USING INTERNATIONAL STUDY SERIES AND META-ANALYTIC RESEARCH SYNTHESES TO SCOPE PEDAGOGICAL DEVELOPMENT AIMED AT IMPROVING STUDENT ATTITUDE AND ACHIEVEMENT IN SCHOOL MATHEMATICS AND SCIENCE

Taking lower-secondary schooling within the English educational system as an example, this paper illustrates the contribution of two bodies of international scholarship to the scoping of research-based pedagogical development aimed at improving student attitude and achievement in science and mathematics. After sketching the English context of systemic reform, the paper uses findings from the Trends in International Mathematics and Science Study (TIMSS) series to illuminate changes in performance, analysed within a framework of cross-system and between-subject comparison. Contrary to the optimistic picture from national assessment, the TIMSS findings suggest that systemic reform has produced fundamental gains only in student achievement in mathematics, and serious declines in student attitude towards both mathematics and science. Prompted by more favourable patterns elsewhere, the paper then triangulates the findings of recent meta-analytic research syntheses to identify promising lines of pedagogical development. Despite important differences in the conceptual frameworks and analytic methods of these syntheses, reasonably robust conclusions can be drawn about the effectiveness of four teaching components: domain-specific inquiry for student achievement in both subjects, student attitude in science, and learning processes in mathematics; cooperative group work for learning and attitude in science; contextual orientation for achievement in science; and active teaching for achievement in mathematics. Equally, discrepancies between findings or insufficiencies of evidence highlight a number of impacts particularly deserving deeper analysis or further investigation: cooperative group work on achievement outcomes, differing forms of learning assessment on both attitude and achievement outcomes, contextual orientation on outcomes in mathematics, and active teaching on outcomes in science.     

SCIENCE AND MATHEMATICS ACHIEVEMENT IN AUSTRALIA: THE ROLE OF SCHOOL SOCIOECONOMIC COMPOSITION IN EDUCATIONAL EQUITY AND EFFECTIVENESS

In this study, we systematically unpack relationships among student socioeconomic status (SES), science and mathematics achievement, and student interest in science in the context of varying school socioeconomic composition. Using the most recent Programme for International Student Assessment dataset for Australia, we found that increases in school SES are consistently associated with substantial increases in science and mathematics performance. This pattern of association held for all groups regardless of their individual SES. However, our findings also show that students’ interest in science was not associated with varying school SES, and only marginally and inconsistently associated with individual SES. We discuss policy implications and strategies for mitigating the influence of school socioeconomic composition on science and mathematics performance, and for the achievement of more equitable and effective educational outcomes generally.     

EQUITY IN MATHEMATICS AND SCIENCE OUTCOMES: CHARACTERISTICS ASSOCIATED WITH HIGH AND LOW ACHIEVEMENT ON PISA 2006 IN IRELAND

Equity in education is a key concern internationally; however, it is rare that this issue is examined separately for low- and high-achieving students and concurrently across different subject domains. This study examines student and school background characteristics associated with low and high achievement in mathematics and science on the Programme for International Student Assessment. Based on the results of a multilevel multinomial model of achievement for each domain, findings indicate that a greater number of the variables examined are associated with low rather than high achievement. At student level, home language, intention to leave school early, socioeconomic status, grade level, cultural capital, and books in the home are significantly associated with achievement in mathematics and science. At school level, only school average socioeconomic status is statistically significant in the models. Significant gender differences are found in the distribution of high and low achievers, which vary across the domains. In mathematics, females are more likely to be low achievers while males are more likely to be high achievers. In science, gender interacts with early school-leaving intent whereas males intending to leave school early are more likely to be in the low-achieving group than females intending to leave early. Conclusions emphasise the need for targeting resources aimed at promoting equity in outcomes at student level as well as at school level. Future work may extend the current analyses by incorporating domain-specific variables or examining cross-country differences.     

