On Friday, we gave the students a quiz over solving systems of linear equations and inequalities by graphing, substitution, and elimination. It seemed as though half the class was confident using substitution and elimination while the other half was still struggling somewhat. However, graphing seemed to be the easiest because we have been graphing practically since the beginning of the semester and they have been graphing even before then. On quiz day, we reviewed, touching on most topics but especially substitution and elimination because that was what the majority was struggling with. We handed out the quizzes and all but one student did not finish before class ended. They turned in their quizzes and we decided to finish them on Monday. We looked through their unfinished quizzes to see what they were struggling with the most. Surprisingly, their graphing both systems of linear equations and inequalities seemed to be the biggest problem. Their graphs were everywhere. There was one problem that involved fractions that most of the students had skipped or gave a very strange graph.
It really shocked us that they were mostly able to answer the problems involving substitution and elimination (there were still some students who did not get it) and instead had problems with graphing. We did not expect them to be stumped by these problems. Because of this quiz, we see that we need to review and practice different methods of graphing and probably need to make sure they know how to check their graphs in their calculators. I discovered it is very difficult to measure if they know the concepts we are trying to test them on when they are struggling with a basic concept that is part of the foundation of the material.
Because my experience is, at this point, mainly with teaching dance I'm going to equate this to my dance teaching. Often times I'm shocked that students will pick up parts so quickly and have trouble with what I think are easier things. I can't help but wonder if maybe part of it is because we anticipate that they'll struggle with certain things so we explain them slower, more in depth and just overall better. If I think the students will pick it up quickly I tend to go over it less thoroughly. However, I get the satisfaction that dance is always in an informal assessment because I can always watch the kids dance. With math we need to make sure we do quizzes and assessments so that we do get the valuable feedback that they are meant to provide (although many students still think it's meant to torture them!)
ReplyDeleteIt is amazing, students always seem to suprise you even when you think you know what to expect. I think it is a great idea you are going back and reviewing because it is important that they learn the material.
ReplyDeleteI was thinking the same thing as Patrick as I read your post. When you think you can predict the outcome of something, what you actually get can sometimes surprise you!
ReplyDeleteHow much time do we spend on reviewing? How much time do we have? When is it appropriate to review as a class? These were all questions that came to mind. It can be a struggle to find the time, but it is essential to make sure they know the fundamental ideas so they can reach the higher level thinking that involved in the lessons. I like the idea incorporating review problems in their homework or in the warm up activity. So many times you see the case: if you don't use it, you loose it. We need to emphasize the concepts that will continue to be important as we progress through topics in our classes. And as Caitlin said, we need to make sure to use assessments to capture the misconceptions and gaps in knowledge and give feedback!
You have no doubt heard the comment that you should start where your students are. It is difficult for me to say this know the current demands that are placed on teacher through common core standards and processes and accountability measures everywhere you turn. So, if there is something that you can do, albeit informal, to tap into what students know about graphing - that is the place to start.
ReplyDeleteI realize that I am saying this as if it is something simple you can do -- when I understand the challenges. However, it may save time and help you identify misconceptions in order to plan for the upcoming lesson...has anyone done these kinds of informal pre-assessments - might be a ticket out the door? might be one problem at the beginning of class?
Pre-assessment is one thing that I have noticed is not really present in many of the math classes that I have observed at Maryville. This shocked me a little bit because we talk about how important this is in our classes. I think next semester I will implement some kind of informal pre-assessment.
ReplyDeleteI understand this situation. I have stopped assuming things are easy.
ReplyDelete