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Enhancing Engineering Mechanics Statics Instruction Using Manipulative Truss Models Joel A. Mejia, Wade Goodridge, and Christopher Green Department of Engineering Education Utah State University Logan, UT 84322 - 4160 Abstract—Enhancing a student’s ability to mentally visualize and intuitively assess foundational concepts in engineering mechanics - statics can create a significant advantage for students in their pre-professional engineering courses. Concepts such as forces and moments often prove to be challenging for students lacking hands-on mechanical experience or those who are visual and kinesthetic learners. Showing students these “intangible” mechanics principles is not an easy task and usually requires proactive measures to improve learning. In an effort to improve visualization and tactile learning in a college mechanics – statics course, hands-on and visual truss models were developed based on the concept of physical manipulatives. Mathematics instructors use manipulative models to help students identify different mathematical concepts. These models not only allow the students to see and feel different objects but also to manipulate the objects to form a concrete representation of the concept. Furthermore, manipulative models help students visualize, feel, and analyze the behavior of the material being manipulated. This study examines the relationship between the use of a physical model of a truss and the students’ framing of information during task interpretation to successfully attain conceptual understanding about truss analysis. Keywords—manipulatives; statics; task interpretation; constant comparative analysis I. INTRODUCTION Statics is the branch of mechanics that is concerned with the analysis of loads and forces on stationary structures and machines. It is a fundamental course that prepares students for subsequent courses such as dynamics and mechanics of materials. Studies have shown that students tend to have different conceptual understanding misconceptions in statics. Students “fail to account for the mutual nature of forces between connected bodies that are separated for analysis” [1]. One example that illustrates this difficult concept for students in engineering statics is the internal and external force analysis in a truss problem. Trusses are structures comprised of units, also called members, connected to one another through joints. These structures provide stability and shape to different larger structures and machines such as crates, cranes, buildings, and bridges. Simple mathematical analysis often leads to a solution that may not have a true intuitive meaning for the student. Manipulatives can be used as a tool tying together students’ analytical capabilities and their engineering intuition. Research has indicated that the manipulatives are most effective when students’ exploration is somewhat guided, either by their instructor in lecture or by homework, lab, or recitation activities using guided-inquiry approach to learning [2]. For example, mathematics instructors use manipulative models to help students identify different mathematical concepts [3]. The advantage of using physical manipulatives is the fact that manipulatives enhance spatial visualization for engineering students [4]. Nonetheless, there is a gap between how the students understand the problem and how they plan and execute solutions for the problem. Therefore, investigating the students’ task interpretation during the analysis of the truss is important in order to incorporate the three layers of information construction: explicit, implicit, and socio- contextual information about tasks [5]. These three factors influence how the student creates a strategy for task understanding and execution. The framing of the information gathered through task interpretation, in terms of underlying concepts, helps students decode the requirements of a particular task [6], which, along with other aspects of self– regulated learning, help develop work habits in their learning activities. This also helps create empowering pedagogies where students can use their task interpretation in new productive and meaningful ways. II. ANALYSIS OF LITERATURE A. Physical and Virtual Manipulatives The challenges college students face when learning statics was investigated using learning activities [7]. The study addressed different misconceptions and problems for students in statics, including the forces between rigid bodies, moments, and forces on inanimate objects. The study described different techniques that could be used in the classroom to improve learning, especially the use of physical manipulatives to demonstrate the “invisible” and help develop mechanical intuition for the students. Instruction with these physical manipulatives was accompanied by a series of group discussions, collaborations, and feedback activities in the classroom. The authors described two core ideas: 1) students have difficulty perceiving forces between inanimate objects but physical manipulatives can help students see and feel what is “invisible” and abstract, and 2) the necessary assessment and feedback required in the statics course. The authors argued that learning modules that use physical manipulatives and other activities could be applicable to a wide variety of engineering 978-1-4673-5261-1/13/$31.00 ©2013 IEEE

Enhancing Engineering Mechanics Statics Instruction Using

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Enhancing Engineering Mechanics Statics Instruction Using Manipulative Truss Models

Joel A. Mejia, Wade Goodridge, and Christopher Green Department of Engineering Education

