Wednesday, May 7, 2014

Day 153: Reviews and Proofs

I have a ton of grading that I have to do and I am reminded how much easier this job was when I was doing it poorly.  When I only used multiple choice tests and checked homework only for completion, grading was a snap!

This whole "wanting to be a better teacher" thing sure is exhausting.

We spent geometry going over the sheets that I gave them yesterday.  The students really struggled with the first page, on which they were given a quadrilateral with certain properties and asked to determine if it had to be a parallelogram.

I liked this page because it required a ton of lateral thinking and students needed to be able to justify their reasoning.

Almost everyone was able to come up with counterexamples when they existed, but the reasoning for the proofs was much more difficult.  I purposely did not work out the problems ahead of time because I think it's important for the students to see the way I think as a process rather than a finished product.

It was immediately obvious that this is a tactic that they are not used to.  I saw several eyes glaze over until I was done asking myself questions, pens poised to write the answers instead of the ideas that lead to it.

Most of them, however, seemed to really enjoy the puzzle that is a geometric proof.  I think that by emphasizing formal proof structure, we take away the fun that can exist in proofs.  They are, essentially, a puzzle with each piece leading to the next.  There is no set path that a student must take, but they do have to justify each step.

I think there is great freedom and beauty in it, but with very few exceptions, I may have been the only on the room to think so.  I've also found that when it's something they don't think they should know, they work MUCH harder to figure it out.  I can understand this as the simpler concepts should "just come" to us and if they don't, it's harder to motivate ourselves to work on them.  "It'll just come to me later."

In pre-algebra, we went over the practice test from yesterday in the hopes of getting them prepared for the actual test tomorrow.  I had students putting their work and answers up on the board to try to get them more active, but several refused and the ones who did, were rudely talked over or even heckled by their classmates.

I truly feel as though we've made much less progress this year than we have in previous year, and don't just mean about content.  At this point last year and the year before, my students were not nearly as rude to each other or to me.

One of the major problems with changing styles or routines in educations is that it's VERY hard to tell if it's the procedure that doesn't work, or the specific dynamic of the students in the room.

I try to make them understand what I'm attempting to do and why, but with this year's pre-algebra classes, I feel as though I have missed the mark by a mile.  I hate to think that they need Old-Teacher Justin while the geometry class needs New-Teacher Justin because it feels like giving up.

In period 8/9, there were three specific students out and it made all the difference.  The rest of the class, though boisterous, worked VERY well on the review, asking good questions and volunteering to show the class what they did.  I'm always amazed at how the addition or subtraction of one or two students can completely change a class dynamic.

I'm also quite tired of having to tamp down the urge to start each of these blog posts with "I'm so tired."  I'm starting to think that the recharge that I need isn't just emotional, but physical as well.  I've been going full-steam this year and haven't really given myself a chance to recover.

No matter how awesome and dynamic your lessons are for Monday and Tuesday, there is still a Wednesday.


  1. Your last sentence is exactly how I feel every week! I feel like there's never enough time to plan a GREAT week, only a few great days. I see 1st, 2nd, 3rd, and 4th grade during the week. Many times at least 2 of the classes in each grade are on different topics/standards and it becomes very difficult to do everything I want with them.

    I agree that it's hard to gauge your efficiency in less than a year with a new group, but it seems that you're doing exactly what you need to do to foster a good learning can only take them to the water though, you can't force them to drink!

  2. Justin
    Your comments about the beauty of proof and the process of proof interest me. When I last taught Geometry I would often let kids lead me down proof paths that I knew would not be fruitful. I felt that this was a wonderful exercise in choice and in seeing patterns that work and those that don't. I was in the distinct minority in seeing it that way - many students were frustrated with me. I tend to think that I just did not do a good enough job in establishing the right culture of thought, but perhaps there is no culture of thought that circumvents that tendency to just want to know the answer.

    1. I was thinking about how to introduce the idea of it being ok to spend a long time going in the wrong direction. I'm considering the idea of starting the section on proofs by having the kids solve mazes and put together puzzles. The concept would be that it's ok to make mistakes and go down dead ends as long as you don't give up. I wonder if seeing it in that light might help them to see that it's fine to not be right the first time, even in math.

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