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Full-Text Articles in Mathematics
The Effects Of Blended E-Learning On Mathematics And Computer Attitudes In Pre-Calculus Algebra, Balarabe Yushau
The Effects Of Blended E-Learning On Mathematics And Computer Attitudes In Pre-Calculus Algebra, Balarabe Yushau
The Mathematics Enthusiast
This study examines the influence of blended e-learning on students' attitude towards mathematics and computers. A random sample of 70 students of the preparatory year program of King Fahd University of Petroleum & Minerals (KFUPM), Dhahran served as the sample of this study. Data were collected at the beginning (pre-program) and the end (post-program) of the semester using Aiken Mathematics Attitude Scale and Greessen and Loyd Computer Attitude Scale. The result indicates that the subjects have positive attitude towards mathematics and computer. However, analysis of variance shows no statistically significant change in students’ attitudes towards mathematics and computer except for …
How Students Conceive Function: A Triarchic Conceptual-Semiotic Model Of The Understanding Of A Complex Concept., Iliada Elia, Panayotis Spyrou
How Students Conceive Function: A Triarchic Conceptual-Semiotic Model Of The Understanding Of A Complex Concept., Iliada Elia, Panayotis Spyrou
The Mathematics Enthusiast
This study explores conceptions for function amongst 164-second year students of the Department of Education at the University of Cyprus and their relationship with students’ abilities in dealing with tasks involving different modes of representations of function. The test that was administered to the students included recognition tasks given in various representations and questions requesting definition and examples of function’s applications in real life situations. Results have shown that students’ definitions and examples of the notion are closely related to their ability to use different modes of representations of function. These three factors, i.e., definitions given by the students, functions …
World-Class High Quality Mathematics Education For All K-12 American Students, Om P. Ahuja
World-Class High Quality Mathematics Education For All K-12 American Students, Om P. Ahuja
The Mathematics Enthusiast
In September 1989, the United States’ Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that “By the year 2000, United States students will be first in the world in mathematics and science achievements”. However, recent results of the ‘Programme for International Student Achievement’ and ‘Trends in International Mathematics and Science Study’ indicate that the United States students’ achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also …
Building Blocks Problem Related To Harmonic Series, Yutaka Nishiyama
Building Blocks Problem Related To Harmonic Series, Yutaka Nishiyama
The Mathematics Enthusiast
In this discussion I give an explanation of the divergence and convergence of infinite series through the building blocks problem and at the same time I touch on the fact that mathematics is not just about manipulating complicated numerical formulas but also a field in which logical ways of thought are learnt. I emphasize that in order to overcome the aversion of university students to mathematics, teachers must pour their energies into developing study materials taken from topics relevant to the students.
Problems To Discover And To Boost Mathematical Talent In Early Grades: A Challenging Situations Approach, Viktor Freiman
Problems To Discover And To Boost Mathematical Talent In Early Grades: A Challenging Situations Approach, Viktor Freiman
The Mathematics Enthusiast
Several studies of mathematical giftedness conducted in the past two decades reveal the importance of creation of learning and teaching environment favourable to the identification and nurturing mathematically talented students. Based on psychological, methodological and didactical models created by Krutetskii (1976), Shchedrovtiskii (1968), Brousseau (1997) and Sierpinska (1994), we have developed our challenging situation approach. During 7 years of field study in the elementary K-6 classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical talent in very young children keeping and increasing their interest towards more advanced mathematics curriculum. …
Not Out Of The Blue: Historical Roots Of Mathematics Education In Italy, Fulvia Furinghetti
Not Out Of The Blue: Historical Roots Of Mathematics Education In Italy, Fulvia Furinghetti
The Mathematics Enthusiast
In this note I outline some elements of the history of mathematics education in Italy. Initially the chief characters were mathematicians who played a role in designing curricula and in editing textbooks. The development of the Italian community of mathematics educators towards the present day trend in research was fostered by participation in international activities after the Second World War. I also identify some elements of continuity with the past to stress the influence of some mathematicians in the development of present research.
Editorial: Growth & Change, Bharath Sriraman
Editorial: Growth & Change, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Automated Geometric Theorem Proving: Wu's Method, Joran Elias
Automated Geometric Theorem Proving: Wu's Method, Joran Elias
The Mathematics Enthusiast
Wu’s Method for proving geometric theorems is well known. We investigate the underlying algorithms involved, including the concepts of pseudodivision, Ritt’s Principle and Ritt’s Decomposition algorithm. A simple implementation for these algorithms in Maple is presented, which we then use to prove a few simple geometric theorems to illustrate the method.
