Can Mathematics Education and History of Mathematics Coexist?

Despite the wide interest in combining mathematics education and the history of mathematics, there are grave and fundamental problems in this effort. The main difficulty is that while one wants to see historical topics in the classroom or an historical approach in teaching, the commitment to teach the modern mathematics and modern mathematical techniques necessary in thepure and applied sciences forces one either to trivialize history or to distortit. In particular, this commitment forces one to adopt a Whiggish approach to the history of mathematics. Two possible resolutions of the difficulty are (1) radical separation – putting the history of mathematics on a separate track from the ordinary course of instruction, and (2) radical accommodation – turning the study of mathematics into the study of mathematical texts.     

TPACK and Pre-Service Teacher Mathematics Education: Defining a Signature Pedagogy for Mathematics Education Using ICT and Based on the Metaphor “Mathematics Is a Language”

National professional standards for teachers in Australia (AITSL, 2011) expect teacher education graduates to demonstrate technological, pedagogical and content knowledge (TPACK). Those standards have emerged concurrently with the development of a new Australian mathematics curriculum. Thus, the expectation is that graduates can demonstrate the use of information and communication technologies in mathematics teaching and learning. The authors argue that “signature pedagogy” (Shulman, 2005 Shulman, L. S. 1986. Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2): 4–14. [Crossref] , [Google Scholar]) is the use of a key metaphor which views mathematics as a language and suggests that mathematics should be taught and learned as any other language. This article provides a summary of the findings of an action research project involving two cohorts of undergraduate mathematics education students in an Australian university. Data collected was used to inform targeted changes to improve the technological pedagogical approach employed by the course team across two offers of the course to enhance student learning and align the course with the expectations for graduate teachers. The implications of this action research are provided to inform the design and implementation of pre-service teacher education courses with respect to the development of TPACK capabilities specifically in mathematics education.     

Confidence is Everything” – Perspectives of Teachers and Students on Learning Mathematics

This paper problematises confidence as a frequently used explanation for performance in the mathematics classroom. I report on an interview-based study of how some English Advanced level (16+) students who have chosen to study mathematics, and their teachers, speak about confidence with respect to the learning of mathematics. I outline what constitutes confident learners for these teachers and, differently, for their students and what the students feel teachers could do to improve the students confident state. I discuss the implications of this for the education of prospective teachers of mathematics.     

Teachers’ Perspectives on the Human-Nature Relationship: Implications for Environmental Education

This study based on a theoretical framework of three main environmental perspectives in the human-nature relationship (anthropocentrism, biocentrism and ecocentrism), aimed to identify their incidence in teachers involved with environmental projects when confronted with diverse environmental issues. 60 teachers drawn from four school cycles in Portugal (crèche; 1st cycle, 6–9 years old; 2nd cycle, 10–11 years old; 3rd cycle and Secondary school, 12–17 years old) were interviewed and divided into two groups: generalist teachers (crèche and 1st cycle) and specialists in different subjects (2nd and 3rd cycles and secondary). The results showed a higher occurrence of biocentric perceptions in all teachers (more significantly in those from the 1st group). Comparatively, the teachers from the 2nd group showed more ecocentric perceptions. These differences can be explained by the models of teacher education (initial and inservice) and by the influence of the specific characteristics of the cycles in question. In contrast, the teachers' environmental projects were mostly centred on sustainable use of resources, which inevitably favours anthropocentric arguments. The results allow us to conclude that different environmental approaches are possible, especially if teachers are aware of the importance of dealing with more controversial environmental issues.     