BUILDING MATHEMATICS ACHIEVEMENT MODELS IN FOUR COUNTRIES USING TIMSS 2003

Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries hugely influential in world events (the USA and Russia). In each country, students’ self-concept of ability in mathematics, mathematics values, perception of school, teachers’ and principals’ perceptions of school and other characteristics related to the classroom and school were incorporated to build an achievement model through hierarchical linear modelling. The final achievement models suggested that among student variables, self-concept of ability in mathematics had the highest relation to 8th graders’ mathematics achievement in all 4 countries. The relation between mathematics achievement and other student characteristics, along with the family, teacher and school variables, differed across the 4 countries. This suggests that self-concept of ability is a key variable for understanding achievement in high and low achieving countries and that other contextual variables vary in the magnitude of relations to mathematics achievement across countries.     

QUALITY OF THE TASKS IN THE NEW TURKISH ELEMENTARY MATHEMATICS TEXTBOOKS: THE CASE OF PROPORTIONAL REASONING

This study examines new Turkish elementary school mathematics textbooks to provide perspectives on the quality of the tasks related to the proportion concept and the ways they are presented. Tasks were analysed for several dimensions with a particular focus on their level of cognitive demands (LCD). Tasks were distinguished in two groups in terms of LCD: lower-level demand and higher-level demand. The findings revealed that 75 % of the tasks were related to higher-level demand in that they requested a certain level of interpretation, required connecting knowledge and procedures related to each other, demanded responses with some explanation and reinforced students’ non-algorithmic thinking. Only 25 % of the tasks were related to a lower-level demand, and these tasks could be resolved by recalling and implementing rules, procedures and factual knowledge without reflecting upon the meaning behind them. Most of the tasks were presented in multiple representations and framed in non-mathematical contexts. All these task characteristics indicate that the new elementary school textbooks have the capacity to promote students’ proportional reasoning. The findings also inform the international community about crucial aspects of the curriculum reforms in Turkey and provide suggestions for teachers and textbook writers concerning the quality of the tasks and their selection and implementation in the classrooms.     

CREATING OPTIMAL MATHEMATICS LEARNING ENVIRONMENTS: COMBINING ARGUMENTATION AND WRITING TO ENHANCE ACHIEVEMENT

The issue of mathematics underachievement among students has been an increasing international concern over the last few decades. Research suggests that academic success can be achieved by focusing on both the individual and social aspects of learning. Within the area of mathematics education, the development of metacognitive skills and the incorporation of discourse in classroom instruction has resulted in students having deeper conceptual understandings of the content and increased mathematical achievement. However, studies in this field tend to focus on the effects of these practices separately, making research that seeks to harness the potential of both quite rare. This paper reports on a study that was aimed at addressing this gap in the literature by examining the effects of writing and argumentation on achievement. Two hundred and eleven students and five teachers participated in this multimethod study that investigated the effects of three treatment conditions on mathematical achievement. These conditions were writing alone, argumentation alone, and writing and argumentation combined. Analysis of covariance revealed significant differences between the groups, and tests of the contrasts showed that students who engaged in both argumentation and writing had greater knowledge gains than students who engaged in argumentation alone or neither activity.     

PREDICTING MATHEMATICS ACHIEVEMENT: THE INFLUENCE OF PRIOR ACHIEVEMENT AND ATTITUDES

Achievement in mathematics is inextricably linked to future career opportunities, and therefore, understanding those factors that influence achievement is important. This study sought to examine the relationships among attitude towards mathematics, ability and mathematical achievement. This examination was also supported by a focus on gender effects. By drawing on a sample of Australian secondary school students, it was demonstrated through the results of a multivariate analysis of variance that females were more likely to hold positive attitudes towards mathematics. In addition, the predictive capacity of prior achievement and attitudes towards mathematics on a nationally recognised secondary school mathematics examination was shown to be large (R ²  =  0.692). However, when these predictors were controlled, the influence of gender was non-significant. Moreover, a structural equation model was developed from the same measures and subsequent testing indicated that the model offered a reasonable fit of the data. The positing and testing of this model signifies growth in the Australian research literature by showing the contribution that ability (as measured by standardised test results in numeracy and literacy) and attitude towards mathematics play in explaining mathematical achievement in secondary school. The implications of these results for teachers, parents and other researchers are then considered.     

