Thesis (M.A.). / Written for the Dept. of Integrated Studies in Education. Title from title page of PDF (viewed 2008/08/07). Includes bibliographical references.

The purpose of this study is to investigate gender differences in mathematics anxiety and its relationship to test anxiety, trait anxiety, high school mathematics participation, and mathematics attitudinal factors in community college students. It takes place at a small rural community college in California, in which the majority population is Hispanic. The study relies primarily on quantitative methods, but includes a small qualitative component in the form of focus group interviews to confirm and enhance the findings. There were several main findings in the sample studied. Women scored significantly higher in mathematics anxiety than males among all age groups, ethnicities, and mathematics levels. Furthermore, the size of the gender gap in mathematics anxiety was not affected by age, ethnicity, or mathematics level. Significant relationships were found between mathematics anxiety and test anxiety, worry, emotionality, trait anxiety, self-confidence in mathematics, effectance motivation in mathematics, perceived usefulness of mathematics, and number of years of high school mathematics. Moreover, these relationships appeared to be approximately the same across samples of females and males, regardless of age, ethnicity, or mathematics level. Among the significant predictors of mathematics anxiety of particular importance were a lack of self-confidence in mathematics, a high presence of test anxiety—specifically emotionality—and a low presence of effectance motivation in mathematics. Follow-up focus group interviews suggested additional factors that could be related to mathematics anxiety, among which were an unpleasant experience with mathematics at the elementary or junior high school level, the requirement of having to follow precise steps in obtaining an exact answer, and the perception that the terminology of the mathematical language was confusing.

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.

The purpose of this study was to explore the relationship between the attitude toward mathematics, including related mathematics anxiety, and the frequency of classroom observations of mathematics lessons by elementary school administrators. This study considered Approach-Avoidance Motivation as part of the conceptual framework guiding the research. Approach-avoidance motivation refers to a person's approach of tasks that are pleasant or enjoyable and avoidance of tasks that are disliked or not enjoyable. This research sought to answer the questions: 1. What is the academic background in mathematics of elementary school administrators? 2. What is the attitude toward mathematics of elementary school administrators? 3. What is the frequency of classroom observations of mathematics lessons by elementary school administrators? 4. What, if any, is the relationship between the attitude toward mathematics, including related mathematics anxiety, and the frequency of classroom observations of mathematics lessons by elementary school administrators? The participants in this study included elementary school principals and assistant principals in one school division in Virginia. Data were collected to investigate the mathematics background, attitude toward mathematics, and frequency of classroom observations of mathematics lessons by elementary school administrators. This study also examined the possible relationship between the attitude toward mathematics, including related mathematics anxiety, and the frequency of classroom observations of mathematics lessons. The attitude toward mathematics, including related mathematics anxiety, was found to have no relationship with the frequency of both formal and informal classroom observations of mathematics lessons conducted. The sample population data indicated positive attitudes toward mathematics and low levels of mathematics anxiety, which conflicts with some previous research (Dorward and Hadley, 2011; Hembree, 1990). The mathematics background of participants was found to be limited in the number of mathematics courses completed and teaching licensure endorsements specific to mathematics instruction. The findings provide educational leaders with relevant research related to attitude toward mathematics and the instructional leadership practice of observing mathematics classrooms. Central office and school leaders could benefit from explicit expectations relating to the observation of mathematics lessons in schools. / Ed. D. / The purpose of this study was to explore the relationship between the attitude toward mathematics, including related mathematics anxiety, and the frequency of classroom observations of mathematics lessons by elementary school administrators. This study considered aspects of avoidance theory as part of the conceptual framework guiding the research. Approach-avoidance motivation refers to a person’s approach of tasks that are pleasant or enjoyable and avoidance of tasks that are disliked or not enjoyable. Elementary school principals and assistant principals in one school division in Virginia participated in this study. Data were collected to investigate the mathematics background, attitude toward mathematics, and frequency of classroom observations of mathematics lessons by elementary school administrators. This study also examined the possible relationship between the attitude toward mathematics, including related mathematics anxiety, and classroom observations of mathematics lessons. The attitude toward mathematics, including related mathematics anxiety, was found to have no relationship with the frequency of classroom observations of mathematics lessons conducted. The study data indicated positive attitudes toward mathematics and low levels of mathematics anxiety in study participants, which conflicts with some previous research (Dorward & Hadley, 2011; Hembree, 1990). The mathematics background of participants was found to be limited in the number of mathematics courses completed and license endorsements specific to mathematics teaching. The findings provide educational leaders with relevant research related to attitude toward mathematics and the instructional leadership practice of observing mathematics classrooms. Central office and school leaders could benefit from explicit expectations relating to the observation of mathematics lessons in schools.

