Some Thoughts about Fractions

2007 ◽  
Vol 12 (7) ◽  
pp. 370-373
Author(s):  
Zalman P. Usiskin

The writing of “The future of fractions” in 1978 was motivated by a single incident, the quote that begins the article. That quote—indicating that fractions would become obsolete—is from an editorial essay in the Virginia Mathematics Teacher by Lucien Hall. Hall was an active, responsible, and knowledgeable member of the mathematics education community, and when I saw what he had written, I knew that his statement represented the beliefs of many other mathematics teachers and educators. I felt that his statement and this broader view of the impending demise of fractions had to be addressed.

2020 ◽  
Vol 1 (191) ◽  
pp. 120-123
Author(s):  
Lyubov Mykhaylenko ◽  

In the article we reveal the influence of methodical training of the future teacher of mathematics on the development of logical thinking of future teachers. We substantiate that the effectiveness of the development of logical thinking of students in mathematics lessons depends on the quality of methodological training of mathematics teachers in the free economic zone. Our experience in training future teachers of mathematics, allowed us to identify the criteria of methodological competence of mathematics teachers in the development of logical thinking of students: motivational, cognitive and activity; to characterize indicators of methodical competence of the teacher of mathematics in the course of development of logical thinking of pupils. We characterize the motivational criterion as the need of future mathematics teachers to master the methodological knowledge, skills and abilities for the development of logical thinking of students. The motivational criterion is revealed by the following indicators: professional orientation on the development of students' logical thinking; motivation for self-improvement in methodical activity. The cognitive criterion reflects the knowledge of future mathematics teachers of the logical component of students' mathematical competence. Indicators of the cognitive criterion of methodological competence of a mathematics teacher in the process of development of logical thinking of students are: completeness of theoretical knowledge of the logical component of mathematical competence of students; familiarity with the methods of developing students' logical thinking in mathematics lessons. The activity criterion shows the ability of future mathematics teachers to develop students 'logical thinking and involves mastery of methods for developing students' logical thinking. Indicators of the activity criterion of methodical competence of a mathematics teacher in the process of developing students' logical thinking are: the ability to use theoretical knowledge in practice; ability to develop the logical component of students' mathematical competence; the ability to generate new ideas aimed at improving the development of logical thinking of students. Selected criteria and indicators of methodological competence of mathematics teachers in the development of logical thinking of students reveal the importance of the ability to form a logical component of mathematical competence of students and determine the content of methodical activities of teachers in the development of logical thinking of students.


1971 ◽  
Vol 2 (2) ◽  
pp. 124-129
Author(s):  
Thomas J. Cooney

The purpose of this article is to examine the relevance of the International Study of Achievement in Mathematics to those mathematics educators in volved in the preparation of teachers. While the explicit purpose of the Study is not to provide directions for teacher-education programs, the Study nevertheless examines questions which indirectly involve the training of mathematics teachers. While all of the hypotheses in the Study deal with some aspect of education as they relate to mathematics, some hypotheses, namely Hypotheses 12–26, arc involved with probl ems more directly related to the mathematics education community. In particular, Hypotheses 12, 13, 14, 15, 18, 19, and 20. in the opinion of the writer, take on added significance when considering the preparation of mathematics teachers.


Author(s):  
Alessandro Ramploud ◽  
Silvia Funghi ◽  
Maria Mellone

AbstractIn this study, we address the issue of mathematics teachers' personal and professional responsiveness to changing circumstances, such as the shift in external demands made on teacher practice due to the COVID-19 pandemic. For investigating a such delicate issue, we take a theoretical approach, which is quite novel in the field of mathematics education: Lacan's psychoanalytical lens. Specifically, we will use this psychoanalytical lens to analyze a case study focusing on a primary school teacher during the first lockdown in Italy, during which school was organized exclusively in the form of distance education. The analysis of the teacher’s crisis and the strategies she adopted to overcome this crisis give some suggestions about possible directions and issues to consider for future mathematics teacher training proposals.