Students’ Perspectives on Worldwide “Greening” of Tertiary Education Curricula

Several scholars have suggested the introduction of an environmental literacy requirement into the curricula of Non-Environmental Science disciplines in tertiary institutions of the world as a “greening” strategy for fostering global environmental stewardship necessary for enhancing understanding and collaboration in tackling the major environmental risks facing our global village today. However, there is no study on students’ opinion on this issue. This study was therefore initiated to 1) evaluate the opinion of undergraduate students on the introduction of a worldwide environmental literacy into the curricula of Non-Environmental science majors as a graduation requirement; and 2) identify any possible demographic differences in opinions among the student subjects polled. We sought the opinion of 800 undergraduates from African, North American and European universities on the subject and 99% responded. The result showed that a majority (67%) of them supported the worldwide environmental literacy requirement and those already trained were significantly (P < 0.0001) more likely to support it than those untrained. Students from developing countries were significantly (P < 0.0001) more likely to support it than those from developed countries; similarly students in the Arts’ disciplines were more likely to support it than Non-Arts’ students as a group. However, no significant differences were observed between students from Francophone versus Anglophone countries; Social Sciences versus Non-Social Sciences majors and between Education versus Non-Education majors. Some similarities were observed between the opinion of university-age students in this study and 15-year old secondary school students from two major international surveys (Research on Science Education-ROSE, and Program for International Student Assessment-PISA) on science education; further studies comparing these two categories of students is suggested. The need for all professionals to be literate about the science of their surroundings was the most identified reason for supporting the literacy requirement by the students polled. The results of this study thus provide evidence of support by students in the on-going paradigm shift towards “greening” the curricula of tertiary institutions and thus reinforces its implementation by leaders of academe and policy makers worldwide.     

John Wilson’s confused ‘Perspectives on the Philosophy of Education’

In his ‘Perspectives on the Philosophy of Education’ John Wilson laments the confusion that surrounds the current state of the philosophy of education. Unlike other branches of philosophy, he claims, it is not clear what the philosophy of education is about, and a snapshot of current work in the field reveals its lack of coherence. To remedy this he advocates starting ‘from scratch’: the philosophy of education is to be understood as a discipline concerned with the logic of value judgements and focused on questions of learning. While the present paper acknowledges the extent of Wilson’s contribution to the field, it draws attention to the confusion in the position that he holds, and shows that his assessment of the current state of the philosophy of education is both inaccurate and politically blinkered. In the process, the paper challenges his account of the philosophy of education as a branch of philosophy and offers a more coherent characterisation.     

How Chinese Teach Mathematics: Canadian Teachers’ Perspectives

As part of a large reciprocal learning partnership project between Canada and China, this study explored Canadian teachers’ perceptions of mathematics teaching in elementary schools in China. Using reciprocal learning and Activity Theory as the theoretical lens, we collected data, i.e., classroom observations, group discussion, and informal exchanges from teachers in a pair of research sister-schools in Canada and China. Qualitative data analyses revealed four themes in Canadian teachers’ perceptions of the characteristics of Chinese mathematics teaching: an active teacher-student interaction model of questioning-responding, a mathematical knowledge-package summary at the end of each lesson, integration of the history of mathematics into teaching, and the development and implementation of well-structured lessons. Contributions, implications, and limitations of the study in mathematics education and research are discussed.     

Pre-service Mathematics Teachers’ Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

This study examined pre-service mathematics teachers’ knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4–8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males’ knowledge scores are significantly higher than females’ scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers’ knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers’ positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.     

African American Pre-Service Teachers’ Perspectives on Urban Education: An Exploration at an HBCU

This paper aims to better understand African American pre-service teachers?? perspectives on urban education. Over a 2-year period, pre-experience and post-experience surveys were conducted at a Historically Black University (HBCU) after pre-service teachers completed an urban education immersion course in order to frame their understanding of perspectives on urban education. Ultimately, the results indicate that the African American pre-service teachers?? perceptions of urban teachers, urban administrators, and a career in urban education were statistically more positive after the immersion course, but their views of urban parents became more negative. These results provide further implications for teacher education programs.     

Whose Ethics? Toward Clarifying Ethics in Mathematics Education Research

The philosophical branch of ethics is foundationally concerned with the question of right or wrong, benevolent or harmful, and ultimately what is proper conduct. The present inquiry addresses two related questions: (1) How have theories of ethics been applied to mathematics education research? and (2) What alternatives have not been considered? What might the implications be if these alternative formulations were considered? To answer the first question, I offer a review of the philosophy of mathematics education literature, considering those articles which discuss ethics and mathematics education together. The ethical perspectives adopted within the literature span normative and non-normative, modern and postmodern orientations towards ethics. To answer the second question, I explored philosophy literature to identify which philosophical perspectives of ethics have (not) been adopted by philosophers of mathematics education research. The structure of this paper parallels these two questions: the first part considers the philosophy of mathematics education research and how researchers have defined ethics while the second part discusses additional philosophical approaches to ethics and puts those approaches into conversation with those identified in part one. I conclude by intertwining these two strands into my central thesis: ethics per se is construed too narrowly in the philosophy of mathematics education literature and considering additional ethical perspectives from philosophy can be generative of new ideas.     