Children show large individual differences in numerical skills, even before they begin formal education. These early differences have significant and long-lasting effects, with numerical knowledge before school predicting mathematical achievement throughout the primary and secondary school years. Currently, little is known about the dispositional factors influencing children's numerical development. Why do some children engage with and succeed in mathematics from an early age, whilst others avoid mathematics and struggle to acquire even basic symbolic number skills? This thesis examines the role of two dispositional factors: First, spontaneous focusing on numerosity (SFON), a recently developed construct which refers to an individual's tendency to focus on the numerical aspects of their environment; and second, mathematics anxiety (MA), a phenomenon long recognised by educators and researchers but one which is relatively unexplored in young children. These factors are found to have independent effects on children's numerical skills, thus the empirical work is presented in two separate parts. The SFON studies start by addressing methodological issues. It is shown that the current measures used to assess children's SFON vary in their psychometric properties and subsequently a new and reliable picture-based task is introduced. Next, the studies turn to theoretical questions, investigating the causes, consequences and mechanisms of SFON. The findings give rise to three main conclusions. First, children's SFON shows little influence from parental SFON and home numeracy factors. Second, high SFON children show a symbolic number advantage. Third, the relationship between SFON and arithmetic can be explained, in part, by individual differences in children's ability to map between nonsymbolic and symbolic representations of number. The MA studies focus primarily on gender issues. The results reveal no significant differences between boys' and girls' overall levels of MA; however, there are gender differences in the correlates of MA. Specifically, boys' (but not girls') MA is related to parents' MA. Moreover, the relationship between MA and mathematical outcomes is stronger for boys than it is for girls. Possible causal explanations for these gender differences are explored in two ways: First, by examining the reliability of the scales used to assess MA in boys and girls. Second, by investigating the relationship between girls' (and boys') mathematics anxiety and their societal math-gender stereotypes. The findings from both sets of studies draw a link between children's emerging dispositions towards mathematics and their early numerical skills. Future research needs to examine how these dispositional factors interact with other (cognitive and non-cognitive) predictors of mathematics achievement.

A solid understanding of basic mathematics is essential for many practical, everyday tasks and good mathematical skills are increasingly necessary in the workplace. For some, however, mathematics can evoke an adverse emotional reaction, increasingly recognised in both psychology and education as 'Mathematics Anxiety' (MA); nationally funded projects are currently undertaking research in this area. Studies show that MA can develop in early childhood and increase in intensity with age; this emphasises the importance of early intervention and educational psychologists are well-placed to promote and support this. Paper One details a systematic literature review evaluating the impact and effectiveness of interventions on the reduction of MA in school-aged children. Nine studies, published between 2010 and 2017, met inclusion criteria and were assessed using quality frameworks. Findings indicated that MA might be amenable to intervention in children aged between seven and eighteen years; potential factors contributing to effective amelioration were identified and discussed. In Paper Two, the relationship between MA and working memory (WM) is highlighted and explored. Having established a possible bi-directional relationship, a quasi-experimental, empirical study aimed to assess the potential benefits of WM training for reducing MA. A comparison group completed activities encompassing many of the potentially effective factors identified in Paper One. 50 children, aged between eight and nine years, participated in six-week long interventions. MA was measured through self-report and qualitative questionnaires; data were analysed quantitatively (using descriptive and inferential statistics) or qualitatively (using content analysis) respectively. Findings question the validity of self-report measures of MA in this age group and implications for effective intervention are considered. Paper Three provides an overview of the concepts of evidence-based practice and practice-based research in addition to considering current literature in relation to effective dissemination of research. Implications resulting from the current research are discussed alongside the proposed dissemination strategy.