Modeling Interdisciplinary Activities Involving Mathematics And Philosophy, Steffen M. Iversen
Modeling Interdisciplinary Activities Involving Mathematics And Philosophy, Steffen M. Iversen
The Mathematics Enthusiast
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series …
Mathematically Promising Students From The Space Age To The Information Age, Linda Jensen Sheffield
Mathematically Promising Students From The Space Age To The Information Age, Linda Jensen Sheffield
The Mathematics Enthusiast
On October 4, 1957, with the launch of Sputnik 1 by the Soviet Union, the world entered the Space Age and the United States became quite concerned that the Soviet Union had a head start in the space race. A year later, realizing that the support of gifted and talented mathematics and science students was critical to national security, the United States federal government passed the National Defense Education Act (NDEA), providing aid to education in the United States at all levels, primarily to stimulate the advancement of education in science, mathematics, and modern foreign languages. Also, during this time, …
Algorithmic Problems In Junior Contests In Latvia, Agnis Andžans, Inese Berzina, Dace Bonka
Algorithmic Problems In Junior Contests In Latvia, Agnis Andžans, Inese Berzina, Dace Bonka
The Mathematics Enthusiast
Mathematical contests are of great importance for advanced education in Latvia today. Their content must be well-balanced and must correspond to the inner logic and recent trends of mathematics. A classification of algorithmic problems and characteristic examples are considered.
Tme's Worldwide Circulation Statistics
Tme's Worldwide Circulation Statistics
The Mathematics Enthusiast
No abstract provided.
A Comparison Of The Danish And The Virginia Secondary Teacher Education System: Their Values And Emphasis On Mathematics Content Knowledge, Bettina Dahl
The Mathematics Enthusiast
In this paper I will first examine an example of secondary mathematics teacher education in the USA, namely Virginia, then compare it with the secondary teacher education in Denmark. The purpose is both to investigate how much mathematics the students get in the respective systems and secondly to see what this type of teacher education communicates about the values emphasized in the various countries’ education systems. I spent more time on explaining the Danish education system than that of the USA and the single states since it is assumed that the reader is familiar with these systems. One cannot necessarily …
Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman
Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce
Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce
The Mathematics Enthusiast
Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students …
Von Neumann And Computers, Steve Humble
Von Neumann And Computers, Steve Humble
The Mathematics Enthusiast
The title of this paper should not be Von Neumann and computers, but Von Neumann and the Von Neumann machine. Von Neumann may be famous for many things but humility was not one of them. Yet no one had anything bad to say about 'good time' Johnny Von Neumann; he just was too likeable. He gave massive parties and loved women, fast cars, jokes, noise, Mexican food, fine wine, and, most of all, mathematics. 'Unbelievable', said one of Von Neumann's old friends, 'He knew how to have a good time. His parties were once if not twice a week at …
Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi
Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi
The Mathematics Enthusiast
In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students …
Instrumented Techniques And Reflective Thinking In Analytic Geometry, Nurit Zehavi, Giora Mann
Instrumented Techniques And Reflective Thinking In Analytic Geometry, Nurit Zehavi, Giora Mann
The Mathematics Enthusiast
In a previous study that explored epistemological perspectives on solving problems with Computer Algebra Systems (CAS) we concluded that awareness of the special ways that the software utilizes symbols in algebraic manipulations and in implicit plotting should be encouraged (Zehavi, 2004). Such awareness is required for, and encouraged by treating geometry analytically with a symbolic-graphical system. In this paper we compare a traditional solution of a problem in analytic geometry with CAS-based solutions to the same problem. The discussion will focus on the role of reflective thinking, namely selection of techniques, monitoring of the solution process, insight, and conceptualization, play …
A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott
A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott
The Mathematics Enthusiast
The National Council of Teachers of Mathematics (NCTM) has taken a very firm stand on the issue of equity in mathematics education. Not only is equity incorporated in the Curriculum and Evaluation Standards for School Mathematics (1989) and Principles and Standards for School Mathematics (2000), equity is the first plank of NCTM’s legislative platform.
Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein
Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein
The Mathematics Enthusiast
It is a pleasure, challenge, and an honor to respond to the thoughtful and innovative debate started by Braver, Micklus, Bradley, van Spronsen, Allen, & Campbell on teaching mathematics for social justice. They take seriously the issues in, and raise many interesting views about, my article, Teaching and Learning Mathematics for Social Justice in an Urban Latino School (JRME, January, 2003). I would like to respond to (connected) two points in particular: the relationship of functional to critical literacies, and the relationship of “critical thinking” in mathematics to learning mathematics for social justice. However, I would first like to clarify …
Taxi Cab Geometry: History And Applications!, Chip Reinhardt
Taxi Cab Geometry: History And Applications!, Chip Reinhardt
The Mathematics Enthusiast
We will explore three real life situations proposed in Eugene F. Kraus e's book Taxicab Geometry. First a dispatcher for Ideal City Police Department receives a report of an accident at X = (-1,4). There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third …
Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou
Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou
The Mathematics Enthusiast
Through this research into the solution of the cubic, I hope to learn the thoughts of mathematicians during this period of history. This knowledge must be conveyed in a way that is historically and mathematically accurate, yet comprehensible and readily available to use in a class of eighth grade math students. It is my wish that as we begin to delve into the world of algebraic and graphical solutions to the problems in the eighth grade text, students will be able to make a connection with this information to that they are currently using to solve their problems. They should …