Meaningful mathematics in the middle years

This paper describes an action research project that investigated issues concerning the teaching and learning of numeracy in the middle years. Building on research concerning the middle years of schooling, and their own experience of teaching mathematics in years 5 - 8, a group of teachers, drawn from four schools, trialed strategies intended to improve the engagement, attitudes and outcomes of their students in mathematics. The group recommended at the end of the study that mathematics needs to be meaningful for young adolescents. The concept of meaningful mathematics is explored through a description of the actions and findings of the teachers participating in this project.

The "strugglers" in selected computer based mathematics classrooms

In this paper, the experiences of lower achieving mathematics students in two secondary mathematics classrooms in which computers were regularly used are described. A year 8 and a year 9 mathematics class from one secondary school participated in the ethnographic study. The results show that in these two classrooms the learning relationships and power relationships did not, in general, support the learning and engagement of lower achievers in mathematics. Research into computer based teaching methods that engage low achieving students in computer based mathematics is needed.

Questions in primary mathematics classrooms

In this paper the types of questions that primary teachers use when teaching mathematics are discussed. Teachers from five primary schools participated in a professional development program designed to improve the quality of questioning in mathematics classrooms. Changes in their practice as they perceived them are presented.

Windows on practice : investigating equity in technology based mathematics classrooms

The strengths and weaknesses of using ethnographic research to investigate equity in a study of a grade 9 class that used a dynamic geometry program with laptop computers will be presented. It will be argued that research approaches that involve “windows on practice” provide understanding of not only who is advantaged and disadvantaged in technology-mediated classrooms but how this occurs. The way that other paradigms such as reflexive methods may enhance qualitative research will be proposed. Studies that involve “windows on equitable practice” will provide mathematics educators with models for advancing equity in mathematics learning when teaching with technology.

Trends and factors concerning gender and mathematics in Australasia

For many years now gender differences in average mathematics achievement in Australia and New Zealand have not been significant in large-scale domestic and international studies. However there is some recent evidence, from Australia at least, that gender differences in achievement favouring males may be re-emerging and, despite some positive affective findings and trends with respect to affect and participation leading up to the turn of the century, a pattern of lower interest and declining participation in mathematics among girls is evident. In this paper, trends in gender equity with respect to participation, achievement and affect reported in the literature over the past decade will be presented and analysed. Of particular interest are the factors that may have influenced these trends. Findings from recent research will be discussed. However it would seem that the attempts made by researchers to explain these trends are either limited in their capacity to establish an explanation or imply a deficit view of girls. An alternate position on gender equity and explanation of these trends will be presented in this paper with the purpose of making a contribution to the debate on curriculum and pedagogy in mathematics education.

Girls back off mathematics again : the views and experiences of girls in computer based mathematics

The views and experiences of girls in two co-educational mathematics classrooms in which computers were regularly used were researched. Data were collected by observation and videotaping of lessons, questionnaire, and interviews of students and the teachers. In this paper case studies of six girls are presented. Their ‘stories’ reveal a diversity of experiences and views and multiple gender identities. High achieving girls persisted as “outsiders within,” other girls “backed off”, and exceptional girls challenged gender stereotypes. Implications for social justice in mathematics in the age of the super highway are discussed.

Showcasing recent Australian research in gender and mathematics

In this paper findings from a recent review of Australian research on gender issues in mathematics education (Vale, Forgasz & Horne, 2004) are presented.

Student views of computer based-mathematics in the middle years : does gender make a difference?

How the use of computers in mathematics classrooms was viewed by students in two middle years mathematics classrooms was the focus of the research described in this paper. The primary data sources consisted of questionnaires, classroom observations supported by videotaping of mathematics lessons, and interviews with two girls and two boys from each class. Thus both qualitative and quantitative methods were used. Girls viewed the computer-based lessons less favourably than did boys. In general, the boys were likely to believe that computers contributed to their experiencing pleasure in these lessons, and to making mathematics more relevant to them. Girls were typically more concerned about whether computers facilitated learning and enabled success in mathematics. The attitudes of students to computer-based mathematics were related to their views of computers.

Teaching and learning mathematics and science in a second or third language

 This study investigates the interaction between languages used for particular purposes in mathematics and science classrooms and the accompanying multimodal resources that support teachers’ strategies. The dual investigation sets this study apart, and produces its originality and contribution to the field. It develops a novel multimodal description of pedagogic strategies in multilingual mathematics and science classrooms in Malaysia.

