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Problem-solving is a typical type of assessment in engineering dynamics tests. To solve a problem, students need to set up equations and find a numerical answer. Depending on its difficulty and complexity, it can take anywhere from ten to thirty minutes to solve a quantitative problem. Due to the time constraint of in-class testing, a typical test may only contain a limited number of problems, covering an insufficient range of problem types. This can potentially reduce validity and reliability, two crucial factors which contribute to assessment results. A test with high validity should cover proper content. It should be able to distinguish high-performing students from low-performing students and every student in between. A reliable test should have a sufficient number of items to provide consistent information about students’ mastery of the materials. In this work-in-progress study, we will investigate to what extent a newly developed assessment is valid and reliable. Symbolic problem solving in this study refers to solving problems by setting up a system of equations without finding numeric solutions. Such problems usually take much less time. As a result, we can include more problems of a variety of types in a test. We evaluate the new assessment's validity and reliability. The efficient approach focused in symbolic problem-solving allows for a diverse range of problems in a single test. We will follow Standards for Educational and Psychological Testing, referred to as the Standards, for our study. The Standards were developed jointly by three professional organizations including the American Educational Research Association (AERA), the American Psychological Association (APA), and the National Council on Measurement in Education (NCME). We will use the standards to evaluate the content validity and internal consistency of a collection of symbolic problems. Examples on rectilinear kinematics and angular motion will be provided to illustrate how symbolic problem solving is used in both homework and assessments. Numerous studies in the literature have shown that symbolic questions impose greater challenges because of students’ algebraic difficulties. Thus, we will share strategies on how to prepare students to approach such problems. 

Practice plays a critical role in learning engineering dynamics. Typical practice in a dynamics course involves solving textbook problems. These problems can impose great cognitive load on underprepared students because they have not mastered constituent knowledge and skills required for solving whole problems. For these students, learning can be improved by being engaged in deliberate practice. Deliberate practice refers to a type of practice aimed at improving specific constituent knowledge or skills. Compared to solving whole problems requiring the simultaneous use of multiple constituent skills, deliberate practice is usually focused on one component skill at a time, which results in less cognitive load and more specificity. Contemporary theories of expertise development have highlighted the influence of deliberate practice (DP) on achieving exceptional performance in sports, music, and various professional fields. Concurrently, there is an emerging method for improving learning efficiency of novices by combining deliberate practice with cognitive load theory (CLT), a cognitive-architecture-based theory for instructional design. Mechanics is a foundation for most branches of engineering. It serves to develop problem-solving skills and consolidate understanding of other subjects, such as applied mathematics and physics. Mechanics has been a challenging subject. Students need to understand governing principles to gain conceptual knowledge and acquire procedural knowledge to apply these principles to solve problems. Due to the difficulty in developing conceptual and procedural knowledge, mechanics courses are among those that receive high DFW rates (percentage of students receiving a grade of D or F or Withdrawing from a course), and students are more likely to leave engineering after taking mechanics courses. Deliberate practice can help novices develop good representations of the knowledge needed to produce superior problem solving performance. The goal of the present study is to develop deliberate practice techniques to improve learning effectiveness and to reduce cognitive load. Our pilot study results revealed that the student mental effort scores were negatively correlated with their knowledge test scores with r = -.29 (p < .05) after using deliberate practice strategies. This supports the claim that deliberate practice can improve student learning while reducing cognitive load. In addition, the higher the students’ knowledge test scores, the lower their mental effort was when taking the tests. In other words, the students who used deliberate practice strategies had better learning results with less cognitive load. To design deliberate practice, we often need to analyze students’ persistent problems caused by faulty mental models, also referred to as an intuitive mental model, and misconceptions. In this study, we continue to conduct an in-depth diagnostic process to identify students’ common mistakes and associated intuitive mental models. We then use the results to develop deliberate practice problems aimed at changing students’ cognitive strategies and mental models. 

Practice plays a critical role in learning engineering dynamics. Typical practice in a dynamics course involves solving textbook problems. These problems can impose great cognitive load on underprepared students because they have not mastered constituent knowledge and skills required for solving whole problems. For these students, learning can be improved by being engaged in deliberate practice. Deliberate practice refers to a type of practice aimed at improving specific constituent knowledge or skills. Compared to solving whole problems requiring the simultaneous use of multiple constituent skills, deliberate practice is usually focused on one component skill at a time, which results in less cognitive load and more specificity. Contemporary theories of expertise development have highlighted the influence of deliberate practice (DP) on achieving exceptional performance in sports, music, and various professional fields. Concurrently, there is an emerging method for improving learning efficiency of novices by combining deliberate practice with cognitive load theory (CLT), a cognitive-architecture-based theory for instructional design. Mechanics is a foundation for most branches of engineering. It serves to develop problem-solving skills and consolidate understanding of other subjects, such as applied mathematics and physics. Mechanics has been a challenging subject. Students need to understand governing principles to gain conceptual knowledge and acquire procedural knowledge to apply these principles to solve problems. Due to the difficulty in developing conceptual and procedural knowledge, mechanics courses are among those that receive high DFW rates (percentage of students receiving a grade of D or F or Withdrawing from a course), and students are more likely to leave engineering after taking mechanics courses. Deliberate practice can help novices develop good representations of the knowledge needed to produce superior problem solving performance. The goal of the present study is to develop deliberate practice techniques to improve learning effectiveness and to reduce cognitive load. Our pilot study results revealed that the student mental effort scores were negatively correlated with their knowledge test scores with r = -.29 (p < .05) after using deliberate practice strategies. This supports the claim that deliberate practice can improve student learning while reducing cognitive load. In addition, the higher the students’ knowledge test scores, the lower their mental effort was when taking the tests. In other words, the students who used deliberate practice strategies had better learning results with less cognitive load. To design deliberate practice, we often need to analyze students’ persistent problems caused by faulty mental models, also referred to as an intuitive mental model, and misconceptions. In this study, we continue to conduct an in-depth diagnostic process to identify students’ common mistakes and associated intuitive mental models. We then use the results to develop deliberate practice problems aimed at changing students’ cognitive strategies and mental models. 

