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Why can't i be a mathematician?
... The male body, as an object, can symbolise intellect but it is often depicted in media as fragile and socially inept ). These peculiarities of mathematical masculinity often manifest in media and social discourse as mental illness, personality disorders and the like (Doxiadis 2004, Gadanidis 2012). ...
... . Usefully, for this paper, Holland et al.'s example of addiction and mental illness facilitates an understanding of how mathematical identity can be similarly read. For it is claimed mathematicians' lives are read through their mathematics as though it is their identity(Mendick et al. 2010, p. 5) and images of mathematicians (as mad, obsessional, genius) are ingrained in the media and public consciousness(Doxiadis 2003, Andreasen 2014, Gadanidis 2012 p. 4). For example, mathematicians depicted in theatre and films are often portrayed for the dramatic elements such as their struggle against, and obsession with, the mathematical problem as well as struggles with poor mental health and personal and social relationships(Doxiadis 2003(Doxiadis , 2004Gadanidis 2012; Abbot 2015). ...
... For it is claimed mathematicians' lives are read through their mathematics as though it is their identity(Mendick et al. 2010, p. 5) and images of mathematicians (as mad, obsessional, genius) are ingrained in the media and public consciousness(Doxiadis 2003, Andreasen 2014, Gadanidis 2012 p. 4). For example, mathematicians depicted in theatre and films are often portrayed for the dramatic elements such as their struggle against, and obsession with, the mathematical problem as well as struggles with poor mental health and personal and social relationships(Doxiadis 2003(Doxiadis , 2004Gadanidis 2012; Abbot 2015). Mathematics as obsession further alludes to a vice or addiction, which, through Holland et al.'s understanding is conceived as mental illness.Doxiadis (2003) claims these conflicts are dramatic and entertaining because of the inherent paradox and dichotomy between the commonly held views of mathematics and mathematicians as both rational and irrational (mentally disturbed). ...
The stereotypical mathematical identity story of the 'mad mathematician' (consumed by mathematics and socially inept) is widely reported as problematic to understanding what it means to be mathematical, and to engaging students in mathematics. This problem is explored in the improvisational parody 'Math Therapy', which occurred during my filming of 'Performatics'(https://vimeo.com/147449932); an Arts Based Research (ABR), using filmed-drama. 'Performed' and informed by the lived experiences of three post graduate students studying courses with mathematical content, their mathematical experiences are juxtaposed with those of a socially imagined 'mad mathematician' in a fictional, generic therapy context entitled 'Math Therapy'. The ABR facilitated a performance of embodied ways of imagining and performing mathematical identity; subverting, making ridiculous, and disordering the stereotypical 'mad mathematician' identity, so as to critically question and challenge its authority. Through the performance, the mathematical identities available to us are also revealed as a parody; between the imagined identity and lived experience. © 2018 The Author(s) & Dept. of Mathematical Sciences-The University of Montana.
... Therefore, the main aim of this study is to explore and identify the range of perceptions, beliefs and attitudes towards mathematics as it is perceived by the secondary school students. It is widely claimed that, negative perceptions and myths of mathematics are widespread among the students, especially in the developed countries (e.g.,Mtetwa & Garofalo, 1989;Ernest, 1996;& Gadanidis, 2012).Sam (2002)claimed that many students are scared of mathematics and feel powerless in the presence of mathematical ideas. They regarded Mathematics as "difficult, cold, abstract, and in many cultures, largely masculine" (Ernest, 1996, p.802). ...
... Therefore, the main aim of this study is to explore and identify the range of perceptions, beliefs and attitudes towards mathematics as it is perceived by the secondary school students. It is widely claimed that, negative perceptions and myths of mathematics are widespread among the students, especially in the developed countries (e.g., Mtetwa & Garofalo, 1989;Ernest, 1996;& Gadanidis, 2012). Sam (2002) claimed that many students are scared of mathematics and feel powerless in the presence of mathematical ideas. ...
