Jesse L. M. Wilkins

Mathematics and Science Self-Concept: An International Investigation

Using data from different countries, the author conducted an international investigation of the relationship between mean country mathematics and science self-concept and respective mean country achievement and geographic region. In addition, the relationship between self-concept and gender and age was compared for the different countries. Findings showed, at the student level, an overall positive relationship between achievement and self-concept in the countries investigated. However, at the country level, a negative relationship was found. Overall, there was a gender gap in favor of males and a developmental gap suggesting that mathematics and science self-concept decline as students grow older. Implications for mathematics and science education are discussed.

Using Self-Efficacy as a Construct for Evaluating Science and Mathematics Methods Courses

The focus of this study was elementary preservice teachers’ development as effective teachers of science and mathematics as influenced by their participation in elementary science and mathematics methods courses. Preservice teachers’ reports of factors that influenced their perception of their teaching abilities were analyzed according to Bandura’s (1994) 4 sources of efficacy: mastery experiences, vicarious experiences, social persuasion, and stress reduction. This investigation allowed the researchers to evaluate the courses based on these sources. The analysis indicated all 4 sources influenced preservice teachers’ teaching self-efficacy beliefs, with mastery experiences considered the most influential. Embedded within discussions of mastery experiences were references to the other sources of efficacy, which suggest an interrelationship between mastery experiences and the other sources.

Time in the Arts and Physical Education and School Achievement.

With the increase in state‐mandated high‐stakes testing across the USA, schools and school districts are considering ways of increasing instructional time for core curricular subjects such as mathematics, science, English, and social studies. One seemingly logical approach to improving test scores is to reduce the time spent in subjects that are not tested, most notably art, music, and physical education, thus increasing time for the tested subjects. In this study, data was collected from 547 Virginia elementary school principals who completed a survey indicating the time specialists taught art, music, and physical education in their schools. After controlling for socio‐cultural opportunities associated with the school community, partial correlations between time allocation and school‐level passing rates on the Virginia Standards of Learning tests indicated no meaningful relationship between time allocation to art, music, and physical education and school achievement. The findings from the study do not support the notion that a reduced time allocation to art, music, and physical education is related to higher test scores.

Predicting Student Growth in Mathematical Content Knowledge

Abstract Using national longitudinal data, the authors investigated factors related to student learning or growth in statistics, algebra, and geometry in middle school and high school. The authors used hierarchical linear models to model variation in student rate of growth with factors associated with student characteristics and instructional and environmental factors. In addition, the authors designed the study to identify factors that differentially affect student growth at different levels of secondary school (middle school vs. high school) and for different mathematical content areas (statistics, algebra, geometry). Results indicated substantial growth in all 3 content areas in both middle school and high school. Factors related to student learning were identified and found to differ by level of secondary school and content area.

INVESTIGATING CORRELATES OF MATHEMATICS AND SCIENCE LITERACY IN THE FINAL YEAR OF SECONDARY SCHOOL

The concepts of mathematics and science literacy have been ongoing subjects of debate in both the mathematics and science education communities, at large, and within TIMSS, in particular. While many reform initiatives in mathematics and science education around the world point to mathematics and science literacy as an important goal of education (e.g., Australian Education Council, 1991; National Council of Teachers of Mathematics [NCTM], 2000; National Research Council, 1989, 1996; New Zealand Ministry of Education, 1992), there is no clear consensus as to what constitutes mathematics and science literacy, because the notion of “literacy” has a complex and dynamic nature, and it is not easily defined (Bybee, 1997; Koballa, Kemp, & Evans, 1997; Shamos, 1995; Steen, 1997). Many scholars have discussed the significance of literacy as an overarching goal of education (Apple, 1993; Ferdman, 1990) and the problems associated with defining and developing mathematics and science literacy (Lee, 1997; Pollack, 1994; Pool, 1990; Steen, 1997). Further, there is a need to understand the factors that influence the development of mathematics and science literacy. With this in mind this chapter outlines one conceptualization of mathematics and science literacy employed in TIMSS—facility with mathematics and science as it may occur in real life (Orpwood & Garden, 1998)—and attempts to identify factors related to the development of this literacy in 16 countries that participated in the literacy component of TIMSS. An important step towards a richer understanding of literacy is exploring its sociocultural aspects. This suggests that the notions of mathematics and science literacy do not only refer to educational achievements but also to social ones; consequently, such notions evolve over time. Moreover, what constitutes and influences literacy may differ from one region of the world to another. Therefore, an international exploration of the sociohistorical circumstances under which mathematics and science literacy evolve—such as the student or school level factors

