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.     

The transition to secondary school geometry: can there be a “chain of school mathematics”?

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels.     

Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks

This study is grounded in the theoretical position that solving problems in different ways creates mathematical connections when learning and teaching mathematics. It acknowledges the central role teachers play in providing students with learning opportunities, and it is based on the empirical finding that mathematics teachers are reluctant to solve problems in different ways in the classroom. In this paper we address the contradiction between theory-based recommendations and school mathematics practice. Based on analysis of individual interviews and two group meetings with 12 Israeli secondary school mathematics teachers, we demonstrate that in the context of multiple-solution connecting tasks this discrepancy is caused by the situated nature of the teachers’ knowledge. We also reveal the complex relationship between different types of teacher knowledge and argue the significance of developing a common language between members of the mathematics education community, including teacher educators and researchers. The names of the teachers have been changed to protect their privacy.     

The effects of motivational constructs and engagements on mathematics achievements: a comparative study using TIMSS 2011 data of Chinese Taipei,Singapore, and the USA

Motivational constructs and students’ engagements have great impacts on students’ mathematics achievements, yet they have not been theoretically investigated using international large-scale assessment data. This study utilized the mathematics data of the Trends in International Mathematics and Science Study 2011 to conduct a comparative and empirical study on exploring: (1) the changes of motivational constructs from 4th grade to 8th grade; and (2) the effects of motivational constructs from the expectancy-value model and students’ engagements on mathematics achievements. The countries investigated include Chinese Taipei, Singapore, and the USA. The results showed that: (1) students’ motivations deteriorate over school years; (2) self-confidence in mathematics (SCM) has the strongest relationship with mathematics achievements. Furthermore, it is evident that Singapore has the most effective schools in students’ mathematics education. More findings of this comparative study are subsequently discussed.     

Poles Apart? An exploration of single-sex and mixed-sex educational environments in Australia and England

This paper contributes to debates on the benefits of single-sex and co-educational school environments by considering both single-sex versus co-educational schools and single-sex versus co-educational classes in co-educational schools. Two research studies provide the empirical basis for this discussion. One study was a 10-year-long investigation of two Australian secondary schools which had been single-sex schools and became co-educational secondary schools over a two-year period. The second study involved a two-year investigation in an English co-educational secondary school where single-sex mathematics classes were introduced for one cohort of pupils for five school terms, after which mixed-sex classes were reintroduced. Evidence relating to academic self-concept, pupil, parent and staff perceptions and academic achievement are discussed. Overall, the evidence suggests that co-educational environments create possible social/interaction disadvantages for girls, but that academic self-concept is not adversely affected by transferring from single-sex environments into mixed-sex ones.     

微课教学技术支持下的中职数学教学反思

数学是中职教育阶段一门非常重要的基础学科,由于长期以来人们对中职教育存在错误的认识,中职院校的生源普遍基础很差,因此,在数学知识的学习方面很多学生都感到压力很大。文章通过对中职数学教学中存在问题的反思,提出利用微课技术这种新的教学方式改善中职数学教育的方法,以此来提高中职数学教学的质量。     

Effects of an Ancient Chinese Mathematics Enrichment Programme on Secondary School Students’ Achievement in Mathematics

Ancient Chinese mathematics has been the focus of many research studies and scholarly works from a historical perspective. However, no move has been made to investigate its role in the teaching and learning of mathematics. This pilot study examined the effects of an Ancient Chinese Mathematics Enrichment Programme (ACMEP) on the academic achievement of second-year students from a secondary school in Singapore – a strand of a principle study with the intent of investigating the possible roles of ancient Chinese mathematics in the Singapore secondary school mathematics curriculum. Analysis of covariance was used to examine the difference in mean scores on a variety of formal assessments in mathematics between students who participated in the ACMEP and those who did not. In addition, the scores on formal assessments of other relevant subjects were analyzed to further investigate the ACMEP’s scope of influence.     

Effects of an Ancient Chinese Mathematics Enrichment Programme on Secondary School Students’ Achievement in Mathematics

Ancient Chinese mathematics has been the focus of many research studies and scholarly works from a historical perspective. However, no move has been made to investigate its role in the teaching and learning of mathematics. This pilot study examined the effects of an Ancient Chinese Mathematics Enrichment Programme (ACMEP) on the academic achievement of second year students from a secondary school in Singapore—a strand of a principal study which had the intent of investigating possible roles of ancient Chinese mathematics in the Singapore secondary school mathematics curriculum. Analysis of covariance was used to examine the difference in mean scores on a variety of formal assessments in mathematics between students who participated in the ACMEP and those who did not. In addition, scores on formal assessments of other relevant subjects were analyzed to further investigate ACMEP’s scope of influence.     

“‘数学文化’教育观”下中学数学教学模式

数学被看作是一种特殊的文化,已经被纳入新课程理念中来。但是把数学文化作为一种教育观提出还是第一次,文章将从“‘数学文化’教育观”的角度,对中学数学教学模式进行初步的研究和探索。旨在使中学数学教学模式的研究再上一个新的层次。     

Modeling Change in Student Attitude Toward and Beliefs About Mathematics

Abstract

The authors used data from the Longitudinal Study of American Youth to investigate variables related to change in students' attitude toward and beliefs about mathematics in middle school and high school. Using hierarchical linear modeling techniques, the authors modeled variation in students' rate of change with variables associated with student characteristics, instructional experiences, and environment. They also identified variables that differentially affect change at different levels of secondary school (i.e., middle school vs. high school) and for different affective dimensions (i.e., attitude toward mathematics, beliefs about the social importance of mathematics, and beliefs about the nature of mathematics). Results showed a substantial negative change in students' attitudes toward and beliefs about the social importance of mathematics throughout secondary school. However, students' notions of the nature of mathematics did not change throughout secondary school. The authors identified variables related to change and found that they differed according to the level of secondary school and affective dimensions.     

