Now entering my second year of teaching at my new school, I am in the process of submitting a portfolio for my contract renewal (3 more years). Until now, I’ve never had to actually sit down and write an honest to God teaching philosophy. We discussed the concept in my MAT program, but I don’t remember ever really typing out what I thought about teaching–then again, I’m not sure what I could have said about my teaching philosophy with 0 hours in a classroom under my belt back in the day. So today, I present to the internet-world, my Teaching Philosophy and Self Evaluation statements for my contract renewal. I felt it was important to share this as I attempt to enter the #MTBoS world of putting my teaching life out there on the world wide web 🙂
Philosophy of Teaching Statement
I spent the vast majority of my educational career telling myself that I was never going to be a teacher. Math was a subject that never really came ‘naturally’ to me while in primary and secondary school. I always enjoyed the puzzle-like nature of mathematics problems, but I was never good at memorizing algorithms for completing math problems—which was the instructional method implemented by the majority of my teachers at the time. I decided to study mathematics in college with the intent of going into logistics or some other similar field, but never dreamed that I would one day become a teacher.
That changed when shortly after college I joined the Peace Corps and spent twenty-seven months serving in the rural foothills of the Andes Mountains in northern Peru as a Community Health Volunteer. My town was small, with no electricity, no telephones or cell phones, minimal access to running water, and limited vehicle transportation. My town was not the ideal location for young Peruvian teachers starting their career. We didn’t get the committed teachers, the ones who would stick around to inspire young minds. Instead, we got the teachers with the lowest test scores on their national exam and the least interest in the teaching and learning process. Three teachers left the town two weeks into the rainy season my first year in town, which coincided with the second month of the school year. Shortly afterwards the parent’s group contacted me with a simple request: to teach 3rd grade mathematics at the primary school. I was hesitant to agree, my Spanish was limited to health topics and small talk, not the mathematical language needed for teaching, but I agreed to teach for a few weeks, just until their teachers were replaced. Next thing we all knew, I was finishing my Peace Corps service having taught mathematics and science to my town’s youth for two years. We learned about addition and subtraction by running a small business selling snacks with a local storeowner. We studied multiplication, ratios, and areas of shapes while designing houses for our student’s families and creating murals to paint around campus. It wasn’t traditional teaching…I knew I didn’t want to do that…but my students learned math while learning about life – and in the process I found my life calling, to teach.
I first learned the pedagogical term for the type of mathematics instruction I used in Peru while studying at Duke University to earn my Master of Arts in Teaching: Project-Based and Problem-Based learning. The idea is to use real world context to teach mathematics by focusing less on the mathematical theory that persists in the traditional direct instruction methods of teaching and shifting the focus to applications of mathematics with hands on activities. I have bounced back and forth from full-scale implementation of the Project-Based Learning curriculum to a scaled back combination of problem based learning with direct instruction over my teaching career.
I have come to believe that mathematics is best taught through its applications, not as a set of rules, regulations, and restrictions that are to be memorized and then restated. When students are given the opportunity to model a real world situation with mathematics they are more likely to retain the information being presented rather than learning the material in a traditional algorithmic method. With this in mind I strive to create student centered learning tasks such as labs, engaging problems, and projects, in which students need to utilize the mathematics they know to argue a point or to create a hypothesis to be tested. A mathematics classroom should look a lot like a science classroom—students should work in groups, create and perform experiments, test hypotheses, and interact with the math they are learning.
In my first year of teaching at UNCSA I made the decision to integrate student-centered problems, period-long group tasks that tie together short sections of direct instruction, into my teaching practices. This decision was partially driven, or at least sustained, by my involvement with an online mathematical professional development group called the Math-Twitter-Blog-o-Sphere (#MTBoS on Twitter). The MTBoS brings together math teachers, district-wide curriculum coordinators, technology developers, and instructional support staff from around the United States and the world.
I discovered that most of the students whom I teach at UNCSA are math-phobic; they have spent a fair amount of their academic career either feeling as though they are not good at math, or earning grades that would make them feel so. I noticed in my students last year a hesitation to participate in class, resistance to voice an opinion about an answer or to even make an educated guess as to where to begin a problem. I believe that this shyness stems from a feeling of never being “correct” while in a math classroom. I noticed that the same students who were quiet and reserved in math were outspoken and opinionated in their social studies and English classes. The MTBoS had suggested over the summer that perhaps this math-phobia could be eased by providing students a safe start to every class period – A question or discussion topic that has multiple entry points, or easy access for all skill levels, and that most importantly, that don’t have a correct answer.
