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1. Evaluating the differential impact of dichotomous and partial credit scoring models on student problem-solving assessment outcomes.

   May, T.; Koskey, K.; Bostic, J.; Stone, G.; Kruse, L.; Matney, G. (February 2023, School science and mathematics)

   Determining the most appropriate method of scoring an assessment is based on multiple factors, including the intended use of results, the assessment's purpose, and time constraints. Both the dichotomous and partial credit models have their advantages, yet direct comparisons of assessment outcomes from each method are not typical with constructed response items. The present study compared the impact of both scoring methods on the internal structure and consequential validity of a middle-grades problem-solving assessment called the problem solving measure for grade six (PSM6). After being scored both ways, Rasch dichotomous and partial credit analyses indicated similarly strong psychometric findings across models. Student outcome measures on the PSM6, scored both dichotomously and with partial credit, demonstrated strong, positive, significant correlation. Similar demographic patterns were noted regardless of scoring method. Both scoring methods produced similar results, suggesting that either would be appropriate to use with the PSM6. 

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2. Examining how using dichotomous and partial credit scoring models influence sixth‐grade mathematical problem‐solving assessment outcomes

   https://doi.org/10.1111/ssm.12570  

   May, Toni A.; Koskey, Kristin L. K.; Bostic, Jonathan D.; Stone, Gregory E.; Kruse, Lance M.; Matney, Gabriel (February 2023, School Science and Mathematics)

   Abstract Determining the most appropriate method of scoring an assessment is based on multiple factors, including the intended use of results, the assessment's purpose, and time constraints. Both the dichotomous and partial credit models have their advantages, yet direct comparisons of assessment outcomes from each method are not typical with constructed response items. The present study compared the impact of both scoring methods on the internal structure and consequential validity of a middle‐grades problem‐solving assessment called the problem solving measure for grade six (PSM6). After being scored both ways, Rasch dichotomous and partial credit analyses indicated similarly strong psychometric findings across models. Student outcome measures on the PSM6, scored both dichotomously and with partial credit, demonstrated strong, positive, significant correlation. Similar demographic patterns were noted regardless of scoring method. Both scoring methods produced similar results, suggesting that either would be appropriate to use with the PSM6. 

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3. Validity and Test-Length Reduction Strategies for Complex Assessments

   Kruse, Lance; Stone, Gregory; May, Toni; Bostic, Jonathan (November 2023, Journal of applied measurement)

   Smith, Richard (Ed.)

   Lengthy standardized assessments decrease instructional time while increasing concerns about student cognitive fatigue. This study presents a methodological approach for item reduction within a complex assessment setting using the Problem Solving Measure for Grade 6 (PSM6). Five item-reduction methods were utilized to reduce the number of items on the PSM6, and each shortened instrument was evaluated through validity evidence for test content, internal structure, and relationships to other variables. The two quantitative methods (Rasch model and point-biserial) resulted in the best psychometrically performing shortened assessments but were not representative of all content subdomains, while the three qualitative (content preservation) methods resulted in poor psychometrically performing assessments that retained all subdomains. Specifically, the ten-item Rasch and ten-item point-biserial shortened tests demonstrated the overall strongest validity evidence, but future research is needed to explore the psychometric performance of these versions in a new independent sample and the necessity for subdomain representation. Implications for the study provide a methodological framework for researchers to use and reduce the length of existing instruments while identifying how the various reduction strategies may sacrifice different information from the original instrument. Practitioners are encouraged to carefully examine to what extent their reduced instrument aligns with their pre-determined criteria. 

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4. Best 2019 PIC III Paper: Do They Understand Your Language? Access Their Fluency with Vector Representation

   https://doi.org/10.18260/1-2--34205  

   Davishahl, Eric; Haskell, Todd; Davishahl, Jill; Singleton, Lee; Goodridge, Wade (June 2020, 2020 ASEE Virtual Annual Conference Content Access)

