Mathematics as a Constructive Activity

Teaching and learning involve reflexive actions and should be chosen thoughtfully and deliberately, not because someone has decided “what works.” In this study, I examine how complex conversations might offer pedagogical and theoretical (re)considerations in a teacher education course on mathematics. The term “math methods” is a doubly weighted phrase, for both mathematics and methods connote particular ideologies prevalent in current educational rhetoric. In order to unpack the impact of these words, I engage in research based on inquiry, historical analysis, and personal reflections, all of which I use in an eclectic, thoughtful, and explorative manner. The two main research questions I will explore in this dissertation involve effort by “teacher” and “student” in which both are learners, knowers and participants. The first question is how can complex conversations—those involving multiple perspectives—aid pre-service teachers in becoming reflective practitioners, effective professionals, and inquiring pedagogues? Specifically, teaching mathematics as a relational activity—in which a hermeneutical perspective is crucial—brings forth epistemological questions and issues. The historical situatedness of teacher education and mathematics education become relevant with respect to current epistemological perspectives of teachers and researchers, and these influences are examined in the context of pre-service teachers’ positionalities. The second question involves an examination of how I am transformed as I experience and reflect on participation in these complex conversations. While engaged as an instructor, I am simultaneously influenced by research in complexity theory, curriculum theory, and teacher education. In complex conversations, we can find possibilities for teaching and learning, even potential ways of being that we do not yet know. Complex conversations encourage a different form of interaction, a different way of imagining the world—different from a Ramist method of hierarchies, different from a patriarchal positioning of supervisors over teachers and teachers over students, and different from mathematics as what is. In (re)imagining what mathematics can be, it is important to recognize how mathematics is currently construed. May mathematics education be(come) a field of study that allows for differences, multiple perspectives, and authentic questions, where ideas do not converge or diverge but co-emerge.

The objective of this study was to follow up changes in knowledge related to the mathematics education field work of preliminary early childhood teachers. The subjects of this research were 28 students who were taking mathematics education courses in early childhood education departments at various universities. This research ran for 15 weeks and was conducted through field work relating to mathematics education. The study collected data from pre-service teachers' knowledge, the diagram of concept, writing journals, interviews, and materials from the internet. Through this procedure, pre-service teachers' knowledge for mathematics education could later be expanded, ordered, and integrated. In addition, pre-service teachers not only understood the importance of contents and levels of lesson plans, but also learned how to utilize educational media to make effective lessons. Furthermore, pre-service teachers realized that the mathematical concepts of students could be expanded depending on the contents and methods of pre-service teachers' lesson plans and students could then apply these concepts into daily situations.

One of the key ideas of the modern-day elementary mathematics teacher education deals with mediating learning by visual thinking to enable transition from seeing and acting on concrete objects to describing the visual and the physical through culturally accepted symbolic representations. This paper shares mathematical activities designed originally for teacher candidates and used with students in upper elementary classrooms at a school in Upstate New York with minority student enrollment 97%. Because successful use of conceptual thinking by young students does have positive impact on their future teachers, connection of work in the school to a master’s level elementary mathematics education course taught by the authors is discussed. It is shown how using a spreadsheet and Wolfram Alpha allows for the research-like extension of the activities to the secondary level of mathematics education.

Foreword, Ubiratan D'Ambrosio Acknowledgments Introduction, Brian Greer, Swapna Mukhopadhyay, Sharon Nelson-Barber, and Arthur B. Powell Part I: Foundations and Backgrounds 1. Culture and the Development of Mathematics: An Historical Perspective, Frank J. Swetz 2. New Philosophy of Mathematics: Implications for Mathematics Education, Paul Ernest 3. An Ethnomathematical Perspective on Culturally Responsive Mathematics Education, Swapna Mukhopadhyay, Arthur B. Powell and Marilyn Frankenstein 4. Seeing With Many Eyes: Connections Between Anthropology and Mathematics, Jim Barta and Mary E. Brenner 5. What Mathematics Teachers Need to Know about Culture and Language, Judit Moschkovich and Sharon Nelson-Barber 6. The Politics of Mathematics Education in the United States: Dominant and Counter Agendas, Eric Gutstein 7. Conceptions of Assessment of Mathematical Proficiency and their Implications for Cultural Diversity, Dalton Miller-Jones and Brian Greer Part II: Teaching and Learning 8. Preparing Culturally Responsive Mathematics Teachers, Geneva Gay 9. Mathematics Literacy and Liberation: Reframing Mathematics Education for African American Children, Danny Bernard Martin and Ebony O. McGee 10. Culturally Responsive Mathematics Education in the Algebra Project, Robert Moses, Mary Maxwell West and Frank E. Davis 11. A Two-Way Process for Developing Effective Culturally Based Math: Examples from Math in a Cultural Context, Jerry Lipka, Evelyn Yanez, Dora Andrew-Ihrke and Shehenaz Adam 12. Native-American Analogues to the Cartesian Coordinate System, Ron Eglash 13. Privileging Mathematics and Equity in Teacher Education: Framework, Counter-Resistance Strategies and Reflections from a Latina Mathematics Educator, Julia M. Aguirre 14. Latina Mothers' Perceptions about the Teaching and Learning of Mathematics: Implications for Parental Participation, Marta Civil and Beatriz Quintos 15. Culturally Responsive College Level Mathematics, Mark K. Davis, Shandy Hauk and M. Paul Latiolais Index

