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Collaborative Evaluative Inquiry: A Model For Improving Mathematics Instruction In Urban Elementary Schools, Iman C. Chahine, Lesa M. Covington Clarkson 2010 Georgia State University

Collaborative Evaluative Inquiry: A Model For Improving Mathematics Instruction In Urban Elementary Schools, Iman C. Chahine, Lesa M. Covington Clarkson

Middle-Secondary Education and Instructional Technology Faculty Publications

In this article, the authors describe the cyclical process of a collaborative evaluative inquiry project and the data collected throughout the project—data that not only informed "next steps" during the project but also show promise in documenting the benefits of such projects. Over a period of 18 months, seven elementary teachers from a K–6 urban elementary school collaborated with university personnel using Parsons’s (2002) Evaluative Inquiry Model, a 5-stage, cyclical model that includes defining, planning, and investigating challenges; collecting, analyzing, and synthesizing data; and communicating findings that transpire through collaborative inquiry. Overall, the project focused on improving ...


The Nuts And Bolts: A Review Of Culturally Specific Pedagogy In The Mathematics Classroom: Strategies For Teachers And Students, Shonda Lemons-Smith 2010 Georgia State University

The Nuts And Bolts: A Review Of Culturally Specific Pedagogy In The Mathematics Classroom: Strategies For Teachers And Students, Shonda Lemons-Smith

Middle-Secondary Education and Instructional Technology Faculty Publications

The author reviews Jacqueline Leonard's Culturally Specific Pedagogy in the Mathematics Classroom: Strategies for Teachers and Students.


Polysemy Of Symbols: Signs Of Ambiguity, Ami Mamolo 2010 University of Montana

Polysemy Of Symbols: Signs Of Ambiguity, Ami Mamolo

The Mathematics Enthusiast

This article explores instances of symbol polysemy within mathematics as it manifests in different areas within the mathematics register. In particular, it illustrates how even basic symbols, such as ‘+’ and ‘1’, may carry with them meaning in ‘new’ contexts that is inconsistent with their use in ‘familiar’ contexts. This article illustrates that knowledge of mathematics includes learning a meaning of a symbol, learning more than one meaning, and learning how to choose the contextually supported meaning of that symbol.


Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi 2010 Syracuse University

Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi

Mathematics - Faculty Scholarship

Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.


Internal And External Comments On Course Evaluations And Their Relationship To Course Grades, Hilary Smith Risser 2010 University of Montana

Internal And External Comments On Course Evaluations And Their Relationship To Course Grades, Hilary Smith Risser

The Mathematics Enthusiast

The validity of student evaluations of courses and the relationship between evaluations and course outcomes has frequently been examined. Since many course evaluations give students an opportunity to provide answers to open-ended questions in addition to giving Likert scale ratings, it is important to understand the relationship between these responses and course outcomes. This study examined the relationship between student responses to open ended questions (specifically whether they attributed their achievement to factors within their control or factors not within their control) and their outcomes in the course. The results of the study indicate that students that identified external factors ...


Tme Volume 7, Numbers 2 And 3, 2010 University of Montana

Tme Volume 7, Numbers 2 And 3

The Mathematics Enthusiast

No abstract provided.


Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit 2010 University of Montana

Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit

The Mathematics Enthusiast

This paper describes a singular process that has been transforming mathematics education in Israel over the past 20 years, as a result of a massive influx of mathematics teachers from the former Soviet Union (FSU). It traces the key points of conflict that marked the initial contact between Israel's mathematical and educational culture and the codes and values brought with the immigrant teachers from the FSU. It then shows how this conflict is gradually becoming resolved, as the two disparate cultures merge into a single, new culture, based on 'the best of both worlds.' This case, we claim, can ...


The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer 2010 University of Montana

The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer

The Mathematics Enthusiast

This study examined a professional development project for K-12 science teachers that engaged participants in an authentic scientific investigation along with explicit-reflective attention to nature of science (NOS). The Views of Nature of Science (VNOS) and Views of Scientific Inquiry (VOSI) Questionnaires (Lederman, Abd-El-Khalick, Bell, & Schwartz, 2002; Schwartz, Lederman, & Thompson, 2001) were used to examine the relationship between teachers’ views of NOS and specific aspects of the professional development project. Results of the study show that teachers’ views of NOS were influenced by the multidisciplinary, primarily non-experimental research that they engaged in, the opportunity to observe interactions of scientists from different disciplines ...


Women Belonging In The Social Worlds Of Graduate Mathematics, Abbe H. Herzig 2010 University of Montana

Women Belonging In The Social Worlds Of Graduate Mathematics, Abbe H. Herzig

The Mathematics Enthusiast

The participation of women in post-graduate mathematics still lags substantially behind that of men. Drawing upon sociocultural theories of learning, I argue that success in graduate school necessitates learning mathematical content, participating in mathematical practices, and developing a sense of belonging in mathematics. Using an institutional ethnography approach, I interviewed 12 women graduate students from three mathematics departments in the U.S. to document their experiences within the social relations of graduate mathematics. They described both intrinsic and extrinsic obstacles to belonging, including a tension between their desire to belong and their needs to distance themselves from what they perceived ...