This study investigates the influence of students’ perceptions on mathematics performance at a selected South African secondary school. The influence of factors such as strength and weaknesses in mathematics, teacher support/learning material, family background and support, interest in mathematics, difficulties or challenges in doing mathematics, self-confidence and myths and beliefs about mathematics were identified as constructs of perceptions that influence students’ performance. Five of the seven constructs were found to be influential on students’ performance in mathematics. Quantitative methods were used to analyse the data collected from a questionnaire which was administered to randomly selected secondary school students (n=124) in Polokwane, South Africa. From the regression analysis of the data, the following hierarchy of themes emerged as components of students’ perceptions of mathematics. These were (i) weaknesses in mathematics (ii) family background and support, (iii) interests in mathematics, (iv) self-confidence in mathematics, (v) myths and beliefs about mathematics (vi) teacher /learning material support, (vii) difficulties in learning mathematics. Results from t-tests, Anova and suggest that there were significant differences in the perceptions and beliefs about mathematics between males and females, between mature and juvenile students and among students from different language backgrounds respectively. Correlation analysis results showed strong positive relationships between performance and perception constructs such as self-confidence, interests in mathematics, teacher and learning support material as well as myths and beliefs .The respondents tend to view lack of proficiency in mathematics as a challenge, and attribute success in mathematics to effort and perseverance. Students also perceive difficulty in mathematics as an obstacle, and attribute failure to their own lack of inherited mathematical ability. These findings suggest that differences in (i) myths and beliefs about mathematics success, ( (ii) motivation given by mathematics teachers and parents, (iii) mathematics teachers' teaching styles and learning materials and (iv) self confidence in mathematics may lead to differences in perceptions about mathematics. These in turn may lead to differences in attitudes towards mathematics and learning mathematics which have a bearing on performance.
DOI: 10.5901/mjss.2014.v5n3p431
... Cognitive representations are relevant from a reasoning point of view, while attitudes, sentiments, interests, and emotions are relevant from an affective domain. According to Gadanidis (2012), students around the world have largely negative perceptions and misconceptions about mathematics achievement, although they might have an interest in studying the subject. Furthermore, Lent et al. (1991) discovered that student potentials did not add positive significant variability to the forecasting of mathematics interest after managing self-efficacy. ...
Science, technology, engineering, mathematics (STEM) education, the current engine for this technological generation, has made its way into Ghana's education system and is progressively becoming autonomous, particularly at the senior high level. It depends extensively on student mathematics performance to progress into their various dream STEM career programs. It is worthwhile to study the relationships between STEM students' mathematics (perception, self-efficacy, and connection) and mathematics achievement with their study interest mediating between them. The researchers purposively and conveniently sampled 385 general science respondents from eight selected senior high schools in the Kumasi metropolis for this study. The study produces results by quantifying and analyzing the collected data by investigating the six distinct hypotheses with structural equation model (SEM) using SPSS (26) and AMOS (24) software to confirm or refute fundamental assumptions. The study suggests that general science students' mathematics self-efficacy and connection directly impact their mathematics performance and, at the same time, somewhat mediate their ability to perform well in mathematics through their study interest. Moreover, there was no relationship between mathematical perception and student interest or achievement. Students must continue to evaluate the efficacy of their learning tactics to achieve academic excellence, and they must make reliable and self-efficacious evaluations of their mathematical learning as well as their mathematics connections to other STEM subjects to improve their study interest and mathematics achievement. The study recommends that stakeholders, curriculum developers, and implementers of the new STEM curriculum try to connect mathematics to all aspects of STEM as much as possible to either directly improve their performance or increase their interest in improving their mathematics education.
... It is widely claimed that negative perceptions and myths of mathematics are widespread among students, especially in the developed countries (Ernest, 1995;Gadanidis, 2012). Sam (1999) claimed that many students are scared of mathematics and feel powerless in the presence of mathematical ideas. ...
The students' perception of mathematics is equally important for the parents as well as the teachers to deal with them effectively. Therefore, this study is concerned with the secondary level low-performing students' perception of mathematics and its effects on their achievements. The study is based on the mixed-method survey research design consisting of 312 grade IX and X students, 119 male and 193 female students from the 10 community schools of Province No. 1, Nepal. A Likert-type survey questionnaire, 'Perception Towards Mathematics Inventory (PTMI) was developed and administered by the researchers to the participants. Thus, the collected quantitative data were analyzed by using descriptive statistics. The qualitative data collected through semi-structured interviews were summarized and analyzed categorically in high-performing and low-performing groups. The findings revealed that the perception of the low-performing students towards mathematics was found negative or they did not prefer to learn mathematics. Similarly, the student's perception of mathematics was found to have a greater effect on their achievement. The group of higher achiever students was found more positive and confident towards mathematics and the lower achievers were found negative and anxious. However, most of the students were found aware of the value of mathematics.