Utah State University Logan, UT 84322 - 4160

Abstract—Enhancing a student’s ability to mentally visualize and intuitively assess foundational concepts in engineering mechanics - statics can create a significant advantage for students in their pre-professional engineering courses. Concepts such as forces and moments often prove to be challenging for students lacking hands-on mechanical experience or those who are visual and kinesthetic learners. Showing students these “intangible” mechanics principles is not an easy task and usually requires proactive measures to improve learning. In an effort to improve visualization and tactile learning in a college mechanics – statics course, hands-on and visual truss models were developed based on the concept of physical manipulatives. Mathematics instructors use manipulative models to help students identify different mathematical concepts. These models not only allow the students to see and feel different objects but also to manipulate the objects to form a concrete representation of the concept. Furthermore, manipulative models help students visualize, feel, and analyze the behavior of the material being manipulated. This study examines the relationship between the use of a physical model of a truss and the students’ framing of information during task interpretation to successfully attain conceptual understanding about truss analysis.

Keywords—manipulatives; statics; task interpretation; constant comparative analysis

I. INTRODUCTION Statics is the branch of mechanics that is concerned with

the analysis of loads and forces on stationary structures and machines. It is a fundamental course that prepares students for subsequent courses such as dynamics and mechanics of materials. Studies have shown that students tend to have different conceptual understanding misconceptions in statics. Students “fail to account for the mutual nature of forces between connected bodies that are separated for analysis” [1]. One example that illustrates this difficult concept for students in engineering statics is the internal and external force analysis in a truss problem. Trusses are structures comprised of units, also called members, connected to one another through joints. These structures provide stability and shape to different larger structures and machines such as crates, cranes, buildings, and bridges. Simple mathematical analysis often leads to a solution that may not have a true intuitive meaning for the student. Manipulatives can be used as a tool tying together students’ analytical capabilities and their engineering intuition. Research has indicated that the manipulatives are most effective when

students’ exploration is somewhat guided, either by their instructor in lecture or by homework, lab, or recitation activities using guided-inquiry approach to learning [2]. For example, mathematics instructors use manipulative models to help students identify different mathematical concepts [3]. The advantage of using physical manipulatives is the fact that manipulatives enhance spatial visualization for engineering students [4]. Nonetheless, there is a gap between how the students understand the problem and how they plan and execute solutions for the problem. Therefore, investigating the students’ task interpretation during the analysis of the truss is important in order to incorporate the three layers of information construction: explicit, implicit, and socio-contextual information about tasks [5]. These three factors influence how the student creates a strategy for task understanding and execution. The framing of the information gathered through task interpretation, in terms of underlying concepts, helps students decode the requirements of a particular task [6], which, along with other aspects of self–regulated learning, help develop work habits in their learning activities. This also helps create empowering pedagogies where students can use their task interpretation in new productive and meaningful ways.

II. ANALYSIS OF LITERATURE

A. Physical and Virtual Manipulatives The challenges college students face when learning statics

was investigated using learning activities [7]. The study addressed different misconceptions and problems for students in statics, including the forces between rigid bodies, moments, and forces on inanimate objects. The study described different techniques that could be used in the classroom to improve learning, especially the use of physical manipulatives to demonstrate the “invisible” and help develop mechanical intuition for the students. Instruction with these physical manipulatives was accompanied by a series of group discussions, collaborations, and feedback activities in the classroom. The authors described two core ideas: 1) students have difficulty perceiving forces between inanimate objects but physical manipulatives can help students see and feel what is “invisible” and abstract, and 2) the necessary assessment and feedback required in the statics course. The authors argued that learning modules that use physical manipulatives and other activities could be applicable to a wide variety of engineering

978-1-4673-5261-1/13/$31.00 ©2013 IEEE

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subjects and help students understand, observe, and feel concepts that are somewhat abstract [7].

Other studies have investigated the use of both physical and virtual manipulatives in a variety of STEM areas. These studies investigated different frameworks that would describe the best way to integrate, sequence, or “blend” the use of both physical and virtual manipulatives to understand abstract concepts. For example, the use of hands-on (physical) malipulatives helped engineering students in modeling and engineering problem solving [10]. The results from this study showed that students increased their understanding of engineering concepts when they used manipulatives and were able to see and feel reactions created by the manipulative. Another study, involving physical and virtual manipulatives, indicated that manipulatives affected not only learning but also engagement and knowledge transfer [3]. The results from this study showed that the learning of all groups in the study in all conditions increased as the result of the use of manipulatives. Students developed skills to correctly identify variables based on word problems. It was observed that students with concrete materials, or manipulatives, led to better procedural use and therefore a reduced cognitive load.

