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Knowledge Assessment in Statics: Concepts Versus Skills

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Knowledge Assessment in Statics: Concepts Versus Skills Session 1168 Knowledge Assessment in Statics: Concepts versus skills Scott Danielson Arizona State University Abstract Following the lead of the physics community, engineering faculty have recognized the value of good assessment instruments for evaluating the learning of their students. These assessment instruments can be used to both measure student learning and to evaluate changes in teaching, i.e., did student-learning increase due different ways of teaching. As a result, there are significant efforts underway to develop engineering subject assessment tools. For instance, the Foundation Coalition is supporting assessment tool development efforts in a number of engineering subjects. These efforts have focused on developing “concept” inventories. These concept inventories focus on determining student understanding of the subject’s fundamental concepts. Separately, a NSF-supported effort to develop an assessment tool for statics was begun in the last year by the authors. As a first step, the project team analyzed prior work aimed at delineating important knowledge areas in statics. They quickly recognized that these important knowledge areas contained both conceptual and “skill” components. Both knowledge areas are described and examples of each are provided. Also, a cognitive psychology-based taxonomy of declarative and procedural knowledge is discussed in relation to determining the difference between a concept and a skill. Subsequently, the team decided to focus on development of a concept-based statics assessment tool. The ongoing Delphi process to refine the inventory of important statics concepts and validate the concepts with a broader group of subject matter experts is described. However, the value and need for a skills-based assessment tool is also recognized. Thus, initial efforts to delineate concepts and skills in statics are discussed, including an initial inventory of these concepts and skills. Introduction Statics is the first course in a series of courses within the broader subject area commonly referred to as engineering science for virtually all engineering and engineering technology students. It is a fundamental course prerequisite for other important courses like dynamics and strength of 1 materials. Success in these latter courses is directly correlated to success in statics. 9.834.1 Page Proceedings of the 2004 American Society of Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education Demonstrated proof of student learning and mastery of engineering concepts is now required in the Accreditation Board of Engineering and Technology’s (ABET) outcomes-based environment 2. Tools are needed for assessment of individual student learning. Faculty, departments, and institutional administrators all receive benefits from timely measurement of student learning—immediately upon completing the course. Second, engineering faculty need validated instruments for formative use in assessing implementation of new course design strategies and instructional practices intended to increase student learning. Following the lead of the physics community, the bulk of the effort has focused on concept inventories. Typically, these concept inventories focus on determining student understanding of the subject’s fundamental concepts. For instance, the Force Concept Inventory (FCI) was developed and fielded by physics educators. 3 The FCI probes student understanding and misunderstandings of Newtonian physics, primarily as applied to Newton’s Second Law, i.e., things in motion, and has been widely used by physics educators to assess student learning. In engineering education, the Foundation Coalition is currently supporting concept inventory development efforts in a number of engineering subjects—materials, dynamics, mechanics’ of materials—but not statics. A National Science Foundation-supported effort to develop an assessment tool for statics is underway by the author and co-principal investigators. The specific goals of this project are to articulate the concepts and knowledge areas essential to statics, create a set of questions probing those concepts, accomplish field-testing and analysis to validate the questions and instrument, and to disseminate the instrument nationally. This paper reports the progress toward the first of these goals. Initial Compilation of Statics Knowledge Areas An initial list of statics’ knowledge areas had been previously developed by the project co- principal investigators (Danielson and Mehta) and is shown in Table 1. 4 This original list was broken into three categories: fundamental laws, their corollaries and related knowledge. Here, the word “concept” was used in an applied sense. While the most basic concepts of mechanics may be argued to be space, time, mass, and force, initial thoughts were focused on defining the concepts of statics as areas of knowledge critical to mastery of statics. It was, and remains, the intent to develop knowledge areas and tools independent of any particular textbook and applying to virtually any statics course. Table 1. Original Statics Concept Taxonomy Fundamental Concepts Newton’s First Law: equilibrium Newton’s Third Law: action and reaction Concepts that are corollaries to the fundamental concepts Equilibrium of the whole and parts (assuming no deflections) Free Body Diagrams Particle and rigid body analyses External reactions Friction Moment 9.834.2 Page Center of Gravity Proceedings of the 2004 American Society of Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education Moment of Inertia Cables, Springs, and Pulleys Related knowledge (includes both concepts and skills) Vector Mathematics: addition, unit vectors, dot product, cross product, reduction of vector expressions to a scalar form Integral Calculus (used for understanding distributed loads, centroids, etc.) Weight as a Force (using W = mg) Right-Handed Coordinate Systems Units and Calculations (significant digits, etc.) For the purposes of statics, the First Law’s statement of static equilibrium and the Third Law’s statement about the forces of action and reaction between things in contact were viewed as fundamental. The second set of items was originally posited as corollaries of Newton’s First and Third Laws. For instance, Newton’s Third Law is the foundation for applying tools like free body diagrams and understanding external support reactions. It was felt that the concept of a free body diagram was critical to success in virtually all statics problems. The Related Knowledge items in Table 1 consisted of both conceptual knowledge and skills, often intertwined together. For instance, implementing the concept of the moment of a force in a problem is often linked to the mathematical skill of performing a vector cross product. In addition, all of these knowledge areas are often portrayed as classic statics problems (e.g., two- dimensional equilibrium, or force resolution and manipulation). Thus, as a first step in establishing the concepts and knowledge areas essential to statics, the original taxonomy of concept and knowledge areas shown in Table 1 was reviewed by eight other engineering mechanics’ educators. This team (listed in the acknowledgements) formed a diverse and experienced group of educators. After email exchanges, the group met in person to discuss the project and this list of knowledge areas. During the discussion, the group decided that skills should not be a part of a concept test. Thus, each item on the original list was reviewed with the goal of eliminating skill-based items (analysis, problem solving or mathematics). However, the group also felt that since skills are also important, they agreed that fielding a concept inventory might not be sufficient for mechanics educators, as a separate skill-based test would also be useful. Then the group used their judgement to remove from the list what seemed like skill-oriented items, leaving a shorter, more distilled concept list. In addition, the group made a conscious decision to focus on concepts as used or taught in the majority of statics classes. This meant that some aspects of our concept list were not universal to mechanics, merely to statics. For instance, while the assumption of equilibrium with no deflection is not valid for all of mechanics, it is almost universal within the realm of statics’ classes. The resulting concept list is shown in Table 2. However, the group decided that a Delphi process 5 would be a valuable way to obtain and validate consensus about both the concepts and skills of statics. Page 9.834.3 Page Proceedings of the 2004 American Society of Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education Table 2. Statics Concepts after First Review (Pre-Delphi) Newton’s First Law: equilibrium Newton’s Third Law: action and reaction “Nature” of force(s)—but only contact forces—to include parallelogram law (resultants) Equilibrium of the whole and parts (assuming no deflections) Free Body Diagrams Particles and rigid bodies External reactions (which may involve pins, cables, springs, pulleys, etc.) Friction Moment of a force Weight as a Force Distributed forces Center of Gravity (as applied to distributed loads) Statically indeterminate situations (recognition level, not solving) Concept versus Skill As mentioned above, most engineering educators are working on developing concept inventories based on the approach of the Force Concept Inventory (with
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