Last semester, we invited a guest speaker into our Education class and she started her time by leading our group in a community-building activity. She asked us to stand in a circle, state our name, and answer the question: “Why are you or why do you want to be in teaching?” I didn’t have time to prepare a response but without hesitation I answered: “I want to be the face of modern progressive math education on the college level.”
Let me expand on that response. I do want to be the face of modern progressive mathematics education. I want to lead by example and represent what I believe to be necessary change. I want to show students that with enough time and training mathematics achievement is attainable and that mathematics matters. I also want to show students that love and care are a necessary part of the educational experience and that they matter as human beings.
To be more specific about my practices and beliefs that I believe are necessary in today’s mathematics education, consider that educational goals fall into one of two categories: content goals and “meta” goals. Content goals are explicit mathematical objectives and I will discuss my pedagogical practices and beliefs that guide students towards those goals. “Meta” goals are goals that we aim for students to achieve in a course that are not directly tied to content, such as “communicate mathematics effectively” or “develop a positive disposition towards mathematics” and I will also discuss the meta goals that frame my teaching.
Content goals and pedagogy
Although our content goals are specific to an individual course, general pedagogical strategies can be widely applicable and then tailored to the specific content.
First and foremost, I believe in active learning as we learn best by doing rather than simply watching. I recently took some dance classes which served as a reminder that no amount of watching and nodding your head is the same as actually attempting to do something on your own. In the classroom, this translates to providing students with as many opportunities as possible to work on practice problems. This benefits their learning as well as my teaching as it provides opportunities for instant feedback and to cater instruction to the students’ needs.
Opportunities to work on problems during class often involve some form of group work for two main purposes. First, verbalizing your own thoughts can test your own understanding of a concept and second, collaboration invokes diverse perspectives to further engage in the learning process. I have even taught full semesters using a “team-based” approach in which groups of students were randomized each week to formalize the importance I place on active and collaborative learning.
Yet another hallmark of active learning is providing additional opportunities to make mistakes as more often than not mistakes, rather than successes, are where true learning occurs. While many may agree about the importance of making mistakes, their value is often contradictory to our grading and assessment structures. As a result, my perspective on assessment continues to evolve and I am currently teaching a course using a mastery-based grading scheme which rewards initial mistakes that ultimately lead to the understanding of particular course content. Also referred to as “specifications-based” or “standards-based” grading, this grading scheme ties student grades to achievement of learning outcomes rather than the traditional percentage of total points earned.
The most common question asked of instructors who utilize active learning techniques is “How do you have enough time to cover all of the course content?” and I can attest that this has never been a concern for me for a couple of reasons. First, in every class that I teach I provide structured guided notes that save class time by not having to write down certain definitions or theorems. These notes and my attention to detail in my preparation has led to near universal praise over the years as students appreciate structure in their learning. Second, I shift some of the learning outside of class with pre-class readings and online quizzes to introduce sections of material with foundational or review material. This is intended to make students accountable for their learning, have a foundation to more effectively engage with problems in class, and provide additional structure to the content.
Finally, I believe we should strive for a conceptual understanding of mathematics at all levels. This does not ignore the importance of many “mechanical” procedures, but my emphasis on concepts is reflected in my classroom teaching and assessments which require students to demonstrate a deeper understanding of course content.
Outside of explicit content goals, there are various meta goals I strive towards depending on the specific course.
Throughout the course of my teaching experiences and in light of today’s globalization, it became increasingly imperative for me to expose students to authentic connections of mathematics to society and ways in which math impacts policy and decision making. This desire to show students how and why mathematics matters is what motivated me to initially pilot a unit on Gerrymandering. This then led to redesigning a course as “Math and Politics” focusing on Voting, Apportionment, Redistricting, and Game Theory. I was further inspired to create a brand new course on Math and Redistricting, a current course that is cross-listed with Political Science which focuses on the ways in which quantitative, political, and legal information contribute to our maps and notions of fair representation.
Underlying my motivation to create such courses is the importance I continue to place on “service-level” classes. Significant numbers of students come through our departments each semester to “check a box” for their graduation requirement, but for me this represents being responsible for the last formal mathematics experience of many lives. In the general education context, I heavily value the goals of improving students’ disposition towards the field of mathematics and developing a growth mindset towards learning. This even includes a mindset statement on all of my syllabi demonstrating ways to replace disparaging phrases about one’s math learning with phrases that align with a growth mindset.
Beyond our general education students, I place a larger emphasis on the integration of technology to provide additional representations of a concept and develop practical skills. In the Calculus sequence, I regularly use Desmos not only to illustrate concepts, but to show students how to best utilize the resource for their own learning. In Statistics, I incorporate training and assignments in Excel for students to gain experience in analyzing authentic data sets.
Lastly, I believe that education is a holistic human experience and is at its best with an atmosphere that is conducive to learning and personal growth. This includes valuing each student as a person and practicing inclusivity by being aware, empathetic, and responsive towards unique individual needs. Tangible practices attending to the human element of education include mental health advocacy through my hashtag #SpreadLoveAlways, holding ample office hours at various times and locations to accommodate as many students as possible, and attending events to become involved in the campus community.
“Being a leader isn’t always about taking the initiative or having the strongest voice. If people follow you, then you’re a leader.”