The fundamental question for any instructor today is why it is a student should want to be taught by us, rather than enrolling in a Massive Open Online Class (MOOC) where they would watch lectures by one of the best professors available anywhere in the USA. The mathematics we teach and techniques for explaining it are well-known. We each have our own twist on how we present and explain mathematics, but it would be sheer hubris to believe that our lecture is more clear, better organized, or more entertaining than any other.
To answer this challenge, we had better know the answer to the question, “What do students need in order to learn?” First and foremost is always motivation. If they have motivation and the appropriate resources, they will be able to learn. Most undergraduates have a degree of internal motivation and internal and external resources, but not enough to learn from a book or challenging material in an online course.
Math instructors often focus on the mathematical content. We rarely consider the emotional state of our students, but this is the key to opening the door to learning. Subtly and powerfully, I provide motivation through inspiration, relevance, and, most importantly, my relationship with my students.
Psychologists have shown that happy people are better able to learn and solve problems requiring insight. My first and foremost concern in teaching is to create the positive environment in which learning can occur. The key aspects that I work on are
- Knowing and respecting students as individuals.
- Creating camaraderie within the class.
- Catching students doing things right.
- Providing inspiration and challenge.
- Giving meaning to their work.
I have taught eleven different math classes at Texas A&M University over the past six years, classes for freshman non-majors to classes for senior mathematics majors. In order to do this and do this well: I have to know my math. I have to know my students. I have to be able to explain the math to those students. I have to be able to answer questions, and, most importantly, be glad students ask them. I have to relate the math to what my students already know and what they care about. While all these technical skills are important to teaching, the emotional work I have just described is the real key to my success as a teacher, because if I cannot get them to sit down and actually do math, my technical expertise has no impact at all.
The most significant technical contribution I have made in teaching is in setting consequential learning goals and then designing projects and assignments for my mathematical modeling course that require mastering those learning experiences to complete.
In mathematical modeling, we have daily access to computers. I organize the topics required to work the projects and ask students to research them online. Students gain participation credit for explaining their meaning and relevance to the rest of the class. I only fill in details as needed. Thus, students learn to take responsibility for assembling knowledge and being part of a learning community.
My mathematical modeling course is a writing and communication intensive course based on projects and mathematical programming. These are significant skills that are essential to success in the job market or in graduate school. Students have won many awards for class work, but the real accomplishment is getting the vast majority of the class to understand how math matters to them and in the world around them.
I have a breadth of experience in academics and industry coupled with a great hunger for reading about human behavior and the principles of effective leadership. This allows me to bring interesting real-world problems and projects into a math classroom and teach them effectively. My research focus is on finding collaborative projects with other faculty that I can turn into collaborative projects with my students. I have an excellent eye for spotting student interests that can be nurtured into significant projects and for spotting activities, problems, videos, and articles that relate to the math we are doing in the classroom and that will be interesting and meaningful to my students.
In my classroom, a student will not be invited to sit passively for 50 or 75 minutes listening to me. Students will be asked to answer questions and work problems. I will do the hardest thing any instructor ever does; I will shut up and let my students think. I use quizzes in a similar way; they are taken at the beginning of class. Once quizzes are handed in, immediate feedback is provided; we discuss the solutions to reinforce learning.
Aside from the mathematical content, here are key ideas I find myself repeating to my students:
- 90% of success is showing up on time prepared for whatever job it is you are about to undertake.
- Just do the work in front of you.
- If you are struggling to get started, use the power of 15 minutes. 15 minutes of quality effort can move you vastly forward on a problem. Most of the time what we really need to do is to get started in the first place.
- Embrace your mistakes; when you know you have done something wrong, that means now you can fix it.
- The smartest, most powerful person in the room is never afraid to ask her questions, so pretend you are smart and powerful and ask your questions.
- “Courage doesn’t always roar. Sometimes courage is the quiet voice at the end of the day saying, `I will try again tomorrow.’ ” (quote by Mary Ann Radmacher)
Being a teacher goes beyond teaching mathematics. I hope the lessons I teach extend to autonomy and responsibility as life-long skills. Autonomy does not mean not needing help. Autonomy is self-directing, which means asking for help when it is needed and finding and utilizing resources of all sorts. Responsibility is accepting who we are, what we do, and the impact these have on the world around us. It is looking for changes we can make in ourselves that will result in positive changes in our environment. I am interested in making my students better at mathematics, but I use this as a vehicle to help them become better, kinder, more thoughtful and resilient human beings.