The reflective summary should respond to the portfolio’s statement of purpose through a critical reflection on the portfolio itself as well as on the experiences, activities, and learning that have occurred through your participation in the PTP program. You should demonstrate what you learned, how you applied it, and how you have grown as a teacher and a future professional as a result of participating in the program. You should address what you learned from your mentoring experience as well as the PTP seminars. The reflective summary should explain your teaching-related goals and objectives for the future and the way in which the PTP program experience will help you achieve those goals.
I hope that I have conveyed my love of teaching mathematics through the pages you have seen. I try to send this message in the classroom, too. My enthusiasm, my encouragement to discuss math, and the group work I promote all fuel the desire I have to witness a student having an ‘ah-ha’ moment. You might not be able to actually see the lightbulb flash on top of their heads, but a keen observer will know when a student has succeeded in making a connection. I give my students all the tools I can to help them achieve this moment.
I give my students the power to use their own voice. Whether they are reasoning through an argument, providing an example, or simply stating a fact, their input is always welcome in my classroom. Through the PTP experience, I have seen the importance of this tool. It creates a welcoming and relaxed learning environment where everyone’s opinion is respected and desired. My portfolio’s artifacts support this desire. My peers, students, and faculty mentor all indicate positive feedback from using this discussion based model.
I have seen the importance of small group work both as an instructor and as a student. I use small groups and partners in my classroom to keep students actively engaged. It also allows students to self-assess and provides me with the opportunity to check individual student’s progress. While they complete a 3-5 minute task in their group, I can walk through the room to check progress and answer questions. I have also used this time to purposely pair students who may have been absent recently with a student who was present. The advantages are twofold. The student who missed material can receive quick and concise instruction on the basics while the other student can reprocess and explain the material in his or her own words. As a PTP fellow, I was able to partake in numerous small group discussions at the beginning of each seminar. I found that the case studies triggered a lot of discussion within the group about topics that were relevant to all fields of study. All members were able to think critically about topics such as assessment, cheating, plagiarism, and course policies. By taking such an active involvement in the topic, these discussions are some of the most memorable parts of the seminars. Through the PTP experience, my ideas of engaging students through discussion has been further cemented.
I have implemented other topics from the seminars such as motivating students by explaining why I love the subject of mathematics. This includes promoting the historical aspect of mathematics. When relevant, I try to introduce the context with which a topic was discovered or implemented or information about a mathematician’s life. Students are often very surprised to learn of the feuds in Calculus, that L’Hospital’s Rule is incorrectly attributed to L’Hospital, or that Fermat published only one mathematical paper. I have also used the format of a lesson plan promoted by Dr. Honeycutt. As seen on my artifacts page, I have employed a lesson plan which is segmented into 10-15 minute portions. Furthermore, I have made use of creative assessments such as Venn diagrams to organize information and highlight relevant points. These types of assessments were emphasized in the seminar about critical thinking.
From my time spent with my faculty mentor, I feel more competent in fairly assessing students. My faculty mentor helped guide me toward reasonable questions and formats. He helped me establish a balance between homework and quizzes to keep students up to date on recent material. This also gives students study material they can use in preparing for exams.
Finally, I hope to keep learning from my students. From my students, I have discovered new ways to solve problems and heard conjectures that left me pondering. In creating this portfolio, I have been able to reflect and learn from my past teaching experiences. I have seen aspects on which I hope to improve. These include my strictness during the first few weeks of class and my planning of course exams. I have also been able to return to previous semesters of teaching and see what I have strengthened into forming my foundation of teaching practices. I remain open to feedback, welcome students into office hours, and encourage active participation.
I leave you with a critique on my strengths and weaknesses as an instructor from an anonymous student.
She can lift 300 pounds!