A Review of “Seeking Sense in the City: European Perspectives on Religious Education”

If universities can teach about religion, the community colleges cannot be far behind. Here are some impelling reasons     

Team Research at the Biology–Mathematics Interface: Project Management Perspectives

The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics background and an experimentally oriented biology student. The team mentors typically ranked the students'' performance very good to excellent over a range of attributes that included creativity and ability to conduct independent research. However, the research teams experienced problems meeting prespecified deadlines due to poor time and project management skills. Because time and project management skills can be readily taught and moreover typically reflect good research practices, simple modifications should be made to undergraduate curricula so that the promise of initiatives, such as MATH-BIO 2010, can be implemented.     

Educational Inequity from the Perspectives of Those Who Live It: Urban Middle School Students’ Perspectives on the Quality of their Education

In interviews with over 250 urban young adolescents, many students make it clear that they are acutely aware of the educational inequities that exist in their schools and that these inequities are having a negative impact on their education. Student voice is used to highlight urban middle school students’ perspectives on the quality of their education particularly in terms of curricular issues, teacher quality, and lack of resources.

South African Primary Mathematics Teachers’ Experiences and Perspectives About Lesson Study

This study aims to investigate the perspectives of primary school teachers in South Africa, who participated in a Lesson Study (LS) project, on this professional development process and about their professional learning. The study followed a mixed approach, with data collected through a questionnaire, followed up by interviews. A novel approach in this study was to source teachers’ experiences of the individual stages of LS as well as of the integrated process. Teachers’ perspectives on LS were categorised into 5 themes: collaboration — commitment and the free rider effect, confidence issues, teachers’ knowledge and skills, misconceptions about the LS approach, and external issues including concerns over time of teachers and learners, systemic challenges and school management. Using teachers’ individual and focus group inputs in the questionnaire and the interviews, we report about their experiences.

     

“Enactment of Sámi Past in School Textbooks: Towards Multiple Pasts for Future Making”

The article examines the use of archaeological knowledge in elementary history textbooks used in Norwegian schools today. The aim is to determine whether we can find any traces of colonialism by reviewing how these narratives perform in interrelations within and between the Sámi and Norse pasts, and how the narratives allow for hybridity and heterogeneity. Postcolonial theory turns the narrative into an object of analysis. The findings show that the Sámi material remains are outside the system of cultural change and that the temporal and spatial distances produce binary and homogeneous cultures. New material perspectives can intervene in singular performativity. Learning to enact dynamic material heterogeneity may affect the future of pupils’ participation in cultural negotiations of pastsin present.     

Dimensions of Mathematics Mentoring in School‐based Initial Teacher Education

There have been significant advance in educational technology but they have not always brought about measurable shifts in user behavior. This study examined the relationship between teachers’ knowledge about a tool and their use of that tool. In many secondary schools use of a Learning Platforms (LPs) is no longer optional although the degree of engagement with the technology remains a matter of choice. However, individual decisions to use selected functionalities of these systems are not well captured in current models of technology acceptance. In a best-case scenario, self-reported possible and actual use of LPs was acquired for 50 teachers from eight technology-rich schools. Three key barriers to use were identified: the functionality of the software, workloads and personal interest. Based on teachers’ knowledge of LP functionality and perceived barriers to use, four distinct groups of teachers emerged. A low-user group identified all three barriers, showed little enthusiasm for use of this technology and had a markedly impoverished perception of the LP. There were three distinct higher use groups based on perceived barriers. While the functions used by these three groups showed less variation, with innovative functions such Blogs and Wikis remaining aspirational, there were differences in how such limitations were viewed. Whether the response was one of complacency and frustration has implications for professional development programmes.