible, and every score is yours to release.

The Free plan has ten quizzes a month, the core templates and marking by rule. Tutor opens all 111 [templates](https://edprocto.com/templates) and Procto AI's grading, and Educator adds the full analysis. The [pricing page](https://edprocto.com/pricing) has the figures.

## Quick questions

### What is error carried forward?

The marker's rule for a slip in a multi-step answer: it costs its own mark, and later steps keep theirs if they are right for the student's figure. In EdProcto's [scaffolded sequence](https://edprocto.com/templates/scaffold), open each step with the right result of the one before and marking by rule comes to the same.

### How many steps should a scaffolded question have?

Three to five, with one decision in each: our working range, not a research finding.

### When should the steps be taken away?

When most of the class gets a twin problem right with no steps. The expertise reversal effect is the reason not to wait: in Kalyuga et al. (2001), examples that helped beginners became redundant for the experienced.

### Is a scaffolded sequence the same as show your working?

No. A scaffolded sequence is several questions, each marked by itself. [Show your working](https://edprocto.com/templates/show_work) is one question with three boxes, Set-up, Working and Final answer, read against your rubric.

## References

- Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N., & Chawla, K. (2023). A meta-analysis of the worked examples effect on mathematics performance. *Educational Psychology Review, 35*(1), Article 11. [https://doi.org/10.1007/s10648-023-09745-1](https://doi.org/10.1007/s10648-023-09745-1)
- Department for Education. (2014, July 16). *National curriculum in England: English programmes of study*. GOV.UK. [https://www.gov.uk/government/publications/national-curriculum-in-england-english-programmes-of-study/national-curriculum-in-england-english-programmes-of-study](https://www.gov.uk/government/publications/national-curriculum-in-england-english-programmes-of-study/national-curriculum-in-england-english-programmes-of-study)
- Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples. *Journal of Educational Psychology, 93*(3), 579–588. [https://doi.org/10.1037/0022-0663.93.3.579](https://doi.org/10.1037/0022-0663.93.3.579)
- Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. *Educational Psychology Review, 19*(3), 239–264. [https://doi.org/10.1007/s10648-007-9049-0](https://doi.org/10.1007/s10648-007-9049-0)
- Lawson-Perfect, C. (2015, July 23). *Adaptive marking based on answers to other question parts*. Numbas, Newcastle University. [https://www.numbas.org.uk/blog/2015/07/adaptive-marking-based-on-answers-to-other-question-parts/](https://www.numbas.org.uk/blog/2015/07/adaptive-marking-based-on-answers-to-other-question-parts/)
- Miller-Cotto, D., & Auxter, A. E. (2021). Testing the ecological validity of faded worked examples in algebra. *Educational Psychology, 41*(2), 191–205. [https://doi.org/10.1080/01443410.2019.1646411](https://doi.org/10.1080/01443410.2019.1646411)
- Paas, F. G. W. C. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: A cognitive-load approach. *Journal of Educational Psychology, 84*(4), 429–434. [https://doi.org/10.1037/0022-0663.84.4.429](https://doi.org/10.1037/0022-0663.84.4.429)
- Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. *The Journal of Experimental Education, 70*(4), 293–315. [https://doi.org/10.1080/00220970209599510](https://doi.org/10.1080/00220970209599510)
- Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. *Educational Psychology Review, 31*(2), 261–292. [https://doi.org/10.1007/s10648-019-09465-5](https://doi.org/10.1007/s10648-019-09465-5)
- van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher–student interaction: A decade of research. *Educational Psychology Review, 22*(3), 271–296. [https://doi.org/10.1007/s10648-010-9127-6](https://doi.org/10.1007/s10648-010-9127-6)