In another study, three characteristics were observed: instruction, type of knowledge gained, and the use of physical and virtual materials [11]. For this study, the researchers used “mousetrap cars” as the physical manipulative and a digital mousetrap car from a computer program as the virtual manipulative. The analysis focused on open-ended discovery, confidence, and gender effects (male vs. female). The study showed that students learned equally with either medium regardless of constraints. Students were able to increase their knowledge equally using both methods even when time spent on a task was different [11]. However, students using the physical manipulative were able to observe several mistakes with their design while students using the digital manipulative did not experience such observations due to the lack of those features in the computer simulation.

In addition, another study investigated the use of manipulatives and the ability of students to follow specific hand manipulative tasks using instructional animations [12]. The purpose of the study was to show that animated presentations are more effective than static presentations, especially if these depict human movement. The results showed that instructional animations are more effective and lead to better learning and understanding. The study indicated that participants could not imitate actions showed on static images and generated cognitive overload, thus negatively affecting learning.

B. Task Interpretation Task interpretation is a key theoretical component in

students understanding, academic performance, and appropriate and effective task engagement [6]. Task interpretation theorizes that there are three layers of information construction: explicit, implicit, and socio-contextual information about tasks [5]. Explicit features of a task are overtly presented descriptions and are often described in assignments and are the aspects of the task that give it structure and some type of cohesiveness across students [13].

Implicit features of a task include information that students might be expected to extrapolate beyond assignment descriptions such as connection to learning concepts or resources to completing the task [13]. Finally, socio-contextual features include information about the broader course, such as beliefs about knowledge and expertise or beliefs about ability [13]. The importance of task interpretation, or task understanding, when working with a manipulative is that understanding problems is influenced by implicit and explicit aspects that may or may not be accurate. Task understanding is also affected by a social or cultural context that may help the student base a strategy to understand and solve the task. Therefore, it is important to investigate how these three layers of information construction are incorporated when using the manipulative during truss analysis in order to determine if the manipulative can be used in meaningful pedagogical ways.

III. RESEARCH GOALS The use of manipulatives can help the learning outcomes of

engineering students, particularly in the context of ill-structured problems while relating concepts to their own background and prior knowledge. However, not enough studies have been done related to the use of manipulatives and their relationship to task interpretation and students’ problem solving approaches. Therefore, it is important to consider the inclusion of manipulatives in the engineering statics courses and evaluate their relationship to academic achievement in engineering students. The intent of the project is to improve conceptual understanding of the forces involved in truss design and to assess students’ task interpretation (explicit, implicit and socio-contextual) of a truss analysis engineering problem. The fundamental research questions are: (1) Would a physical manipulative help students improve task understanding in an engineering statics course? and (2) How do these students reconcile their initial understanding and interpretation about internal forces in a truss after the use of the physical manipulative?

IV. THE STUDY The study involves a mixed methods approach comprised

of different intervention sessions with selected students. Participants include six engineering students randomly selected from a statics course at a public university. The students are presented with a problem involving a truss analysis. The objective of the task is to predict what is happening on the system followed by a specific explanation or reasoning behind such prediction. The task given to the students involves answering different questions related to the analysis of forces in a truss, such as identifying two force members, zero force members, etc. This problem has posed different challenges for students in the current course due to the students’ unfamiliarity with engineering concepts in statics. Students are asked to solve the problem during a think-aloud process where students identify the information necessary to solve the problem. The think-aloud process helps identify the explicit, implicit and socio-contextual aspects of the task as they work toward understanding the design that

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solves or explains the engineering problem [13]. Knowledge may be in the form of social context (beliefs about understanding and expertise from their relationships and discourse practices), explicit resources (terminology and specific instructions), or implicit resources (different concept connections or extrapolations). Data collection involves think-aloud tasks that elicit students’ task interpretations and perceptions [13]. Broadly speaking, the collection of a protocol involves the recording of a research participant’s verbalization while working to solve a problem, usually one specified by the researcher. This verbal thought process, as well as follow-up interviews and observations, are recorded and transcribed. The purpose is to generate a verbal text that a researcher can analyze to provide an account of cognitive processes [14]. Implicit and explicit layers of information from the students’ verbalizations may or may not be correct, and this allows the researcher to identify how many of their implicit and explicit layers of information are accurate in order to create a coding system for analysis.

