Two Notebooks

[Note: This is a long post, and if you read nothing else, read my last story at the end.]

Sometimes I like to pretend that I really remember what it’s like to be a high school student. I mean, come on. It hasn’t been that long ago, has it? Oh wait. Is that MY ten-year reunion that’s coming up so soon? My boyfriend just made me watch Romy and Michelle’s High School Reunion, so I’m definitely looking forward to it.

I’m going off track.

Anyway, I’m back in the classroom. No, not my own class where I’m the teacher. I still have another week before that happens. I’m back in school — as a student. I finally feel [somewhat] mature enough to pursue my Masters in Applied Mathematics. I’m choosing to go to school because I want to learn, and not because I feel it is what is expected of me.

I did complete one prerequisite course this summer, and I worked my butt off to earn my A+. [Yes, yes, I do feel the need to brag, because I've never studied so hard for a class in my life.] But taking this class made me realize a couple things:

1) Being a teacher made me a much better student.
2) Being a student can teach me how to become a better teacher. (I guess that shouldn’t be a surprise.)

So here are things that I learned that I’m actually going to try this year.

My Problems: Students lose their notebooks. Students write crap from other classes in their notebooks. Notebooks are sloppy and disorganized. Notebooks are falling apart from use. Students don’t reference their notebooks. Students don’t process the information in their notebooks at home because they don’t want to read through it. The list goes on.

My Proposed Solution: Have students maintain two notebooks, one for processing information and future reference, one for all the “dirty work.”

After my first day of class, I realized that my notes were ugly, and not the easiest thing to look back at, so I decided to clean things up. I got a whole new notebook, and started rewriting my notes. (I knew of a couple people who did this before, and I thought they were crazy.) Yeah, yeah, a waste of time, right? Actually, because copying something word for word is annoying and tedious, I instead would try to rewrite my notes from memory (or follow the logical steps), using my scribble-notes as a guide. Examples, proofs, definitions. Then I still left room on the sides (that’s the requirement of Cornell notes at my high school inside of me) to write questions or make notes of things that did not make sense or that I wanted to emphasize.

I did this daily, and it was so much more help than just looking over my notes (which I constantly tell my students is NOT considered studying when it comes to math).

Further, with clearer labels, and definitions, it was much easier to use as a reference when I needed to look back at it. Just a side note — in just five weeks, I went through four entire notebooks for my notes and homework, yet I only used up three-quarters of my “process and reference” notebook, and for my students, I plan to have them keep this special notebook IN CLASS, so it won’t get lost or messed up, and process their notes in class (thanks to block scheduling).

Notecards and Definitions

My Problems: This is more my problem as a teacher. After taking this class, I realize that I often think geometrically and like to think of definitions in terms of pictures. For example, I’ve always favored the definition of absolute value as the distance from 0, when introducing it to my class. However, I often overlook the difficulty students have with taking these more concrete and visual definitions and turning them into the abstract symbols that they are required to work with in Algebra. That, and in the past, I feel I’ve been too light on the rigor of the definitions presented in class. I’m going to change that.

My Proposed Solutions: This is one of the oldest tricks in the book. Create notecards. And I’ve had students make them before, but I think I’m going to make this more integrated throughout the year, rather than just reviewing near the end of the terms. My trick to using notecards is to NOT use them. I hold them in my hands, but never look at the answer unless I really need to.

Pictures and ways to remember them are great, but I also want my students to have them memorized, and have actual vocabulary quizzes. I have failed my students in this area for far too long. I have always wanted my students to see a term or symbol, and have an understanding of what it means, but I feel I may have gone about it wrong by not holding them accountable to having something EXACT memorized first.

Group Work

Story time:I always felt group work was necessary in the classroom, so I would always have activities and opportunities for students to work together. However, when it came to myself, I almost always chose to work alone (I can be very shy at times), and I found that I was successful. 90% of my summer class, I spent studying alone, and I did very well on my tests. Then two days before my final exam, a classmate asked me to study with her since she didn’t do well on her previous test. I was hesitant in my mind, but I agreed.

I met with her and one other student in an empty classroom, and progress was pretty slow. At first we still pretty much did our own thing, sort of comparing solutions and proofs, and providing each other with different resources, like notes and homework examples. But then, she took out here whiteboard markers, and that’s where the real fun began. That’s when we actually started to really discuss the mathematics, critique each other’s writing and logic (and revised proofs together on the board to make clearer or more concise), and just having a blast talking about the math.

At the end of the day, I covered less material than I normally would have alone, BUT there were concepts that I understood at a level that I would not have otherwise reached had I just stuck to the methods and reasoning shown in the text… and I definitely would not have had as much fun! I have that small group to thank for the perfect score on my final test.

With that said, I noted that I felt it was necessary to have group work in the classroom. Now I KNOW it is necessary.

Textbook Pre-Reading

This is a tough one. I’ve never been a fan of textbooks before, and even now, I find them very, very difficult to use, but as a student very, very necessary. By keeping up on the readings prior to lecture, it made things much easier to follow. Even in the areas that I did not understand on my own, being exposed to the vocabulary, and trying some of the simple homework problems prior was one of the biggest reasons for my success. My goal to want to stay AHEAD of the class.

I would love to have students have that kind of discipline. I have no idea how to make it happen, and it probably won’t. But I just wanted to throw it out there.

One Last Story…

I have much more that I want to share, but this is getting long-winded already. But I have one last story for you.

I had a great professor. He had very high standards. He was a nice guy, approachable and always held a pre-class class during his office hours since his office couldn’t handle the number of students that would show up. He also was very open to questions and always provided that little bit of direction you needed when you were stuck on a problem, without giving away the fun part of solving it. He was also very good at providing constructive criticism, as well as praise.

However, like all professors, he was human, and there were a couple times where he would get stuck on a problem as well. One day, he was stuck on something. He asked for input and I raised my hand, and said something stupid. (Well, the picture in my head was correct, but I didn’t say it correctly.) But he quickly gave a short and terse response as to why what I said was wrong; and he had this look in his eye.

Now I bring this up, because he did absolutely nothing wrong. He corrected my error, and he didn’t make any big deal over it, or call me stupid, or put me down, or anything of the sort.

HOWEVER, being a student, I felt humiliated for saying something so stupid, and I took things to heart to the point that I may have allowed myself to believe that he viewed me as some smart-aleck trying to correct the teacher, and that the look in his eye was a little demeaning (although in retrospect, I think he was just thinking really hard still.) This caused me to lose concentration for a good portion of the class, and even worry that he would be extra nit-picky on my test.

The next day, though, I realized that these may be the same thoughts that may flow through the minds of my students. All the praise, feedback, getting to know students, and relationships you think you’ve built with a student could be taken back by just one unintentional “look” in your eyes. And this misinterpretation could hurt the performance of even some of your best students.

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