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

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 serve …

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Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried Jul 2010

Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried

The Mathematics Enthusiast

To shed light on how history of mathematics can play a role in mathematics education, Hernández and López chose well in focusing on the chain rule as a case study. Generally speaking, it is, as they point out, a topic students find difficult to grasp: it is a rule involving a different order of complexity than, say, the rule for differentiating functions of the form f(x)=xn, and, although it can eventually become intuitive, it is far from intuitive at the start. Harel et al. (2009) have pointed out that students’ difficulties with the chain rule involve: “...coordinating three or more …

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Magic Circles In The Arbelos, Christer Bergsten Jul 2010

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.

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Vectors In Climbing, Anne Birgitte Fyhn Jul 2010

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.

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The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe Jul 2010

The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe

The Mathematics Enthusiast

This article explores the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics. In particular, we draw on the mathematically pedigreed but misunderstood development of the Mercator projection and its connection to the integral of the secant function. We discuss the merits and the possible pitfalls of this approach based on a teaching module with undergraduate students. The appendices contain activities that can be implemented as an enrichment activity in a Calculus course.

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Problem Posing From The Foundations Of Mathematics, Libby Knott Jul 2010

Problem Posing From The Foundations Of Mathematics, Libby Knott

The Mathematics Enthusiast

This reflective paper develops a repertoire of questions for teachers to use in their classrooms during episodes of mathematics discussions with and among students. These questions are motivated by an examination of questions posed by Wittgenstein in Zettel, and are connected to underlying tacit assumptions about mathematics, most of which lie subtly below the generally accepted milieu of math-talk. Once classrooms norms have been established to encourage participation by all students in a democratic and just classroom environment, these questions can be used effectively to stimulate meaningful discourse. These questions provide important examples of problem posing designed to encourage student …

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

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 …

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

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 …

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Epilogue, Bharath Sriraman Jul 2010

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 outside …

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So Many Journals, So Many Words... So What?, Bharath Sriraman Jul 2010

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

The Mathematics Enthusiast

No abstract provided.

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Women Belonging In The Social Worlds Of Graduate Mathematics, Abbe H. Herzig Jul 2010

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 to …

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Polysemy Of Symbols: Signs Of Ambiguity, Ami Mamolo Jul 2010

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.

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Chaos In Physics And Recurrence In Arithmetic Sets, Jean Dayantis Jul 2010

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.

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Guest Editorial: A Starting Point, Ke Wu Norman Jul 2010

Guest Editorial: A Starting Point, Ke Wu Norman

The Mathematics Enthusiast

As a new faculty member in the Department of Mathematical Sciences at the University since Fall 2008, I was eager to find possible research partners with whom to build a research network for long term collaboration and support. I wondered “Where shall I start?” and “Whom shall I invite?” After several conversations with my colleague, Dr. Bharath Sriraman, and many phone calls to my good friend, Dr. Anne Kern, a new faculty at the University of Idaho, we came up with the idea of forming a support group of female faculty in the fields of mathematics and science education in …

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

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 …

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

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 …

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

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 of …

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Tme Volume 7, Numbers 2 And 3 Jul 2010

Tme Volume 7, Numbers 2 And 3

The Mathematics Enthusiast

No abstract provided.

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July 2010 News Releases, University Of Montana--Missoula. Office Of University Relations Jul 2010

July 2010 News Releases, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

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Orientation In Technological Space, Albert Borgmann Jun 2010

Orientation In Technological Space, Albert Borgmann

Philosophy Faculty Publications

No abstract provided.

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June 2010 News Releases, University Of Montana--Missoula. Office Of University Relations Jun 2010

June 2010 News Releases, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

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University Of Montana Commencement Program, 2010, University Of Montana--Missoula. Office Of The Registrar May 2010

University Of Montana Commencement Program, 2010, University Of Montana--Missoula. Office Of The Registrar

University of Montana Commencement Programs, 1898-2020

Commencement program from the University of Montana.

