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Full-Text Articles in Physical Sciences and Mathematics
Cubism And The Fourth Dimension, Elijah Bodish
Cubism And The Fourth Dimension, Elijah Bodish
The Mathematics Enthusiast
When one looks into the subject of geometries that attempt to explain fourthdimensional space, it is inevitable that one encounters references to Cubism. The purpose of this paper is to find what the similarities between this mathematical concept and cubism are. There are many historical arguments as to how the cubists encountered literature about the fourth-dimension, and whether they were exposed to it at all, which I will for the most part omit and instead let the art speak for itself. It is important to see how two fields are interrelated in order to gain a better understanding of both …
The Journal (Wheel) Keeps On Turning, Bharath Sriraman
The Journal (Wheel) Keeps On Turning, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
On The Use Of Realistic Fermi Problems For Introducing Mathematical Modelling In School, Jonas Bergman Ärlebäck
On The Use Of Realistic Fermi Problems For Introducing Mathematical Modelling In School, Jonas Bergman Ärlebäck
The Mathematics Enthusiast
In this paper uses an analytical tool refereed to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extramathematical knowledge used …
Small Change - Big Difference, Ilana Lavy, Atara Shriki
Small Change - Big Difference, Ilana Lavy, Atara Shriki
The Mathematics Enthusiast
Starting in a well known theorem concerning medians of triangle and using the ‘What If Not?’ strategy, we describe an example of an activity in which some relations among segments and areas in triangle were revealed. Some of the relations were proved by means of Affine Geometry.
Mathematical Beauty And Its Characteristics- A Study On The Student's Point Of View, Astrid Brinkmann
Mathematical Beauty And Its Characteristics- A Study On The Student's Point Of View, Astrid Brinkmann
The Mathematics Enthusiast
Based on the statement, that the experience of mathematical beauty has a positive influence on students’ motivations and attitudes towards mathematics and its study, the focus of this paper is the aesthetic component of mathematics. First, the role of aesthetics for perception and education is addressed. The appreciation of the beauty of mathematics is one of the wellsprings of this subject, not only in research but also in school education. This should have implications for the teaching of mathematics. However the beauty making elements have not been very well analysed. In particular, it is not clear to what extent the …
Helping Teachers Un-Structure: A Promising Approach, Eric Hsu, Judy Kysh, Katherine Ramage, Diane Resek
Helping Teachers Un-Structure: A Promising Approach, Eric Hsu, Judy Kysh, Katherine Ramage, Diane Resek
The Mathematics Enthusiast
The amount of overt structure in the presentation of a task affects students’ engagement, creativity, and willingness to tolerate frustration. In a professional development project, with algebra teachers from nine American schools, we tried to help teachers make judicious decisions in their use of structure by having them facilitate low-structure tasks, remove structure from overly structured tasks, and observe “at-risk” students engaged in learning through low-structure tasks. Project schools that worked on structuring generally improved their algebra passing rates, both overall and for African-American students.
Who Can Solve 2x=1? An Analysis Of Cognitive Load Related To Learning Linear Equation Solving, Timo Tossavainen
Who Can Solve 2x=1? An Analysis Of Cognitive Load Related To Learning Linear Equation Solving, Timo Tossavainen
The Mathematics Enthusiast
Using 2x = 1 as an example, we discuss the cognitive load related to learning linear equation solving. In the framework of the Cognitive Load Theory we consider especially the intrinsic cognitive load needed in arithmetical, geometrical and real analytical approach to linear equation solving. This will be done e.g. from the point of view of the conceptual and procedural knowledge of mathematics and the APOS Theory. Basing on our observations, in the end of the paper we design a setting for teaching linear equation solving.
If Mathematics Is A Language, How Do You Swear In It?, Dave Wagner
If Mathematics Is A Language, How Do You Swear In It?, Dave Wagner
The Mathematics Enthusiast
Swears are words that are considered rude or offensive. Like most other words, they are arbitrary symbols that index meaning: there is nothing inherently wrong with the letters that spell a swear word, but strung together they conjure strong meaning. This reminds us that language has power. This is true in mathematics classrooms too, where language practices structure the way participants understand mathematics and where teachers and students can use language powerfully to shape their own mathematical experience and the experiences of others.
