To study a problem set without memorizing the solution, explain the decisions in a worked example, hide part of the help and then attempt a new problem independently. Keep a note of the first decision you cannot justify. The goal is to become able to choose a method under new conditions, not reproduce a familiar sequence of lines.
This guide is for computational and analytical courses at Canadian universities, including mathematics, computing and introductory science. It concerns permitted practice material. Follow the course's collaboration and assistance rules for any problem set you submit for marks.
What should you inspect in a worked solution?
Read the problem before the answer. Identify what is given, what must be found and any conditions restricting the method. Try to describe the target in words. Only then compare your interpretation with the worked solution.
For each major step, ask why it is appropriate here. A calculation may be straightforward once chosen; the difficult part may be recognizing which relationship applies. Mark that decision rather than highlighting every line equally.
Waterloo's guidance on problem-solving distinguishes selecting a method for an unfamiliar problem from simply applying an already signposted procedure. Use that distinction to judge your practice. A chapter heading that names the method can provide more help than you notice.
Write a decision note beside the calculation
Keep it short: “Use this relationship because the rate is constant in the stated model” or “This case needs separate treatment because the earlier assumption does not hold.” The reason must come from the task and course material, not a generic phrase added to every answer.
If you cannot explain a step, mark it as unresolved. Do not rename copying as understanding. That mark is a useful question to bring to the tutorial or TA's office hours.
How do you remove help without making the task impossible?
Start by covering the final result and checking whether you can complete the last operation. Then cover a larger portion, including a decision step. Finally, hide the entire solution and attempt the problem from the prompt alone. This is a suggested practice sequence, not a fixed prescription for every learner or topic.
Keep a record of what was visible during each attempt. Finishing with the method supplied is different from selecting the method independently. Both can be useful stages, but they should not receive the same label in your progress notes.
| Stage | Help still visible | What you are checking |
|---|---|---|
| Explain | Complete solution | Whether you can justify the steps |
| Complete | Opening setup only | Whether you can carry the method forward |
| Choose | Original problem only | Whether you can select and execute the method |
| Transfer | A different problem | Whether you can adapt to changed conditions |
Restart after inspecting a stuck point
When you need help, uncover only enough to understand the obstacle. Then close the solution and restart the relevant reasoning yourself. Otherwise the session can turn into reading the answer while writing behind it.
If you repeatedly uncover the same step, make it the subject of a separate explanation or small exercise. It may involve a prerequisite concept rather than the whole problem. Bring that specific difficulty to the next tutorial.
What does a simple transfer exercise look like?
Consider an invented pricing model: a fixed charge of 5 dollars plus 2 dollars per item. For three items, the model gives 5 + 2 × 3 = 11 dollars. This is an arithmetic teaching example, not a real price or a claim about a service.
First explain why the fixed charge appears once and the item charge is multiplied. Then change the number of items. Finally, change the model: suppose the fixed charge covers the first item. You must now decide how many additional items incur the extra charge, rather than blindly reuse the old expression.
The useful question is not “Can I remember 11?” It is “Which part of the description determines how often each charge appears?” The same approach can be adapted to a course example, using the assumptions and notation your instructor has supplied.
Change one condition at a time
If you change every feature at once, it can be hard to tell which change caused the difficulty. Start with a manageable variation, explain its effect and then try a less familiar problem. Use the course's authorized exercises where available rather than generating a large unverified answer bank.
For programming tasks, distinguish tracing a known example from writing a solution to a new specification. For numerical tasks, distinguish substituting different values from recognizing that the method itself must change. Both distinctions keep practice honest.
How should you use solutions provided by the course?
Check your attempt against the reasoning, not just the final output. Two solutions can reach the same number for different reasons, and one may rely on an invalid assumption. Conversely, an arithmetic slip does not necessarily mean your method choice was wrong.
Waterloo's CS135 study guide is one course-specific example of encouraging students to apply understanding and write complete answers to practice questions. Follow the corresponding guidance in your own course; do not assume another course's exam conditions or permitted assistance apply to you.
Keep a small log of method errors, execution errors and interpretation errors. When an issue recurs in later topics, connect it to your cumulative-final revision. Broader first-year workload questions belong in the guide to engineering study in Canada.
Which parts belong on flashcards?
Use a short question for a definition, a condition or the meaning of a symbol. “What must I check before choosing this method?” can be useful if the answer is precise and verified. “Solve the whole assignment” is not a bounded recall prompt.
Notibo can generate notes and flashcards from PDF, PPTX and DOCX documents. Try it with a permitted explanation of the method, then check the result against the original. Its document notes can be edited, while generated cards cannot currently be edited individually. Keep customized decision prompts in your own practice sheet.
The flashcard feature can support those smaller pieces. Your final activity should still be a fresh solution attempt. Close the notes, choose the method, complete the work and inspect whether the result answers the problem you were actually given.