... The other aspect of Design Principle 5 is that the mathematical content at the heart of the task is important. Indeed, when designing "low floor, high ceiling" tasks, Gadanidis (2012) suggests that one should begin with a central mathematical idea that is embedded within the secondary mathematics curriculum (e.g., infinity), and work backwards to design an activity appropriate for students in primary school who are expected to engage with the task. Such an approach resonates with mathematics education researcher calls for advanced mathematical ideas to be explored when contextually appropriate in the primary school curriculum (e.g., infinity; see Holton & Symons, 2021). ...
How can we engage all primary school students in rich mathematical learning, support them to make connections, and develop their mathematical language and reasoning? In this article, we draw on one school’s experience in considering an approach to mathematics instruction that could support teachers in addressing this question, specifically pursuing structured inquiry in a multi-age setting.
... The studies suggest that there is a strong progressive affiliations among the performance and the perception builds such as belief in oneself, schooling and learning support material, interest in mathematics, myths and belief about mathematics [7]. It is also asserted that, adverse perceptions and myths of mathematics are common between the students that, observed in the developed countries [8][9][10]. ...
The attitude of students towards mathematics is most important factor especially for the engineers in their practical observation relating to the understanding of particular problems in their field. To analyze this reservation, the study is conducted using students' feedback towards the performance of students in Calculus and Differential Equation subjects. During the analysis, a case study of 17A and 17B batches of 1 st and 2 nd semesters are selected. The marks of the Mathematics subjects namely Applied Mathematics-I (Calculus) and Applied Mathematics-II (Differential Equation) is collected from the students individually using university students portal and the results is calculated by using Statistical Package for Social Sciences (SPSS v.16) which shows the overall students' perception towards the mathematics subjects. The results imply that there is no significant relationship between the marks of calculus and differential equation. Furthermore, the null hypothesis is rejected for the disciplines such as Civil, Mechanical, Electrical, Mechatronics and Textile of 17A and Civil, Mechanical and Electrical of 17B Batch. Although the null hypothesis is accepted only for the Electronics department of 17A and Mechatronics, Electronics and Textile of 17B Batch. It is recommended that the teachers must put efforts on the students for the understanding of Mathematics concepts and improve their attitude towards it, so that they can perform better in their future practical life.
... For example, in his contribution about curves, Mahmoud included hyperlinks to different pages on the MacTutor History of Mathematics archive (http:// www-history.mcs.st-and.ac.uk/) to explore various curves (e.g., trisectrix of Maclaurin, double folium), allowing himself and the reader to delve into content beyond the secondary mathematics curriculum. Such writing further illustrates the potential of open-ended, 'low-floor, high-ceiling' tasks as a way for students to deeply engage with mathematics (Gadanidis, 2012). ...
... It is widely claimed that, negative perceptions and myths of mathematics are widespread among the students, especially in the developed countries (Ernest, 1996,&Gadanidis, 2012. Sam (2002) claimed that many students are scared of mathematics and feel powerless in the presence of mathematical ideas. ...
This paper presents the perceptions of low-performing secondary level students towards mathematics. In this study, the participants consisted of 180 students, 30 each from the 6 secondary schools in Nepal. Two schools from each ecological region; Hills, Mountains and Tarai were purposively selected. A Likert type survey questionnaire was developed and administered to the participants. The data thus collected were analysed calculating the mean of the responses. The findings revealed that the low performing students' perceptions towards mathematics were negativein that they thought thatmathematicswas a difficult subject although they still perceived mathematics as a subject of value and importance.
... As Steckles [41] notes, with such a restricted definition, it is likely that "most people in the world would probably never meet someone who fits that title." Furthermore, it has been argued that just as individuals can consider themselves to be an athlete without being a professional athlete, and others may consider themselves to be an artist without being a professional artist, why must we only associate the word "mathematician" with a professional mathematician, allowing the title to be permissible only for a select few [18]. ...
... There had been claims that the learners from the developed nations have pessimistic perceptions and beliefs on mathematics (Gadanidis, 2012). Such discipline was viewed to be a highly complicated subject matter that only those brilliant and strong-willed learners can well tackle the same. ...
... Researchers have additionally acknowledged the major potential of personal learning networks (PLNs), which enable students to engage in individualized collaboration and benefit from the community network. For example, Gadanidis et al. (2008 and2012) report that community-based collaboration inspired such a positive image of Mathematics among students of Teacher Training for Primary Education that they subsequently instilled this in their pupils. ...
