Mathematics Commons^™

Values In Mathematics And Science Education: Similarities And Differences, Alan Bishop

The Mathematics Enthusiast

literacy and expertise from their citizens than ever before. At the heart of such demands is the need for greater engagement by students with school mathematics and science. As the OECD/PISA definition of numeracy puts it:

“Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen”(OECD, 2003)

Values are an inherent part of the educational process at all levels, from the systemic, institutional macro-level, …

Critique On Eisenberg's Article, Renuka Vithal

The Mathematics Enthusiast

I enjoyed reading the article and learned some interesting (and disturbing) information about well known mathematicians that is not so well known. However in its current form it is more appropriate for the popular media rather than as an academic or scholarly article.

Having said that it does raise some serious questions of ethics and values that all mathematics educators should be engaging. The increasingly popular view that mathematics teaching be socially contextualised means that this kind of historical information may be communicated in lecture rooms and classroom with little understanding or awareness of the "hidden curriculum" being enacted.

Doin' The Math: On Meaningful Mathematics-Ethics Connections, Kurt Stemhagen

The Mathematics Enthusiast

In this essay mathematics is conceived of as intentional human activity. Since intention implies choice, there are ethical dimensions to making mathematical choices. Embracing these dimensions requires acknowledging the contextual nature of mathematics. First John Dewey’s philosophy of mathematics and a reconsideration of mathematical empiricism are posited as ways to foster a context sensitive understanding of mathematics. Next, I address the ways in which existent conceptions of mathematics—even those which support reform in mathematics education—are insufficient with regard to their ability to recognize its human dimensions. The essay concludes with a distinction between mathematics education that ethically applies existing versions …

The Action Map As A Tool For Assessing Situated Mathematical Problem Solving Performance, Murad Jurdak

The Mathematics Enthusiast

The aim of this paper is to investigate the appropriateness, concurrent and construct validity of action map as a tool for assessing situated problem solving performance. Action map is rooted in activity theory whose stipulations are compatible with situated problem solving. Thirty-one last year secondary students were given three tasks with real –world context. Based on the analysis of the written solutions and interviews, evidence is presented on the appropriateness and validity of action map as an instrument to assess situated problem solving performance.

A Reflection On Mathematical Cognition: How Far Have We Come And Where Are We Going?, Kristin Umland

The Mathematics Enthusiast

Any theory of mathematical cognition and learning must ultimately articulate with our current understanding of how the mind works and with current theories of how knowledge is acquired from both an individual and social perspective. Certainly the human mind is very complex; understanding how it works in general and identifying the components that contribute to “doing mathematics” in particular is no easy task. To understand how the mind does mathematics, we must identify what mathematicians actually do in the context of everyday cognition. Here we discuss some of what is known and about this and point out directions for future …

Relationship Of Some Psychological Variables In Predicting Problem Solving Ability Of In-Service Mathematics Teachers, M. K. Akinsola

The Mathematics Enthusiast

This paper examines some psychological variables in predicting problem solving ability of inservice mathematics teachers. The sample consists of 122 in-service teachers enrolled in degree programme. Five standardized instruments were used to collect the data on teachers’ mathematics anxiety, mathematics teaching efficacy belief, locus of control, study habits and problem solving ability. Multiple regression, Chi-square analysis,and Pearson moment correlation coefficient were used to analyze the data. The results show that mathematics anxiety, mathematics teaching efficacy belief, locus of control and study habits all have significant relationships with problem solving ability with mathematics anxiety having the highest and study habits the …

How Is Mathematics Education Philosophy Reflected In The Math Wars?, David M. Davison, Johanna E. Mitchell

The Mathematics Enthusiast

Throughout the duration of what has been termed the “math wars”, many overlygeneralized statements by both sides have detracted from the quest for a solution to the conflict between conceptual and procedural approaches to mathematics study. In terms of philosophies of mathematics education, the absolutist view posits that mathematical knowledge is certain and unchallengeable while the fallibilist view is that mathematical knowledge is never beyond revision and correction. We suggest that the major mathematics education reforms have been absolutist in focus and have not reflected the changing nature of the discipline. Thus we believe that true reform will reflect changing …

Teaching Proof At Ks4, Sue Waring

The Mathematics Enthusiast

Proof is a fundamental component of mathematics and so, in my opinion, it should be part of mathematical education in schools. It is an important link between topics and so can help pupils achieve a deeper understanding of the “wholeness” of mathematics and, moreover, it is vital for able pupils if they are to be inspired by mathematics and given a firm basis for future mathematical studies.

