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This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with 3D-printed models, build the theoretical basis for how they support learning, and assess their effectiveness in the classroom. We are exploring how such models can scaffold spatial skills and support learners’ development of conceptual understanding and representational competence in calculus and engineering statics. We are also exploring how to leverage the model-based activities to embed spatial skills training into these courses. The project’s original focus was on group learning in classroom activities with shared manipulatives. After a year of development and pilot activities, we commenced data collection in classroom implementations of a relatively mature curriculum starting fall 2019. Data collection ended abruptly in March 2020 when we had to shift gears in the context of a shift to online learning amid the COVID-19 pandemic. With uncertainty as to when the use of shared hands-on models in a collaborative in-person learning context would be feasible again, it was clear a change in approach would be necessary. We have since developed new versions of the models and associated curriculum designed for independent at-home use in the contextmore »
Do They Need To See It To Learn It? Spatial Abilities, Representational Competence, and Conceptual Knowledge in StaticsA growing body of research indicates spatial visualization skills are important to success in many STEM disciplines, including several engineering majors that rely on a foundation in engineering mechanics. Many fundamental mechanics concepts such as free-body diagrams, moments, and vectors are inherently spatial in that application of the concept and related analytical techniques requires visualization and sketching. Visualization may also be important to mechanics learners’ ability to understand and employ common mechanics representations and conventions in communication and problem solving, a skill known as representational competence. In this paper, we present early research on how spatial abilities might factor in to students’ conceptual understanding of vectors and associated representational competence. We administered the Mental Cutting Test (MCT), a common assessment of spatial abilities, in the first and last week of the term. We also administered the Test of Representational Competence with Vectors (TRCV), a targeted assessment of vector concepts and representations, in week one and at mid-term. The vector post-test came after coverage of moments and cross products. We collected this assessment data in statics courses across multiple terms at three different colleges. To understand how spatial skills relate to the development of representational competence, we use a multiple regressionmore »
The landscapes of many elementary, middle, and high school math classrooms have undergone major transformations over the last half-century, moving from drill-and-skill work to more conceptual reasoning and hands-on manipulative work. However, if you look at a college level calculus class you are likely to find the main difference is the professor now has a whiteboard marker in hand rather than a piece of chalk. It is possible that some student work may be done on the computer, but much of it contains the same type of repetitive skill building problems. This should seem strange given the advancements in technology that allow more freedom than ever to build connections between different representations of a concept. Several class activities have been developed using a combination of approaches, depending on the topic. Topics covered in the activities include Riemann Sums, Accumulation, Center of Mass, Volumes of Revolution (Discs, Washers, and Shells), and Volumes of Similar Cross-section. All activities use student note outlines that are either done in a whole group interactive-lecture approach, or in a group work inquiry-based approach. Some of the activities use interactive graphs designed on desmos.com and others use physical models that have been designed in OpenSCAD and 3D-printedmore »
Perusal of any common statics textbook will reveal a reference table of standard supports in the section introducing rigid body equilibrium analysis. Most statics students eventually memorize a heuristic approach to drawing a free-body diagram based on applying the information in this table. First, identify the entry in the table that matches the schematic representation of a connection. Then draw the corresponding force and/or couple moment vectors on the isolated body according to their positive sign conventions. Multiple studies have noted how even high performing students tend to rely on this heuristic rather than conceptual reasoning. Many students struggle when faced with a new engineering connection that does not match an entry in the supports table. In this paper, we describe an inquiry-based approach to introducing support models and free-body diagrams of rigid bodies. In a series of collaborative learning activities, students practice reasoning through the force interactions at example connections such as a bolted flange or a hinge by considering how the support resists translation and rotation in each direction. Each team works with the aid of a physical model to analyze how changes in the applied loads affect the reaction components. A second model of the isolated bodymore »
Modern 3D printing technology makes it relatively easy and affordable to produce physical models that offer learners concrete representations of otherwise abstract concepts and representations. We hypothesize that integrating hands-on learning with these models into traditionally lecture-dominant courses may help learners develop representational competence, the ability to interpret, switch between, and appropriately use multiple representations of a concept as appropriate for learning, communication and analysis. This approach also offers potential to mitigate difficulties that learners with lower spatial abilities may encounter in STEM courses. Spatial thinking connects to representational competence in that internal mental representations (i.e. visualizations) facilitate work using multiple external representations. A growing body of research indicates well-developed spatial skills are important to student success in many STEM majors, and that students can improve these skills through targeted training. This NSF-IUSE exploration and design project began in fall 2018 and features cross-disciplinary collaboration between engineering, math, and psychology faculty to develop learning activities with 3D-printed models, build the theoretical basis for how they support learning, and assess their effectiveness in the classroom. We are exploring how such models can support learners’ development of conceptual understanding and representational competence in calculus and engineering statics. We are also exploring howmore »