By Andrew Miller

Think back to your college mathematics courses. What is one word to describe how students in that class were learning? Does the word “passive” come to mind? Having taken countless math courses throughout my undergraduate and graduate career, I can confidently say that the structure of most courses is the same. Instructors lecture, students take notes, and afterwards students attempt to apply the knowledge they’ve gained on various problems. Students often get stuck and may have no opportunity to get extra help. Of course, most instructors offer to answer student questions, but for the large part of the class, students are processing the new content in a passive manner. With the growing body of literature on active learning strategies and their effect on student’s ability to process new knowledge, moving away from passive learning styles and embracing active learning strategies will be more beneficial for your students. 

As a full time PhD candidate, I teach two courses under my assistantship, and I am a part of the adjunct faculty at my alma mater. I don’t have time to completely rework one of my classes nor have time to record original videos or even scour the internet for acceptable videos on each topic I teach if I wanted to flip my classroom. Thanks to Dr. Robin Grenier of UConn’s Graduate Certificate in College Instruction, I have been introduced to James Lang’s Small Teaching: Everyday Lessons from the Science of Learning. Whether you are a first-time instructor or have been tenured for twenty-five years, you should own this book. In an easy and enjoyable way, Lang offers teaching strategies that are grounded in scientific research and best of all, they are small modifications educators can make to their classroom to bump up the effectiveness of their instruction while moving the needle into the active learning environment.

Small Teaching is broken into three parts: Knowledge, Understanding, and Inspiration. I will describe some of my favorite small teaching changes within the Knowledge and Understanding sections that have had an impact in my own classes or my colleagues’ classes. These strategies can be implemented in any STEM classroom at any educational level.

Knowledge – Retrieving:

It is a little taboo, but let’s admit: students need to have some facts memorized, otherwise their problem solving will be burdened with the need to recall or find these facts, impeding their ability to engage in higher order thinking. One of my favorite ways to test and remind students of the facts they need is through the use of a polling or clicker system. I personally choose Poll Everywhere. The free version allows forty students at a time to text in their responses (I mean, they are on their phones anyways!). I typically propose a statement to my class such as: “If a function is continuous at all x-values in its domain then it is differentiable for all x-values in its domain.” I will then give them four options: “true and I’m certain”, “true but I’m not sure”, “false but I’m not sure”, and “false and I’m certain”. Think for a moment about how much more impactful these four choices are and how much more information you will learn from your class rather than a basic “true” or “false” option. You will be able to quickly assess students’ understanding and adjust on the spot or make small adjustments to future lessons. 

Here are some other options for recalling foundational knowledge inspired by Lang’s book:

• Ask them to recall what was covered in the previous class without looking at their class materials. Note here: This rarely happens the first few times; keep pushing and they will come around.
• Ask students to pair together and summarize the material covered for the day, then ask for a verbal whole class response.
• Engage students in “Do Now” problems that students complete in the first two to three minutes of class and that prompt them to retrieve previous material.

Knowledge – Interleaving:

There is a chance that you may not know what interleaving is—I didn’t until I read Lang’s book (if you do, skip to the next paragraph). To better show the effectiveness of interleaving, let me give you an example of what interleaving is not. A student is studying for a math exam that covers sections 2.1-2.9 of a textbook. The student individually practices problems from 2.1, then 2.2, and so on. Once the student finishes, she starts over on 2.1. The student takes the exam and the questions are in the exact order as the material and the way she studied. Perfect! Well, this is not quite how life, work, or anything else in the real world comes at us. Interleaving, as defined by the University of Arizona, “…is a process where students mix, or interleave, multiple subjects or topics while they study in order to improve their learning.”

We should want students to be able to apply knowledge from any section, multiple sections, or even entire chapters and courses to solve problems. Interleaving allows students to see problems and methods multiple times, moving the knowledge deeper into long term memory. 

How can we get our students to interleave without them even knowing? Let’s circle back to the “Do Now” problems given at the beginning of class. Give students problems on material they haven’t seen in a while, but you know they will need for future material. Ever have an important exam question go horribly wrong and you vow to give it to them again? Give it as a “Do Now”. Students need exposure and practice with problem solving techniques as well as a mixture of problems that focus on your learning objectives throughout the course. This will enable your students to better attack problems on exams and internalize information. I constantly stress to students that once they have their baseline studying done, they should randomize their practice problems. Say students have fifty practice problems to work on, they can use a random number generator to randomly pick a problem to complete. I will admit, they look at me like I have five heads for a moment; however once I explain the idea, they try it and often come back with better results. 

Here are some other options to apply interleaving:

• Teaching an online or hybrid course or have online homework? Assign chapter reviews sporadically throughout the semester to force students to come back to older but important information. 

• Giving a short quiz in class? Include an older but essential concept as a separate or as part of a question.

 

Understanding – Self-Explaining

My guess is that I don’t have to do much convincing here as to why self-explaining would be beneficial for our students. Think about what happens when you teach a course more than once. New connections and different ways of teaching are discovered; this is because you are learning the topic at a deeper level by explaining it to others.

Here is one of my absolute favorite ways to apply self-explaining (and it will make your job easier)! Right around exam time, office hours are busy, and the same questions or problems are being asked by multiple students. Instead of going through the problem again, I ask a student to explain and work through the problem in class. Especially in STEM, we learn best by doing, and giving students a chance to explain themselves to their peers will certainly help them to master the material. This is also low pressure, since it will be 1:1  or 2:1 situation, rather than a student working through a problem to the whole class. 

Be cautious here; this doesn’t always work. You need to have a rapport with your students and have created a comfortable environment in and out of class. With a comfortable environment, students will be more willing to take the risk of teaching another student. In addition, you need to have a feel for if the student has a good baseline for the problem and should keep an eye on their work in case of errors. 

A quick and slightly different version of this that can be used in class is the think-pair-share model. 

• Pose a problem and let students think about it individually.
• Then ask students to turn to a partner and discuss their thoughts and collectively conclude.
• Ask the entire class for a response.

In this model you will see an increase in response time and frequency from the whole class since students already have had the opportunity to discuss their thoughts. This will also help to build that comfortable environment I was speaking to. 

Changes to improve student learning do not always have to be big in order to make an impact. Anyone, in almost any position in academia, is going to be busy with what seems like a never ending to-do list. This should not stop us from being open to adjustments in our teaching. Personally, each time I reteach a course, I incorporate one or two changes (sometimes based off student evaluations).  Small changes to one’s teaching overtime can lead to big changes in student outcomes and course knowledge. To paraphrase Lang; it is the start of a new semester, what changes will you make today?

 

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