This study examines the evolving knowledge and beliefs of a preservice secondary mathematics teacher as she participated in a mathematics education course that emphasized mathematical and pedagogical connections and applications of the function concept. Her conceptions were revealed during a 10-week period through interviews, observations, and written work. The teacher's initial understanding of functions as computational activities (e.g., function machines, point plotting, vertical line test) was consistent with her larger view of mathematics as a collection of “concrete” procedures. Although her understanding of function grew substantially during the study, her anticipated approach to teaching, which was dominated by her narrow view of mathematics, was less significantly affected by course activities.

In this paper we present a model for formative assessment based on peer-review workshops on MOODLE, designed by researchers of te University of Salerno and  the University of Torino. The model has been implemented in the Mathematics and Mathematics education courses in Primary Education at the University of Torino. The peer-review workshops are intended to pursue the following objectives: (1) strengthening the argumentative skills of prospective teachers to direct them towards a relational view of mathematics; (2) provide them with models of formative assessment rooted in peer-review feedback managed by the university lecturer. We present an example of peer-review that intertwines effective feed-back with a relational understanding of mathematical thinking.

The book is a collection of problems in school mathematics specifically written for the teachers. It is an attempt to enrich prospective and current teachers with the deep knowledge of school mathematics and to develop their reasoning and proving skills. Also, it is supposed to help them to anticipate and analyze their students’ errors and use them as teachable moments. The book is intended to be used in mathematics education courses (or professional development) for pre-service or in-service secondary school teachers. It can be used in graduate and undergraduate courses, in accordance with the orientations of different teacher preparation programs. Additionally, it can be used for the independent studies. One can also imagine situations in which teachers might use certain problems from this problem book directly in working with students, but this would constitute a supplementary use of the book.

There is compelling evidence on the effectiveness of bibliotherapy for facilitating one’s development. Arguably, in teacher education, bibliotherapy has been shown to facilitate prospective teachers’ professional development. However, teacher educators may experience difficulties in finding relevant reading to stimulate prospective teachers’ identification process, which is essential if the application of pedagogical bibliotherapy is to be successful. This study is situated in a mathematics education course for prospective elementary school teachers and explores the features of relevant pedagogical reading via analysis of four prospective elementary school teachers’ identification processes with two case descriptions. The identification here relates to the reading of the so-called true stories; prospective teachers read stories of other prospective teachers from the same teacher education context. We outline the recommendations for the selection of reading material when applying pedagogical bibliotherapy in order to assist prospective teachers’ professional development.

There is still a shortage of qualified mathematics teachers in schools in developed and developing countries. It may be because of the problems facing mathematics teachers in schools and the problems facing mathematics teacher-educators in colleges of education who are responsible in producing qualified mathematics teachers. Mathematics teachers and educators are more concerned about the former and the latter is usually neglected. This article tries to trace out the problems facing mathematics teacher-educators in both developing and developed countries on the basis of a study carried out in Nepal and a similar study in England. 15 out of 16 and 135 out of 247 mathematical educators in Nepal and England respectively took part in these studies. It was found that lack of books and journals, teaching facilities and aids and negligible grants for research or personal studies are the main problems for mathematics teacher-educators both in Nepal and England. However it was seen that the problems faced by mathematical educators in Nepal were more serious than those of England.Key words: Mathematics teacher; Developing and Developed countries; Nepal and EnglandTribhuvan University JournalVolume XIV, 1991Page: 15-25Uploaded date: 5 October, 2010

