It is easy for the new (and experienced) instructor to feel lost about how to teach when faced with “learning” methods and paradigm shifts in education. Here’s a bunch of buzz phrases: project-based learning, presentation-based learning, student-centered learning, mobile learning, brain-based learning, flipping the classroom, etc. In addition to standardized tests and national education standards, there is also the peanut gallery quick to point to one failing student who could have been better served if only the instructor had done <insert magical teaching method>. And so what can an instructor do?

There’s a lot of discussion among educators about moving towards engaging students and showing them: “the beauty of math”, “how math is practical”, “why it’s important”. A quick perusal of the myriad of math blogs and math chats can confirm this. The peanut gallery does have a point and there are a lot of good ideas about moving away from the “I lecture. You write. I assign. You do.” style. Instructors oughtn’t just drone on and then give out worksheets and have students solve problems. This is not teaching. This is not conducive to learning. This is laziness. Simultaneously, though, one should keep the instructor’s and the students’ viewpoint in mind. Students are going to be reluctant to speak about a topic if they don’t understand what they are talking about. Equally, instructors do have to give some form of instruction and assignment to keep things organized and students will have to do some amount of writing and “doing.” Active engagement in the subject matter by both sides is essential to classroom learning.

Instructors are going to be forced to speak to some extent so that they may impart some knowledge onto their students. The key thing here is that at some point an instructor should begin to make a switch from a monologue to a dialogue. Then eventually the environment should morph into one where the students are learning on their own and coming to the instructor for guidance and conversation. Then, start the loop again, if necessary, for a new topic. In other words, good teaching is a mix of many methods: lecture a little, converse a little, give group projects, give individual projects, have students present, give exams, give problem sets, go on a field trip (science and math museums do exist), watch a video, have guest speakers, give students a break, let students explore openly, etc. This reminds me of a quote by Robert A. Heinlein from “Time Enough For Love”:

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.

Relying on any one method is not going to produce good results for one simple reason: people learn differently. Some like to know all the pieces before they can understand the big picture. Some like to know the big picture first before any specifics are discussed. Some like tons of examples before being formally taught the theory. Some like to see the theory first and then apply to specific problems. Some like it if they were just given a hard problem to figure out so that they can go off on their own and tinker. Some need step-by-step guidance before they feel comfortable with the topic. And so, with all these orthogonal learning styles, no single teaching method can possibly work.

Instructors have to do two things:

1. understand each student’s learning style
2. vary their pedagogical methods

The first point should be obvious. An instructor cannot possibly hope to teach something if he does not understand how his students learn.

The second point should be the instructor’s dilemma. Her teaching style should be dynamic, not static. She should rely on a variety of pedagogical methods, not just one. She should catch herself and adjust if she always leans towards one way of instruction.