The inverted classroom in introductory calculus

Best practices and potential benefits for the preparation of engineers

Robert Talbert, Grand Valley State University / @RobertTalbert

American Society for Engineering Education, Indianapolis IN 2014-06-17

GVSU

Outline

  • What is the inverted classroom and why consider it?
  • Self-Regulated Learning
  • An inverted Calculus 1 course
  • Results and extensions
  • Q&A

The inverted or "flipped" classroom

A course design paradigm that reverses the contexts of direct instruction and active learning.

Traditional Model

Pre-class: Instructor decides concepts and topics, devises learning objectives, plans direct instruction

In class:Direct instruction, presentation of information

After class:Students assimilate information through homework, projects, etc.

traditional

Inverted or Flipped Model

Pre-class:Direct instruction through reading, video, audio + simple examples

In class:Students assimilate information through directed work on challenging problems, with instructor supervision

After class:Extended work (additional HW, projects, etc.) and preparation for upcoming classes

inverted

What problems does the inverted classroom solve?

Inverse relationship between difficulty of work and accessibility to help

Lack of student control over information flow

Lack of time for exploration of concepts/difficult problems

Lack of explicit instruction on lifelong learning skills

Self-Regulated Learning

Paul Pintrich et al.

  • Learners are active participants in learning process and construct their own meanings
  • Learners have the potential to monitor aspects of the learning process
  • Learners have a standard against which to compare learning processes and make realistic decisions about the adequacy of their learning
  • Learners use self-regulating activities to mediate between personal characteristics and performance

Closely related to lifelong learning

The Engineer of 2020

Given the uncertain and changing character of the world in which 2020 engineers will work, engineers will need something that cannot be described in a single word. In involves dynamism, agility, resilience, and flexibility. [...] Encompassed in this theme is the imperative for engineers to be lifelong learners. They will need this not only because technology will change quickly but also because the career trajectories of engineers will take on many more directions – directions that include different parts of the world and different types of challenges and that engage different types of people and objectives.

Redesign of introductory calculus at GVSU

Components:

Implementation: Pre-Class Work

Using the Guided Practice framework

  • Overview (puts new material in context)
  • Basic and Advanced Learning Objectives
  • Resources (reading and viewing)
  • Exercises on basic objectives

Example: Guided Practice on The Definite Integral

Implentation: In-Class Work

Focus of class time is on questions and group work on Advanced Learning Objectives.

Practical matters

Did student do the pre-class work?

Median completion rates of Guided Practice were 92% for one section and 96% in the other section.

Did students learn through the pre-class work?

Entrance Quiz median values were 78% and 72%.

How much time did it take to make the videos?

With a collaborator, 60 of the 91 videos were completed in a 10-day period prior to the start of classes.

Results from the student experience

The setup for the class is perfect, i dont [sic] understand why all classes are not like this, like you said the hardest part of the class is the homework and other teachers expect us to just pick up from what they said in lectures which is out of date teaching. Like for my Engineering class we do all the hard stuff outside of class.
I really enjoy this style of class. I would like to take one similar to this for my calc 2 experience. Are there any other professors that run class this way? If so I would love to know as I would switch into a class like this in a heartbeat.

Next steps

Large scale study on student gains in flipped vs. non-flipped instruction, using Calculus Concept Inventory and the Motivated Strategies for Learning Questionnaire

Creation of video materials for Calculus 2

The end

Robert Talbert, Associate Professor of Mathematics, Grand Valley State University

talbertr@gvsu.edu / @RobertTalbert

This presentation available at http://roberttalbert.github.io/asee2014

All Calculus materials freely available at http://github.com/RobertTalbert/calculus under a Creative Commons license

Video content available at http://bit.ly/GVSUCalculus

Casting Out Nines blog: http://chronicle.com/blognetwork/castingoutnines