2013 ◽  
Vol 115 (2) ◽  
pp. 1-29
Author(s):  
Lawrence M. Clark ◽  
Toya J. Frank ◽  
Julius Davis

Background/Context Historians and researchers have documented and explored the work and role of African American teachers in the U.S. educational system, yet there has been limited attention to the specific work, role, and experiences of African American mathematics teachers. To meaningfully and responsibly conceptualize the role of African American mathematics teachers and better understand their work in U.S. schools, analytic approaches are needed to help us understand cases of African American mathematics teachers as representations of a complex and ever-evolving series of intertwined contexts, forces, and events that include critical events along historical timelines (i.e., U.S. educational system, mathematics education, technological innovation and development, African American teaching force). Purpose/Objective The purpose of this article is to challenge readers to consider the African American mathematics teacher as a conceptual entity that embodies characteristics, practices, and dispositions that are potentially meaningful for students, particularly African American students, in ways that support students’ capacity to participate and perform within the racialized contexts of mathematics education, the broader schooling experience, and broader society. Design Structured as an analytic essay, this article provides a rationale and potential directions of inquiry for historians and researchers open to explorations of relationships between race, mathematics education, teacher identity, and teacher practice. Conclusions/Recommendations We make two assertions about the African American mathematics teacher that help to conceptualize his or her role as a theoretical construct. First, the African American mathematics teacher is a boundary spanner with membership in multiple communities—a mathematically proficient and intellectually powerful African American person within a historically disempowered African American community with a history of inaccessibility to and underperformance in mathematics. Second, through various implicit and explicit means and micro-interactions, the African American mathematics teacher has the potential to engage in liberatory mathematics pedagogy, a pedagogy that serves to dismantle racialized hierarchies of mathematics ability. We encourage mathematics education researchers to interrogate, challenge, critique, and build on conceptualizations of the African American mathematics teacher as an entity that represents a unique confluence of experiences, perspectives, dispositions, and knowledge domains critical to the education of students. In doing so, it is our hope that theories of student learning, participation, and performance will more willingly embrace, acknowledge, and incorporate the inescapable dynamics of race, class, student identity, and teacher identity.


1953 ◽  
Vol 46 (5) ◽  
pp. 330-332
Author(s):  
John R. Mayor

These lines arc written just after the page proof for the official program of the Thirty-First Annual Meeting of The National Council of Teachers of Mathematics, held last month in Atlantic City, was returned to the printer. The members of our largest Affiliated Group, the Association of Mathematics Teachers of New Jersey, and the officers of the National Council worked hard to make the 1953 annual meeting the “biggest and best”, and more importantly, a meeting of great value to those who attended and to our cause which is that of the improvement of mathematics education at all levels of instruction. Reports on the annual meeting will appear in fall numbers of The Mathematics Teacher.


2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
Eugenia Vomvoridi-Ivanovic ◽  
Jennifer K Ward

Despite decades of social change and institutional reform, the academic gender gap continues to exist in many countries around the world and disproportionately affects women with children. Early indicators suggest that COVID-19 will widen this gap and exacerbate issues academic mothers face. In this essay we seek to raise awareness to the challenges and tensions academic mothers in mathematics education face both outside of and during a pandemic. We use existing literature on academic motherhood to make sense of our lived experiences, working to reframe pieces that are so often viewed as deficits to assets for our work in mathematics education. We hope that this will bring visibility to the invisible ways our identities as mothers inform our work as mathematics teacher educators and researchers. We conclude this essay with a call for the university-based mathematics education community to break the silence around the inequities associated with academic motherhood in our field and to shift the discourse from deficits of academic mothers to asset orientated views.


