Before this course, and what a math tutor does
A good bike teacher does not ride the bike for you. They hold the seat for a bit, watch, ask "what happened there?" and let go when you are ready. A math tutor is the same: you help, you ask, and the learner does the math.
- Before this course: Quantitative Reasoning: models and estimates (course 13.14.3), and before that Math for Life: ratios and statistics (course 13.14.2). Check that you can still do these five things without notes: estimate 487 x 21 (about 10,000), convert 90 km/h to 25 m/s, find the 5 GB break-even between a $20 + $5 per GB plan and a $45 plan, explain marginal versus average rate, and compute an expected value. If one is shaky, redo that lesson first. You cannot teach what you cannot do.
- A tutor has three jobs:
| Job | What it looks like |
|---|---|
| Ask | Questions that make the learner's thinking visible ("How did you get that?") |
| Model | A short worked example of one step, said out loud |
| Check | The learner explains it back and solves a new problem alone |
- Your limits: you do not do graded homework or tests for the learner, you do not decide what help is allowed on graded work (the teacher does), and you do not diagnose learning disabilities. If you notice ongoing struggles or strong worry about math, refer the learner to their teacher, parent or school support.
- A classic problem-solving cycle comes from the mathematician George Polya's book How to Solve It (copyright 1945): understand the problem, make a plan, carry it out, and look back to check. Teach the learner to say which step they are on.
- The US Institute of Education Sciences (IES) What Works Clearinghouse guide "Improving Mathematical Problem Solving in Grades 4 Through 8" (2012) has five recommendations. The one rated strong evidence that fits every session: assist students in monitoring and reflecting on the problem-solving process. Another strong one: teach students how to use visual representations (lesson 3).
- Tutoring can be a job, and some organisations certify tutors. Example (one US body): the National Tutoring Association's page says initial tutor certification requires current NTA membership, completing NTA training, an application with proof of tutoring experience, a background check and fees. Requirements differ between organisations and countries; read the certifying body's own page.
- Do the five "ready" checks above on paper, with no notes. Mark each right or wrong.
- Redo the matching lesson from course 13.14.2 or 13.14.3 for any check you missed.
- Write the four steps (understand, plan, carry out, look back) on a card you will keep on the table in every session.
- Write your tutor's promise in three lines: what you will do (ask, model, check) and what you will not do (do graded work, decide the rules, diagnose).
- Find one practice learner who agrees to work with you during this course (a younger student, classmate or family member).
- Ask them what math they find hardest and what they need it for. Write it down.
- Check: you have five ready checks done, a four-step card, a promise and a practice learner with a goal.
Videos by other creators on YouTube, for reference. They are not made by or affiliated with The Future Market.
Read the video script
[Host] "A bike teacher doesn't ride the bike for you. A math tutor doesn't do the math for you."
[Text on screen: Ask · Model · Check] "Three jobs. Ask questions. Model one step. Check that the learner can do it alone."
[Text on screen: Understand · Plan · Carry out · Look back] "Teach the four steps of problem solving, and ask which step they're on."
[Text on screen: You do not do graded work] "You never do graded work for them. The teacher sets the rules."
[Host] "And before you teach it, make sure you can still do it yourself."
Do the five ready checks and fix any gap. Write your four-step card and your tutor's promise. Meet your practice learner for 10 minutes and write down their goal in one sentence.
ClaudeStuck? Copy a ready-made prompt for Claude
Copy this, open Claude, paste it, and Claude will walk you through the lesson step by step.
For a grown-up: Claude is for adults (18+). Copy this, paste it into Claude, and use the answer to explain the lesson to your child.
I'm learning "Math Tutor: teach" on The Future Market. Lesson 1: "Before this course, and what a math tutor does".
