The short answer
- When you’re stuck: try briefly, study one worked example, then solve a similar problem on your own. That alternation of worked examples and practice is a U.S. Institute of Education Sciences (IES) recommendation with moderate evidence.
- Two habits have the strongest evidence in the IES guides: quizzing yourself to re-expose key content, and answering deep “why” questions about the method.
- For grades 4-8 problem solving, IES rates two practices as strong: monitoring and reflecting on your process, and drawing visual representations.
- Free tools that teach: Khan Academy (through calculus), Desmos and GeoGebra (graphing), Illustrative Mathematics (free curriculum TK–Algebra 2), OpenStax (textbooks), Paul’s Online Math Notes (college), AskRose (grades 6-12 help line).
- Parents don’t need to know the method. Ask “what is the question asking?”, “can you draw it?” and “does the answer make sense?”
Being stuck on math homework is normal and, up to a point, useful — the effort of retrieving a method is part of how it sticks. The goal isn’t to never get stuck; it’s to have a routine for getting unstuck that leaves you able to do the next problem alone. This page gives you that routine, the research behind it, and free tools that teach rather than just answer.
What the research says works for math homework
The best summaries come from the U.S. Department of Education’s Institute of Education Sciences (IES), which publishes practice guides that rate evidence as strong, moderate, low or minimal. Two are directly useful for homework.
| Practice | IES evidence rating | What it looks like at the kitchen table |
|---|---|---|
| Use quizzes to re-expose key content (retrieval practice) | Strong | Cover your notes and redo a problem from memory |
| Ask deep explanatory questions | Strong | “Why does this step work?” “What would change if…?” |
| Monitor and reflect on the problem-solving process (grades 4-8) | Strong | “What’s the question asking? Does my answer make sense?” |
| Teach students to use visual representations (grades 4-8) | Strong | Draw the diagram, number line, table or graph |
| Interleave worked examples with problem-solving | Moderate | Study one solved problem, then do a similar one |
| Space learning over time | Moderate | Revisit last week’s topic for ten minutes |
| Expose students to multiple strategies (grades 4-8) | Moderate | Solve it a second way to check |
Sources: IES practice guide Organizing Instruction and Study to Improve Student Learning (2007) and the IES/What Works Clearinghouse guide Improving Mathematical Problem Solving in Grades 4 Through 8 (2012, revised 2018).
Worked examples vs. struggling on your own
For beginners, studying a worked example beats unguided problem-solving — but the advantage fades as you get better. Researchers call the first part the worked-example effect (Sweller and Cooper, 1985, studying algebra) and the second the expertise reversal effect (Kalyuga and colleagues, 2003). There is also a line of research on “productive failure,” associated with Manu Kapur, in which students try to invent solution methods for a hard new problem before being taught the standard method.
These ideas can sound contradictory. A practical way to combine them — our synthesis, not a single study’s finding — is: try briefly, then study a worked example, then practice. The short attempt shows you what you don’t know. The example fills the gap efficiently. The practice turns it into something you can do on a test.
Retrieval practice backs up the last step: repeated testing beats repeated re-reading for long-term retention, a finding replicated across several meta-analyses. Re-reading the example ten times feels productive; solving a fresh problem without it actually is.
A step-by-step routine for when you’re stuck
Run these steps in order and stop as soon as you’re moving again.
- Restate the question. Write in one line what you’re being asked to find. Many “stuck” moments are really “misread” moments.
- Draw it. A sketch, table, number line or graph — whatever fits. Visual representations have strong evidence in the IES guide.
- Try for a few minutes. Write down whatever you can, even a guess. Circle the exact step where you stop.
- Find one worked example of the same type. Your notes and textbook first; then Khan Academy or OpenStax. Read each step and ask why it’s there.
- Close the example and solve your original problem.
- Check it. Estimate, plug the answer back in, or solve a second way. Ask: does this make sense?
- Do one more similar problem with no help. That’s the retrieval step — the one that makes the method stick.
- Still stuck? Ask a person. A free library tutor, AskRose (grades 6-12) or your teacher tomorrow — bring the circled step.
Worked example of the routine
Say the problem is: a test has 40 questions and you got 6 wrong; what’s your percent? Restate: find the share correct as a percent. Draw: 40 boxes, 6 shaded. Try: 40 − 6 = 34 correct. Study the pattern “part ÷ whole × 100.” Solve: 34 ÷ 40 = 0.85, so 85%. Check: 10% of 40 is 4, so 6 wrong is 15% off — 100 − 15 = 85. Then practice a fresh one: 25 questions, 3 wrong → 22 ÷ 25 = 88%. You can confirm both with the test score calculator.