Children's Mathematics Learning: The Struggle to Link Form and Understanding

Teaching Secondary and Middle School Mathematics combines the latest developments in research, standards, and technology with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics today. In the fully revised fifth edition, scholar and mathematics educator Daniel Brahier invites teachers to investigate the nature of the mathematics curriculum and reflect on research-based "best practices" as they define and sharpen their own personal teaching styles. The fifth edition has been updated and expanded with a particular emphasis on the continued impact of the Common Core State Standards for Mathematics and NCTM’s just-released Principles to Actions, as well as increased attention to teaching with technology, classroom management, and differentiated instruction. Features include: A full new Chapter 7 on selection and use of specific tools and technology combined with "Spotlight on Technology" features throughout clearly illustrate the practical aspects of how technology can be used for teaching or professional development. Foundational Chapters 1 and 2 on the practices and principles of mathematics education have been revised to build directly on Common Core State Standards for Mathematics and Principles to Actions, with additional references to both documents throughout all chapters. A new Chapter 4 focuses on the use of standards in writing objectives and organizing lesson plan resources while an updated Chapter 5 details each step of the lesson planning process. A fully revised Chapter 12 provides new information on teaching diverse populations and outlines specific details and suggestions for classroom management for mathematics teachers. Classroom Dialogues" features draws on the author’s 35-year experience as an educator to present real-world teacher-student conversations about specific mathematical problems or ideas "How Would You React?" features prepares future teachers for real-life scenarios by engaging them in common classroom situations and offering tried-and-true solutions. With more than 60 practical, classroom-tested teaching ideas, sample lesson and activities, Teaching Secondary and Middle School Mathematics combines the best of theory and practice to provide clear descriptions of what it takes to be an effective teacher of mathematics.

This study aims to design online mathematics games using Scratch, Geogebra, and Geogebra AR through multimedia education mathematics courses. This study used the multimedia development life cycle. Participants in the study were 41 students (13 male and 28 female) of fifth-semester in a multimedia course in mathematics education at a university in West Java, Indonesia. The research instrument was a questionnaire through Google Forms, performance appraisal, observation, and interviews. Based on the research results it is known that Scratch, Geogebra, and Geogebra AR can be used in math game design even though previous students have not studied both, but the results are good. The author suggests that students can try out these math games at school during research or teaching practice. In addition, the authors hope that the game can be published on the internet so that it can be used by many students. Keywords: game online, scratch, geogebra AR

The research sought to assess mathematics teachers’ acceptance of Information and Communication Technology (ICT) integration into teaching and learning at the secondary schools. This study was a cross-sectional survey that gathered data with structured questionnaire. The population was mathematics (core and elective) teachers of secondary schools within the Ashanti region of Ghana. Purposive sampling was used to select mathematics teachers from 41 secondary schools in the region. In all, there were 207 usable questionnaires for the study. Structural Equation Modelling (SEM) was run in Amos (v.23) to estimate the path coefficients of the various hypotheses, using Technology Acceptance Model (TAM). The study established that perceived ease of use predicted both perceived usefulness and attitude towards use; perceived usefulness predicted attitude towards use and behavioral intention; attitude towards use of technology predicted the behavioral intention to adopt technology in teaching and learning, while behavioral intention also predicted actual usage of ICT in teaching and learning of mathematics. As an extension to the original TAM, the study found school related factors as percussor to perceived usefulness and perceived ease of use. Similarly, ICT training was found to greatly influence perceived usefulness and perceived ease of use. Keywords: ICT, mathematics education, structural equation modelling, technology acceptance model

The purpose of this study was to investigate beliefs and perceived self-efficacy beliefs of Turkish prospective elementary mathematics teachers in using origami in mathematics education. Furthermore, gender differences in their beliefs and perceived self-efficacy beliefs were investigated. Data for the current study was collected via Origami in Mathematics Education Belief Scale (OMEBS) and Origami in Mathematics Education Self-Efficacy Scale (OMESS). Descriptive analysis results indicated that prospective mathematics teachers strongly believe that origami is beneficial and effective to be used in mathematics education. However, their perceived self-efficacy beliefs were at little higher than moderate level. Lastly, independent sample t-test results revealed that female teacher candidates have significantly higher beliefs and perceived self-efficacy beliefs in using origami in mathematics education when compared with male teacher candidates.

The year 2020 will be remembered as the time when the COVID-19 pandemic swept the world. Almost overnight, all educational activities pivoted to online platforms and teaching and learning was navigated in uncharted terrains. In mathematics education, concerns about sustaining online teaching and learning of mathematics have generated efforts in using digital technologies. In this paper, we use the lens of complexity theory and in particular the constructs of agents, interaction, dispersed control, and emergence to describe top-down and bottom-up mechanisms for change within the sudden shift to emergency remote teaching and learning. The authors’ collaborative work was carried out through online meetings discussing observations on and insights about their experience as mathematics teacher educators during the COVID-19 pandemic and traction data in three locally available online platforms. The main findings indicate two government-led, top-down initiatives, and three community-led bottom-up initiatives. The results suggest that mathematics teachers, mathematics teacher educators, and mathematics teacher consultants served as actors within the larger system. We discuss the possibilities and constraints of mathematics education in a time of crisis through the lens of complexity theory and offer trajectories for further research.