A Controlled Study of the Flipped Classroom with Numerical Methods for Engineers
Completing doctoral research, and writing a PhD dissertation is no small task, so I figure this one gets to count as a project. The abstract does a decent job at describing the dissertation project as a whole, so here it is:
Recent advances in technology and ideology have unlocked entirely new directions for education research. Mounting pressure from increasing tuition costs and free, online course offerings are opening discussion and catalyzing change in the physical classroom. The flipped classroom is at the center of this discussion. The flipped classroom is a new pedagogical method, which employs asynchronous video lectures, practice problems as homework, and active, group-based problem-solving activities in the classroom. It represents a unique combination of learning theories once thought to be incompatible—active, problem-based learning activities founded upon constructivist schema and instructional lectures derived from direct instruction methods founded upon behaviorist principles. The primary reason for examining this teaching method is that it holds the promise of delivering the best from both worlds. A controlled study of a sophomore-level numerical methods course was conducted using video lectures and model-eliciting activities (MEAs) in one section (treatment) and traditional group lecture-based teaching in the other (comparison). This study compared knowledge-based outcomes on two dimensions: conceptual understanding and conventional problem-solving ability. Homework and unit exams were used to assess conventional problem-solving ability, while quizzes and a conceptual test were used to measure conceptual understanding. There was no difference between sections on conceptual understanding as measured by quizzes and concept test scores. The difference between average exam scores was also not significant. However, homework scores were significantly lower by 15.5 percentage points (out of 100), which was equivalent to an effect size of 0.70. This difference appears to be due to the fact that students in the MEA/video lecture section had a higher workload than students in the comparison section and consequently neglected to do some of the homework because it was not heavily weighted in the final course grade. A comparison of student evaluations across the sections of this course revealed that perceptions were significantly lower for the MEA/video lecture section on 3 items (out of 18). Based on student feedback, it is recommended that future implementations ensure tighter integration between MEAs and other required course assignments. This could involve using a higher number of shorter MEAs and more focus on the early introduction of MEAs to students.
If you’re interested in more details, read on!
The prospect of moving classroom lectures online is exciting, and paves the way for several possible educatoinal innovations. Before getting too much into that, however, it’s important to define a few terms 1.
Education: The process of receiving or giving systematic instruction, especially at a school or university.
Effectiveness: The degree to which something is successful in producing a desired result; success.
Educational Effectiveness: The degree to which educational experiences [facilitated by a program, materials, and/or instructor(s)] are successful in producing the desired results.
The way I see it, there are two ways we could go by pairing online educational tools with the in-class experience. These are based on two conceptually distinct educational goals, based on corresponding sets of “desired results” (usually called outcomes in educational lingo): (1) problem solving ability and knowledge-based outcomes (2) other outcomes. I would put most of what we focus our time and effort on in current educational institutions into the first bin. The second bin includes things like problem formulation, mathematical modelling, leadership skills, communication, and ability to work well on teams. One important observation is that the items in the first bin are relatively easy to measure objectively, while those in the second are rather difficult. Now, back to the original assertion I made in the first sentence of this paragraph. There are two main ways we could go. We could either (a) use online educational tools to enhance problem-solving ability and knowledge-based outcomes and also spend classroom time working toward the same goals, or (b) use online educational tools to enhance problem-solving ability and knowledge based outcomes while spending in-class effort working toward other outcomes.
Option (a) focuses exclusively on items in the first bin, while option (b) covers both. If we assume that only items from bin 1 (problem-solving ability and knowledge-based outcomes) are reliably measurable, then success for scenario (a) means that performance on bin 1 items must be higher than performance on bin 1 items would have been without using online educational tools. If option (b) is pursued, however, a successful outcome would mean that performance on bin 1 items would be the same as (or possibly, but not necessarily, higher) performance on these items would have been without using online educational tools. Of course, this only means that time and effort was spent on bin 2 items that would not have otherwise been spent. Although it doesn’t mean those efforts were successful, actually trying seems better to me than not even trying at all.
For this project, we chose to focus in-class efforts on helping students foster the ability to formulate and communicate mathematically meaningful models of engineering problems situated in a realistic context. The specific approach is to use model-eliciting activities (MEAs). MEAs are activities that require students to work in groups to solve realistic, open-ended, client-driven engineering problems. Rather than a closed-form solution, the product of an MEA a written memo that responds to the client’s request with a detailed description and sample results from applying the procedure the group developed to formulate and solve the client’s problem.
The following graph traces the historical foundation for MEAs back approximately 100 years. A brief description of each of these educational theories and frameworks appears within the dissertation itself.
In addition to the above picture, which is based on the chronological development of several different theories and methods, it is also possible to depict how these methods overlap. That is the purpose of the diagram below. To be honest, I’m afraid that while I claim to know what both a Venn and Euler diagram are, I’m not actually sure which one the following diagram is. It isn’t an Euler diagram because Euler diagrams show the actual overlap between regions. I make no claim that the proportions of overlap in the diagram below are strictly accurate, although the intent was to show overlap only where it is theoretically present. It is also not a Venn diagram because Venn diagrams show all possible combinations among the given alternatives. In any case, the main point is that model-eliciting activities typically bring together many different methods to accomplish their task of helping students formulate and communicate mathematically significant models.
A few of the graphs I produced showing the results from this study are given below.