   In teaching mechanics, we use multiple representations of vectors to develop concepts and analysis techniques. These representations include pictorials, diagrams, symbols, numbers and narrative language. Through years of study as students, researchers, and teachers, we develop a fluency rooted in a deep conceptual understanding of what each representation communicates. Many novice learners, however, struggle to gain such understanding and rely on superficial mimicry of the problem solving procedures we demonstrate in examples. The term representational competence refers to the ability to interpret, switch between, and use multiple representations of a concept as appropriate for learning, communication and analysis. In engineering statics, an understanding of what each vector representation communicates and how to use different representations in problem solving is important to the development of both conceptual and procedural knowledge. Science education literature identifies representational competence as a marker of true conceptual understanding. This paper presents development work for a new assessment instrument designed to measure representational competence with vectors in an engineering mechanics context. We developed the assessment over two successive terms in statics courses at a community college, a medium-sized regional university, and a large state university. We started with twelve multiple-choice questions that survey the vector representations commonly employed in statics. Each question requires the student to interpret and/or use two or more different representations of vectors and requires no calculation beyond single digit integer arithmetic. Distractor answer choices include common student mistakes and misconceptions drawn from the literature and from our teaching experience. We piloted these twelve questions as a timed section of the first exam in fall 2018 statics courses at both Whatcom Community College (WCC) and Western Washington University. Analysis of students’ unprompted use of vector representations on the open-ended problem-solving section of the same exam provides evidence of the assessment’s validity as a measurement instrument for representational competence. We found a positive correlation between students’ accurate and effective use of representations and their score on the multiple choice test. We gathered additional validity evidence by reviewing student responses on an exam wrapper reflection. We used item difficulty and item discrimination scores (point-biserial correlation) to eliminate two questions and revised the remaining questions to improve clarity and discriminatory power. We administered the revised version in two contexts: (1) again as part of the first exam in the winter 2019 Statics course at WCC, and (2) as an extra credit opportunity for statics students at Utah State University. This paper includes sample questions from the assessment to illustrate the approach. The full assessment is available to interested instructors and researchers through an online tool. 

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5. Do They Understand Your Language? Assess Their Fluency with Vector Representations

   Davishahl, E.; Haskell, T. R.; Davishahl, J.; Singleton, L.; Goodridge, W. H. (June 2019, ASEE Annual Conference proceedings)

   In teaching mechanics, we use multiple representations of vectors to develop concepts and analysis techniques. These representations include pictorials, diagrams, symbols, numbers and narrative language. Through years of study as students, researchers, and teachers, we develop a fluency rooted in a deep conceptual understanding of what each representation communicates. Many novice learners, however, struggle to gain such understanding and rely on superficial mimicry of the problem solving procedures we demonstrate in examples. The term representational competence refers to the ability to interpret, switch between, and use multiple representations of a concept as appropriate for learning, communication and analysis. In engineering statics, an understanding of what each vector representation communicates and how to use different representations in problem solving is important to the development of both conceptual and procedural knowledge. Science education literature identifies representational competence as a marker of true conceptual understanding. This paper presents development work for a new assessment instrument designed to measure representational competence with vectors in an engineering mechanics context. We developed the assessment over two successive terms in statics courses at a community college, a medium-sized regional university, and a large state university. We started with twelve multiple-choice questions that survey the vector representations commonly employed in statics. Each question requires the student to interpret and/or use two or more different representations of vectors and requires no calculation beyond single digit integer arithmetic. Distractor answer choices include common student mistakes and misconceptions drawn from the literature and from our teaching experience. We piloted these twelve questions as a timed section of the first exam in fall 2018 statics courses at both Whatcom Community College (WCC) and Western Washington University. Analysis of students’ unprompted use of vector representations on the open-ended problem-solving section of the same exam provides evidence of the assessment’s validity as a measurement instrument for representational competence. We found a positive correlation between students’ accurate and effective use of representations and their score on the multiple choice test. We gathered additional validity evidence by reviewing student responses on an exam wrapper reflection. We used item difficulty and item discrimination scores (point-biserial correlation) to eliminate two questions and revised the remaining questions to improve clarity and discriminatory power. We administered the revised version in two contexts: (1) again as part of the first exam in the winter 2019 Statics course at WCC, and (2) as an extra credit opportunity for statics students at Utah State University. This paper includes sample questions from the assessment to illustrate the approach. The full assessment is available to interested instructors and researchers through an online tool. 

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