Zwischen Schule und Universität: Argumentation in der Mathematik

Several studies show that university students in Germany still have problems in reasoning mathematically although this already should be fostered at high school since the implementation of standards for school mathematics. Mathematical argumentation is a core competence and highly important, especially in academic mathematics. To foster mathematical argumentation at the beginning of university studies, competence models are needed which give more detailed insights in the skills that are necessary for reasoning. As mathematical argumentation is a complex process, especially at the higher secondary level or at university, many little steps are needed to complete a competence model for argumentation at the secondary–tertiary transition gradually. A possible step can be to initially identify several aspects of mathematical argumentation competence that influence the reasoning quality. The empirical basis for identifying those aspects is a cross-sectional study with 439 engineering students who participate in a transition course in mathematics. We address the following questions: (1) how is the quality of student’s reasoning? (2) Which kind of arguments do students use? (3) What resources do students who reasoned correctly use for solving the problems? (4) Does the content of the tasks play an important role? The results show a great influence of the content on the reasoning quality, especially if the content is abstract or concrete. Argumentation quality of students decreases with an increasing level of abstraction of the content. Furthermore, the results reveal that students often use routines for solving the problems. That indicates that procedural approaches still play an important role in school mathematics. If procedures could be used for solving the tasks, students are more successful. Competence models for mathematical argumentation at the beginning of the tertiary level should, therefore, include these factors.     

Working for learning: teaching assistants developing mathematics for teaching

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.     

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.     

高等代数观点下的中学数学问题研究

运用高等代数的理论、方法、思想与观点剖析中学数学相关内容的若干问题,加强课程教学中理论联系中学数学实际,探索高等数学观点对中学数学教学的指导作用,深化理解中学数学的相关内容,促进高中数学新课程的改革与实践。     

Teaching students with Down syndrome in regular classrooms in Ghana: views of secondary school mathematics teachers

ABSTRACT

The recent development of making secondary school education free in Ghana has raised concerns about the level of preparedness of teachers to teach students with diverse needs in one classroom. Significantly, mathematics is one of the core areas that the Ghanaian government has prioritised, and it has institutionalised mechanisms to encourage participation by many students. Accordingly, this qualitative study aimed to document the level of preparedness of mathematics teachers to support the teaching of students with Down syndrome in secondary school classrooms. Twenty-seven mathematics teachers from 14 schools, made up of 18 males and nine females, took part in the study. We found that participants were in favour of implementation of inclusive education. However, regarding the prospect of teaching students with Down syndrome, most of the participants thought that the regular secondary school classroom is not a suitable environment for these students to access education, especially due to a number of challenges. The need for the government to support schools with appropriate teaching materials and facilities is discussed extensively.     

Contemporary poetry for the high school

The inadequate number of American young adults selecting a scientific or engineering profession continues to be a major national concern. Using data from the 23-year record of the Longitudinal Study of American Youth (LSAY) and working within the social learning paradigm, this analysis uses a set of 21 variables to predict young people's employment in science, technology, engineering, mathematics, or medicine (STEMM) at ages 36 to 39. The LSAY is one of the longest and most intensive longitudinal studies of the impact of secondary education and postsecondary education conducted in the United States. Using a structural equation model, the study found that mathematics continues to be a primary gateway for STEMM professions, beginning with algebra track placement in grade eight and continuing through high school and college calculus courses. Home and family factors such as parent education and parent encouragement of science and mathematics during secondary school also enhanced the likelihood of entering a STEMM profession.     

中职数学教学中体验式教学法的运用探析

体验式教学法在数学教学中的有效应用,能让学生在开放的思维空间里,通过自我实践,正确理解教学内容,有助于学生合作交流、自主学习、探索发展能力的提高。文章基于中职数学教学中存在的问题,结合运用体验式教学的可行性研究,从激发学习兴趣、注重联系生活、结合专业知识三个方面探讨中职数学教学中运用体验式教学法的策略。     

Single-sex schooling,gender and educational performance: Evidence using PISA data

The advantages and disadvantages of single-sex schooling continue to be a source of policy and public debate. Previous empirical evidence is somewhat ambiguous, with some studies finding a positive impact of single-sex schooling on education achievement and others finding no differences across school types. The relationship between single-sex schooling on academic outcomes is typically problematic to examine, as in most countries single-sex schools are selective and the numbers attending them are relatively small. In Ireland, a high proportion of secondary school children (~1/3) attend a single-sex school. In addition, these schools are largely state-funded and non-selective but differing in composition compared to mixed-sex schools. For this reason, the Irish educational system provides an interesting setting for exploring the outcomes of single-sex schooling. In this context, this study utilises the 2018 PISA data for Ireland to examine the relationship between single-sex education and mathematics, reading and science literacy performance for boys and girls, respectively, as well as differences across gender in these outcomes. We find significant raw gaps in reading, science and mathematics scores between females in single-sex and mixed-sex schools and in mathematics scores for males across the same school types. However, after controlling for a rich set of individual, parental and school-level factors we find that, on average, there is no significant difference in performance for girls or boys who attend single-sex schools compared to their mixed-school peers in science, mathematics or reading. In terms of heterogeneous analysis, this finding is consistent across the performance distribution.