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Montana Kaimin, April 27, 2010, Students Of The University Of Montana, Missoula Apr 2010

Montana Kaimin, April 27, 2010, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

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Minutes From The April 8, 2010 Meeting Of The University Of Montana Faculty, University Of Montana--Missoula. Faculty Apr 2010

Minutes From The April 8, 2010 Meeting Of The University Of Montana Faculty, University Of Montana--Missoula. Faculty

University of Montana Faculty Senate Meeting Minutes

Meeting minutes from the April 8, 2010 meeting of the University of Montana faculty.

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Department Of Mathematical Sciences Newsletter, Spring 2010, University Of Montana--Missoula. Department Of Mathematical Sciences Apr 2010

Department Of Mathematical Sciences Newsletter, Spring 2010, University Of Montana--Missoula. Department Of Mathematical Sciences

Newsletters from the Department of Mathematical Sciences at UM

Studying Abroad in Scotland / Abram McCormick -- Alumni Profile: Aaron Luttman, PhD '06 / John Bardsley -- A PhD Student Describes his Research in Applied Mathematics / John Goldes -- Notes from the Chair / Leonid Kalachev -- 2010 Summer Math Camps at UM -- My Weekend of Math in Nebraska / Stephanie Bell -- Alumni News -- Department News -- Honor Roll of Donors -- 2010 Spring Scholarship and Award Winners -- Degree Recipients 2009-2010 -- Alumni Reply Form -- In Honor of Math Awareness Month

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Montana Kaimin, March 10, 2010, Students Of The University Of Montana, Missoula Mar 2010

Montana Kaimin, March 10, 2010, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

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March 2010 News Releases, University Of Montana--Missoula. Office Of University Relations Mar 2010

March 2010 News Releases, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

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Timing Of Present And Future Snowmelt From High Elevations In Northwest Montana, Bonnie Jean Gillan, Joel T. Harper, Johnnie N. Moore Jan 2010

Timing Of Present And Future Snowmelt From High Elevations In Northwest Montana, Bonnie Jean Gillan, Joel T. Harper, Johnnie N. Moore

Geosciences Faculty Publications

The sensitivity of snowmelt-driven water supply to climate variability and change is difficult to assess in the mountain west, where strong climatic gradients coupled with complex topography are sampled by sparse ground measurements. We developed a model which ingests daily satellite imagery and meteorological data and is suitable for areas >1000 km2, yet captures spatial variability of snow accumulation and melt in steep mountain terrain.We applied the model for the years 2000–2008 to a 2900 km2 snowmelt-dominated watershed in NW Montana. We found that >25% of the basin’s snow water equivalent (SWE) accumulates above the highest measurement station and >70% …

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Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon Jan 2010

Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon

Mathematical Sciences Faculty Publications

This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.

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Trace Gas And Particle Emissions From Domestic And Industrial Biofuel Use And Garbage Burning In Central Mexico, Ted J. Christian, Robert Yokelson, B. Cardenas, L. T. Molina, G. Engling, S. C. Hsu Jan 2010

Trace Gas And Particle Emissions From Domestic And Industrial Biofuel Use And Garbage Burning In Central Mexico, Ted J. Christian, Robert Yokelson, B. Cardenas, L. T. Molina, G. Engling, S. C. Hsu

Chemistry and Biochemistry Faculty Publications

In central Mexico during the spring of 2007 we measured the initial emissions of 12 gases and the aerosol speciation for elemental and organic carbon (EC, OC), anhydrosugars, Cl(-), NO(3)(-), and 20 metals from 10 cooking fires, four garbage fires, three brick making kilns, three charcoal making kilns, and two crop residue fires. Global biofuel use has been estimated at over 2600 Tg/y. With several simple case studies we show that cooking fires can be a major, or the major, source of several gases and fine particles in developing countries. Insulated cook stoves with chimneys were earlier shown to reduce …

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