GENDER DIFFERENCES IN THE INFLUENCE OF EARLY PERCEIVED PARENTAL SUPPORT ON STUDENT MATHEMATICS AND SCIENCE ACHIEVEMENT AND STEM CAREER ATTAINMENT

The lack of females entering STEM careers is well documented. Reasons for the gender gaps at all stages of the educational pipeline include both internal factors such as self-concept and external factors such as the influence of parents, media, and educators. Using latent growth curve analysis and nationally representative longitudinal survey data, this study compares differences in the relationship between a critical external factor (perceived early parental support), student mathematics and science achievement trajectories, and persistence in STEM career by gender. Mathematics and science trajectories were positively related to STEM career persistence for males and females. Perceived early parental support was related to growth in mathematics achievement for males but not females. There was no relationship between early perceived parental support and growth in science achievement for either males or females. These findings indicate differences in the relationship between parental support, achievement, and career persistence depending on content area and gender.     

HOMEWORK AND MATHEMATICS ACHIEVEMENT IN HONG KONG: EVIDENCE FROM THE TIMSS 2003

Though it is generally believed that doing homework promotes better learning, no consensus has been achieved concerning its importance and relevance to students’ achievement. The historical up-and-down status of public attitudes toward homework indicates that understanding about the role of homework in students’ learning is far from comprehensive and clear. The literature shows that much research effort has been devoted to the relationship between amount of homework and achievement, but little on quality of homework and how it has been used. Applying a 2-level hierarchical linear model on the TIMSS 2003 data, this study investigated the relationship between classroom practices on homework and 8th grade students’ mathematics achievement in Hong Kong in three dimensions: frequency and amount of homework, types of homework, and usage modes of homework. The results showed that while the time spent on daily mathematics homework had significantly positive effect on students’ TIMSS results, no effect was observed on the frequency of homework assigned. Out of three types of homework, only homework of the problem/question type demonstrated significant effect. The practice of having students start homework in class had negative influence on students’ learning outcome. Implications and suggestions for educational practice and future research were then discussed.     

THE DIFFERENCES IN SCORES AND SELF-EFFICACY BY STUDENT GENDER IN MATHEMATICS AND SCIENCE

Typically, mathematics and science are seen as linked together, where both subjects involve numbers, critical thinking, and problem solving. Our study aims to develop a better understanding of the connections between student’s achievement scores in mathematics and science, student gender, and self-efficacy. We used the Trends in International Mathematics and Science Study 2007 eighth grade data to answer our research questions and were able to demonstrate that when controlling for self-efficacy, there is a statistically significant difference in the achievement scores between males and females by subject, where females score higher Algebra, but males score higher in the other mathematics subjects. Likewise, we were also able to demonstrate that there is a statistically significant difference in the achievement scores in Earth Science, Physics, and Biology, between males and females where males score higher in science subjects. In both mathematics and science examinations, we controlled for self-efficacy where in mathematics females hold lower self-efficacy then males and in science there is no difference between females and males in terms of self-efficacy. We conjecture that mathematics and science classrooms that consider self-efficacy may impact student’s achievement scores by subject, which can ultimately impact career choices in mathematics- and science-based fields.     

信息与计算科学专业《数学分析》课程的教学改革与实践

在分析<数学分析>课程特点和信息与计算科学专业需要的基础上,围绕素质教育的要求,给出了对信息与计算科学专业<数学分析>课程教学改革的一些体会,提出了一些建议.     