Once the prediction, solution, and subsequent explanation have been made, the students have the opportunity to work with the manipulative. Two types of data are collected during the process: concurrent, in which a participant thinks aloud during the process of completing the task, and retrospective, in which a participant completes components of the task or the whole task and then is prompted to reconstruct the process from memory [14]. Once they have worked with the manipulative, a final interview is conducted to determine if the students concur with the predictions made and determine any assimilation problems and possible elimination of misconceptions. The prediction and final interview may consist of descriptions of design load calculations, reactions and free body diagrams, presentation of engineering calculations, and determination of zero force members. All questions are open-ended questions and help describe the kind of thinking and kind of knowledge the students emphasize during the task assignment. In this process, student may connect different stories that they can relate to the type of assignment being investigated.

Constant comparative analysis is used to critically draw important information about the participants. The constant comparative method consists of identifying a phenomenon, object, or event, then comparing incidents applicable to each category, and finally integrating such categories and their properties [15]. Thus, this method combines category coding with simultaneous comparison of all incidents observed as well as simultaneous comparison across categories. The constant comparative analysis would create a coding system used to compare, contrast and determine frequencies of different sets of beliefs, ideas or perceptions.

V. IMPLICATIONS This project is intended to promote an instructional

technique that is relevant to students in engineering. Providing engineering students with opportunities to communicate

science and engineering through physical manipulatives, drawings, charts, tables, graphs, and computer-developed simulations increases participation and promotes more focus on communication for understanding. It provides the students with the time to build context, common experiences, thinking skills, cooperative learning, comfort level and a positive attitude toward learning. The results obtained from this study will be used to modify and expand further research regarding engineering physical and virtual manipulatives, curriculum materials, and practices to help the linguistically and culturally diverse classrooms. At the time of the FIE 2013 Conference, results from this research will be presented.

REFERENCES [1] Steif, P. S., & Dantzler, J. A. (2005). A Statics Concept Inventory:

Development and Psychometric Analysis. Journal Of Engineering Education, 94(4), 363-371.

[2] Perkins K, Adams W, Dubson M, Finkelstein N, Reid S, Wieman C, LeMaster R. (2006). PhET: Interactive simulations for teaching and learning physics. Physics Teacher, 44(1), 18–23.

[3] Belenky, D. M., & Nokes, T. J. (2009). Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer. Journal Of Problem Solving, 2(2), 102-129.

[4] Alias, M, Black, T. R., & Gray, D. E. (2002). Effect of instructions on spatial visualization ability in civil engineering students. International Education Journal, 3(1), 1-12.

[5] Hadwin, A. F. (2006). Do your students really understand your assignment? LTC Currents Newsletter, II (3), 1-9.

[6] Butler D. L., & Cartier, S. C. (2003). Promoting effective task interpretation as an important work habit: A key to successful teaching and learning. The Teachers College Record, 106, 1729-1758.

[7] Dollár, A., & Steif, P. S. (2006). Learning modules for statics. International Journal of Engineering Education, 22, 381-392.

[8] Olympiou, G., & Zacharia, Z. C. (2012). Blending physical and virtual manipulatives: An effort to improve students' conceptual understanding through science laboratory experimentation. Science Education, 96(1), 21-47.

[9] Lemons, G., Carberry, A., Swan, C., Jarvin, L., & Rogers, C. (2010). The benefits of model building in teaching engineering design. Design Studies, 31(3), 288-309.

[10] Coller, B.D. (2008). An experiment in hands-on learning in engineering mechanics: statics. International Journal of Engineering Education, 24, 545-557.

[11] Klahr, D., Triona, L. M., & Williams, C. (2007). Hands on what? The relative effectiveness of physical versus virtual materials in an engineering design project by middle school children. Journal of Research in Science Teaching, 44, 183 – 203.

[12] Ayres, P., Marcus, N., Chan, C., & Qian, N. (2009). Learning hand manipulative tasks: When instructional animations are superior to equivalent static representations. Computers In Human Behavior, 25(2), 348-353.

[13] Hadwin, A. F., Oshige, M., Fior, M. N., Tupper, K., & Miller, M. F. W. (2008). Examining the agreement between students and instructor task perceptions in a complex engineering design task. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), New York.

[14] Smagorinsky, P. (2008). The method section as conceptual epicenter in constructing social science research reports. Written Communication, 25, 389-411.

[15] Glaser, BG. & Strauss, AL. (1967). The Discovery of Grounded Theory: Strategies for Qualitative Research. New York: Aldine De Gruyter.