Teaching candidates must have a strong understanding for the subject they teach, as well as the ability to clearly explain it to their students. Without thoroughly understanding the material, it would be impossible to teach it to others, specifically I believe identifying gaps in understanding or coming up with new ways to explain an idea are only possible when the teacher fully understands the topics. This element is really important to me, it’s actually the reason why I chose to study Mathematical Sciences opposed to education. I truly believe that to be a good math teacher I need a deep and thorough understanding of Math. So for me, this element means I must not only show a strong understanding of the Math content covered in the courses, but also be able to help my students understand it too.

At WPI I’ve had the amazing opportunity to study a wide variety of Math and STEM classes. I’ve been able to take many math classes beyond the scope of the high school curriculum like Linear Algebra, Linear Algebra II, Ordinary Differential Equations, Modelling with Ordinary Differential Equations, and Real Analysis. Classes that have given me the opportunity to more deeply study STEM, and specifically computer science and algorithms, include Introduction to Programming for Non-Majors, Systems Programming for Non-Majors, Discrete Math, and Numerical Methods for Calculus and Differential Equations. Additionally I’ve refined my teaching skills by working as a Mathnasium Tutor for the past few summers and winter vacations, and working as a PLA in WPI's Math department. During the pandemic both of these positions moved online, and I was able to practice my online teaching skills, too.

Well structured lessons are key to good teaching as confusion and frustrations are barriers to learning. Through our lesson plan template I was able to consistently create well-structured lessons based on state standards. I always planned out measurable objectives to meet each class, and typically used my Exit Ticket as a formative assessment in that way. I started each day with a Do Now to get students thinking and reviewing past material, and as a segue into the next content each day. I planned activities to help students practice the skills needed to reach the days’ goals, and always built in time for questions. Provided below is a link to an example of a lesson plan for my Algebra I class. Many more lesson plan can be found at my Instructional Materials page.

Algebra I Distributive Property Lesson Plan

Adjustment to practice is another important element of CAP. This element focuses on the student teacher’s ability to take in feedback from students and use it to inform their teaching. This can mean realizing the pace of some topic is too fast or slow, leading to an adjustment in the goals for the day or plans for the next classes. It could also be the review of classwork, homework, or quizzes, and realizing that certain ideas didn’t “click” with students. This is so important since units, and math as a whole, build on past knowledge. If students struggle with a concept, then they will struggle with other related ideas unless misunderstands are addressed. It’s the same concept of building a house on a shaky foundation; you can build it anyway but it won’t last. To help gauge my students’ understanding I implemented Do Nows and Exit Tickets daily. I used Google Forms to get feedback from students on their answers, and always made a point that it’s ok to submit “I’m not sure” if a student was really stuck, since that information helped me more than no answer at all. Here is an example of a Do Now from Algebra I about writing expressions, a foundation for the new material of writing equations. These responses let me know most students had understood and remembered the topics from last unit, and the I could move onto the new material with little review:

Meeting diverse needs and differentiating instruction is another important aspect of teaching, and one that looked very different this year, in an online classroom, than it would have in the past. Many of my students had IEP or 504 plans, but the accommodations listed for them were designed for an in person class. For example, preferential seating away from distractions is not something I can implement when we meet virtually. Additionally, discreetly checking in on students and reminding them to stay on task is not possible in a Google Meet with the whole class present. So to help accommodate for this I regularly announced goal and time reminders to my students during independent work time and repeated directions many times for all students to hear. Additionally, many of my students were English Language Learners, ranging from level 2-5. I could use some of the same techniques to help cater to these students' needs, but repeating myself often, and using synonyms to help with understanding ideas and directions. I also made sure to emphasize important vocabulary, give examples, and provide visuals. To further help students succeed, I made sure to offer a variety of independent work activities each class, so students could pick the order they completed their work based on their personal preference and needs. I offered EdPuzzle videos as an important supplement at least once per week, so students could hear and see additional examples of the kinds of problems we were working with, then offering worksheets and practice problems to continue working on their skills. As it’s often said, differentiated teaching is good teaching, and I believe these techniques helped all my students learn.