Consecutive Numbers, Steve Humble

The Mathematics Enthusiast

The hidden secrets of our number system can often reveal the magical quality of mathematics. Through the process of discovery and discussion with fellow classmates, the hidden depths of maths takes on new appeal. Consecutive numbers is one such area that gives this excitement.

New And Noteworthy Books From Sense Publishers

The Mathematics Enthusiast

No abstract provided.

Tme Worldwide Daily Circulation [Dec 6-11, 2007]

The Mathematics Enthusiast

No abstract provided.

The Correlation Coefficients, Rudy Gideon

Mathematical Sciences Faculty Publications

A generalized method of defining and interpreting correlation coefficients is given. Seven correlation coefficients are defined — three for continuous data and four on the ranks of the data. A quick calculation of the rank based correlation coefficients using a 0-1 graph-matrix is shown. Examples and comparisons are given.

A Hexagon Result And Its Generalization Via Proof, Michael De Villiers

The Mathematics Enthusiast

This paper presents the discovery of a hexagon result on Geometer’s Sketchpad and its generalization via proof for any 2n-gon. The result is : If ABCDEF is a hexagon with opposite sides parallel (not necessarily equal), then the respective centroids G, H, I, J, K and L of triangles ABC, BCD, CDE, DEF, EFA and FAB, form a hexagon with opposite sides both equal and parallel.

Introduction Of A New Construct: The Conceptual Tool "Flexibility", Mette Andresen

The Mathematics Enthusiast

This paper presents a new construct: the conceptual tool ‘Flexibility’. The construct was a result of an attempt to extract experiences of teaching and learning with the use of laptops. It was further developed and refined on the basis of four small-scale teaching experiments. The teaching experiments, being part of a development project in upper secondary school mathematics, investigated the use of laptops for teaching differential equations from a modeling point of view. The research was double-aimed: one objective was to conclude the project with some recommendations for the design of teaching, in the form of guidelines suitable for a …

New And Noteworthy Books From Sense Publishers

The Mathematics Enthusiast

No abstract provided.

Tme Volume 4, Number 2

The Mathematics Enthusiast

No abstract provided.

Editorial: New Horizons-Four Years Later, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Objective Truth Versus Human Understanding In Mathematics And In Chess, Olle Häggström

The Mathematics Enthusiast

This paper begins with a review of the collection 18 Unconventional Essays on the Nature of Mathematics edited by Hersh (2006). Inspired especially by the contribution by Thurston to that collection, I then go on to discuss, by means of a couple of thought experiments involving computer "oracles", the nature of mathematics as a human activity, hopefully providing some balance to the simplified view (sometimes held by research mathematicians such as myself) of the discipline as purely a quest for objective truth.

The Philosophy Of Mathematics, Values And Keralese Mathematics, Paul Ernest

The Mathematics Enthusiast

This paper explores the philosophical significance of the Keralese and Indian subcontinent contribution to history of mathematics. Identifying the most accurate genesis and trajectory of mathematical ideas in history that current knowledge allows should be the goal of every history of mathematics, and is consistent with any philosophy of mathematics. I argue for the need of a broader conceptualization of philosophy of than the traditional emphasis on scholastic enquiries into epistemology and ontology. For such an emphasis has been associated, though I add need not necessarily be so, with an ideological position that devalues non-European contributions to history of mathematics. …

Mars Exploration Rover: Mathematics And People Behind The Mission, Uffe Thomas Jankvist, Bjørn Toldbod

The Mathematics Enthusiast

This paper is a selective study of the mathematics and people involved with a specific space mission, namely the Mars Exploration Rover (MER) mission launched in 2003. The specific mathematics of the MER mission are sought uncovered through interviews with applied scientists who worked with different aspects of the mission at the Jet Propulsion Laboratory (JPL). Some of the more specific questions attempted answered through this article for instance concerns if the aerospace industry, exemplified by the MER mission, calls for new developments in mathematics or if it mostly relies on well established theories; how much independence the scientists have …

On The Solution To Octic Equations, Raghavendra G. Kulkarni

The Mathematics Enthusiast

We present a novel decomposition method to decompose an eighth-degree polynomial equation, into its two constituent fourth-degree polynomials, as factors, leading to its solution. The salient feature of the octic equation solved here is that, the sum of its four roots being equal to the sum of the remaining four roots. We derive the condition to be satisfied by coefficients so that the given octic is solvable by the proposed method.