Free math resources by level
All of these are free to use; a few have paid add-ons, noted in the table.
| Level | Resource | What you get |
|---|---|---|
| K-12 to early college | Khan Academy | 840+ free courses, math from early grades through calculus; nonprofit |
| TK to Algebra 2 | Illustrative Mathematics | Full curriculum online at no cost, with lessons and printable PDFs |
| Middle school to college | Desmos | Free graphing and scientific calculators; built into the SAT, PSAT and certain AP Exams |
| All levels | GeoGebra | Free graphing, geometry, 3D and scientific apps, plus 1M+ community resources |
| High school and college | OpenStax | Free textbooks including algebra, precalculus, calculus and statistics |
| High school and college | Wolfram|Alpha | Free computation; step-by-step solutions need the paid Pro plan |
| College (Algebra, Calc I–III, Diff Eq) | Paul’s Online Math Notes (Lamar University) | Free notes and practice problems |
| Advanced and competition | Art of Problem Solving | Free community forums, wiki and the Alcumus practice tool |
| Grades 6-12 | AskRose (Rose-Hulman) | Free math and science help by phone (877-ASK-ROSE), chat or email |
| Any level | Your public library | Free live tutoring for cardholders at many libraries |
Photo-solver apps such as Photomath, Mathway and Symbolab offer free basic steps with paid upgrades — see homework scanner apps for prices and Gauth vs Brainly vs Photomath for a comparison. For more places to get a live tutor, see free homework help.
Using AI and photo solvers without losing the learning
A solver is a worked example on demand — useful exactly where step 4 of the routine sits, harmful anywhere earlier. If you open the app before you’ve tried, you skip the part that shows you what you don’t know. If you copy the last line, you skip the practice entirely.
The rule of thumb: an app may show you how only after you’ve circled the step where you got stuck, and the problem isn’t done until you’ve solved a similar one with the app closed. General chatbots add a second risk — they can explain well and still get the arithmetic wrong. Our guide to AI math help covers when to trust them and how to check.
How parents can help with math homework
You don’t have to remember how to factor a quadratic. The most useful things a parent can do are questions, not explanations — and they line up with practices the IES rates as having strong evidence.
- “Walk me through it.” Asking your child to explain their reasoning is a deep explanatory question.
- “Can you draw it?” Visual representations help students in grades 4-8 solve problems.
- “What’s the question asking? Does the answer make sense?” That’s monitoring and reflecting on the process.
- Spread practice out. Short self-quizzes over several days beat one long cram session.
- Set a rule for apps: an honest attempt first, then the app as an example, then a similar problem without it.
If homework is taking far longer than it should, compare it against the homework time calculator, and plan the week with the homework planner so the hardest subject isn’t left until bedtime.
Sources
- IES, Organizing Instruction and Study to Improve Student Learning (Pashler et al., NCER 2007-2004, Table 2): https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/20072004.pdf
- IES/WWC, Improving Mathematical Problem Solving in Grades 4 Through 8 (2012, rev. 2018): https://ies.ed.gov/ncee/wwc/PracticeGuide/16
- Worked-example effect and expertise reversal (Sweller & Cooper 1985; Kalyuga et al. 2003): https://en.wikipedia.org/wiki/Worked-example_effect
- Testing effect (Roediger & Karpicke 2006 and later meta-analyses): https://en.wikipedia.org/wiki/Testing_effect
- Productive failure (Manu Kapur): https://www.manukapur.com/productive-failure/
- Khan Academy: https://www.khanacademy.org/about
- Desmos on College Board tests: https://bluebook.collegeboard.org/students/tools
- GeoGebra: https://www.geogebra.org/about
- Illustrative Mathematics: https://illustrativemathematics.org/math-curriculum/
- OpenStax: https://openstax.org/about
- Wolfram|Alpha Pro for students: https://www.wolframalpha.com/pro/pricing/students
- Paul’s Online Math Notes: https://tutorial.math.lamar.edu/
- Art of Problem Solving: https://en.wikipedia.org/wiki/Art_of_Problem_Solving
- AskRose: https://askrose.org/
Checked October 14, 2026. Spotted something out of date? Tell us via the about page.