The lesson during my observation was about special systems of linear equations. We started discussing the topic the day before this observation so the students had some prior knowledge on the subject matter. The goal of this lesson was to make connections between systems of linear equations with “no solution”, “infinitely many solutions” and what we have been previously learning about slope and the y-intercept of graphs.
This class is right after lunch and is often quite chatty. I attempted to make a lesson that would increase our communication and collaboration skills, because as a class they are struggling with these skills as we change to the common core standards. I’ve noticed my students desire to simply be robotic in mathematics, we have to get away from that! I want to teach them to think and problem solve.
The activity I had planned didn’t go as well as I hoped it would. We ran out of time to fully make the connections I intended. The first activity where the students needed to group themselves into fours (one graph, one equation, one slope, and one y-intercept) was supposed to let the students review slope intercept form and connecting the equation to it’s graph as well as showing how some systems of linear equations have no solution. We did not get to the part where the students were supposed to find another group with the same slope as them to create a system with no solution.
The second activity was intended to review transforming equations in standard form to slope-intercept form. By finding a partner whose equation transformed to the same equation in slope-intercept form, the goal was to establish an understanding of systems with infinitely many solutions.
I hope to try this activity again and make some adjustments so it works better. I know I need to explain the directions better, perhaps I could write them out and have them posted on the board so the students can refer back to them. I really like the skills that this activity could help the students learn.
This week, I gave a quiz to my Course 3 Math students (normal 8th grade math). I was feeling a bit uncertain about it the day before. I made the quiz myself, but used the textbook’s assessment generator.
The quiz covered sections 2.1-2.4. It was about using a table to graph a line, calculating slope, slope-intercept form, and graphing by finding the x and y intercepts. From my informal assessment, I knew that there was quite a range of understanding in my classes. I knew many students were understanding the process, but others really didn’t grasp the entire concept.
With having to do the MEAP the past few weeks, the lessons haven’t been completely normal. Four days out of the past two weeks had short class periods of only 30 minutes. Yet, I didn’t feel as if we were rushing through the sections. I strategically picked the less complex lessons to teach during those short class periods. We only covered one concept per day. I did give short homework assignments though. I gave them worksheets that covered the concepts well but were only about 10 problems long. I didn’t want to overwhelm them with work during the MEAP weeks. The students have been really lazy about homework though. They “complete” it but they don’t actually read all of the directions. For example, they transform an equation into slope-intercept form but then they are asked to graph it and they don’t! This is a key concept…they must make the connections between the equation and graphs as well as between the table and the graph. I gave the students a stern talking to about the issues I have been seeing with homework. I said if it didn’t improve for the next day’s homework assignment, they would earn themselves extra problems. Well…they certainly earned the extra problems.
The problem is, the same issues I saw on their homework appeared on the quiz! I just don’t understand how to “teach” someone to care about the quality of the work they are doing. I want them to see that there is a direct relationship between how much effort they put in and what they get out (including both learning and grades). I am at a loss of how to change this…I can control what happens in my classroom but I can’t control what they do at home.
In the past week, my students have completed two days of MEAP testing, a quiz, and a test. That is a whole lot of time devoted to testing. I have wondered whether this is really the best way to assess learning and understanding from our students. I know that these things have become “a necessity” in education so that we as teachers can prove that we are teaching. Yet, is this really in the best interest of the students? I don’t think it is but at the same time I can’t come up with a sound way to gather this information without testing students.
Project based learning seems like it is one alternative. If students are working in a group though to complete a project, how can we assess each individual’s learning? I personally have never been a huge fan of group projects because I typically felt that I was taking on a majority of the work. To look at the other side of the coin though, society functions in a similar way. In a job you are not tested on what you know, rather you are expected to perform and work together with coworkers to accomplish tasks that benefit the company.
I am just thinking aloud here, but I really wish we could find a way to reduce the amount if time we spend formally testing our students but still be able to gather the same kind of individualized data.
During my observation today, I wanted to focus on questioning techniques. I really wanted to think about the types of questions I was asking in terms of variation and depth as well as determine if I was giving students enough time to think about a question before calling on someone for a response. Over the past few weeks, I have been trying to move away from questions such as “what’s next” while moving towards encouraging students to genuinely share their thinking, whether it be right or wrong.
From the observation notes, I noticed that I often ask the same questions. In some aspects this can be good, because the students know what I am expecting, but as a whole I don’t think I want to work to change this. I want to constantly engage the students in mathematical thinking, not just letting them go through the motions.
One highlight of this lesson for me, was diving into common misconceptions. I hadn’t necessarily planned on doing that today, but it seemed to fit well so I decided to give it a try! I like having students identify errors in order to understand why that way does not work so they can in turn avoid it as well!
In the debriefing part of the observation, we discussed several things I would like to implement in my every day teaching. I am going to conscientiously make an effort to have the students discuss with their neighbor often so I can hear responses from several people on one topic. Also, I really like the idea of having students write down the answer to a question I pose, my only worry with this is that it could get time consuming to do walk arounds so often. The set up of my classroom, which my CT doesn’t really want to change, isn’t the most conducive to getting to all the students quickly.
I do want my students to become independent math students where they can think and reason mathematically without having to be spoon fed so often. I feel that we need to work on problem solving and critical thinking. I want to implement more collaboration and communication between the students. I believe I received several good suggestions today and I look forward to trying them out in the days ahead!
Quick side note: I tried some of these techniques just this afternoon and I liked the results! Using “thumbs up/down” for agree or disagree and stimulating a class discussion was cool to see. The discussion did not quite bring about the necessary points, but it helped me know what they were thinking and a base for my explanation.