You do not have to be perfect to learn math.
You are allowed to make mistakes, ask for help, and learn at a human pace.
The truth is that you've probably had a bad math instructor at some point in your life. They were very likely someone that had their own anxieties about the subject passed down to them from someone in the same boat. It's generational, it's tragic, and it can stop with you. You likely don't know how to study, and that's okay! This page will get you started, but it's up to you to learn how to learn. I know you may come to this course tired. You may come after work, before work, after caring for a child, a parent, a partner, a sibling, or a friend. You may come in carrying anxiety, depression, grief, embarrassment, or the memory of that bad teacher telling you that you were "not a math person." I want you to know that you are still allowed to learn.
What to do with a wrong answer.
Let's start with some good news: a wrong answer is not some kind of verdict on you. There is no math god looking down and judging you, and I certainly am not judging you. All a wrong answer is... is information, and some of the most useful information you will get all week. But it only helps if you go back and look at it. The mistake on its own does not teach you anything. The looking does.
So when you miss a problem, take a moment and find the first line where it went sideways and write one sentence about what happened there. After that, try a fresh problem of the same kind with the answer covered. That last step is the one that proves it stuck.
The worst mistake you can make is not learning from mistakes.
How to study from a worked example.
It was graduate school before I learned how to study myself. I made it all the way through four years of college having no idea I had no idea how to study. I used to read a worked solution, nod along, and feel like I had studied. I had a few professors that disabused me of that notion and showed me how little I really knew. It was only then that I was able to start really learning. It's humbling, but it's not as bad as the shame of "not being a math person." You can be a math person. Just know that reading the answer is not the same as being able to produce it. So make the example work for you. Cover the next line, try to come up with it yourself, and only then look. Take any solved problem, from class, the book, or a Canvas assignment, and go through it in the steps below.
- Read the problem, not just the solution. Say what it asks in your own words.
- Cover the next line with your hand or a card.
- Predict the next move. What would you do, and why?
- Uncover it and compare. Did it match? Where did it differ?
- Write one sentence: why did that step happen?
- Now try a similar problem with the solution closed.
Once a type feels familiar, mix them
Doing ten of the same problem in a row feels great and fades fast. A test might not tell you which method to use, so the real skill is choosing. Practice that.
- Pull problems from a few different sections and shuffle them.
- For each one, name the type and the method before you solve.
- Return to the same skills across several days instead of all at once.
Stuck is fine.
Getting stuck is not a sign that you are bad at this. It's a sign that you need to learn more. Good news there is that you're in a class to do just that! Being stuck is most of what learning actually feels like, and a lot of the real progress happens right there in the stuck part. There is a catch, though. Being stuck only helps while you still have a move to try. Once you are just staring, nothing is happening but the tick of the clock.
Give yourself a real limit. Try for about ten focused minutes. If you have no next move, that is your cue to ask a question, not to quit.
This is working
- You draw a picture, table, graph, or number line.
- You compare the problem to a worked example.
- You find the first line that stops making sense.
- You estimate, then check whether the answer is reasonable.
- You write one specific question to ask.
This has stalled
- You stare at the page for 30 minutes.
- You copy a solution without working it yourself.
- You reread notes without doing any problems.
- You guess and move on without checking.
- You decide "I am just bad at math" and stop.
What should I do?
You don't always have a ton of time; I get that. So pick the plan that fits the time you have today, not the time we all wish we had. Even ten minutes is worth doing. It can keep a skill warm.
- Retrieve: redo one problem from memory, no notes.
- Check it against a worked example.
- Write one question for class or a tutor.
- Study one worked example with the cover-and-predict steps.
- Try two similar problems with the solution closed.
- Check both and fix the first wrong step.
- Write down exactly where you got stuck.
- Warm up: redo two old problems from memory.
- New practice on this week's skill.
- Mixed review: a few problems of different types.
- Update your mistake log.
- Write the one question you still have.
Keep a mistake log.
Humans are terrible at fixating on when things are going well, but we're great at seeing the bad. While that might have helped us not be a tiger's dinner, we're just trying to learn math. We can't see our progress if we don't track it, so keep a log of your mistakes. It can be one page in a notebook, or a note on your phone. This does a lot of things, but what it doesn't do is serve as some kind of record of failure. You'll need this log less and less as you go on, and one day you'll be buzzing through the work and will realize you haven't needed this thing in a while. This can be the short list of things that will not catch you twice. Add a row whenever you miss a problem you care about, and skim it before a quiz or test.
| Problem type | Where I got stuck | What I tried | What the correction taught me | What I will try next time |
|---|---|---|---|---|
| Solving for x with fractions | Clearing the denominators | Distributed across only one term | Multiply every term by the common denominator | Write the denominator under each term first |
| Word problems | Did not know where to start | Stared at it, then guessed | Writing down what they actually want makes it doable | Underline the question, then list what I know |
| Graphing lines | Mixed up which number was the slope | Plugged numbers in kind of randomly | In y = mx + b, the m is the slant and the b is where it starts | Say "slope, then start" before I draw it |
| Negative signs | Kept losing the minus partway through | Rushed the middle steps in my head | A dropped minus sign changes the whole answer | Slow down and rewrite every line, even the easy ones |
Use AI as a coach, not a shortcut.
AI can help you get unstuck. It can also hand you an answer before your brain has done the work, which feels productive and teaches you almost nothing.
The move that works is to make it ask you questions instead of just handing over the answer. These prompts do that.
After it helps, close it and try a fresh problem on your own. That second problem is what tells you whether you actually learned.
Ask me what I would try first. Do not solve it yet.
Find the first wrong step and ask me about it.
Give me a similar problem after I explain this one.
Quiz me on mixed problem types from this section.
Help me make a 25-minute study plan for this topic.
Do not give the final answer unless I ask after trying.
When life interrupts, do not disappear.
Many of you carry real responsibilities outside this classroom. You may be working full time. You may be raising children. You may be caring for family. You may be sharing one car. You may be helping someone with appointments, food, bills, translation, or transportation.
None of these make you any less serious as a student, and I and your other instructors know that. If you're in one of my classes, my email address is at the top of my syllabus. Send me an email and I'll help.
When something gets in the way, I would rather hear from you than lose you. Send a message. Ask the question. We will make a plan.
Something come up? Try this.
- Before or after workOne 10-minute practice session. Keep the skill warm.
- Missed classOpen the matching lesson, do one worked example, then bring one question to the next class.
- Kids or family nearbyAim for a 10-minute block, not a perfect hour. Tell them it is your math ten minutes. They might listen.
- Bad quizCorrect the first two missed problems, add them to your mistake log, and email me.
- Several days awayDo not restart from zero. Redo two problems you already knew, then add one new one.
- Freezing or anxiousStart by copying what the problem asks and one thing you know. Moving your pen breaks the freeze.
I missed class and want to catch up. What should I do first?
I did poorly on the quiz. Which two skills should I practice before the next one?
I understand the examples in class, but I freeze on homework.
I have limited study time this week. What should I prioritize?
I am dealing with family responsibilities. I want to stay in the course. What is the recovery plan?
I freeze on tests even though I can do the homework. What can I try?
I have been away a couple of weeks. Where do I restart?
Which worked examples match what we did in class?
You can learn this!
After years of watching people learn this, I've come to believe that math is not a thing you are nor a thing you are born with. It grows, through practice, feedback, better strategies, and a little help. You can come back after falling behind. You can recover from a bad quiz. You can learn math even if math has hurt you before. And you belong in my classroom regardless of what you fully believe.