Over the course of my teaching career, many of my students have described their past experiences with mathematics and/or their mathematics teachers as demotivating and unpleasant. To begin fostering relationships, I meet with my students individually early in the semester to discuss their interests and become acquainted with their background. I also convey that mathematical achievement is possible for everyone, regardless of geographic, demographic, and economic boundaries. My teaching philosophy is centered around the relationships formed between my students and with me. My main priority as an instructor is to cultivate a classroom environment where students feel comfortable making mistakes and exploring questions about the material with their peers. I further support peer discussion by arranging the desks in groups when possible.
I use specifications grading (specs) in my classes to aid students in learning from their mistakes and in improving their skills through the process of reassessment. Specs is an alternate grading scheme that allows students multiple attempts at individual problems that are correlated to course learning outcomes. For any problems that are not fully correct, the student can later retry a similar problem on the same topic to earn a higher score. This type of grading scheme also supports a growth mindset by emphasizing how making mistakes is a necessary part of the learning process. Expecting my students will be unfamiliar with alternative grading, I discuss my rationale for implementing specs and emphasize the benefits of the reassessment process embedded in its structure. There is also evidence this grading system may alleviate test anxiety. In an article (2019), I describe my implementation of standards-based grading in mathematics courses across the curriculum.
To become increasingly effective as a teacher, I elicit frequent student feedback to assess my teaching techniques, activities, and my student’s enjoyment of the topics or applications. Teaching is a two-way street, and this feedback offers an avenue for students to connect with me and suggest how I might improve their experience. I often use active breaks during my lectures to have students consider their understanding of new material and to promote discussion with their peers. For example, students discuss a problem with a peer (e.g. think-pair-share), review and compare their notes with a peer, order the steps to a complex process, or work together to paraphrase a new concept.
To promote teamwork and critical thinking among my calculus students, I give each group pieces of information about the continuity and differentiability of a function and have them share their given information and work together to build the graphs of the function and its derivative. I also promote inquiry-based learning using process oriented guided inquiry learning (POGIL) worksheets—for example, students collaborate to explore the idea of a limit and how algebra is used to determine its value. In my statistics class, students work together using a website or statistical software to simulate samples that match the details of a null hypothesis to gain intuitive insight into the meaning of a P-value. I also have students use simulations to understand the law of large numbers, the central limit theorem, and the idea of a sampling distribution, which tend to be difficult concepts for students to grasp theoretically.
To address any misconceptions, I use readiness assurance tests, which comprise a two-step process where students first complete a set of questions meant to address prerequisite knowledge needed for upcoming material. Then students address the same questions but with a partner using IF-AT scratch off cards that reveal the answers. During the second phase, students check their understanding and discuss their reasoning with a peer, which often corrects any misconceptions before moving to new material. In linear algebra for example, students recall how to find solutions to a system of linear equations before covering an application such as the Leontief input-output model in economics.
It is an unfortunate truth that many students have had poor experiences with mathematics by the time they graduate high school. By showing students a positive and meaningful experience with mathematics and promoting a growth mindset, students gain an increased perception of their abilities and engagement in their learning process. I have witnessed many students become more confident in themselves and gain an appreciation of the applications of mathematics. All my pedagogical strategies are dedicated to increasing student motivation to learn, and helping students observe some of the most powerful tools human beings have created.