I have noticed that the students in math class pay attention or do not according to their motivation. Understanding the problem is not as big of an affect on focus as is the motivation to do the problem in order to find the answer. The students who stay focused through out the whole lesson are motivated to practice their skills. They have self efficacy; they are not afraid to try and perhaps have an error, and they want to be capable of doing the problem. The students who do not, about 6 students are very hyper in math class. They are constantly calling out or playing with something; they are not focused for a long period of time. I believe each students is completely capable of following along and understanding the concepts because when I go to them and ask them how to solve they problem, they will come up with at least the right steps, if not proceed to the correct answer. They are simply not motivated. Perhaps the problems are not engaging enough, perhaps they do not want to put in the effort, or perhaps they do not like thinking critically and would rather think abstractly in their own way about a problem. Consequently, I believe to grasp these students attention and motivation, problems should be more open-ended and many entry points should be available. Creating these problems is difficult and it is something I need to practice so I can incorporate them into my unit.
Another thing I have notice is that the teacher still does not foster student interaction. The answer is just one part of evidence that the students are learning. Their thought process development is another major factor in evidence of their learning. Evaluating their thought process is accomplished through using a T chart for multiple problems; however, students may not be able to express their thinking in written form. Talking their way through their thinking may be easier and more natural, which is why I believe it will be extremely beneficial to not only ask for student's to justify the answer, but to facilitate student discussions so students can learn and compare student's thinking to their own, adjusting thoughts as discussion progresses.
I think this is an important observation; however, you want to be careful that when you say that a student fails to succeed because "they are not motivated", that you don't fall into the common teacher trap of attributing student struggles solely to the student's disposition. It sounds, to your credit, that you are not doing this, and instead highlighting how the nature of the task may be a factor: it is probably a combination of both characteristics you mention, namely, the tasks not having enough entry points and the tasks lacking sufficient student to student interactions. There is an easy litmus test. Put yourself in the place of the student: Would you be motivated to sit quietly and mindlessly listen to the teacher model procedure after procedure day after day? If the tasks do not motivate the students to think, and if the students have few "entry points" into the activity (either you know how to do the procedure or you don't; either you catch on, or you don't), then it is almost inevitable that some students will become "unmotivated". As you mention, one remedy is to try to structure math instruction that provides multiple entry points into thinking about the big idea and that facilitates student-student interactions where students can defend and share their thinking.
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