Notes for Students

If you’re reading this page, you’re already on the right track.  It means you want to get the most out of what you’re doing, and that you’re willing to work for it.  Bravo.  Keep this attitude; it will serve you well.

There are many reasons students take algebra, but one thing most of them have in common is that they need to know this material later.  There are arguably more important things that you will gain from taking this course, but we’re going to focus here on course performance and retention.

During high school most of us got in the habit of viewing learning as something we did for a test.  That, as it turns out, isn’t the most helpful way to think about learning.  For example, by the time you take the next course, whatever exam you took on this material will be long gone.  So how do you learn things in such a way that you understand them, and can recall and reconstruct them, rather than place them in short-term memory for a test?

  • Focus on the material, not the exam.  If you know the material, you’ll do well on the exam, even if it has a few surprises.  Studying for the exam won’t teach you much and will probably stress you out.
  • Real learning is long-term learning.  Repeated exposure is key.  Watch the videos before class.  Be engaged during class.  Do your homework.  Go to office hours.  Watch the videos again if you’re stuck.  Ask questions.  Work with peers in a group.

This is your education.  You are in charge of what you learn and how well.

  • Math is like basketball: to learn mathematics, you must do mathematics.  Watch each video with a pencil and paper.  Stop the video to try to do the problems yourself before they are completed in the video and whenever you need to write down a question.
  • Try to solve the problems even if you don’t know how.  Your brain learns when you fight for it.  You sit like a dead fish, your brain is going to act like a dead fish.  It is absolutely vital that you: believe you can learn to material; that you attempt to solve the problems; that you analyze patterns in where you get stuck or make mistakes; that you get help from your classmates and your teachers.
  • Keep careful notes.  This is a learning process.  You want to be able to keep track of the evolution of your own ideas.  See how your approaches change.  Consider the difference between: “Professor, I didn’t understand the video last night?”  Okay, what did you have trouble with?  “I don’t know.  Everything.  I just didn’t understand.”  compared with: “Professor, I was watching the video about solving quadratic equations last night, and they put THIS equation up and then said it was the same as THIS.  I couldn’t figure out how.  Can you help me?”

The second person is going to get the answer to the question they actually have and learn something.  The first student’s question is unanswerable.  No matter how much the professor wants to, it isn’t possible to figure out what that student is struggling with.  Even when you don’t understand, it’s on you to ask questions.

If you get stuck at some point, like the second student did, going from one point to another, make a note of your question and then keep going.  See if you can follow the rest of the solution from there.  Don’t give up.  Remember.  Repeated exposure is part of the learning process, struggle is part of the learning process, and productive failure is part of the learning process.  As a student, it’s your job to make the inevitable failures that are part of the learning process productive for you.  Keep track of what you do and don’t understand.  Ask questions.  Keep trying.  Write clear notes to yourself.

-Sheila Miller