Monday, January 28, 2013

How the Math Twitterblogosphere Has Changed Me

Before I tweeted, blogged, and organized Twitter Math Camp, I was a much different teacher. I did mostly lecture-style teaching. I had very little contact with other math teachers outside of my district. I spent little time outside of my school day thinking about mathematics and teaching mathematics.

And then I found Twitter. (Well, actually my husband asked me to check it out for something else and here I am. :-) ) I saw all these great and wonderful teachers and what they were doing in their classes and thought to myself, "Maybe I can do that in my classes." I went to visit one of my Twitter friends and saw that I wasn't totally off base in how I taught (because after reading all of these great things others are doing, you do start questioning what you are doing in your class). I started incorporating more and more things that I learned and read about from my fellow members in the Math Twitterblogosphere.

Fast forward to today. It is now about 2 weeks after my midterm exams have been completed by my students. I am still sitting here frustrated. I have never sat and obsessed worried about how my students have done on their exams. I did what I thought was best - gave them a chance to see the types of problems that they would encounter. I know the reason they did poorly is that they didn't practice. But I cannot stop myself from thinking about things to do differently, even though I realize that at this point there's not a whole lot I can do to change it.

I am still sitting here wondering what the point of the semester exam is. I know partially it's supposed to let students demonstrate what they learn (and for evaluation purposes, that is part of it). But when students don't take these kinds of exams on any semblance of a regular basis, they don't know how to prepare for them. Students focus on doing what they need to do to get by and when that assessment is asking them to remember stuff from 4 months ago, it is difficult for them if they are not using it on a regular enough basis. But when what we learned back in September is not directly related to what we are doing in December and January, that's difficult. We have so much material we are tasked with teaching these students that it creates a culture at times of learning the material for the short term and move on to the next. With all of the different viewpoints on teaching mathematics, there are good points to each (and some not good points). I can see what some of the "reformers" are getting at, but I go back sometimes to "what was so wrong with how we learned math?" (Side note - here's an interesting article from Education News about how maybe what we were doing wasn't so wrong.)

I didn't use to obsess think about my teaching this much. As I come up on the next topic, I start  to think about what I can do to help my students learn the material. I read way too much education and math education material and haven't read much of anything for pleasure in a while (which I miss sometimes). I spend lots of time putting together materials for my classes than I ever used to. And sometimes, I think I am doing a better job as a teacher (although since semester exams, I really don't feel that way). As much as I like that I am making changes in my classroom, sometimes I wonder if I am making the right changes. Sometimes I think I think way much about all of this and I need to step back. Maybe that's why I'm not blogging as much this year (although I'm sure that keeping on top of my curriculum has a pretty good part of that as well). I am starting to reach the point though that I feel I need to find the right balance - between thinking about/preparing for my classes and thinking about other things. I hope I can get there soon.

Sunday, January 20, 2013

My Weekly Diigo Links (weekly)

Posted from Diigo. The rest of my favorite links are here.

Saturday, January 19, 2013

Polynomial Questions

Normally, I post questions like this to Twitter, but I need to use more than 140 characters to ask it. Please feel free to tweet me (@lmhenry9) your answers or post them in the comments. Thanks!

We are starting the polynomial unit in Algebra 2. I have some students who have graphing calculators. We do not have BYOD and cell phones and i-devices are not permitted in school. I have four computers in my classroom. We do have a computer lab, but there are not enough computers for all of my students to have access at the same time. Some students have access to computers at home. My district has about 55-60% of its students on free or reduced lunches. I have students of many ability levels in my classroom.

So, given that background knowledge... how would you deal with the graphing polynomials (and eventually exponential and logarithmic equations as well as rational and radical equations) with these students? Common Core says (from here):

  • CCSS.Math.Content.HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    • CCSS.Math.Content.HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
    • CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
    • CCSS.Math.Content.HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
    • CCSS.Math.Content.HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
    • CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude

    So, how would you do it? In the past, I have always used the graphing calculator as a part of the process. I have asked my principal for permission to use other devices in and she is thinking about it, but I am not confident I am going to get a yes answer. What would you do? Thanks for your thoughtful answers.

    Frustrated and Discouraged

    I haven't posted in a while. To be honest, I have been rather busy trying to keep on top of school work and life in general. However, I am compelled to post about midterm exams.

    **Blogger's Note: I know at the end of this I am posing a lot of questions. Right now, I have no answers. Please feel free to add your own answers and comments at the end. Thanks. --LMH

    I generally feel that this year has gone well. I have been doing what I felt was a good job teaching, although I know there are a lot of things to improve on. Students have been doing well. Some have been reassessing. Grades for the grading period have looked pretty good this year. Generally, I feel that my students have been "getting" what I have taught. Then midterm exams hit.

    In my 21 years teaching, this has to be the worst year yet for midterm exams for me. My students did so poorly. We were to give exams over two days and I did a multiple choice portion and a non multiple choice portion, both of which I made up. I went through as I have done in previous years and put together a review sheet that had one or two of each type of question on the review (although I did find out that I missed one). I gave two days in class time to work on the review so that 1) students would (hopefully) complete the problems and 2) students would have time to ask questions. I allowed students to compile an 8 1/2" by 11" sheet of notes and formulas (they could not have example problems on it).

    Students did NOT do well on the non-multiple choice portion at all. I had some of my more motivated students ask me about a couple of the questions that were on the review that were a little different than questions they had seen before. I knew when I put them on there that they were not the exact type of question I had on an assessment before, but I also felt that they had the requisite knowledge of the mathematics involved to solve the problems. There were two word problems on there that students had seen before. The one question I had inadvertently left off the review was a question that involved algebraic manipulation and I felt that students should have had the requisite background knowledge to successfully solve the problem. They struggled and in some cases, didn't even attempt these problems.

    What I cannot for the life of me figure out is that in spite of warning students that they needed to do all of the problems on the review, they did not listen. In spite of telling them they really should take the time to put together their own note page so they could review the material, I had many students come in without a note page and I had several students who had a copy of a note page that another student had compiled for himself and that he shared. I cannot figure out why students who had done decent or well on assessments over the course of the year did so poorly on the midterm exam. What in the world did I do wrong? How can their midterm exam grades not even come close to what their grades have been all along?

    Is Standards Based Grading to blame? Are my students so focused on the short term that they truly don't focus on really learning and owning the material for the long term? I honestly think this last question is a good part of the reason. I am thinking of a few students who choose to reassess (and reassess often in some cases) and they earn 4's, 4 1/2's and 5's many times but then did not do well or attempt some of these other problems at all. Am I setting up a culture in my classroom (not intentionally) emphasizes short term learning? How do I change that?

    Sunday, January 13, 2013

    My Weekly Diigo Links (weekly)

    Posted from Diigo. The rest of my favorite links are here.

    Sunday, January 06, 2013

    My Weekly Diigo Links (weekly)

    Posted from Diigo. The rest of my favorite links are here.