# Modeling as a Design Practice in Engineering

Modeling is often part of the engineering design process (Carberry & McKenna, 2014; Lammi & Denson, 2017; Moore, Miller, Lesh, Stohlmann, & Kim, 2013). Engineering, perhaps more than the other disciplines, also uses modeling in connection with mathematics, science, technology, or computational thinking. Modeling is focused primarily on representations of the possible design, a problem or a system. As a principle for K-12 engineering education,

The design process, the engineering approach to identifying and solving problems, is (1) highly iterative; (2) open to the idea that a problem may have many possible solutions;

• (3) a meaningful context for learning scientific, mathematical, and technological concepts; and (4) a stimulus to systems thinking, modeling, and analysis. In all of these ways, engineering design is a potentially useful pedagogical strategy.
• (National Research Council, 2009, p. 4)

While mathematical modeling is a part of engineering, this section will focus more on modeling as part ot the design process. A significant component of the design process is iterating and considering the purposes ot the design. This sense of modeling also includes creating, designing, and refining prototypes (Moore et al., 2014; Wendell & Rogers, 2013). The design process also supports students’ learning of scientific models (Capobianco, Nyquist, & Tyrie, 2013; Wendell & Lee, 2010).

Engineering activities regularly include math and science applications. However, when considering integrated STEM, there are some engineering-based ways ot incorporating modeling. Modeling appears in engineering in three ways related to the design processes which are essential to engineering as a discipline. The first is modeling as generating a prototype or initial design. So, students might design an initial model house (Wendell & Rogers, 2013) as part of their design and problem solving. That prototype can then be tested and revised in subsequent design cycles. This sense of prototypes is language distinctive to engineering and is not regularly seen in mathematics or science.

The second way modeling is used in engineering is to generate mathematical models (e.g., functions, equations, formulas) to describe phenomena. This mathematical modeling can be a component of model-eliciting activities (Moore et al., 2013; Tank et al., 2018). The mathematical modeling might serve an engineering goal in the design process. Related to mathematical models, engineering also relies on computational thinking tor simulations, calculations, and the development of algorithms.

Third, modeling in engineering is also the application of scientific models. Engineering tasks can be used to support or elicit students’ understanding of scientific constructs (e.g., heat transfer in the design of a model house; Wendell & Rogers, 2013). Another aspect ot science modeling is the application of scientific models that students need to carry out their design. Throughout the design process, students need to consider science knowledge and may design artifacts that demonstrate that knowledge.

The fourth aflordance of engineering to modeling is the role of context. A design activity typically includes a realistic context, including its constraints. A client may be used to set constraints like financial resources or material selection. As modeling is the connection between representations and the structure of the real world, engineering is an opportunity for the theoretical to meet the practical in terms of modeling. The context is the distinction between modeling and other types of problem solving since students need to engage with the world of the context in a meaningful and sometimes messy way (English, 2009).

The final way modeling is used for engineering is to represent students’ conceptual understanding and hence a method of developing understanding of concepts (sometimes from math and science). So, the process of design creates natural opportunities to develop understanding of required concepts. For instance, designing a model house will require development of knowledge of materials science, and it presents an applied opportunity to use and develop knowledge (Wendell & Lee,2010). Those representations (in the form of designs) are models of students’ thinking. When students must express their conceptual understanding in the form of engineering design, their knowledge is tested. For instance, as they use different materials, their knowledge of the properties of those materials is tested (e.g., when selecting materials for a paper basket, they can begin to examine properties of materials) (Tank et al., 2018). Where science is modeling the real world, engineering is designing for the world using models.

# Models and Simulations in Computational Thinking

Although computational thinking (CT) is often described as modeling with computers (Israel, Pearson, Tapia, Wherfel, & Reese, 2015), computer scientists define it more broadly as an analytic competency that supersedes computer programming (National Research Council, 2010). CT is a problem-solving process with specific characteristics related to problem formulation, organization and representation of data, use of abstractions such as models, procedural or algorithmic thinking, efficiency of solutions, and transferability of problem-solving processes (Grover & Pea, 2013; Wein- trop et al., 2016).