Learning is usually conceptualized as a process during which new information is processed in working memory to form knowledge structures called schemas, which are stored in long-term memory. Practice plays a critical role in developing schemas through learning-by-doing. Contemporary expertise development theories have highlighted the influence of deliberate practice (DP) on achieving exceptional performance in sports, music, and different professional fields. Concurrently, there is an emerging method for improving learning efficiency by combining deliberate practice with cognitive load theory (CLT), a cognition-architecture-based theory for instructional design. Mechanics is a foundation for most branches of engineering. It serves to develop problem-solving skills and consolidate understanding of other subjects, such as applied mathematics and physics. Mechanics has been a challenging subject. Students need to understand governing principles to gain conceptual knowledge and acquire procedural knowledge to apply these principles to solve problems. Due to the difficulty in developing conceptual and procedural knowledge, mechanics courses are among those which receive high DFW rates (percentage of students receiving a grade of D or F or Withdrawing from a course) and students are more likely to leave engineering after taking mechanics courses. Since deliberate practice can help novices develop good representations of the knowledge needed to produce superior problem solving performance, this study is to evaluate how deliberate practice helps students learn mechanics during the process of schema acquisition and consolidation. Considering cognitive capacity limitations, we will apply cognitive load theory to develop deliberate practice to help students build declarative and procedural knowledge without exceeding their working memory limitations. We will evaluate the effects of three practice strategies based on CLT on schema acquisition and consolidation in two mechanics courses (i.e., Statics and Dynamics). Examples and assessment results will be provided to evaluate the effectiveness of the practice strategies as well as the challenges. 

Free-body diagrams (FBDs) are diagrammatic representations of external forces and moments exerted on an object of interest for solving kinetics problems. Several studies have reported different ways of teaching FBDs in terms of pictorial representation of forces (e.g., placement of vectors or labeling). However, there is little research on practice strategies for helping students learn how to draw FBDs. Through the use of task analysis and a model of subgoal learning, we will develop task-analysis-guided deliberate practice to enhance learning. Task analysis is often used in instructional design to extract knowledge requirements for acquiring a skill. Skill acquisition is usually divided into three phases including declarative, knowledge compilation, and procedural. Task analysis in our study will identify relevant declarative and procedural knowledge related to drawing FBDs. The findings will be used to develop deliberate practice. Deliberate practice can help novices develop good representations of the knowledge needed to produce superior problem solving performance. This has been viewed as a gold standard for practice. Although deliberate practice is mainly studied among elite performers, the recent literature has revealed promising results for novices. Considering cognitive capacity limitations, we will apply cognitive load theory to develop deliberate practice to help students build declarative and procedural knowledge without exceeding their working memory limitations. A knowledge extraction expert will take an iterative approach to conduct task analyses with a subject matter expert (or experts)to distill knowledge to a level that is appropriate for students in the dynamics course. We will then integrate the task analysis results with instructional design strategies derived from cognitive load theory and the subgoal learning model to develop deliberate practice and assessment materials. Examples and assessment results will be provided to evaluate the effectiveness of the instructional design strategies as well as the challenges. 

Learning is usually conceptualized as a process during which new information is processed in working memory to form knowledge structures called schemas, which are stored in long-term memory. Practice plays a critical role in developing schemas through learning-by-doing. Contemporary expertise development theories have highlighted the influence of deliberate practice (DP) on achieving exceptional performance in sports, music, and different professional fields. Concurrently, there is an emerging method for improving learning efficiency by combining deliberate practice with cognitive load theory (CLT), a cognition-architecture-based theory for instructional design. Mechanics is a foundation for most branches of engineering. It serves to develop problem-solving skills and consolidate understanding of other subjects, such as applied mathematics and physics. Mechanics has been a challenging subject. Students need to understand governing principles to gain conceptual knowledge and acquire procedural knowledge to apply these principles to solve problems. Due to the difficulty in developing conceptual and procedural knowledge, mechanics courses are among those which receive high DFW rates (percentage of students receiving a grade of D or F or Withdrawing from a course) and students are more likely to leave engineering after taking mechanics courses. Since deliberate practice can help novices develop good representations of the knowledge needed to produce superior problem solving performance, this study is to evaluate how deliberate practice helps students learn mechanics during the process of schema acquisition and consolidation. Considering cognitive capacity limitations, we will apply cognitive load theory to develop deliberate practice to help students build declarative and procedural knowledge without exceeding their working memory limitations. We will evaluate the effects of three practice strategies based on CLT on the schema acquisition and consolidation in two mechanics courses (i.e., Statics and Dynamics). Examples and assessment results will be provided to evaluate the effectiveness of the practice strategies as well as the challenges.