So this year I made the decision to introduce several types of warm ups with no correct answers that would easily generate discussion and constructive criticism in my classroom. To start some classes we will do a Which One Doesn’t Belong? activity where students are given 4 images, graphs, numbers, or shapes, and they must give a reason for why each image does not belong to the entire group. We then spend time elaborating on student responses and increasing the amount of mathematical vocabulary utilized to justify their responses. I have noticed that even my weakest students, the ones with the least self-confidence in math, have the most unique answers for these warm ups and are usually the first to point out a reason for their argument. Other days in class we use 1001 Math Puzzles, an online resource of non-grade specific brainteasers and logic puzzles, where students are asked to visualize shapes and colorings or objects to make an argument for their rationale in answering the prompt of the day. Every Friday we play Set, a math game in which students are given 12 cards and asked to find sets of 3 cards that meet a specific set of criteria. Even though we are only 2 months into the school year, I have seen a huge improvement in my students’ willingness to voice an opinion, mathematical or otherwise, growth in the ways in which they describe and argue with mathematics, and a higher overall sense of confidence while in the classroom. I look forward to continuing this practice over the course of the school year and hope to continue to see improvement in students’ willingness to participate and an increase in the mathematical vocabulary utilized when making an argument.
This year I have also used a variety of new online technology resources in the classroom, such as the Desmos Activity Builder, to integrate formative assessments into my weekly instruction. This tool allows me to create an interactive iPad task for the students to work with where I can see their work and provide feedback as we move through a chapter. Recently I vetted a Desmos Activity that I created to the MTBoS community and received invaluable feedback as to ways to improve the content of the activity and to differentiate the activity to suit a variety of learning levels. The lesson was a huge success not only in terms of the content in which students demonstrated mastery, but also in the engagement level of the students. I am currently working on integrating the use of iClickers, a student response system, into my classroom as well. This will allow the collection of formative assessments to gauge students learning throughout a class period through the use of multiple choice or matching style questions. I plan to have the iClicker system up and running in my classroom by fall break at the latest.
In addition to these new warm ups and instructional resources, I also created a new non-routine problem or lab to every unit in my classes this year. The math department decided to introduce non-routine problems into the PreCalculus curriculum in order to better prepare students for AP Calculus. These problems are somewhat open ended, related to current and/or past content, and intentionally worded differently than other problems from class. The idea is to give the non-routine problems to groups of students and to assess, utilizing a department created rubric, how they handle the problem in terms of group collaboration, mathematical language utilized by the group members, content cited, and problem solving methods used by the students. I have decided to introduce these non-routine problems into my Standard Algebra 2, and AFM classrooms, to assess the critical thinking skills of my students. I hope to see them succeed in these problems with the confidence they seem to be gaining from the non-math warm ups this year.
I am currently in the process of redesigning the Algebra 2 and AFM curriculum to better meet the needs of our students. Currently that involves shifting the focus of a few units and the sequencing of the year so as to stay within the current course descriptions for both courses. I look towards next academic school year, however, I would like to propose a major overhaul of how we treat the AFM class at UNCSA and what standards we cover as a course. With its current focus as written in the course description, AFM is a repeat of Algebra 2 with an increase in the amount of hands on activities and labs that students perform. I feel that we would better serve our students if AFM provided the opportunity for our weaker math students to explore new mathematics. For instance, there is a topic in number theory, called modular arithmetic, that is the foundation for how credit cards, ID key cards, encryptions on your email, and how your personal information is transferred over the web, which can be explained using basic arithmetic and understandings of functions. That is to say it is accessible to students who can perform basic arithmetic operations such as addition, subtraction, multiplication, and division, but separate from the curriculum they have already been provided while in Algebra 1, Geometry, and Algebra 2. While a sophisticated application of mathematics, the security of your information is not rooted in the complexity of the mathematics involved, but rather the tedium of calculating the products of very large numbers. The concept of how to securely design encryptions to protect your information on the web is well within the grasp of our students’ abilities and could provided an interesting shift in how we view an upper level math course at UNCSA that is not on the AP curriculum path. I feel that the shift away from the repetition of Algebra 2 with AFM would not only increase the mathematical confidence of the students, but vastly improve their reasoning skills and problem solving abilities—both of which are key to success not only in college and beyond, but for the preparations for college like the SAT and ACT. I would also like to have students modeling with combinations of linear, quadratic, exponential, and trigonometric equations from the beginning of the year with the use of a graphing calculator or online calculator rather than waiting until after an in depth review of Algebra 2 so that students would solve the equations by hand. It is my belief that students in a course such as AFM would benefit more from the critical thinking and problem solving skills required for modeling with combinations of functions than the process of using algorithms to solve and create these equations by hand.
It is my hope to have a newly drafted AFM curriculum to present to the Educational Policy Committee by fall 2016 with the hopes of introducing the new curriculum changes in fall of 2017. I want to redesign the course with the input and feedback of my peers to create a course that pulls the focus of AFM from Algebra 2 and moves towards new math for the students to explore that will meet the requirements for admittance to university of a math beyond Algebra 2 to ensure that AFM students are eligible for college.