1. Pre- and Post-Assessment for Dividing PolynomialsWhen I was teaching an advanced Algebra course, I chose to teach the students polynomial long division. I did this over the course of three class periods, with a pre-assessment on the first day and a short quiz in the third class. In the pre-assessment, none of the students attempted long division. I chose not to tell them to use this method because I wanted to see what approaches they would use. One of the most common methods I saw students using in the pre-assessment was dividing the polynomial expression by just part of the divisor. For example, instead of dividing by (x+2), students divided by just (x).
Many of the students remembered how to do long division after a refresher on the first day, and dividing by a monomial was picked up pretty quickly. I used the data from the pre-assessment to place students in groups for the second day of instruction, which involved some review. I had emphasized to students at the beginning of this mini-unit that practice and taking their time was extremely important. The students who did the practice and wrote out all the steps of the long division did extremely well on the final quiz. Below are various examples of student work. Each student’s pre- and post-assessment are grouped together to easily compare the two. |
I had the opportunity to conduct two interviews with an Algebra I Part 1 student to determine their level of understanding of various fraction schemes. After the interviews, I analyzed their responses to determine what their current level of understanding was and then created an action plan. The action plan was what I would do next to help this student further their knowledge. I did not get to enact this action plan, but I think this still shows my ability to determine a student’s current level of understanding and develop a plan that will allow them to grow in their knowledge of a certain concept.
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