Computational thinkers solve problems, design systems, and understand human behavior by drawing on computing concepts (Wing, 2008, p. 3717). Within this broader conceptualization of CT beyond programming, modeling becomes both the process and the product of abstraction (Brennan & Resnick, 2016; Wing, 2008). More specifically, instruction in CT prepares students to model the attributes of computational systems, to use computational systems and data to model problems in other STEM disciplines, and to leverage and challenge the predictive quality of models.

The consistent classification of modeling and simulation as major categories in multiple CT frameworks (Grover & Pea, 2013; Shute, Sun, & Asbell-Clarke, 2017; Weintrop et al., 2016) make it clear that CT extends tar beyond computer programming because it builds the necessary problemsolving skills students need to model with computers and interpret data. Thus, we associate modeling with CT as “the conceptual foundation required to solve problems effectively and efficiently (i.e., algorithmically, with or without the assistance of computers) with solutions that are reusable in different contexts” (Shute et al., 2017, p. 142). Shute and colleagues (2017) identify six facets of CT in their exhaustive literature review (p. 153). These facets align with use of models for problem solving in K-12 mathematics and science:

a. Decomposition: Break problems down into smaller problems, which are then systematically solved separately.

b. Abstraction: Identify essential features of a problem. This includes data collection and analysis, identifying patterns within problems and solutions, and developing models to represent how a system operates.

c. Algorithms: Design a sequence of logical instructions to develop a solution to a problem. These instructions may be followed by a person or by a computer.

d. Debugging: Detect, identify, and fix errors when a system does not work as it should.

e. Iteration: Repetition of the design process to refine solutions.

f. Generalization: Transfer of CT skills to efficiently solve problems in similar and different domains.

The intentional development of CT can be made explicit in mathematics and science modeling activities beyond computer science instruction. Modeling and simulation of systems of varying complexity become exercises in CT which connect mathematical reasoning, scientific inquiry, and engineering thinking. Student processes of designing, creating, assessing, and using models as CT practices may offer a common language tor connecting problem solving across STEM disciplines.

# Modeling as an Integrated Practice Across the Disciplines

This section examines how modeling serves as a natural component ot integrated STEM learning. The previous sections described how each discipline includes modeling (often using aspects ot the other disciplines), but modeling is also an interdisciplinary, transdisciplinary, and multidisciplinary practice critical tor integrated STEM learning (English, 2009). Three characteristics ot modeling are themes in all of the disciplines.

• 1. Modeling and models as connected to real phenomenon as abstractions or representations with explanatory or descriptive relevant
• 2. Modeling process as cyclic or iterative (express, test, revise)
• 3. Modeling as an opportunity to express and to develop disciplinary knowledge and students’ ways ot thinking

Models and modeling are paradoxically both about real, often tangible phenomena but also about the abstract, non-tangible description ot those phenomena. For prototyping in engineering, the model is not the real object but a stand-in used for testing. For mathematics and computational thinking, the model may be a program or a function that abstracts features of the real world. So, the modeling process is about both creating a representation that is as close as possible to the real phenomenon and also highlighting or emphasizing certain features and perhaps neglecting other features. For the second feature, modeling and model creation are cyclic and iterative. Students are expected to test and revise their own models when asked to design a model as part of the solution. This process includes situations where students may compare different models, similar to situations in science and engineering where new methods of measurement are regularly studied. The question is not about whether a model is “correct” or “right” but whether the model is the best one for the situation at hand.

The third feature, modeling as an opportunity for students to express and develop disciplinary knowledge and develop their own ways of thinking, refers specifically to modeling as a learning experience. Common across many ot the examples is that modeling is an opportunity tor students to explore phenomena and create models that reveal their current thinking and understanding. Another sense of the learning experience is that models as simulations allow students to develop understanding of possibly intangible concepts (e.g., the solar system). The other way simulation is used is for students to use a modeling environment to play with variables that cannot be quickly changed in the real world (e.g., traffic simulations, environmental populations). Modeling as a learning experience, including simulation, can bring phenomena into the classroom that might be impossible otherwise.