(0) Unsatisfactory | (1) Progressing | (2) Proficient | (3) Distinguished |
The candidate provides no outside resources from professional mathematics organizations. | The candidate collects outside resources but they are not related to the mathematics of the unit. | Appropriate resources are collected and the candidate explains how they relate to the content of his or her math unit. | The outside resources selected by the candidate either effectively extend students’ learning of a topic in the unit or provide scaffolding to students in need of support. |
This year, one of our TAs, Brock Walsh, submitted the following entry. (He granted his permission for me to share this with you.) I was completely unprepared for this approach since it did not meet my experience or expectations. Consequently, I scored it as "Progressing" - surprise, I was wrong.Outside Resources
The Process Standards from the NCTM website are a useful tool that I continuously find myself looking for and applying to my teaching philosophy. In particularly, I used these standards during one of my lessons this semester as I put myself at the front of the classroom to analyze a rational function problem on the white-board. I told the students that the purpose of this was for them to see what a good problem solver would look like so that they could reciprocate those ideas when they problem solved in the investigation. Showing the students my thought processes of problem solving, using reasoning and proof, and making connections were all things that I acted out in class for them to see. I then communicated to them what my thinking was and represented my work through graphs and charts. I had so much fun with this lesson and was able to improve on it teaching that lesson three times. I had an action plan set for that class as well looking to increase students’ engagement in problem solving and in the end, I felt that I did a very good job in my objective.
The Process Standards should always be a crucial framework to follow whenever I plan a lesson for my students. I want to make sure that when they are doing math, that they are able to somehow use these standards to show that they are mastering their work. My unit in particular needed a lot of connections to be made to understand new material. The students themselves needed to show me that they knew the material by communicating their thinking to me through formative assessments. We had projects where the students were able to represent their thinking on posters that were hung in the hallway. And lastly, they use reasoning during problem solving to work through problems and generate answers. My students will be successful when they are successfully using each of these standards appropriately.
Brian Cambourne’s Conditions of Learning is another great resource for really knowing how to engage my learners. Being an effective teacher means that I am reaching each student at the appropriate level that they should be learning. Being at Black River, we have high expectations for our students to be responsible for their own learning. In several lessons we allowed students to make approximations before we stepped in to demonstrate the correct way to problem solve. By doing that we gave them opportunity to achieve their own way of understanding the problem, which is powerful when it is accomplished. From the formative assessments, I was able to give students immediate response to their work and let them know how to make corrections to their understanding. All of these conditions truly make students progress towards better literacy of mathematics.
Cambourne’s conditions should be on my mind whenever I lesson plan. I need to know my students and present material to them in a way that they are engaged and are able to progressively develop their thinking. This is a framework that I should keep on hand and refer back to on occasion to make sure that I am reaching my student’s needs.To be continued...
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