Mathematics Education And Neurosciences: Relating Spatial Structures To The Development Of Spatial Sense And Number Sense, Fenna Van Nes, Jan De Lange

The Mathematics Enthusiast

The Mathematics Education and Neurosciences (MENS) project is aimed at exploring the development of the mathematical abilities of young (four- to six-year old) children. It is initiated to integrate research from mathematics education with research from educational neuroscience in order to come to a better understanding of how the early skills of young children can best be fostered for supporting the development of mathematical abilities in an educational setting. This paper is specifically focused on the design research that is being conducted from the perspective of mathematics education in which we are investigating the relationship between young children’s insight into …

Non-Linear Functions In Secondary School Of Lower Qualification Level (German Hauptschule), Astrid Beckmann

The Mathematics Enthusiast

This article reports of the effectiveness of introducing non-linear functions in a German Hauptschule. Some research based recommendations are provided for practitioners with the goal of improving student competencies in lieu of PISA.

Looking Back At The Beginning: Critical Thinking In Solving Unrealistic Problems, Mark Applebaum, Roza Leikin

The Mathematics Enthusiast

We believe that problem-solving skills engage critical thinking at every phase of problem solution. In this research a special attention is given to the fist phase - "understanding the problem". We consider this phase as a continuation of all the previous mathematical experience, in which understanding of new problems requires "looking back" at those solved in the past. Evaluation of the givens in the problem sometimes allows immediate solution whereas in other cases it shows that solution does not exist. We found that it is not easy for mathematics teachers to discover that a problem includes contradictory (i.e. unrealistic) conditions. …

The Need For An Inclusive Framework For Students' Thinking In School Geometry, Jaguthsing Dindyal

The Mathematics Enthusiast

This study is the outcome of a research that investigated how students who were assigned varying levels of geometric thinking attempted problems requiring some amount of algebraic thinking in geometry. The study reports that students’ thinking in geometry also requires facility with algebra and as such there is a need for a framework that provides a more inclusive view of what constitutes geometric thinking in school mathematics.

Lagrange: A Well-Behaved Function, Benjamin Harris

The Mathematics Enthusiast

This paper outlines the biography and achievements of Joseph Louis Lagrange (1736–1813) and includes a detailed explanation, with examples, of the Lagrange Multiplier method for optimizing multivariate functions subject to constraint. The Lagrange Multiplier is widely used in chemistry, physics, and economics, in particular. The paper considers the origin of economics’ use of the multiplier and provides a concrete example of how it is used in microeconomic theory. While the focus is on the multiplier’s application to microeconomics, the intended audience includes all teachers and students who encounter any of Lagrange’s contributions. Since Lagrange’s contributions to mathematics are numerous, so …

Learning Mathematics With Understanding: A Critical Consideration Of The Learning Principle In The Principles And Standards For School Mathematics, Andreas J. Stylianides, Gabriel J. Stylianides

The Mathematics Enthusiast

Learning with understanding has increasingly received attention from educators and psychologists, and has progressively been elevated to one of the most important goals for all students in all subjects. However, the realization of this goal has been problematic, especially in the domain of mathematics. To this might have contributed the fact that, although the vision of students learning mathematics with understanding has often appeared in curriculum frameworks, this vision has tended to be poorly described, thereby offering limited support to curriculum development and policy. The Learning Principle in the Principles and Standards for School Mathematics, an influential mathematics curriculum framework …

Today's Mathematics Students, Carmen M. Latterell

The Mathematics Enthusiast

A common mistake that undergraduate mathematics professors make when teaching is to assume that students are younger versions of themselves. Since many mathematics professors are above average in intelligence and were quite good students, the assumption that students are just like themselves can cause pedagogical difficulties (Krantz, 1993). To teach effectively, it is important to understand students. Yet, understanding today's students is literally like bridging a generation gap (Hawk, 2005).

Tme Volume 4, Number 1

The Mathematics Enthusiast

No abstract provided.

Adult Students' Reasoning In Geometry: Teaching Mathematics Through Collaborative Problem Solving In Teacher Education, Raymond Bjuland

The Mathematics Enthusiast

This article reports research that is concerned with pre-service teachers2 working collaboratively in a problem-solving context without teacher involvement. The aim is to focus on the students’ heuristic strategies employed in the solution process while working on two problems in geometry. Two episodes from the dialogues in one group of students with limited mathematical backgrounds have been chosen to illustrate some mathematical movement throughout the group meetings, from working with the first problem to working with the second one. The findings reveal that three categories of strategies, visualising, monitoring, and questioning, play an important role in order to make progress …