Potential scenarios for Internet use in the mathematics classroom

Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation of tools. This kind of research led to the theoretical perspective presented in this paper: knowledge is constructed by collectives of humans-with-media. In this paper, I will discuss how media have shaped the notions of problem and knowledge, and a parallel will be developed between the way that software has brought new possibilities to mathematics education and the changes that the Internet may bring to mathematics education. This paper is, therefore, a discussion about the future of mathematics education. Potential scenarios for the future of mathematics education, if the Internet becomes accepted in the classroom, will be discussed. © FIZ Karlsruhe 2009.

Dynamics of change of mathematics education in Brazil and a scenario of current research

Mathematics education in Brazil, if we consider what one may call the scientific phase, is about 30 years old. The papers for this special issue focus mainly on this period. During these years, many trends have emerged in mathematics education to address the complex problems facing Brazilian society. However, most Brazilian mathematics educators feel that the separation of research into trends is a theoretical idealization that does not respond to the dynamics of the problems we face. We raise the conjecture that the complexity of Brazilian society, where pockets of wealth coexist with the most shocking poverty, has contributed to the adoption and generation of different strands in mathematics education, crossing the boundaries between trends. At a more micro level, we also raise the conjecture that Brazilian trends in research are interwoven because of the way that Brazilian mathematics educators have experienced the process of globalization over these 30 years. This tapestry of trends is a predominant characteristic of mathematics education in Brazil. © FIZ Karlsruhe 2009.

Trends in Brazilian academic production in the History of Mathematics Education: directions from EBRAPEM

The number of papers on History of Mathematics Education presented at EBRAPEM (Brazilian Meeting of Graduate Students in Mathematics Education) has increased significantly between 2003 and 2008. This article presents a study with the aim of identifying themes, periods in focus, and sources and theoretical and methodological references used by the authors of the papers on History of Mathematics Education published in the proceedings of VII, VIII, IX, X, XI and XII EBRAPEM. The study indicates that the approach of ongoing research in History of Mathematics Education in Brazil has been similar to the approach of research in History of Education in general. However, the institutional separation between these two areas of investigation is noted as a factor rendering communication between both groups of researchers difficult.

A causal model of mathematics performance in early adolescence: the role of sex

Using path analysis, the present investigation was done to clarify possible causal linkages among general scholastic aptitude, academic achievement in mathematics, self-concept of ability, and performance on a mathematics examination. Subjects were 122 eighth-grade students who completed a mathematics examination as well as a measure of self-concept of ability. Aptitude and achievement measures were obtained from school records. Analysis showed sex differences in prediction of performance on the mathematics examination. For boys, this performance could be predicted from scholastic aptitude and previous achievement in mathematics. For girls, performance only could be predicted from previous achievement in mathematics. These results indicate that the direction, strength, and magnitude of relations among these variables differed for boys and girls, while mean levels of performance did not.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

The Impact of Language Opacity and Proficiency on Reading Strategies in Bilinguals: An Eye Movement Study

Reading strategies vary across languages according to orthographic depth - the complexity of the grapheme in relation to phoneme conversion rules - notably at the level of eye movement patterns. We recently demonstrated that a group of early bilinguals, who learned both languages equally under the age of seven, presented a first fixation location (FFL) closer to the beginning of words when reading in German as compared with French. Since German is known to be orthographically more transparent than French, this suggested that different strategies were being engaged depending on the orthographic depth of the used language. Opaque languages induce a global reading strategy, and transparent languages force a local/serial strategy. Thus, pseudo-words were processed using a local strategy in both languages, suggesting that the link between word forms and their lexical representation may also play a role in selecting a specific strategy. In order to test whether corresponding effects appear in late bilinguals with low proficiency in their second language (L2), we present a new study in which we recorded eye movements while two groups of late German-French and French-German bilinguals read aloud isolated French and German words and pseudo-words. Since, a transparent reading strategy is local and serial, with a high number of fixations per stimuli, and the level of the bilingual participants' L2 is low, the impact of language opacity should be observed in L1. We therefore predicted a global reading strategy if the bilinguals' L1 was French (FFL close to the middle of the stimuli with fewer fixations per stimuli) and a local and serial reading strategy if it was German. Thus, the L2 of each group, as well as pseudo-words, should also require a local and serial reading strategy. Our results confirmed these hypotheses, suggesting that global word processing is only achieved by bilinguals with an opaque L1 when reading in an opaque language; the low level in the L2 gives way to a local and serial reading strategy. These findings stress the fact that reading behavior is influenced not only by the linguistic mode but also by top-down factors, such as readers' proficiency.