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.

Summarization in Math Class

This action research study of twenty students in my sixth grade mathematics classroom examines the implementation of summarization strategies. Students were taught how to summarize concepts and how to explain their thinking in different ways to the teacher and their peers. Through analysis of students’ summaries of concepts from lessons that I taught, tests scores, and student journals and interviews, I discovered that summarizing mathematical concepts offers students an engaging opportunity to better understand those concepts and render that understanding more visible to the teacher. This analysis suggests that non-traditional summarization, such as verbal and written strategies, and strategies involving movement and discussions, can be useful in mathematics classrooms to improve student understanding, engagement in learning tasks, and as a form of formative assessment.

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.

THE IMPACTS OF MITEP ON MY CAREER IN EDUCATION

MiTEP, the Michigan Teacher Excellence Program, provides current teachers the opportunity to partner with Michigan Technological University to obtain graduate credit towards a Master’s degree in applied science education. In exchange, the university collects data on the implementation of inquiry and earth science concepts into science classrooms. This paper documents my experience within this program, including how it has affected my personal and professional learning.

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.

Construction of Structures I in Moodle: a new teaching methodology in the Degree of Building Engineer

The subject of Construction of Structures I studies, from a constructive point of view and taking into account current legislation, reinforced concrete structures used in buildings, through the acquisition of knowledge and construction criteria required in the profession of a Technical Architect. The contents acquired in this course are essential for further professional development of technicians and are closely related to many of the subjects taught in the same or other courses of the Degree in Technical Architecture at the University of Alicante. The aim of this paper is to present, analyze and discuss the development of a new methodology proposed in the mentioned subject, as it supposed an important change in the traditional way of teaching Construction and Structures I. In order to incorporate new teaching tools in 2013-2014, the course has been implemented by using a Moodle software tool to promote blended learning with online exercises. Our Moodle community allows collaborative work within an open-source platform where teachers and students share a new and personalized learning environment. Students are easily used to the interface and the platform, value the constant connection with teachers or other fellows and completely agree with the possibility of making questions or share documents 24 hours a day. The proposed methodology consists of lectures and practical classes. In the lectures, the basics of each topic are discussed; class attendance, daily study and conducting scheduled exercises are indispensable. Practical classes allow to consolidate the knowledge gained in theory classes by solving professional exercises and actual construction problems related to structures, that shall be compulsorily delivered online. So, after the correction of the teacher and the subsequent feedback of students, practical exercises ensure lifelong learning of the student, who can download any kind of material at any time (constructive details, practical exercises and even corrected exams). Regarding the general evaluation system, goals achievement is assessed on an ongoing basis (65% of the final mark) along the course through written and graphic evidences in person and online, as well as a individual development of a workbook. In all cases, the acquisition of skills, the ability to synthesize, the capacity of logical and critical thinking are assessed. The other 35 % of the mark is evaluated by a complementary graphic exam. Participation in the computing platform is essential and the student is required to do and present, at least 90% of the practices proposed. Those who do not comply with the practices in each specific date could not be assessed continuously and may only choose the final exam. In conclusion, the subject of Construction of Structures I is essential in the development of the regulated profession of Technical Architect as they are considered, among other professional profiles, as specialists in construction of building structures. The use of a new communication platform and online teaching allows the acquisition of knowledge and constructive approaches in a continuous way, with a more direct and personal monitoring by the teacher that has been highly appreciated by almost 100% of the students. Ultimately, it is important to say that the use of Moodle in this subject is a very interesting tool, which was really well welcome by students in one of the densest and important subjects of the Degree of Technical Architecture.

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Pre-Service Teachers’ Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Thesis (Ph.D.)--University of Washington, 2016-06

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.

Predegree Polynomials of Plane Configurations in Projective Space

2000 Mathematics Subject Classification: 14N10, 14C17.

Causal attributions for success or failure by passing and failing students in College Algebra

Success in mathematics has been identified as a predictor of baccalaureate degree completion. Within the coursework of college mathematics, College Algebra has been identified as a high-risk course due to its low success rates. ^ Research in the field of attribution theory and academic achievement suggests a relationship between a student's attributional style and achievement. Theorists and researchers contend that attributions influence individual reactions to success and failure. They also report that individuals use attributions to explain and justify their performance. Studies in mathematics education identify attribution theory as the theoretical orientation most suited to explain academic performance in mathematics. This study focused on the relationship among a high risk course, low success rates, and attribution by examining the difference in the attributions passing and failing students gave for their performance in College Algebra. ^ The methods for the study included a pilot administration of the Causal Dimension Scale (CDSII) which was used to conduct reliability and principal component analyses. Then, students (n = 410) self-reported their performance on an in-class test and attributed their performance along the dimensions of locus of causality, stability, personal controllability, and external controllability. They also provided open-ended attribution statements to explain the cause of their performance. The quantitative data compared the passing and failing groups and their attributions for performance on a test using One-Way ANOVA and Pearson chi square procedures. The open-ended attribution statements were coded in relation to ability, effort, task difficulty, and luck and compared using a Pearson chi square procedure. ^ The results of the quantitative data comparing passing and failing groups and their attributions along the dimensions measured by the CDSII indicated statistical significance in locus of causality, stability, and personal controllability. The results comparing the open-ended attribution statements indicated statistical significance in the categories of effort and task difficulty. ^

Predictors of success: Medical Laboratory Associate in Science Degree Program

Hospitals and healthcare facilities in the United States are facing serious shortages of medical laboratory personnel, which, if not addressed, stand to negatively impact patient care. The problem is compounded by a reduction in the numbers of academic programs and resulting decrease in the number of graduates to keep up with the increase in industry demands. Given these challenges, the purpose of this study was to identify predictors of success for students in a selected 2-year Medical Laboratory Technology Associate in Science Degree Program. ^ This study examined five academic factors (College Placement Test Math and Reading scores, Cumulative GPA, Science GPA, and Professional [first semester laboratory courses] GPA) and, demographic data to see if any of these factors could predict program completion. The researcher examined academic records for a 10-year period (N =158). Using a retrospective model, the correlational analysis between the variables and completion revealed a significant relationship (p < .05) for CGPA, SGPA, CPT Math, and PGPA indicating that students with higher CGPA, SGPA, CPT Math, and PGPA were more likely to complete their degree in 2 years. Binary logistic regression analysis with the same academic variables revealed PGPA was the best predictor of program completion (p < .001). ^ Additionally, the findings in this study are consistent with the academic part of the Bean and Metzner Conceptual Model of Nontraditional Student Attrition which points to academic outcome variables such as GPA as affecting attrition. Thus, the findings in this study are important to students and educators in the field of Medical Laboratory Technology since PGPA is a predictor that can be used to provide early in-program intervention to the at-risk student, thus increasing the chances of successful timely completion.^