... Therefore the ultimate aim of this study is to examine, explore, identify and analyze a range of student's perceptions, beliefs and attitudes that influences their take on mathematics in secondary school. It is extensively said that student's unenthusiastic perceptions and myths towards mathematics are very broad mainly in the developed economies (Mtetwa & Garofalo, 1989;Ernest, 1996;Gadanidis, 2012). Sam (2002) argues that many students are petrified of mathematics and feel powerless in the presence of mathematical ideas. ...
... The mathematics-for-teachers activities are the same mathematics activities we have been developing in K-8 research classrooms for approximately a decade in Canada and in Brazil (Gadanidis & Borba, 2008;Gadanidis, 2012). The online component of our blended program (www.researchideas.ca/wmt) ...
In this survey paper we focus on identifying recent advances in research on digital technology in the field of mathematics education. We have used Internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals. We identify five sub-areas of research, important trends of development, and illustrate them using case studies: mobile technologies, massive open online courses (MOOCs), digital libraries and designing learning objects, collaborative learning using digital technology, and teacher training using blended learning. These exemplary case studies may help the reader to understand how recent developments in this area of research have evolved in the last few years. We conclude the report discussing some of the implications that these digital technologies may have for mathematics education research and practice as well as making some recommendations for future research in this area.
... The mathematics-for-teachers activities are the same mathematics activities we have been developing in K-8 research classrooms for approximately a decade in Canada and in Brazil (Gadanidis & Borba, 2008;Gadanidis, 2012). The online component of our blended program (www.researchideas.ca/wmt) ...
This paper surveys the notions, conceptualisations and roles of mathematical competencies and their relatives in research, development and practice from an international perspective. After outlining the questions giving rise to this survey, the paper first takes a brief look at the genesis of competency-oriented ideas as a prelude to identifying and analysing recent trends. The relationships between different notions and terms concerning competencies and their relatives are discussed, and their roles in the 2015 PISA framework are presented. Two kinds of research, on and by means of mathematical competencies, are surveyed. The impact of competency-oriented notions and ideas on curriculum frameworks and documents in a number of countries is being charted, before challenges to the implementation of such notions in actual teaching practice are identified. Finally the paper takes stock of the international state-of-the-art of competencies and similar notions, with a focus on the need for further research.
... Many have long suggested that in order to improve mathematics education, we need to-among other things-disrupt traditional ways of teaching (Gadanidis 2012), make the content more coherent and connected with reality (Stanic 1986;Woodhouse 2012), and make available the benefits of mathematical knowledge to everyone (Apple 1992). These are admirable aims; however, in this paper, I have argued that to a large extent, we may need to go further if we are to disrupt the root of the problem: that, perhaps after a certain point, mathematics is simply unnecessary for most students to flourish. ...
In this essay, I examine the extent to which mathematics education and education for quantitative literacy support students’ present and future flourishing, a concept that entails realizing objective goods in a life lived from the inside. This perspective requires disentangling philosophical assumptions about the aims of mathematics education, which—in the context of flourishing—I take to be a hybrid of those that have informed curricular discussions over the past two centuries. In the process, I problematize ("make strange") many of the common reasons given for students learning mathematics, including: learning it for one’s career, for one’s logical reasoning skills, or for its own sake. My conclusion is that, through the end of compulsory schooling, all students should take coursework that fosters quantitative literacy, or the ability and disposition to use, interpret, and criticize numbers as they manifest in daily life. In addition, in the same environment, traditional mathematics should be included and compulsory up to grade eight, but afterward required only insofar as it is necessary for fulfilling one’s goals. I pursue this line of argument with full cognizance of sociopolitical elements of mathematics education and other challenges in implementation, noting that appealing to consequences—while fine as a justification for avoiding change in the short-term—is not a tenable justification for doing so in the long-term. I challenge readers to reflect on our ability to empower students for future flourishing, and to consider the role that mathematics has in doing so.
... The mathematics-for-teachers activities are the same mathematics activities that have been developed in K-8 research classrooms for approximately a decade in Canada and in Brazil Gadanidis 2012). The online component of the blended program (available at http://researchideas.ca/, see Fig. 7) serves a number of purposes: it is a form of research dissemination; it is a collection of mathematics-for-teachers activities; it is a resource freely available to teachers in the field to use in their classrooms; and it is a set of mathematics-for-teachers courses that they offer through the Fields Institute for Research in Mathematical Sciences. ...
