1. Subject Matter
Definition of "Subject Matter"
A teacher must understand the central concepts, tools of inquiry, and structures of the disciplines taught and be able to create learning experiences that make these aspects of subject matter meaningful for students. To be a subject matter expert, a math teacher needs to understand the calculations and thought processes of mathematicians. He or she also needs to understand how people of a variety of backgrounds come to understand math. To gain expertise in both of these areas, a teacher needs a deep background in theoretical math (as it was taught in school), applied math (as used by engineers, scientists, economists, and others), and tutoring (where common hang-ups can be learned and troubleshooted). A student has the best opportunity to learn from a subject matter expert because subject depth makes it possible for a teacher to modify, and even completely reinvent, curriculum to fit the learning styles and interests of each student.
Supporting Artifacts and Analysis
To be a subject matter expert, I need a rich background in theoretical mathematics, a variety of experiences applying mathematical thinking, and the ability to teach math to children of many backgrounds. My artifacts support these requirements. Note: for privacy reasons, I did not post my transcripts and test scores to the site -- contact me at andypethan at gmail.com and I will send you a copy.
Transcript from Olin College of Engineering:
Olin is a highly applied engineering and design school in Needham, MA. Over the course of four years, I completed countless projects related to computer science, applied programming, control systems, material science, statistics, computer architecture, physics, and other areas. These projects all required significant mathematical reasoning applied to solving a real-world problem. My transcript is a record of the effective completion of courses and independent studies in all of these topics. It demonstrates my work ethic and desire to succeed as a student in the classroom.
My theoretical math education led me through calculus, differential equations, linear equations, discrete math, and statistics at Olin College. With a deep understanding of upper-level math, I can confidently answer student questions about the difficult nuances of foundational subjects like algebra. Common questions I can answer include the reason 0! must equal 1, why matrices are useful beyond solving linear equations, and the reasons why textbooks use such goofy notation to say that all values are in the domain of a function. More commonly, however, students ask me why we learn the many topics in algebra. My experiences at Olin allowed me to see how designers, systems engineers, programmers, mechanical engineers, electrical engineers, and biologists (just to name a few) use math to solve problems in their fields. For example, when students ask why we use f(x) notation for functions, I can explain that functions with clearly defined inputs and outputs are the core concept behind modern programming languages and drive the software behind every device they use. Going a step beyond this simple explanation, I can point students towards online resources that can get them started with programming and extending the topics of the classroom.
Transcript from Winona State University:
On the education side, I started my growth through a couple classes and a variety of volunteering experiences at Olin College. However, I greatly expanded this into a deeper, more formal education at Winona State University in Rochester, MN. My coursework provided a wide overview of critical skills including instructional planning and assessment, teaching literacy, identifying interests and learning styles, and working with students with special needs. I grew my understanding of the backward-design process that allows me to work from the purpose of a course to a clearly defined set of goals and objectives. Using these, I can develop targeted assessments, and just as importantly, create homework, projects, and lessons that prepare students for these assessments. I gained greater insight into the importance of student-developed goals and self-reflection that allow me to serve as more of a facilitator for a classroom of unique individuals than sage on the stage. I took my classes at Winona State seriously and produced my best work for every course I took. By doing this and iterating on my work with professor feedback, I greatly improved my ability to plan for a course, unit, and class. My transcript shows that I completed all of my coursework at a high level and achieved mastery in keys areas while preparing to teach.
MTLE Scores:
The Minnesota Teacher Licensing Exam assesses prospective math teachers on their understanding of high school math and their understanding of how to effectively teach high school math through a series of four 1-hour tests. By successfully passing all of the tests, I have shown my competency in math and my ability to use appropriate strategies in the math classroom.
Content review and addressed gaps:
The content review was a multi-step process that forced me to connect my engineering background to my new role as a math teacher. The first step required me to create a document that aligned each math teaching requirement to specific courses and experiences in my past. Besides listing the relevant content, I needed to explain the connection. This process of connecting and reflecting helped me grow in confidence in my areas of strength and shed light on gaps in my prior education. The second step, a review by a content expert at Winona State University, formalized this process by laying out a set of specific suggestions on how to shore up areas of concern, particularly around my indirect background with Geometry instruction. Finally, going through and addressing these concerns in the context of my internship allowed me to both learn these areas and connect it to my day-to-day work. This page includes the content review document and the work I did to address gaps in my background.
The modern math classroom does not stop at the walls of the school building, nor is it confined by the bell schedule. Each week, I am adding multiple new videos on YouTube to teach or re-teach content to students. My YouTube channel contains many snippets of me teaching Algebra 1, Algebra 2, and Statistics. Everything is accessible to students 24/7. I learned a lot about effective math videos from my intern coaches in Byron -- videos must be short and clear, and to be most effective, need a set of guided notes so students can follow along as active listeners. With over 100 videos uploaded, there is a wide variety of styles of explanations in use. Most of my videos are very short and visual -- about 3 minutes long using at least two pre-typed example problems. Some of the videos are much longer, especially on topics with many exceptions to the primary rule, but I still try to keep these as clear and organized as possible. As a math teacher, it is important for me to build a library of self-developed content that I can make available to my students when I am not able to help them in person. The in-person lessons I deliver at the SMARTboard in my algebra-based classes are very similar to these videos with the addition of wait time, questioning of students, and peer discussion. This content collection demonstrates my ability to clearly explain mathematical concepts.
Synthesis
To be an effective math teacher, it is absolutely necessary to be a content expert. Content expertise in math requires a theoretical base in mathematics, an exposure to many real-world applications of mathematical reasoning, and an ability to help a variety of students understand and use math. My experiences at Olin College and Winona State provided me a strong background in both the subject and the ability to teach it. My deep interest in education while I was still in engineering school gave me a head start with many of the processes that I strengthened at Winona State and applied at Byron High School during my internship. As a content expert, I will continue to develop my own digital content that students can use to pre-learn material with the reverse classroom approach or re-learn material that didn't stick the first time. Through my experience teaching algebra and statistics-based courses at Byron High School, I understand the importance of subject expertise in order to become the most adaptable and creative math teacher I can be.