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Articles 1 - 23 of 23
Full-Text Articles in Physical Sciences and Mathematics
Numbers And Polynomials- 50 Years Since The Publication Of Wittgenstein's Bemerkungen Über Die Grundlagen Der Mathematik (1956): Mathematical And Educational Reflections, Giorgio T. Bagni
The Mathematics Enthusiast
According to L. Wittgenstein, the meaning of a mathematical object is to be grounded upon its use. In this paper we consider Robinson theory Q, the subtheory of firstorder Peano Arithmetic PA; some theorems and conjectures can be interpreted over one model of Q given by a universe of polynomials; with respect to nonconstant polynomials some proofs by elementary methods are given and compared with corresponding results in the standard model of PA. We conclude that the creative power of the language can be pointed out in how the language itself is embedded into the rest of human activities, and …
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 …
Editorial: A Global Intellectual Collage, Bharath Sriraman
Editorial: A Global Intellectual Collage, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
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 …
An In-Depth Investigation Of The Divine Ratio, Birch Fett
An In-Depth Investigation Of The Divine Ratio, Birch Fett
The Mathematics Enthusiast
The interesting thing about mathematical concepts is that we can trace their development or discoveries throughout history. Most cultures of the ancient world had some form of mathematics, and these basic skills developed into what we now call modern mathematics. The divine ratio is similar in that it was used in many different sections of history. The divine ratio, sometimes called the golden ratio or golden section, has been found in very diverse areas. The mathematical concepts of the golden ration have been found throughout nature, in architecture, music as well as in art. Phi is an astonishing number because …
Using Manipulatives In Mathematical Problem Solving: A Performance-Based Analysis, Catherine A. Kelly
Using Manipulatives In Mathematical Problem Solving: A Performance-Based Analysis, Catherine A. Kelly
The Mathematics Enthusiast
This article explores problem solving in elementary classrooms while focusing on how children use (perform tasks) manipulatives and/or tools in problem solving while working on mathematical tasks. Ways for teachers to assess children’s learning through performance-based tool (manipulative) use will also be examined and suggested. Current research reveals that teachers need to teach and assess children’s mathematical knowledge in ways that will allow them to show (perform) what they really understand. And, teachers must be able to see beyond obvious correct or incorrect answers into children’s thinking processes by testing with “tests that allow students the opportunity to show what …
Frames Of Reference And Achievement In Elementary Arithmetic, Eddie M. Gray, Demetra Pitta-Pantazi
Frames Of Reference And Achievement In Elementary Arithmetic, Eddie M. Gray, Demetra Pitta-Pantazi
The Mathematics Enthusiast
This paper considers the relationship between 8-11 years old students’ numerical achievement and a possible disposition towards the construction of particular frames of reference. The paper uses the characteristics of a variety of kinds of images to focus upon frames of reference and explores a possible relationship between children’s verbal descriptions of concrete and abstract nouns and the different ways they respond to aspects of elementary arithmetic. It seeks to establish whether or not children towards the extremes of arithmetical achievement (low and high achievement) have a disposition towards different kinds of frames of reference. The analysis suggests that at …
Sunrise… Sunset…, Alex Friedlander, Tzippora Resnick
Sunrise… Sunset…, Alex Friedlander, Tzippora Resnick
The Mathematics Enthusiast
Sunrise and sunset are obviously a part of our everyday life. Our connection to the movement of celestial bodies, including the Sun, has been somewhat diminished by modern life, in contrast to the practical interest, fascination or even awe of earlier civilizations. Mathematics and astronomy have a long history of cooperative work, but due to their complexity and technical difficulty, usually those who participated in this endeavor were at the advanced studies level, or occupied high religious positions.
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 …
A Classification Of Strategies Employed By High School Students In Isomorphic Combinatorial Problems, Martina Janácková, Jaroslav Janácek
A Classification Of Strategies Employed By High School Students In Isomorphic Combinatorial Problems, Martina Janácková, Jaroslav Janácek
The Mathematics Enthusiast
The aim of the paper is to discuss some aspects of the combinatorial thinking of high school students. We took one student - Jane and gave her 4 isomorphic testing problems. Then we tried to classify the different strategies the students took in their solutions.
Tme's Worldwide Circulation Statistics
Tme's Worldwide Circulation Statistics
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.
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.
Editorial: Growth & Change, Bharath Sriraman
Editorial: Growth & Change, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
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. …
Tme's Worldwide Circulation Statistics
Tme's Worldwide Circulation Statistics
The Mathematics Enthusiast
No abstract provided.
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.
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.
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 …