In this literature survey we focus on identifying recent advances in research on digital technology in the field of mathematics education. To conduct the survey we have used internet search engines with keywords related to mathematics education and digital technology and have reviewed some of the main international journals, including the ones in Portuguese and Spanish. We identify five sub-areas of research, important trends of development, and illustrate them using case studies: mobile technologies, massive open online courses (MOOCs), digital libraries and designing learning objects, collaborative learning using digital technology, and teacher training using blended learning. These examples of case studies may help the reader to understand how recent developments in this area of research have evolved in the last few years. We conclude the report discussing some of the implications that these digital technologies may have for mathematics education research and practice as well as making some recommendations for future research in this area.
... Such learning experiences disrupt the common fragmentation of mathematical ideas in grade-sized chunks, by making what is assumed to be a secondary school concept accessible across grades 1-12. They also provide young students representations for sharing their learning in ways that offer others (such as family and friends and the wider community) mathematical surprise and conceptual insight (Hughes and Gadanidis 2010;Gadanidis and Hughes 2011;Gadanidis 2012). ...
There is currently an increased focus on technology and on making, pointing to new opportunities for engaging learners in constructionist practices with digital technology. In this context, we share our investigations of elementary school mathematics applications of Arduino and Chibitronics, two popular environments for making digital circuits and controlling them with code. We are especially interested in affordances typically associated with coding and more generally with computational thinking--low floor, high ceiling, abstraction, automation and dynamic modelling (Papert 1980; Wing (Commun ACM 49(3);33-35, 2006), (Philos Trans R Soc A 366(1881):3717-3725, 2008))--and how these affordances manifest themselves in making experiences with digital tangibles.
... That is, will the activities we design prepare students to answer the question "What did you do in math today?" by sharing a learning experience that will offer the pleasure of mathematical surprise and insight? (Gadanidis and Borba 2008;Gadanidis and Hughes 2011;Gadanidis 2012). Fourth, we do not present the approach we use as an either/or choice. ...
Wing’s (2006; 2008) advocacy for computational thinking in K-12 education, along with calls from technology leaders for computer programming for all students, have prompted educators and education leaders to reconsider the potential of computational thinking in K-12 education. Currently, computational thinking tends to be viewed as its own objective, rather than integrated with curriculum to enrich existing subject areas. However, there is a natural (and historical) connection between computational thinking and mathematics—in terms of logical structure and in the ability to model and investigate mathematical relationships. To better understand the potential of computational thinking in mathematics education, we consider a classroom case where computational thinking was used with Grade 1 students to investigate (a) patterns with squares and (b) rudimentary ideas of the Binomial Theorem. Our analysis focuses on computational thinking affordances as “actors” in the teaching and learning process.
... The mathematics-for-teachers activities are the same mathematics activities that have been developed in K-8 research classrooms for approximately a decade in Canada and in Brazil Gadanidis 2012). The online component of the blended program (available at http://researchideas.ca/, see Fig. 7) serves a number of purposes: it is a form of research dissemination; it is a collection of mathematics-for-teachers activities; it is a resource freely available to teachers in the field to use in their classrooms; and it is a set of mathematics-for-teachers courses that they offer through the Fields Institute for Research in Mathematical Sciences. ...
Online mathematics teacher education is characterized as an emergent area of research in mathematics education. We identify some key topics that require further research: communities and networks of teachers in online environments; sustainability of these communities and kinds of organizational structures; knowledge-building practices in technology-mediated work group interactions; and online interactions among teachers. The emergence of new research issues also gives rise to new theoretical approaches or the adaptation of existing theoretical perspectives that are presented in this special issue. We summarize some of these theoretical perspectives and attempt to show how online environments have changed them, as well as some theoretical problems that remain to be solved.
In this chapter, the authors describe the design of an approximation for the elementary mathematics methods classroom, focused on providing feedback that builds on children's strengths. This approximation is premised on the idea that using student strengths can be a first step toward designing more equitable instruction in the mathematics classroom. In the multi-phase approximation, prospective teachers (PTs) first complete a fractions task written for third grade. Next, PTs are provided with a set of student work, which they examine with an eye to identifying student strengths. PTs are then asked to use both what they know about the student strengths and appropriate practices to write student feedback. Following the approximation is a discussion of key design decisions and future directions.