Author(s):  
Yulia HALAYKO ◽  

Theoretical results of research of revealing of influence of research work in the context of develop-ment of readiness for innovative pedagogical activity of future mathematics teachers in the conditions of magis-tracy are considered. The components that have a positive influence on the development of the readiness of the stu-dents of the magistracy for research work in the condi-tions of the master's environment are revealed. Dominant among them is recognized cognitive-semantic component as a set of theoretical and methodological research knowledge, providing not only the fundamental prepara-tion, but also the development of those qualities of the undergraduate personality, contributing to the implemen-tation of procedural and activity flow of his cognitive functions, aimed at personality mathematics. Methods.Considering the purpose of the research, the following methods were selected: theoretical analysis of national and foreign scientific literature. The research method is a psychological and pedagogical analysis of the influence of research work, which determines the level of formation of the practical readiness of the future mathe-matics teacher for innovative pedagogical activity.Originality.The results obtained are important be-cause they reveal the essence, professional significance of the research work of the students of the magistracy and the levels of its formation, which include scientific-cognitive, project-modeling and activity-creative with appropriate content context, mastering which contributes to the development of professionalism of future teacher’s mathematics. Results.Revealing the essence of research work and outlining its content, structural components, levels of its development determines the creative approach to solving the problem of preparing future masters, mathematics teachers to innovate their professional activity.Conclusion. The conducted research allows to confirm that the effectiveness of research work in the context of the development of the readiness of future masters, math-ematics teachers for innovative pedagogical activity will be fruitful if based on the following positions: ensuring professional and personal expression of students of the magistracy; transition to subject-subject relations between the teacher and the undergraduate in the organization of the educational process. It is important that: enhancing the dialogue of learning through the use of appropriate variant technologies; detailing the system of procedures and operations of supportive learning on the basis of diagnosis, whole-assignment, design and construction in the context of students mastering the cognitive style of thinking of pro-fessional and mathematical activity in the process of research work; creation of conditions for the creative development of the personality of the future mathematics teacher by updating the subjective experience of research activities in the acquisition of modeling technologies, the development of new forms and means of various studies, including mathematization and computerization; the transition of teachers to a humanistic position and the creation of educational cooperation and creativity, the desire for innovation, flexibility in decision-making, the ability to rethink pedagogical experience, both profession-al and personal. In general, revealing the essence of research work, mutually determine outlining its content, structural com-ponents, levels of its development contributes to the pur-poseful solution of the problem of preparation of future masters, mathematics teachers for innovative professional activity activities in terms of magistracy. The problem of more substantive research of the con-cept of research work of students of the magistracy, re-vealing its connection with the formation of research com-petence of the undergraduates and justification of peda-gogical conditions that contribute to the development of readiness in the context of innovative activity of a future mathematics teacher is urgent


2016 ◽  
Vol 3 (1) ◽  
pp. 45
Author(s):  
Masta Hutajulu ◽  
Marchasan Lexbin E.J.R

The research is conducted to observe if Mathematics teacher who use PMRI base consistently apply the characteristic especially to students of grade 4 primary. The  purpose of this research is to give contribution to all Mathematics teachers who apply PMRI. The data collection technique that use is observation method. The results of research are: 1) the application of PMRI in collaborator school (grade 4 primary) is consistent to the characteristics of PMRI. 2) Mathematics teachers who apply PMRI use the method according to the standard.Keyword: Realistic Mathematics Education of Indonesia (PMRI)


1972 ◽  
Vol 65 (7) ◽  
pp. 637-641
Author(s):  
Lowell Leake

THE current wealth of good literature in mathematics education is a great blessing for mathematics teachers at all levels —high school, elementary school, and college. For many teachers, especially the beginners, this horn of plenty presents a perplexing problem; with limited time or financial resources, the mathematics teacher needs guidance as to what literature would be most beneficial for him to read and, it is, hoped to own.


2020 ◽  
Vol 5 (2) ◽  
pp. 95-102
Author(s):  
Yoppy Wahyu Purnomo ◽  
Irfan Wahyu Prananto

The mathematics teacher profession has become a challenging and interesting profession in the era of technological advancement and global competition. The fact that mathematics is difficult is not able to stop interested (students) to become mathematics teachers. This is a basic asset that they have seen the opportunities behind challenges. This article aims to provide an overview of prospective mathematics teacher candidates regarding the opportunities, hopes, demands, and challenges of becoming a mathematics teacher. To accommodate these objectives, the article is divided into three main sections related to the question: Why choose a mathematics education study program? What does it take to be a math teacher? What needs to be prepared to become a mathematics teacher? These three questions are answered in their respective sections in the hope that they can give an idea of ??what needs to be done, what has been done, and how the students of mathematics teacher candidates follow the lectures.


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