Exam Preparation Reflection

Last year I tried something new with my seniors.   A lot of my students(and I'm sure yours too) tend to not realize that their preparation for a test has a lot to do with the outcome.  So many seem to think that you are just born with math ability and that directly determines how well you end up doing on tests.  I wanted them to be able to reflect on how they prepared for an exam, and how that led to their grade.  I started crafting a project for my students to help with this.  I had the following goals:

1) Students who give 100% in every class and don't have to study much shouldn't be punished
2) Students should have the option of not doing anything at all.  The fact is some kids don't study, and I want them to be able to face it without punishing them further.
3) Students who work hard should be rewarded.
4) Students would be forced to think about how they prepared while seeing their exam grade.

So, I decided that for the project they would hand in all of the materials they used to study and write up a one paragraph explanation detailing exactly what they did.  I made it clear that if they wanted to they could hand in a paper that said "I didn't do anything to prepare" and it wouldn't be detrimental to their grade so long as they did well on their exam.  The worst grade they could get on their project was their exam grade but they could do better on their project if they prepared well.  I gave them the previous year's exam as practice and gave them some general suggestions on what they could do to best prepare.

I thought this would be a good reflection for my students and that they would learn a lot and it was, but it turned out that I learned from it too.  I had been under the assumption that some students studied well, but struggled on my tests and that other students didn't prepare at all, but ended up doing well.  To my surprise, students' grades lined up almost exactly with the way they prepared.

We spent the whole class on the Monday after exams reflecting on exam prep. I opened by having each student write down their answers to the questions below.

In preparing for your exam...

What did you do that worked?

What did you do that didn't work?

What could you have done better?

I handed back their graded exams and we went through the following stats one at a time(red results are from this year):

Class Average: 83% (83.9%)
Highest grade : 93% (99%)
Average of Students who didn't turn anything in: 72%
Average of Students who "looked over their notes": 74%
Average of students who didn't do any of the practice exam: 75%
Average of students who did the easy problems for them on the practice exam: 79% (76.8%)
Average of the students who did all of the hard parts of the practice exam: 87.4% (88.2%)
Average of students who identified and targeted what was difficult for them: 90% (97.25%)

Then we discussed the results and talked about effective studying.  We talked about how "looking over notes" didn't do much of anything, and how even doing problems that are easy for them didn't really do much either.  We talked about how the largest jump came from the people who made sure to figure out how to do the problems that were harder for them and practiced those problems.  We went over some highlights of the Sweeney Study Method and their answers to the questions from the beginning of class, then used the remaining time to start on test corrections.

Overall, I was really happy with the results of this project.  It forced my students to see how their study habits directly influence their exam grades, and was an interesting learning experience for me as well.  I'd really be interested in seeing results from other classes, so if you try something like this, make sure to let me know how it works out!

The Banana Rule

Another concrete rule I use to help my students is the Banana Rule.  I noticed that my students often struggle with simplifying things like this(when we aren't directly learning about it):

Sometimes they don't realize that you can add them, but often times they realize they are like terms but end up messing with the exponents.  To me, it's really just a matter of how they are looking at it.  My best attempt at getting my students to see this problem the way that I see it is by telling them that if everything in a term is the same except for the coefficient(1) is the same you can think of it as a banana. Therefore, the problem above is simply:

Now, they see the answer is 4, but don't totally get it right away, so the banana explanation is quickly followed by:

"So, when you add a banana and 3 bananas, does the fact that you're adding bananas change?"  

"No!"  

"So the answer is 4 bananas, and what did we say was a banana?", etc

During that exchange the lightbulb goes off and they get it.

Just like the rainbow rule, I'll go through this with a class the first time time it comes up naturally in some problem, and then refresh it as it comes up throughout the year.  This method seems to reinforce that it's a tool, and not just "this is how you do this kind of problem".  If I have time, I might go off on a tangent about how it works with anything even if they haven't seen it before and go through some quick examples with trig, logs, integrals or crazy fractions and roots.  Also like rainbow rule, it helps kids put a name to something they struggle with and attaches an intuitive process to it.

(1)Okay, I usually say "number in front" instead of coefficient at this juncture, but we're trying to make it simple right? Please let me keep my math teacher card.

The Rainbow Rule

A couple weeks ago Sam urged people to talk about little tips and tricks done in their classrooms.  Since I found THE CLAW so helpful, I thought it would be only fair if I shared a trick of mine.

The Rainbow rule, a Sweeney original, is my favorite as it's useful for all of my classes from Algebra 1 to Honors Calculus.

Whether my algebra students come across this...

or my calculus students come across this...

...they either don't seem to know how to do it, or are confident about doing it the wrong way.

 Enter the rainbow rule:

Since we don't all have the luxury of excess time and image editing software when working out problems, the actual version looks and works like this:

This rule has been very helpful for my students because it gives a name to this situation which is both easy to remember and helps to avoid the common mistake of crossing the two lines (rainbows don't do that, after all).  While not every students gets it totally right, it still has really improved my students' ability to deal with fractions, especially those who I've had for more than a year.