Este artigo discute resultados de uma pesquisa realizada com licenciandos em Pedagogia de uma instituição de ensino superior da mata norte do estado de Pernambuco, cujo objetivo foi compreender qual a impressão destes futuros professores sobre a matemática e seu ensino. A pesquisa em estudo tem um caráter qualitativo e foi realizada com apenas 6 estudantes do 5° período. Os dados foram produzidos com base em questionamentos realizados em sala de aula pelo professor regente do componente curricular - fundamentos teórico e metodológico da matemática na educação infantil relacionados a importância da matemática para tais estudantes e analisados a partir do que as literaturas discutem sobre o tema. Os resultados indicam que embora entendam a importância da matemática no desenvolvimento da sociedade e na formação do indivíduo para o exercício da cidadania, verificou-se que durante a trajetória escolar dos estudantes envolvidos nesta pesquisa teve influência negativamente a forma que a matemática foi ensinada e, isso, pode ser evidenciado nos protocolos desta pesquisa. São explicitados ainda estereótipos voltados a não capacidade de aprender matemática, ou seja, os sujeitos deste estudo afirmaram que a matemática é para gênios e, que a escolha pelo curso de Pedagogia se deu em virtude de acreditarem que não havia matemática ao longo do curso. Isso implica dizer que há uma grande necessidade de repensar e reelaborar os currículos das instituições que oferecem o referido curso no que diz respeito ao desenvolvimento de competências para o ensino de matemática na educação básica.
Task design is an important element of effective mathematics teaching and learning. Past research in mathematics education has investigated task design in mathematics education from different perspectives (e.g., cognitive and cultural) and offered a number of (theoretical) frameworks and sets of principles. In this study, through a narrative research in the form of autoethnography, I reflected on my past teaching and research experience and proposed a (theoretical) framework for task design in mathematics education. It contains four main principles: (a) inclusion, (b) cognitive demand, (c) affective and social aspects of learning mathematics, and (d) theoretical perspective(s) toward learning mathematics. This framework could be used as a tool for critically reflecting on current practices in terms of task design in teaching mathematics and research in mathematics education. It may also contribute to ongoing research in mathematics education about task design and enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to design rich mathematical tasks for teaching and research purposes.
A common, widespread view on the field of mathematics entails that “mathematics is dry as dust [and] as exciting as a telephone book” (Davis & Hersh, 1981, p. 169), and that the professional mathematician is merely “a kind of calculator” (Krull, 1987, p. 48). Even more provocatively, mathematics is conceived by many of the general public as a “deadend” discipline in which all questions have already been answered, where nothing worthwhile is left for further investigation (Movshovitz-Hadar, 2008). However, mathematics is an active, growing, open-ended field – a fact which can be illustrated, amongst others, by the exponential growth in the number of new articles that are published per year (Dunne, 2019). Furthermore, the common perception of the subject by the people who are working within the field – the mathematicians themselves – is that mathematical work is creative in nature and often driven by its intrinsic aesthetic dimension (e.g., Brinkmann & Sriraman, 2009; Gadanidis, 2012; Sinclair, 2004).
Currently, a major trend in teacher education is the use of blended learning, which allows institutions to use the advantages of online learning while maintaining the regular course structure and professors' role. The authors present a case study of a mathematics methods course in a teacher education program at Western University. In this blended course, the online component consisted of three elements: (1) online modules publicly available at researchideas.ca/wmt, (2) online journal assignments through threaded forums, and (3) collaborative mind maps through Mindomo (https://www.mindomo.com). In this chapter, the authors look specifically into the latter two online components. Through a qualitative data analysis of teacher candidates' online discussion (both in online forums and mind-maps), the researchers respond to the question: What are the roles that each online activity played in the participants' education as mathematics teachers?
While change has been a constant in the faculty, grappling with a transition from a one-year
consecutive professional Bachelor of Education (B.Ed.) program to a two-year B.Ed. program is a
particular challenge. In addition to the challenges inherent in any process of curriculum reform,
the faculty also strives to we differentiate itself. While dealing with the teething pains that are
inevitable in such a fundamentally seismic and sudden change, University of Windsor Education
looks to seize opportunities presented to provide exceptional learning experiences for teacher
candidates manifested in transferrable and transformative competencies required for teaching and
living in diverse contexts.