A mixed methodological approach was used to examine the effects of fourth- and first-grade students cross-age tutoring on mathematics anxiety. 37 Fourth-grade tutors, both trained and untrained, helped 37 first graders use multiple strategies to solve mathematical word problems for 10 weeks. A control group of 16 first-grade students completed the problems independently. Pre-test and post-test mathematics anxiety measures were used. Observations were also conducted throughout the study. The measures used for both primary and intermediate students were effective in identifying students with mathematics anxiety. However, quantitative findings showed no difference for fourth- or first-grade students on mathematics anxiety measures. Results of an ANOVA were not significant. The qualitative findings revealed the trained tutors and their partners were the most structured. They tried more strategies to solve problems and stayed on task better than other groups. Untrained tutors and their partners needed more redirection and engaged in more off-task conversations. First graders with tutors received more positive reinforcement than those who worked independently.

A convenience sample of 123 Hispanic/Latino students from a predominantly Hispanic/Latino South Texas community college was used to determine if gender and/or journal-writing had any effects on mathematics anxiety or achievement. Eight sections of college-algebra courses were administered the Mathematics Anxiety Rating Scale (MARS) to determine levels of mathematics anxiety and the Texas Higher Education Assessment (THEA) to determine levels of mathematical achievement. Results of the study suggest that journal-writing decreases levels of mathematics anxiety among students. In addition, the study suggests that males and females do not differ in terms of mathematical achievement. These finding are consistent with previous studies. However, the study also suggested that males and females report the same levels of mathematics anxiety and that journal-writing does not increase mathematical achievement. This is in contrast to previous published studies.

A convenience sample of 123 Hispanic/Latino students from a predominantly Hispanic/Latino South Texas community college was used to determine if gender and/or journal-writing had any effects on mathematics anxiety or achievement. Eight sections of college-algebra courses were administered the Mathematics Anxiety Rating Scale (MARS) to determine levels of mathematics anxiety and the Texas Higher Education Assessment (THEA) to determine levels of mathematical achievement. Results of the study suggest that journal-writing decreases levels of mathematics anxiety among students. In addition, the study suggests that males and females do not differ in terms of mathematical achievement. These finding are consistent with previous studies. However, the study also suggested that males and females report the same levels of mathematics anxiety and that journal-writing does not increase mathematical achievement. This is in contrast to previous published studies.

My dissertation research explored the experiences of mathematics anxieties in women elementary preservice teachers while learning mathematics as K-12 students and while learning to teach mathematics. Previous studies conducted in mathematics teacher education have emphasized the importance of preservice teachers' mathematical knowledge for teaching, as a confident and competent mathematics teacher is a vital necessity in the classroom (Beilock, Gunderson, Ramirez, & Levine, 2010; Gavin & Reis, 2003; Huebner, 2009). As evidence of elementary preservice teachers' anxiety, I analyzed three women preservice teachers' oral and written narratives about their experiences with learning mathematics and learning to teach mathematics, which I collected over eighteen months at key moments in their teacher preparation program. My findings have revealed that for some women elementary preservice teachers, mathematics anxiety may be an issue or concern that remains consistent and recurs for decades. In fact, the multiple stories that the three preservice teachers had to tell indicated that their experiences in learning mathematics led them to develop a unique coping strategy to deal with mathematics anxiety. They continued to utilize their strategy repeatedly across their experiences as a student learning mathematics and learning to teach mathematics, even when the strategy sometimes failed to protect them from stress, embarrassment, and demoralization. Moreover, these coping strategies appeared to become so powerful that when the women confronted situations in which they felt expected to know mathematical content that they did not understand, they used their unique strategies for coping with mathematics anxiety rather than seriously attempting to learn that content. In this manner, these coping strategies often appeared to have injurious effects on their mathematics learning. Given that my study only included three participants, I suggest future research that mathematics teacher education researchers may want to consider. I also propose ways in which mathematics teacher educators might address issues of mathematics anxiety in elementary teacher preparation programs.