2023 ASEE Annual Conference & Exposition

Over the last ten years, there has been increased inclusion of engineering in K-12 education. One particular instruction method used to integrate engineering into science courses, in particular, has been engineering design challenges. Even though mathematics is part of engineering design challenges, its role remains understated. The joint report from the National Academy of Engineering and National Research Council (2009), Engineering in K-12 Education: Understanding the Status and Improving the Prospects, offered guidance on incorporating mathematics in engineering design challenges to make explicit connections between engineering and mathematics content. The recommendation was to use mathematical modeling as the connector between engineering and mathematics to strengthen how mathematics is used for engineering.

Engineers use mathematical modeling during design to assist with ruling out designs that seem reasonable but will fail, and to determine the range of physical models or processes to test. These types of design decisions using mathematics are underdeveloped in the engineering design process students use at the K-12 level. As a result, students may see design as a "loosely structured process of trial and error" instead of a systematic process to arrive at multiple design solutions that can be tested. Proponents of pre-college engineering education advocate that the mathematics included in engineering design challenges should be instrumental to the design problem to assist students with creating feasible solutions.

The concerns brought forth by the National Academy of Engineering, the National Research Council committee, and the pre-college engineering community focus on mathematics integration; this study was designed to describe the role of mathematical modeling in pre-existing K-12 engineering design challenges. We sought to answer the following research question: to what extent do K-12 engineering activities with the K-12 mathematical modeling standard reflect the characteristics of engineering-based mathematical modeling problems? A subset of activities in the K-6 grade band (n=14) was selected from those published on TeachEngineering. Each activity was reviewed using content analysis methods and an a priori framework based on the six guiding principles of engineering-based mathematical modeling problems adapted from Lesh and colleagues' work. These principles are model construction, reality, self-assessment, model documentation, model shareability, reusability, and effective prototype.

Each activity's instructional overview, the connection to engineering, the prerequisite student knowledge, the individual educational standards, worksheets, and the student introduction to the design challenge were read, analyzed, and summarized into a spreadsheet. These categories were analyzed by the first author in several rounds with the six guiding principles with oversight from an expert in engineering education and mathematical modeling. The first author coded categories using the six guiding principles to make sense of the different roles mathematical modeling can have in the activities.

The outcome of this analysis provides an overview of how to achieve a balance between significant mathematical work and skills from engineering in design challenges. A balance is needed to make the connection between the two disciplines' content obvious and further strengthen students learning within K-12 engineering activities.