This chapter discusses a diverse suite of courses designed to enhance experiential learning,
internationalization and global education, and community service-learning. This reinforces our
commitment to preparing holistic teachers who understand the multiple roles of teachers and the
social, political and moral imperatives of teaching.
Digitization in University Teaching – Experiences with the MathEdu Digital Teaching Concept and Students´ Acceptance of Digital Teaching Elements
When it comes to the digitization of university teaching, there is no shortage of available options, approaches, and tools. Based on the research literature a total of five different approaches is identified: mobile technologies, online course programs, learning objects and digital libraries (repositories), technological environments for collaborative learning, and digitized teaching concepts. In the MathEdu Digital project at the University of Education Schwäbisch Gmünd, Germany, digital approaches and tools are subject to critical analysis and testing as part of a specially developed teaching concept, which is based on experiences and student surveys initially before becoming methodical and empirical. The objective is to structure the math-didactical teaching so that the students gain versatile digital experiences, while at the same time, there's a focus on the identification and elimination of barriers for university teachers also/especially for those of having few digital experience. Based on the findings, as a basic concept, the blended learning format featuring digital and non-digital elements and the use of a learning management system with a well-maintained digital library including learning objects can both be classed as suitable methods. Video demos and webinars also come highly recommended, with the various integrated functions of the latter providing a particular boost to communication and interaction. For a smooth webinar planning, the use of a «direction plan», a prepared spreadsheet, has been successfully proven and tested, which is attached to this paper.
In this paper, we discuss a research we investigated the production of Digital Mathematical Performance (DMP) involving Public Image of Mathematics (PIM). Basically, DMP refers to use of the arts and digital technology in teaching and learning mathematics. In this case, one produced music and digital videos to communicate ideas about infinity. We report a qualitative case study communicating itself through Arts-Based Research following our analysis of two of the seven DMPs produced by pre-service Mathematics teachers in a university`s mobilization knowledge course that was carried out at Sao Paulo State University (UNESP), campus of Sao Jose do Rio Preto. Audiovisual recording of the course’s classes, video analysis of conceptual DMPs, semi structured interviews and surveys and questionnaires composed the production and analysis of data. In terms of findings, we observed alternative PIMs, as those visions promotes feelings such as love and follows dynamic aspects, which regards to mathematics as a human endeavour. We also stress that DMP environment offered ways to contribute with pre-service Mathematics teachers’ education, as undergraduates were engaged in alternative use of digital media and the Arts while developing mathematical activities, forming thinking collectives of humans-with-media.
The recent change in teacher education in Ontario, moving from a single year to a two-year program, has offered us an opportunity to rethink and redesign our Kindergarten – Grade 12 (K-12)teacher education programs. A major shift has been happening within and outside of education due to a renewed focus on different mathematical ways of thinking, including computational thinking (CT) (Grover & Pea, 2013; Wing, 2006, 2008, 2011; Yadav, Mayfield, Zhou, Hambrusch & Korb, 2014). In this chapter we discuss how CT has been integrated into teacher education programs at two Ontario universities and its connection to mathematics education.
I have investigated interfaces about the arts and digital media in mathematics education, conceptualizing the notion of digital mathematical performance (DMP). In this article, I discuss connections between: (a) the mathematical strands and processes of the K-8 Ontario Mathematics Curriculum in Canada, and; (b) DMP produced by students. Based on the analysis of twenty-two DMP, I argue that DMP may offer ways to: (1) explore most of the mathematical processes of the Ontario Curriculum, and; (2) open windows into the exploration of math contents. I highlight the educational significance in practicing DMP as an innovative process that integrates multimodality, playfulness, and creativity. In contrast, I have found that the production of DMP does not guarantee the in-depth connection between the math strands and processes of the Curriculum. Generally, students explored contents about Geometry, which is not surprising, regarding the visual nature of both: geometrical and digital media representations.
In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular cultural texts, we argue that popular discourses overwhelmingly construct mathematicians as white, heterosexual, middle‐class men, yet also construct them as ‘other’ through systems of binary oppositions between those doing and those not doing mathematics. Turning to the analysis of a corpus of 27 focus groups with school and university students in England and Wales, we explore how such images are deployed by learners. We argue that while learners’ views of mathematicians parallel in key ways popular discourses, they are not passively absorbing these as they are simultaneously aware of the clichéd nature of popular cultural images.
