Posted in Algebra 2, AP Calculus, Education, Math, Writing

The Power of Reflection

When I went back to school to get my certification, I was required to take a class called Technology in the Classroom. Oddly enough, the most important thing I learned from this class really had nothing to do with technology. We were required to publish an online portfolio detailing our philosophy of teaching. My online portfolio was composed of several different written reflections that demonstrated key aspects of my philosophy. At the time, it was agonizing work. I hate talking about myself, and it had to be about me. It was torture.

Fast forward a few months, and with a brand new certification in my hand, it was now time to find a teaching job. The pool of candidates in the system was HUGE, and I was a total newbie. I knew I had to do something to set myself apart from the rest of the candidates. I decided to expand my portfolio.

After doing some research, I divided my portfolio into four sections; the first section contained my philosophy of education, The second section contained personal data – transcripts, resume, and letters of recommendation. The next section showcased carefully selected artifacts from my work as a graduate student, as well as my student teaching experience. I organized the artifacts around the ten principles of teaching developed by the Interstate New Teacher Assessment and Support Consortium (INTASC). Associated with each artifact was a rationale page, explaining why the artifact was chosen to support a particular standard. The last section contained a final reflection on my previous experience and my goals for the future. I chose an attractive theme, and peppered the document with quotes that reflected the themes. It took hours, but when I finished, I had it printed and bound and I took it with me for every interview that I had. It was gold.

“I’ve failed over and over and over again in my life…and that is why I succeed.”

-Michael Jordan

Reflecting on my experiences in writing allowed me to connect my attitudes, values, and beliefs to the work that I had done in grad school. Making these connections gave me a clearer view of my own philosophy, which ultimately translated directly into my classroom instruction. Realizing the value of this experience, I knew I had to figure out how to incorporate the same process into my math classroom.

During the summer of 2015, I began to do some research on incorporating portfolios into the classroom. I decided that my students would have to do one submission per quarter, for a total of four submissions. The format of the final portfolio submission was modeled after my own teaching portfolio. At the beginning of the school year, I handed out a project overview, found here.  I talked about the portfolio process and introduced the project.

I knew that I had to provide some instruction to help the students create their portfolios. So, over the first 2 weeks of school, I did a few in-class activities to introduce the process of reflective writing and the eight mathematical practices. The students were now ready to begin.

The portfolios were required to contain four samples of student work (called artifacts) – one from each quarter. After the first two weeks of work, I assigned the first artifact. I was careful to give lots of detailed feedback when I graded the artifacts, so that students had the opportunity to improve for the next submission.  I also peppered in several activities over the course of the year to help students improve their writing. Each quarter, I assigned a new artifact. Part of the beauty of this project is the ease with which I can change the theme for each artifact. For example, during the third quarter we were studying exponential functions. I decided to have the students use an in-class activity for their third quarter artifact.  During the fourth quarter, I have students write an introduction and conclusion for the overall project along with their fourth artifact. The result of this year-long process is a project that documents the students’ journey through the class.

For the last two years, I have done this project in my Algebra 2 and AP Calculus classes. Students have a love/hate relationship with the project; though it takes a lot of time, they do ultimately learn the value of analyzing their own work. Throughout the year, I try to highlight the importance of making mistakes in the learning process. Students learn that the analysis of their mistakes is where the learning happens. I often tell them that if they get A’s all the time in my class, then I probably haven’t taught them anything.

The biggest challenge that I have encountered is keeping students from repeating the same paper four times throughout the year. One way to help alleviate this situation is to have students think of one word to describe themselves, tell a personal story that illustrates that description, and then select an artifact to discuss. This will allow them to better connect their problem solving skills to their personal lives – something that math teachers always strive to do.



Wife, mom, aerospace engineer, math teacher...

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