As an instructor, this card can help you...
1. Explain why engineers use a particular problem solving format to document their work.
2. Develop student ownership in shaping the way they think about the world as distinct from, but connected to, engineering and math equations and laws used by engineers.
3. Guide students in thinking through example and homework problems.

Overview

A three-model framework provides a foundation and context for developing engineering analysis skills, helping students create connections between the real world, their thinking, and the engineering models taught in class; inspiring curiosity about the world around them, and helping them see how their work results in improvements in the world. To the degree that a student's mental model aligns with real world and can leverage engineering and math models, a student can create value as an engineer.

The three models are 1) reality, 2) mental models, and 3) engineering and math models. A diagram of these models supports the engineering problem solving format (Given, Find, Procedure, Solution, Answer) and illustrates the interaction between engineering application (reality), engineering judgement (mental model), and scientific theory (engineering/math model). Engineers work with each of these models as they develop their understanding of a concept or solve a particular problem.

Please see this brief YouTube video to see the models explained as they might be in class.

Method

This ASEE PEER paper contains the complete details for the concepts and demos in the card. The high level outline looks something like this:

1. Introduction: The Three Model Framework presentation is typically best achieved through a chalk and talk approach allowing for active interaction with the students. A PowerPoint presentation version of the The Models is included below.

2. Application: Once established, the framework is a useful way to breakdown engineering analysis problems in courses like statics, dynamics, and mechanics of materials. The card author looks forward to seeing author instructors apply to framework to additional disciplines.

3. Assessment: The framework is easily assessed alongside course specific content. As students work example problems their descriptions of givens, finds, and sketches illustrate their interpretation and mental model. Their ability to identify appropriate procedures and models assesses their ability to plan their work. Their actual solving of the problem and final checks should illustrate the degree to which they are able to validate alignment between the three models.

Discussion Points

Reality is the way the world actually works; in general, reality tends to be complex. The engineer works to shape reality creating value for humanity, and therefore, must be a student of reality, learning how the world works through thoughtful observation. As engineers consider reality, they build mental models of how the world works.

The mental model is qualitative and often intuitive. The mental model is the single greatest asset an engineer has; in the qualitative and intuitive world of the mind curiosity and creativity flourishes. An engineer who wishes to communicate or refine a mental model will draw sketches or diagrams. The mental model should lead to the proper selection of an engineering/math model.

Engineering/math models are often the primary focus of the formal classroom. These models are quantitative and lead to numerical predictions of various outcomes. However, engineering/math models, by nature, require simplification; the mental model must make connections and check the assumptions required to build a solvable engineering/math model. The engineering/math model is usually expressed using logic and mathematics; often computers facilitate numerical predictions. Active integration of the mental model and engineering/math model equips the engineer to properly shape reality.