Supporting Active Learning with PreTeXt

While the benifits of using PreTeXt are numerous, one in particular that has been transformative in my own teaching is utilizing the html format of PreTeXt to embed interactive components which opens the door to a variety of potential active learning implementations.

These implementations can vary in flavor and depth, a very simple example is in the Team Based Inquiry Learning Linear Algebra workbook. By setting up and solving the appropriate system of equations, students are able to explore a variety of topics throughout this course. But as we all know, actually solving these systems can be tedious, time consuming and error prone. Such a task can overwhelm the conceptual exploration that is meant to take place, and students can find themselves focused on the tedium of this arithmetic excercise and put off from the actual topic at hand. By embedding Octave cells throughout the text, for example Activity 2.4.6, students and instructors can circumvent all this and get right to the thinking and discussion meant to take place!

Another way embedded ineractive technology can be used to implement inquiry learning is in bringing ideas to life that are hard to do with theoritical computations, and static examples or images. Probability and any topic that involves randomization is a good example, since any given example or question is in some sense no longer written once it is written down. In this activity, I wrote in embedded R cells to visualie and simulate different confidence intervals generated by randomly sampled data from the same distribution. Students are able to run this code in groups and compare results between groups, and then have a robust discussion on what the confidence interval means in a way that is not possible with any fixed hypothetical sampling situation. This really brings the idea to life in a way static exercises cannot.

A related type of example is to use a visualization or interactive to have students develop their own conjectures, and to see the key findings before we formally establish them. In the first activity of my in progress Linear Optimization text, an embedded Doenet interactive allows students to form conjectures about the properties of the solutions to a linear optimization problem before we formally establish them. A similar activity in the TBIL Linear Algebra text has students similarly using an active Doenet visualization to conjecture properties about determinants.

The potential applications and exploratory activities that are possible are barely explored. I hope that you will be inspired to not only use some of these in your teaching, but to be inpsired to think of new creative ways to use embedded interactive technology to support active and inquiry learning in your own classes! A robust community of creators and contributors is how we build a new era of active and engaged learning and teaching!