What the lesson teaches:
- Before this course: Quantitative Reasoning: models and estimates (course 13.14.3), and before that Math for Life: ratios and statistics (course 13.14.2). Check that you can still do these five things without notes: estimate 487 x 21 (about 10,000), convert 90 km/h to 25 m/s, find the 5 GB break-even between a $20 + $5 per GB plan and a $45 plan, explain marginal versus average rate, and compute an expected value. If one is shaky, redo that lesson first. You cannot teach what you cannot do.
- A tutor has three jobs:
- Job - What it looks like
- Ask - Questions that make the learner's thinking visible ("How did you get that?")
- Model - A short worked example of one step, said out loud
- Check - The learner explains it back and solves a new problem alone
- Your limits: you do not do graded homework or tests for the learner, you do not decide what help is allowed on graded work (the teacher does), and you do not diagnose learning disabilities. If you notice ongoing struggles or strong worry about math, refer the learner to their teacher, parent or school support.
The exercise I'm working on:
Do the five ready checks and fix any gap. Write your four-step card and your tutor's promise. Meet your practice learner for 10 minutes and write down their goal in one sentence.
I'm stuck. Please:
1. Explain the main idea in plain, simple words with one everyday example.
2. Walk me through the exercise one small step at a time. Ask me what I've done so far before giving the next step.
3. Don't just give me the final answer. Help me do it myself, and check my work when I share it.I'm a parent helping my child (about 8 years old) with a lesson called "Before this course, and what a math tutor does" from the course "Math Tutor: teach". Here's what the lesson says: A good bike teacher does not ride the bike for you. They hold the seat for a bit, watch, ask "what happened there?" and let go when you are ready. A math tutor is the same: you help, you ask, and the learner does the math. The activity: Do the five ready checks and fix any gap. Write your four-step card and your tutor's promise. Meet your practice learner for 10 minutes and write down their goal in one sentence. Please explain this so an 8-year-old understands: short sentences, a fun everyday example, and no hard words. Then give me 3 simple questions I can ask my child to check they understood, and a way to do the activity together, one tiny step at a time.
Sources
- IES What Works Clearinghouse, Improving Mathematical Problem Solving in Grades 4 Through 8 (2012): ies.ed.gov/ncee/wwc/PracticeGuide/16
- Princeton University Press, How to Solve It (G. Polya): press.princeton.edu/books/paperback/9780691164076/how-to-solve-it
- National Tutoring Association, Certification: www.ntatutor.com/certification.html
Diagnose: slips, missing steps and misconceptions
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Explain it many ways: words, pictures and numbers
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Worked examples, fading and practice that sticks
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Teaching word problems and simple models
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Teaching data and chance honestly
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Measure progress, give feedback and review other tutors
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Final project
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Quiz
What are a tutor's three jobs in this course?
Ask, model and check.
What are the four steps of the classic problem-solving cycle?
Understand, plan, carry out, look back.
What is the difference between a slip and a misconception?
A slip is a one-time mistake with the right method; a misconception is a wrong idea that keeps causing the same mistake.
A learner says 1/2 + 1/3 = 2/5. Give a quick counter-example.
2/5 = 0.4 is smaller than 1/2 alone; the right answer is 5/6.
A price goes up 20% and then down 20%. Where does 100 end up?
At 96.
Using a bar diagram, split 40 in the ratio 3:2.
24 and 16 (5 parts of 8).
What is a fading worked example?
A sequence that starts fully solved and leaves more steps to the learner each time, until they solve one alone.
Saving $15 a week, how many weeks to reach $500?
34 weeks (33 weeks only gives $495).
Class A (20 students) averages 70 and class B (30 students) averages 80. What is the combined mean?
76.
What is Simpson's paradox?
A pattern that holds in every group reverses when the groups are combined.
A filter flags 90% of phishing and 5% of normal messages, and 1% of messages are phishing. About what share of flagged messages are phishing?
About 15.4% (90 of 585 per 10,000).
A score goes from 45% to 75%. How do you report the change?
A rise of 30 percentage points, or about 66.7% relative.
Final exam
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Certificate
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