Practice Pages (Day 3)

I promised this was for students, so you're probably wondering when we're going to talk about schoolwork!  Let's do that today.  But first...

Revisiting Sleep

How was last night's bedtime routine?  Turn to your page on SLEEP and note down what happened last night.  Did you get through the routine?  What was the time when you last checked it?  (That's close enough to when you fell asleep for us).  What time did you wake up this morning, and how did you feel?  Can you stick with it for one more night?  I hope so!

Practice Pages

I have a great tip for you that comes from the old idea of flash cards, but it's updated for advanced mathematics.  The basic idea is to write common problems and solutions out, then practice until you know them very, very well.  Let's see how it works.

I have a comprehensive exam coming up in April, so I'll use my prep for that as an example of the actual method.  First you find example problems.  For this course I have a handful of worked problems from class, plus example exercises from two online sources the prof gave us, and finally some suggested exercises she posted.  You might also have questions from a textbook, or from tutorial.  Work on them in a rough order according to how critical they are.  For each question, grab a piece of scrap paper.  On one side at the top, write the question, plus a reference for where you found it (if you like you can also put the course code, but they're going to stay together so it doesn't really matter).  On the other side, write out the solution.  Put as many steps as you need to, to really convince yourself you understand each step.  I like to write little notes to myself on the side in a different colour - they're not part of the solution, but they're reminders of tricky things that I know I might forget.

You should get Habitica gold for this, right?  Of course right!  Add a Habit that's called something like "chunk of work".  These are going to be 25-minute timed bursts of work that you can do any time you have 25 minutes available.  You'll need a timer - the handy clock on your phone works, or you can use an online timer, an app, or whatever you like.  I use Focus Booster because it automatically sets to 25 minutes plus a 5 minute break.  Set the difficulty to whatever feels right to you - I do recommend "Hard", though, because this is not something you're likely to sit down and do for fun.

Now, there are two kinds of problems you'll be dealing with; some you will know the solution for, because it was given to you.  More often, though, you will be putting a solution down that you might have some questions about.  (I guess there is an in-between situation where you have an answer in the back of the book, but it's just the final answer with no steps.)  If you aren't given a solution, here are the steps I recommend:

1. Look for a similar problem from your class notes, tutorial notes, textbook, or (last resort) online.  You are probably doing this anyway to work the solution, so don't stop here. 
2. Get together with a classmate and compare answers.  Make sure it's someone who will actually do the work ahead of time and have them written down.  When you have different answers, of course, it's a perfect opportunity to work together to figure out which one is right, which will automatically deepen your understanding.
3. Ask your TA.  As a TA, I can tell you that we LOVE it when you come with questions written down!  If you show up and say "I don't get geometric series", it's hard for us to know where to start. It's always better if you come and say "I'm looking at this problem, and I know how to get this far... (show them)... but then I'm stuck on this step...(show them)."  That gives us a far better picture of what you understand and what concepts you've missed, and we can jump right in and fill the gaps. Also, you can be pro-active by asking "would I get full marks for this answer?".
4. Once you've exhausted your TAs knowledge or time, go to your prof's office hours. Now, I am pretty sure you don't want to do this, just because of how little it happens. (You can go to any university and overhear conversations between profs where they bemoan the fact that students never come to their office hours.)  Buck the trend!  Don't worry about seeming stupid - they will be in so much shock that you're there that they won't even notice.  Think about how wonderful it will be later on when you have to ask for a reference letter or ask someone to be your supervisor - they will already know your name and have an idea of what a persistent, hard worker you are.

Now, you might ask, what are you going to do with these sheets when you are done with them? One of your chunks of work you have available to you is to work with them.  To do that, you take out the stack, put it to your left, look at the top one, and try to work out the solution.  When you think you have it, turn over the paper and check how well you did.  If you got it right, put a checkmark and the date on the front of the page, and put it in a pile to your right.  If you got it wrong or got stuck, put an X and the date on the front, and put it in a pile right in front of you.  When the timer for your chunk of work is done, pick up the stacks from left to right, clip them together, and put them in the file for that course.  Next time you're ready to repeat the process.  (Notice that piling and stacking them in this order automatically puts the stack in the order you want - questions you haven't done recently on top, then questions you were stuck on, and finally questions you got right.  So you'll still review the questions you got right, just not as soon).

I have two Habits set for this task.  I have one of difficulty "Medium" that's called "Practice with flash cards", and one of Difficulty "Hard" that's called "Make new flash cards".   I find the updating (meaning, creating questions every week based on new material) to take much more brainpower. 

I hope you will also see that assignments and tests are goldmines for this process.  As soon as you get an assignment or test back, do two things...

1. The obvious one - make pages for the questions that weren't super-easy for you.
2. The less obvious one - go back through the questions you've been practicing with, and add a star to each one where a very similar question appeared on the test or assignment. This does two things - it helps you identify which questions you should focus on for the final exam, and rewards you for having correctly identified material you absolutely need to know.

Now, I hope you realize that the goal is not to memorize these problems and their solutions.  Approach them fresh each time and apply the knowledge you've gained.  You should find over time that your solutions get shorter, and the steps become more natural.

FAQ:
These are the questions I can hear you asking me!

Q. Do I really have to write it by hand? Can't I type and print, or photocopy them?
A.  Yes, you need to write by hand. Although nobody quite knows why yet, there is something different that happens in your brain when you write by hand instead of typing. Photocopying is a definite no, because you need to write out your solution that makes sense to you.

Q. Isn't this a waste of paper?  Does it really have to be one question per sheet?
A. I feel a little guilty about that, but hopefully you have enough scrap paper to create the questions. (Find a printer anywhere in your school, and there will probably be a recycling bin of paper nearby you can mine).  You need each question on a physical sheet, but if you have space left on the sheet, you can cut it across to leave room for another question.  When you are practicing, you need to write, but it doesn't have to be on paper.  You can use a whiteboard or chalkboard, a writing app on your device, or anything else you have available that's erasable.

Q.  Wouldn't something like the Khan Academy be better for this?
A.  I love the Khan Academy and I highly recommend you use them, yes. I am assuming you are at a level where the material you're learning is not available in their quizzes.

Get out your Journal!

Questions to think/write about:  (Now)  What part of this sounds hardest to you?  What benefits can you see from following this practice?  (In a day or two)  Were you right about the hardest part?  Was there anything easier than you expected?  (After your next test)  How much do you think this practice helped?  Will you stop, continue, or modify this practice?


Reference:
I got this idea from a website that I have unfortunately lost the URL to, and I can't seem to find again. I guess we'd better talk about reference tracking soon!