EXAMINING THE RELATIONSHIPS AMONG CLASSROOM CLIMATE, SELF-EFFICACY, AND ACHIEVEMENT IN UNDERGRADUATE MATHEMATICS: A MULTI-LEVEL ANALYSIS

For nearly 50 years, leaders in American industry, military, education, and politics have focused considerable attention on STEM (science, technology, engineering, and mathematics) education. Given the increased societal demand for STEM careers, the relationships among classroom climate, self-efficacy, and achievement in undergraduate mathematics needed to be examined. A purposeful sample of college algebra instructors (n = 15), employed at public 4-year universities in various states (n = 10) across the nation, was administered the Principles of Adult Learning Scale at the beginning of the semester to assess classroom climate. At the end of the course semester, their college algebra students (n = 326) were administered the Mathematics Self-Efficacy Scale-Revised and final college algebra examinations. The results of the multi-level analysis indicated: (a) students having higher mathematics self-efficacy also had higher mathematics achievement, (b) teacher-centered classroom climates had greater mathematics self-efficacy levels, (c) classroom climate was not a significant predictor of mathematics achievement, (c) classroom climate did not moderate the relationship between mathematics self-efficacy and achievement, and (d) although boys reported higher mathematics self-efficacy than girls, gender differences were not found to exist in regard to mathematics achievement.     

RESIDENTIAL SCHOOLS OF MATHEMATICS AND SCIENCE IN THE USA: OVERVIEW OF THE ADMISSION PROCESS

The admission procedures for identifying and selecting students in special residential schools of mathematics and science in the United States were studied through interviews with school officials and examination of the schools’ literature on admissions. The selection criteria included tests of verbal and mathematical aptitudes, home school grade‐point averages, ratings of behavioral characteristics, and interviews. The selection stages included recruitment, application file development, file reviews, interviews, and selection decision making.     

EVALUATING SELECTED PERCEPTIONS OF SCIENCE AND MATHEMATICS TEACHERS IN AN ALTERNATIVE CERTIFICATION PROGRAM

In 2003 the University of Missouri (with the aid of US National Science Foundation funding) initiated an alternative certification program (ACP) to address the well-documented need in the US for increasing the quantity and quality of mathematics and science teachers for the middle and secondary levels. Nationwide current certification programs do not provide the quality and quantity of mathematics and science teachers needed in schools. As a result most American states have begun to experiment with ACPs as a way to address the shortage of math and science teachers. To evaluate the success of this program, we collected data from ACP participants regarding perceived preparation, self efficacy, and outcome expectancy at three time points in the program. State standards for beginning teachers were used to construct a perceived preparation instrument. Analysis of data suggests that over time, ACP participants exhibited an increasingly positive view toward their preparation for classroom teaching, as well as increased self efficacy. However, there was little change in the students’ outcome expectancy over time. In this article we share details of the unique ACP program and we describe steps taken to collect and evaluate a project data set. Our work provides useful guidance to researchers and practitioners in the field of science and mathematics teacher education.     

THE PRACTICALITY OF IMPLEMENTING CONNECTED CLASSROOM TECHNOLOGY IN SECONDARY MATHEMATICS AND SCIENCE CLASSROOMS

Connected classroom technology (CCT) is a member of a broad class of interactive assessment devices that facilitate communication between students and teachers and allow for the rapid aggregation and display of student learning data. Technology innovations such as CCT have been demonstrated to positively impact student achievement when integrated into a variety of classroom contexts. However, teachers are unlikely to implement a new instructional practice unless they perceive the practical value of the reform. Practicality consists of three constructs: congruence with teacher’s values and practice; instrumentality—compatibility with the existing school structures; and cost/benefits—whether the reward is worth the effort. This study uses practicality as a framework for understanding CCT implementation in secondary classrooms. The experiences of three science teachers in their first year implementing CCT are compared with matched-pair mathematics teachers. Findings suggest that despite some differences in specific uses and purposes for CCT, the integration of CCT into regular classroom practice is quite similar in mathematics and science classrooms. These findings highlight important considerations for the implementation of educational technology.