Proof is an essential characteristic of mathematics and as such should be a key component in mathematics education. Translating this statement into classroom practice is not a simple matter, however, because there have been and remain differing and constantly developing views on the nature and role of proof and on the norms to which it should adhere. Different views of proof were vigorously asserted in the reassessment of the foundations of mathematics and the nature of mathematical truth which took place in the nineteenth century and at the beginning of the twentieth, a reassessment which gave rise to well-known and widely divergent philosophical stands such as logicism, formalism and intuitionism. These differences have now been joined by disagreements over the implications for proof of ‘experimental mathematics’, ‘semi-rigorous mathematics’ and ‘almost certain proofs’, concepts and practices which have emerged on the heels of the enormous growth of mathematics in the last fifty years and the ever-increasing use of computers in mathematical research. If these and earlier controversies are to be reflected usefully in the classroom, mathematics educators will have to acknowledge and become familiar with the complex setting in which mathematical proof is embedded. This chapter aims at providing an introduction to this setting and its implications for teaching. It is not merely as a reflection of mathematical practice that proof plays a role in mathematics education, however. Proof in its full range of manifestations is also an essential tool for promoting mathematical understanding in the classroom, however artificial and unnatural its use there may seem to the beginner. To promote understanding, however, some types of proof and some ways of using proof are better than others. Thus this chapter also aims at providing an introduction to didactical issues that arise in the use of proof. The chapter first discusses the great importance accorded in mathematical practice to the communication of understanding, pointing out the place of proof in this endeavour and the implications for mathematics teaching. It then identifies and assesses some recent challenges to the status of proof in mathematics from mathematicians and others, including predictions of the ‘death of proof’. It also examines and largely seeks to refute a number of challenges to the importance of proof in the curriculum that have arisen within the field of mathematics education itself, sometimes prompted by external social and philosophical influences. This chapter continues by looking at mathematical proof, and the mathematical theories of which it is a part, in terms of their role in the empirical sciences. There are important insights into the use of proof in the classroom that may be garnered through a deeper understanding of the mechanism by which mathematicians, nominally practitioners of a non-empirical science, make an indispensable contribution to the understanding of external reality. Later sections examine the use of proof in the classroom from various points of view, proceeding from the premise that one of the key tasks of mathematics educators at all levels is to enhance the role of proof in teaching. The chapter first reports upon some ambivalent but nevertheless encouraging signs of a strengthened role for proof in the curriculum, and turns to a discussion of proof in teaching, offering a model defining its full range of potential functions. The important distinction between proofs which prove and proofs which explain is then introduced, and its application is presented at some length with the help of examples.
Argues that teaching should be based on Piaget's constructivism because it explains the nature of human knowledge; explains children's knowledge construction from birth to adolescence; and informs educators how Piaget's distinction among physical, social, and logicomathematical knowledge changes the way many subjects should be taught. Elementary mathematics instruction is used to elucidate these arguments. (KDFB)
Growing out of a child's cognitive developmental history, formal operations become established at about the age of 12-15 years. Reflected in his ability to reason hypothetically and independently on concrete states of affairs, these structures may be represented by reference to combinatorial systems and to 4-groups. The essence of the logic of cultured adults and the basis for elementary scientific thought are thereby provided. The rate at which a child progresses through the developmental succession may vary, especially from one culture to another. Different children also vary in terms of the areas of functioning to which they apply formal operations, according to their aptitudes and their professional specializations. Thus, although formal operations are logically independent of the reality content to which they are applied, it is best to test the young person in a field which is relevant to his career and interests.
This paper describes a research project that had two goals: (1) to design and develop a tool with which to investigate pupils'
images of mathematicians; and (2) to use the device to compare those images held by lower secondary pupils (ages 12–13) in
five countries. We report that with small cultural differences certain stereotypical images of mathematicians are common to
pupils in all of these countries and these images indicate that for pupils of this age mathematicians and the work that they
do are, for all practical purposes, invisible.
The infinitely small and the infinitely large are essential in calculus. They have appeared throughout its history in various
guises: infinitesimals, indivisibles, differentials, evanescent quantities, moments, infinitely large and infinitely small
magnitudes, infinite sums, power series, limits, and hyperreal numbers. And they have been fundamental at both the technical
and conceptual levels – as underlying tools of the subject and as its foundational underpinnings. We will consider examples
of these aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. We will also present `didactic observations' at relevant places in the historical account.
Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage
of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured
interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about
themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about
mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore,
each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable
and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate
degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to
pursue mathematical careers.