Thesis advisor: Larry H. Ludlow / The focus on science, technology, engineering, and mathematics fields has noticeably increased in recent decades with the rapid growth in technology. Mathematical knowledge and competence is in many ways a gateway to scientific and technical development, and therefore careers (Prieto & Delgado, 2007). Unfortunately, national and international assessments of mathematics achievement (e.g., Kena et al., 2016; NCES, 2015; OECD, 2013) show that schools in the United States are not helping students achieve acceptable levels of mathematical and numerical proficiency. Therefore, we need to understand how various factors, including mathematics anxiety, affect student performance and persistence in STEM. To do this, a valid and reliable measure of mathematics anxiety is needed. Existing instruments to measure mathematics anxiety have been insufficient in several ways, including in their conceptualization of the construct and use of classical test theory over Rasch measurement theory methods.In this study, an instrument – the Comparative Mathematics Anxiety Scale (CMAS) – was developed to measure the three-dimensional conceptualization of mathematics anxiety that Dr. Caroline Vuilleumier and I originated. A unique, comparative item format adapted from Ludlow et al. (2014, 2019) and Rasch measurement theory (Rasch, 1960/1980) were utilized to mitigate some of the limitations of existing instruments. The overarching research question and three sub-research questions explored whether the CMAS could measure mathematics anxiety in a valid, reliable, and meaningful way. This study employed a seven-step iterative scale development process and was accomplished across three rounds. Ultimately, twenty-three third-person items were developed to capture the emotional-attitudinal, mental-cognitive, and physical-somatic dimensions of mathematics anxiety. Using the Rasch rating scale model, the outcome was the 23-item CMAS that reliably and validly measures increasing levels of three dimensions of mathematics anxiety. The distribution of the items mostly confirmed their hypothesized order and the Rasch measurement theory principles. The scale also provides meaningful interpretations of what a raw score means regarding a student’s experience of emotional-attitudinal, mental-cognitive, and physical-somatic mathematics anxiety. Overall, the findings suggest that the novel approach of combining Rasch measurement theory with third-person items and comparative response options can be successful in developing a scale that measures an important construct. Furthermore, the scale can provide the evidence needed in the provision of interventions and in research to reduce students’ overall experience of mathematics anxiety. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

Background: The use of outcome measures to evaluate upper extremity function after stroke is highly recommended in clinical practice and research. The Chedoke Arm and Hand Activity Inventory (CAHAI) is a recommended measure as it has strong psychometric properties and clinical utility. However, the measure has not been validated in Asia and there are also gaps in the knowledge about the psychometric properties of the CAHAI. Aim & Objectives: This thesis is dedicated to the continued evaluation of the CAHAI with two main objectives: (1) to develop a Singapore version of the CAHAI, and (2) to re-evaluate the original CAHAI using modern test theories. Method: We conducted a study to cross-culturally adapt the CAHAI and evaluated the psychometric properties in a stroke sample in Singapore. Two studies were conducted to re-evaluate the original CAHAI using modern test theories. In the first study, item response theory and Rasch measurement theory were used to evaluate the psychometric properties of the measure. Following which, both measurement theories were used to revise the CAHAI in the second study. Results: Two test items were modified for the Singapore version of the CAHAI, and the measure had good inter-rater reliability (intra-class correlation coefficient = 0.95 – 0.97) and construct validity. The evaluation of the original CAHAI using modern test theories identified three main problems: (1) the scoring scale was not working as intended, (2) local dependency, and (3) the measure was not unidimensional. Revisions to the CAHAI included collapsing the 7-category scale to four categories, deleting two test items, and developing two new shortened versions. Conclusion: The Singapore version of the CAHAI is a valid and culturally relevant outcome measure that can be used to evaluate post-stroke upper extremity function. The original CAHAI was refined into a new 11- and 5-item versions with a 4-category scale which clinicians may find easier to use. / Thesis / Doctor of Philosophy (PhD)