Testing the MUSIC Model of Academic Motivation through confirmatory factor analysis

The purpose of this study was to provide empirical evidence to confirm the theoretical factor structure of the MUSIC Model of Academic Motivation that was developed to help instructors understand how current motivation research can be applied to instruction. We hypothesised the MUSIC model as a hierarchical five-factor correlated model and compared its fit to alternative models. Our research question was: Is a hierarchical five-factor correlated model a valid representation of the MUSIC model? The study included 1228 undergraduate students from three different types of university courses. We measured the constructs associated with the main components of the MUSIC model: empowerment, usefulness, success, interest and caring. Results of the confirmatory factor analyses provided strong evidence that the hierarchical five-factor correlated model was a valid representation of the MUSIC model. Thus, the MUSIC model consists of components that are theoretically and empirically correlated, yet distinct.

Modeling Quantitative Literacy

Quantitative literacy is a habit of mind that is characterized by the interrelationship among a person’s everyday understanding of mathematics, his or her beliefs about mathematics, and his or her disposition toward mathematics. To assess quantitative literacy, it is important to devise measurement tools that provide valid and reliable information about a person’s quantitative literacy. In this study, exploratory factor analysis and confirmatory factor analysis were used to build and evaluate a measurement model of quantitative literacy. Data from the Second International Mathematics Study (SIMS) were used to create calibration (N = 1,429) and validation samples (N = 1,429) of high school students for testing an initial model and cross-validation. An additional sample of high school students (N = 1,429) collected from the midwestern part of the United States was used in a replication study. In each stage, a hierarchical three-factor model was compared with two alternative rival models: a one-factor model and a hierarchical two-factor model. The results of the analyses supported the structure of the hierarchical three-factor model. Implications and limitations associated with the findings from the study are discussed.

Social Interactions and Instructional Artifacts: Emergent Socio-Technical Affordances and Constraints for Children's Geometric Thinking

The reported exploratory study consisted primarily of classroom visits, videotaped sessions, and post-treatment interviews whereby second graders (n = 12) worked on problems in planar geometry, individually and in triads, using physical and virtual manipulatives. The goal of the study was to: 1) characterize the nature of geometric thinking found within the interrelationships of social interactions and instructional artifacts; and 2) describe this nature of thinking in terms of instructional artifact transparency. Juxtaposing collective and individual views of mediated inquiry, we analyze interrelationships to reveal qualitatively different influences on geometric thinking for three conceptually related tasks using manipulatives. Our examination of interrelationships between social interactions and instructional artifacts leads to insights for designing and evaluating instructional technologies for early elementary mathematics, including emerging multi-touch, multi-user systems.

Students’ Quality of Mathematical Discussion and Their Self-Determination in Mathematics

Abstract Mathematical discussion allows for students to reflect upon math concepts and understand such concepts at a deeper level. This process of reflection requires a certain amount of internalization on the part of the student. This internalization is facilitated by meeting the needs of autonomy, competence, and relatedness as advocated by Self-Determination Theory. The current study provides evidence of a relationship between fulfillment of these psychological needs and the quality of mathematical discussion students report they engage in. Correlational analyses and structural equation modeling of data from 176 high school Geometry students were conducted to examine this relationship. Results support the claims of a connection between fulfillment of students’ autonomy, competence, and relatedness and their reported engagement in mathematical discussion.

Communicating Quantitative Literacy: An Examination of Open-Ended Assessment Items in TIMSS, NALS, IALS, and PISA

Quantitative Literacy (QL) has been described as the skill set an individual uses when interacting with the world in a quantitative manner. A necessary component of this interaction is communication. To this end, assessments of QL have included open-ended items as a means of including communicative aspects of QL. The present study sought to examine whether such open-ended items typically measured aspects of quantitative communication, as compared to mathematical communication, or mathematical skills. We focused on public-released items and rubrics from four of the most widely referenced assessments: the Third International Mathematics and Science Study (TIMSS-95): the National Adult Literacy Survey (NALS; now the National Assessment of Adult Literacy, NAAL) in 1985 and 1992, the International Adult Literacy Skills (IALS) beginning in 1994; and the Program for International Student Assessment (PISA) beginning in 2000. We found that open-ended item rubrics in these QL assessments showed a strong tendency to assess answeronly responses. Therefore, while some open-ended items may have required certain levels of quantitative reasoning to find a solution, it is the solution rather than the reasoning that was often assessed.