I fully believe that every student is capable of achieving a certain level of understanding in math. I see my job as an educator is to help students gain and develop the tools necessary to achieve this understanding. This is best expressed in the idea that I want to teach students how to be mathematicians. To me, a mathematician not only has a grasp of a wide range of mathematical content, but they also have important skills needed to acquire new knowledge when necessary. In general, I can summarize these skills into three broad categories: effective communication of mathematical knowledge, ability to collaborate with peers, and appropriate use of technology. In order to increase the success of my students, it is important to teach them these skills and give them plenty of opportunities to practice them. In order to teach these skills, I have employed a variety of strategies through making small changes in the way a traditional math course is taught. Namely, incorporation of active learning activities, a strong emphasis on written work, and teaching the use of technology.
To teach students how to better communicate and collaborate with their peers it is necessary to put them in situations where they are required to do so. In my opinion, math is learned best when actually doing math. I have seen evidence of this through my numerous one-on-one interactions tutoring students, providing supplemental instruction sessions, and in the many studies I have read in my own research of teaching methods. Since listening to lectures and taking exams is not the ideal way to learn I have worked to incorporate a variety of active learning activities in my classes. This not only lets students practice their communication skills but has also improved student engagement.
One of the ways I introduce active learning is by merging the settings of a traditional lecture with those of a discussion. As a discussion leader, I taught in the Enzi STEM building where classrooms are designed to encourage group learning. What I discovered was that a classroom space designed for group learning was not enough to encourage collaboration. When I handed out the worksheet, students still tended to work individually. In response to this, I began to require that students be at the board working through problems together. Although students initially felt uncomfortable in this setting, they eventually saw the benefits of such an approach. This environment allowed them to get feedback from peers, receive assistance from the instructor, and develop confidence with the material. A consequence of this was that my sections frequently had higher exam averages compared to sections that did not conduct discussion in this way. Now when I teach, I almost always complement my lectures with a worksheet facilitated in this manner. In addition to worksheets, I have also incorporated other in-class group activities like gallery walk style review sessions, peer teaching activities, and learning to use software to solve problems.
In furthering the goal of improving students' communication skills in mathematics I always have a heavy emphasis on the quality of written work. I have discovered that students do not truly know what is required in a well written solution and that students better meet expectations if they are in writing. Additionally, I have learned that if students are not held accountable to expectations on written work they will often fail to meet them. This is why I also dedicate a portion of my rubric to assessing their ability to follow these written requirements. Many instructors communicate verbally what they expect to see in student work but it is difficult for students to keep track of everything said in class. Te remedy this, I always provide my students with a list of my written work requirements. Although many students initially view these as a list of arbitrary requirements, they are merely a list of what we would expect any successful math student to do. Over time, and usually after the first exam, students do begin to see the benefits of changing how they do their work. A version of my written work requirements can be seen in my teaching samples.
When incorporating technology into student learning I have found there are two challenges to face. The first is that asking purely computational questions is no longer effective in my teaching. As students have easy access to online solution sites, videos and computational engines like WolframAlpha, calculation processes are easy to find and copy. While students can more quickly and correctly complete assignments, their level of knowledge tends to be poor. The second, is that although students are able to find answers to questions online, they often lack essential knowledge about computers and technology in general. This includes the ability to know when it is appropriate to use technology in their learning and when it is not. This has become most evident in my time as the instructor for Intro to Scientific Computing Lab where students often have no computational experience. As a result, I have found it necessary to incorporate technology in my teaching.
When using technology in the classroom I have discovered that it is important to use tools that are easily available, easy to learn for basic use, and that expectations for its use must be clear to the students. I always spend at least one day in a computer lab showing them how to use Mathematica. Since UW has a site license that permits students to have a personal copy of the software, I have found it an easy and affordable way for students to be introduced to the appropriate use of technology in their education. Since we often use certain tools ourselves, I think it only fair that I show the students how to do the same in their own work. I make no attempts to hide these tools from students and encourage their use. This has the added benefit that it tends to support my high standards for their written work. The importance of technology also extends to upper level students where we need to teach them how to use tools like LaTeX and Beamer. As the teaching assistant for Scientific Computing, I advocated the use of LaTeX for students to type and submit their homework assignments. Over the course of both semesters I have seen many students drastically improve not only their understanding of the material, but also show significant improvement in their mathematical writing skills.
I strive to achieve a balance between the ``old school'' methods by blending them with the ``new school'' approaches. When doing anything that is seen as ``new'' I have found that it is important to be organized, intentional, and have clear expectations that are communicated to the students. I also always employ a means for students to provide feedback on each of the activities we do in class. This gives me an additional way to evaluate the effectiveness of these activities beyond just looking at exam scores or overall pass rates. Through this feedback I have seen that some of the changes I have made in my teaching have dramatically changed outcomes for many of my students.
When implementing non-traditional forms of teaching it is crucial that outcomes can be replicated in future courses. To aid in this, I find it important to construct materials that complement what we do in class. Each time I teach a course I create a set of worksheets, quizzes, reading assignments, lecture notes, and Mathematica notebooks. They are not only easy to re-use, but easy to improve upon. This has the added benefit of making it simple to share resources with fellow graduate students and instructors. Feedback I receive from students is carefully reviewed and used in guiding updates to any materials and activities I create.
In summary, I work hard to be approachable and available to my students. When my students feel like I am invested in their success then they begin to invest in their own success. Although I have only been teaching for a few years I am always working to improve my teaching through research, attending workshops, and consulting other instructors in a variety of fields. I see my role in any of these approaches as a facilitator of the learning environment, keeping the student as the focus of my efforts rather than the material. The goal is then to encourage the student to explore the content, rather than leading them to it directly.