Here is an Edpuzzle I edited to include questions relating to our class.

Another way I worked to meet diverse needs was through gamifying learning. Gamifying is one of the culturally responsive teaching strategies I like best, and it was especially useful during review periods. Students of all levels were incentivized to review when we played games, even if they felt really confident or completely lost, simply because the activities were fun. I turned writing equations into a Bingo game, and used Kahoot! to practice finding roots, but my favorite game was an Escape Room activity for solving equations practice. This activity used Google Slides and Google Forms to structure a virtual series of math puzzles. The starting form and the Google slide "room" are linked here.

A safe learning environment is necessary for student success, thus earning it a place on the list of seven essential elements. A safe place helps students feel comfortable taking risks and trying new things. A safe environment can be cultivated through positive norms and well developed routines. To help foster a positive learning environment in my classes, I used the same daily structure to build a routine, which I believe was especially important with all the unknowns that came with online learning. Each day students started with a Do Now, had some kind of lecture that could include any mix of practice problems, discussion, lecture, videos, or examples, then students would have time to do independent work that was always posted on the Google Classroom. And finally we’d regroup at a specified time to go over questions and complete an Exit Ticket. With a 70 minute period, fitting in a variety of activities was important for maintaining focus and learning. Here is an example of a Google Slides I used during a Topics class to guide students through the activities for the class, also provided to view below:

High expectations are necessary to help students learn and reach their full potential. Students need to be challenged daily to maintain effort, interest, and growth. These challenges need to be at the correct level though, or else they are more of a deterrent than a motivation. Student teachers are assessed on their ability to set high expectations and help their students reach them. Moreover, teachers must model the way that mastery is achieved through practice and effort, not through any innate ability or skill. One thing I was surprised to face in class was students calling themselves “dumb” in class when they didn’t know an answer or got a bad grade. This was something I would not tolerate, and shut down whenever I heard (or read) it. I made sure to emphasize that the only way to learn math is to do math and try problems, and that if a student was struggling it was never due to them being “stupid.” I set the expectation in my classroom that students always had to try and show an effort. This was reflected in the grading policy of worksheets being graded on completion, but other assignments (like Edpuzzles or ALEKS work) being graded on mastery. But all assignments that were graded on accuracy had unlimited tries, so students could always try problems over and be rewarded for that work.

Reflective practice is another essential element of CAP that student teachers must demonstrate. Being able to reflect on your own choices, methods of teaching, and interactions with students is important to improving on them. This reflection can be done alone, or with colleagues, and I tend to reflect a lot with my mentor. One big challenge we faced during the semester was finding fair forms of assessment in an online world. Many factors played into the decisions we made on quizzes. Firstly, we wanted to be able to meet student accommodations for extra time, and the way we thought that to be most fair was giving students class time and keeping assignments open through the end of the day or midnight that night. But that leads to another problem, when students have that much time in an unproctored space, cheating can be a problem. So we chose to make assignments open notes, but we still wanted students to show the work was authentically theirs. This led us to many different options like ALEKS quizzes, Screencastify video assignments, and Google Forms. In my Topics class, we realized ALEKS quizzes, and online software that can provide each student with a unique version of the test then automatically grade it, was not serving as a fair form of assessment. It gave students no credit for partially correct answers or their work, but grading that many unique tests would be impossible for me. So we tried using Screencastify, a screen recording browser extension, to have students make videos of their explanation to problems. But this also came with complications as many students struggled to record and submit assignments. Ultimately we had to just offer the video as a bonus point since so many students were unable or unwilling to record. An example of a Screencastify quiz is provided here. Finally we tried Google Forms, which has become our preference. Now we offer an open note, 6 questions, multiple choice quizzes. Students only get one submission, but are able to do quiz corrections if they get below a 60%. Additionally, though it’s 6 points offered, it’s graded out of 5 points, lowering the stakes and in term reducing students’ potential urge to cheat. An example of one of these quizzes for Algebra I is also provided here. The many iterations of quiz forms we worked through is a great, long term example of reflective practice.