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Full-Text Articles in Mathematics
Mars Exploration Rover: Mathematics And People Behind The Mission, Uffe Thomas Jankvist, Bjørn Toldbod
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 …
Introduction Of A New Construct: The Conceptual Tool "Flexibility", Mette Andresen
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 …
Mathematics Education And Neurosciences: Relating Spatial Structures To The Development Of Spatial Sense And Number Sense, Fenna Van Nes, Jan De Lange
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 …
A Hexagon Result And Its Generalization Via Proof, Michael De Villiers
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.
Non-Linear Functions In Secondary School Of Lower Qualification Level (German Hauptschule), Astrid Beckmann
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
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. …
New And Noteworthy Books From Sense Publishers
New And Noteworthy Books From Sense Publishers
The Mathematics Enthusiast
No abstract provided.
Objective Truth Versus Human Understanding In Mathematics And In Chess, Olle Häggström
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.
On The Solution To Octic Equations, Raghavendra G. Kulkarni
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.
Editorial: New Horizons-Four Years Later, Bharath Sriraman
Editorial: New Horizons-Four Years Later, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
The Philosophy Of Mathematics, Values And Keralese Mathematics, Paul Ernest
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. …
Adult Students' Reasoning In Geometry: Teaching Mathematics Through Collaborative Problem Solving In Teacher Education, Raymond Bjuland
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 …
Students' Conceptions Of Limits: High Achievers Versus Low Achievers, Kristina Juter
Students' Conceptions Of Limits: High Achievers Versus Low Achievers, Kristina Juter
The Mathematics Enthusiast
Learning an advanced mathematical concept, limits of functions in this case, is not a linear development equal for all learners. Intentions and abilities influence students’ learning paths and results. Students’ learning developments of limits were studied in terms of concept images (Tall & Vinner, 1981) in the sense that their actions, such as problem solving and reasoning, were considered traces of their mental representations of concepts. High achievers’ developments were compared to low achievers’ developments to for the duration of a semester to reveal differences and similarities.
The Interplay Of Processing Efficiency And Working Memory With The Development Of Metacognitive Performance In Mathematics, Areti Panaoura
The Interplay Of Processing Efficiency And Working Memory With The Development Of Metacognitive Performance In Mathematics, Areti Panaoura
The Mathematics Enthusiast
The present study outlines a specific three level hierarchy of the cognitive system and especially the relations of specific cognitive and metacognitive processes in mathematics. The emphasis is on the impact of the development of processing efficiency and working memory ability on the development of metacognitive abilities and mathematical performance. We had used instruments measuring pupils´ metacognitive ability, mathematical performance, working memory and processing efficiency. We administered them to 126 pupils (8-11 years old) three times, with breaks of 3-4 months between them. Results indicated that the development of each of the abilities was affected by the state of the …
Today's Mathematics Students, Carmen M. Latterell
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).
The Need For An Inclusive Framework For Students' Thinking In School Geometry, Jaguthsing Dindyal
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.
Numerical Methods With Ms Excel, M. El-Gebeily, B. Yushau
Numerical Methods With Ms Excel, M. El-Gebeily, B. Yushau
The Mathematics Enthusiast
In this note we show how MS Excel can be used to to perform numerical Integration, specifically Trapezoidal Rule and Simson’s rule. Futhermore, we illustrate how to generate Lagranges Interpolation polynomial.
Can Our Learners Model In Mathematics?, Vimolan Mudaly
Can Our Learners Model In Mathematics?, Vimolan Mudaly
The Mathematics Enthusiast
Mathematical modeling of real world conditions should be part ofl mathematics classroom activities. In this paper I argue that when real world problems are taught at schools learners are not able to cope on their own, without the assistance of their educator. There is very little or no emphasis placed on this aspect of mathemtics at schools, although it is just beginning to make an appearance in our new Outcomes Based Curriculum. I also discuss an experiment conducted with Grade 10 learners (15 year old) and their responses to real world problems and the conditions that need to be considered. …
Lagrange: A Well-Behaved Function, Benjamin Harris
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 …
Erratum: An Improvement On The Article Taxi Cab Geometry: History And Applications, Tmme, Vol2, No.1, P. 38 - 64, Benjamin Urland
Erratum: An Improvement On The Article Taxi Cab Geometry: History And Applications, Tmme, Vol2, No.1, P. 38 - 64, Benjamin Urland
The Mathematics Enthusiast
As a high school student from Germany I did a Mathematics research paper entitled Taxicab Geometry: Fundamentals and Applications. During my research I found the article Taxicab Geometry: History and Applications by Chip Reinhardt which was published in the edition Vol.2, no. 1 (p. 38 – 64) of this journal. The article was very helpful for my coursework and I’d like to compliment the author and everyone who is involved in the journal on their work. In my coursework I created an application example similar to the one Chip Reinhardt used in his article. I solved my example in the …
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
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 …