Mathematics Commons^™

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 …

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 …

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.

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.

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.

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 …

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 …

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 …

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 …

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

The Mathematics Enthusiast

No abstract provided.

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 …

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.

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.

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 …

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 …

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 …

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 …

Tme Volume 7, Numbers 2 And 3

The Mathematics Enthusiast

No abstract provided.

Early Intervention In College Mathematics Courses: A Component Of The Stem Rrg Program Funded By The Us Department Of Education, Rohitha Goonatilake, Eduardo Chappa

The Mathematics Enthusiast

Student preparedness in entry level college mathematics courses has decreased in the past. In order for students to be successful in these courses, early intervention is required. Texas A&M International University (TAMIU) has implemented an early intervention program, the Mathematics Enrichment Program (MEP), which will target freshman students entering College Algebra courses in Spring 2009. This project is part of the STEM Recruitment, Retention, and Graduation program, recently funded by the US Department of Education. This paper will highlight the components of the project, most importantly the extent of the intervention, how the project is planned, and preliminary results.

New Year Tidings, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Leading Learning Within A Plc: Implementing New Mathematics Content, Ann Heirdsfield, Janeen Lamb, Gayle Spry

The Mathematics Enthusiast

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Tme Volume 7, Number 1

The Mathematics Enthusiast

No abstract provided.

Mathematical Reasoning In Service Courses: Why Students Need Mathematical Modeling Problems, Kris H. Green, Allen Emerson

The Mathematics Enthusiast

In this paper we argue that conventional mathematics word problems are not aligned with the typical learning goals and expectations partner disciplines, especially business, have in requiring that their students take mathematics courses. Using the taxonomy of educational objectives presented by Anderson and Krathwohl (2001) we show how mathematical modeling problems can be used to promote the needed alignment and contrast two examples to illustrate the differences. We then demonstrate how the more conventional word problem can be rewritten as a modeling problem. Sample assessment materials and instructional activities are included to support teachers in making the transition to the …

Gender And Mathematics Education In Pakistan: A Situation Analysis, Anjum Halai

The Mathematics Enthusiast

This paper reports from a situation analysis of gender issues in mathematics education in Pakistan. It was undertaken at the initiation of a large scale project which aimed to understand how curriculum change in mathematics and science education may be implemented in ways that contribute to poverty alleviation and promote gender equity in disadvantaged rural settings. The paper posits that issues of access, achievement and quality of mathematics education are integrally linked with questions of equity, in this case gender equity. It identifies several questions and arenas for further research and makes recommendations for policy and practice in mathematics education.

High School Teachers Use Of Dynamic Software To Generate Serendipitous Mathematical Relations, Manuel Santos-Trigo, Hugo Espinosa-Pérez

The Mathematics Enthusiast

In this study, we document and analyse problem-solving approaches that high school teachers exhibited as a result of using dynamic software (Cabri-Geometry) to construct and examine geometric configurations. What type of questions do teachers pose and pursue while representing and exploring mathematical tasks or objects dynamically? To what extent their initial problem solving strategies are enhanced with the use of the tools? Results indicate that the use of the tool offered the participants the opportunity of constructing geometric configuration (formed by simple mathematical objects) that led them to identify and explore key mathematical relations.

“What Was Really Accomplished Today?” Mathematics Content Specialists Observe A Class For Prospective K–8 Teachers, Andrew M. Tyminksi, Sarah Ledford, Dennis Hembree

The Mathematics Enthusiast

One of the important activities mathematics teacher educators engage in is the development of teachers at both the in-service and pre-service levels. Also of importance is the professional development of these professional developers. In the summer of 2004, a summer institute was held that allowed mathematics teacher educators watch the teaching of a mathematics content course for prospective K–8 teachers. This paper examines the manner in which a specific group of mathematics content specialists experienced this professional development.

Randomness: Developing An Understanding Of Mathematical Order, Steve Humble

The Mathematics Enthusiast

Is randomness merely the human inability to recognise a pattern that may in fact exist?

The three activities described show how order can be found in seemly random activities. The author has found that by using these activities on randomness, his students have developed a greater understanding of mathematical pattern and sequence. The teaching mathematical concepts in this way, engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can sometimes occur in the classroom. By taking the maths beyond the classroom, …

The Constructs Of Phd Students About Infinity: An Application Of Repertory Grids, Serdar Aztekin, Ahmet Arikan, Bharath Sriraman

The Mathematics Enthusiast

Infinity has been one of the more difficult concepts for humanity to grasp. A major component of the research on mathematics education related to infinity has been the study of student’s conceptions and reasoning about calculus subjects, particularly limits and series. Some related studies are about Cantor’s ordinal and cardinal infinity. However since most students at the high school and college level are unfamiliar with symbolic representations and terminology, such as a set theoretic approach, a context (generally geometric) is used for investigating notions of infinity indirectly. In this paper we report on a study on the constructs of PhD …

When Is .999... Less Than 1?, Karin Usadi Katz, Mikhail G. Katz

The Mathematics Enthusiast

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999... be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.

The Journal (Wheel) Keeps On Turning, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.