Magic Circles In The Arbelos, Christer Bergsten 2010 University of Montana

Magic Circles In The Arbelos, Christer Bergsten

The Mathematics Enthusiast

In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.


Chaos In Physics And Recurrence In Arithmetic Sets, Jean Dayantis 2010 University of Montana

Chaos In Physics And Recurrence In Arithmetic Sets, Jean Dayantis

The Mathematics Enthusiast

After briefly recalling the concepts of recurrence and chaos in physics, the recurrence properties of arithmetic sets are examined following Gauss’ method, as exposed in part three of his Disquisitiones Arithmeticae. This problem in number theory is related to the physical problem of recurrence in deterministic chaos. Most possible forms of moduli are examined in detail with respect to their recurrence properties, for application to the generalized Bernoulli mapping. The emphasis is put on period lengths, rather than on congruences. In an annex the recurrence properties of Arnold’s cat map are briefly examined.


Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn 2010 University of Montana

Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher’s understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry.


Vectors In Climbing, Anne Birgitte Fyhn 2010 University of Montana

Vectors In Climbing, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this article, the work on mesospace embodiments of mathematics is further developed by exploring the teaching and learning of vector concepts through climbing activities. The relevance and connection between climbing and vector algebra notions is illustrated via embedded digital videos.


Pre-Service Teachers In Mathematics Lesson Study, Elizabeth A. Burroughs, Jennifer L. Luebeck 2010 University of Montana

Pre-Service Teachers In Mathematics Lesson Study, Elizabeth A. Burroughs, Jennifer L. Luebeck

The Mathematics Enthusiast

This paper presents qualitative evidence to answer the questions, “What are the outcomes of engaging pre-service and in-service teachers in a collaborative lesson study experience” and “How can the outcomes of this experience inform future ways to include preservice teachers in lesson study?” The data gathered demonstrate that including pre-service teachers in lesson study can introduce them to lesson-building as a process and cross-grades teacher collaboration. It can give them opportunities to be critical thinkers in the context of mathematics education and encourages them to think as teachers. One weakness the pre-service teachers demonstrated was an incomplete understanding of the ...


Epilogue, Bharath Sriraman 2010 University of Montana

Epilogue, Bharath Sriraman

The Mathematics Enthusiast

The table of contents of this double issue included the above quote from the historian Howard Zinn which might seem puzzling to the reader. Why was this quote included and what is it supposed to mean? In the opening editorial, I mused over the whole enterprise of scholarly publishing and what it amounts to in the grand scheme of things. Zinn’s quote reminds us that academia is a cloistered unit and many of the things we place importance on in the academic culture of publish or perish seem insignificant when viewed through the lens of real problems that occur ...


So Many Journals, So Many Words... So What?, Bharath Sriraman 2010 University of Montana

So Many Journals, So Many Words... So What?, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.


A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez 2010 University of Montana

A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez

The Mathematics Enthusiast

According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and ...


Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher 2010 University of Montana

Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher

The Mathematics Enthusiast

This paper reports on the strategies chosen by a group of sixth-grade students in an urban informal learning program as they worked to solve an open-ended, nonroutine task. In particular, the paper focuses on the ability of these students to rise above their previous, procedure-based misconceptions and arrive at a mathematically reasonable solution. Aspects of the problem task, the problem-solving environment, and, importantly, of the nature of the teacher’s interventions are analyzed to determine the conditions that encouraged students to approach mathematics as a logical, meaningful, sense-making activity.


Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams 2010 University of Montana

Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams

The Mathematics Enthusiast

This study presents two critical cases illustrating distinct patterns in teachers' use of literacy strategies in secondary mathematics classes. The cases are part of a professional development project designed to enhance teachers' pedagogical skills by developing content literacy strategies for use in secondary mathematics and science classrooms. Teachers' beliefs about teaching mathematics, their uses of writing and vocabulary development strategies, and goals for student learning were examined via interviews, classroom observations, reflections on teaching, and teacher posts to an online discussion forum. Results show patterns of literacy strategy use were related to teachers' views of pedagogy and of mathematics. Ned ...


A Graduate Level In-Service Teacher Education Curriculum Integrating Engineering Into Science And Mathematics Contents, Ke Wu Norman, Tamara J. Moore, Anne L. Kern 2010 University of Montana

A Graduate Level In-Service Teacher Education Curriculum Integrating Engineering Into Science And Mathematics Contents, Ke Wu Norman, Tamara J. Moore, Anne L. Kern

The Mathematics Enthusiast

This paper presents the curriculum of a master’s level in-service teacher education course that integrates engineering into mathematics and science for high school mathematics and science teachers. The curricular design of the course including learning goals, reading list, course assignment and grading rubric, and a sample of Model-Eliciting Activities (MEAs) are discussed. In addition preliminary research results on teachers’ perception of engineering show that prior to taking this course, teachers’ understanding of engineering mainly focused on the professions of the engineering discipline. After the participation in the course, teachers’ perceptions of engineering were broadened and included the design process ...


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