Mathematical Curiosities About Division Of Integers, Jérôme Proulx, Mary Beisiegel
Mathematical Curiosities About Division Of Integers, Jérôme Proulx, Mary Beisiegel
The Mathematics Enthusiast
As mathematics educators, our focus of attention is mainly placed on the learning and teaching of mathematics. But, as we study phenomena of mathematical learning and teaching, we often come across intriguing mathematical phenomena that capture our interest. We find ourselves often bouncing mathematical ideas back and forth, not just looking for (new/better) ways of teaching or presenting a mathematical concept, but also of uncovering and discovering potential understandings of the concept. These mathematical issues we encounter represent for us a significant aspect of our work, and are also very stimulating. One of these issues arose for us as we …
An Application Of Gröbner Bases, Shengxiang Xia, Gaoxiang Xia
An Application Of Gröbner Bases, Shengxiang Xia, Gaoxiang Xia
The Mathematics Enthusiast
In this paper, we program a procedure using Maple's packages, with it we can realize mechanical proving of some theorems in elementary geometry.
Graph Isomorphisms And Matrix Similarity: Switching Between Representations, Thierry Dana-Picard
Graph Isomorphisms And Matrix Similarity: Switching Between Representations, Thierry Dana-Picard
The Mathematics Enthusiast
A proof whether two graphs (possibly oriented graphs or multigraphs, etc.) are isomorphic or not can be derived by various methods. Some of them are reasonable for small numbers of vertices and/or edges, but not for larger numbers. Switching from iconic representation to a matrix representation transforms the problem of Graph Theory into a problem in Linear Algebra. The support provided by a Computer Algebra System is analyzed, in particular with regard to the building of new mathematical knowledge through a transition from graphical to algebraic representation. Moreover two important issues are discussed: a. the need for more than one …
From Trapezoids To The Fundamental Theorem Of Calculus, William Gratzer, Srilal Krishnan
From Trapezoids To The Fundamental Theorem Of Calculus, William Gratzer, Srilal Krishnan
The Mathematics Enthusiast
The philosophy of Mathematics Education undergoes changes from the school to college level and students generally have a tough time coping with the transition. It is our endeavor to impress the importance of introducing college level topics at an early stage, so that students are not lost in the transition. Keeping this in mind, we suggest an early exposure to an important topic from Calculus; approximating the area of a planar region. Traditionally this topic is introduced using Riemann Sums but in this paper we try to follow a student’s natural inclination in approximating areas and explain how this approach …
Sum Of "N" Consecutive Integers, Steve Humble
Sum Of "N" Consecutive Integers, Steve Humble
The Mathematics Enthusiast
For all n , it is always possible to find at least one sum of n consecutive numbers with an equivalent sum of n - 1 consecutive numbers?
The Contributions Of Comprehension Tests To Cognitive And Affective Development Of Prospective Teachers: A Case Study, Yüksel Dede
The Contributions Of Comprehension Tests To Cognitive And Affective Development Of Prospective Teachers: A Case Study, Yüksel Dede
The Mathematics Enthusiast
The aim of this study was to investigate the role of comprehension tests while teaching algebra and its effects on students’ success. This study was carried out with 108 third year undergraduate students enrolled in math education in faculty of education. Several data collection instruments were used for gathering data from the participants such as; comprehension test, written documents, semi-structured interviews schedule, and participant and nonparticipant observations sheets. Collected data were subjected to content analysis and triangulation among the data was ensured. Results indicated that three different major categories emerged from the content analysis of the data: (1) measure of …
Book Review: What's All The Commotion Over Commognition? A Review Of Anna Sfard's Thinking As Communicating, Bharath Sriraman
Book Review: What's All The Commotion Over Commognition? A Review Of Anna Sfard's Thinking As Communicating, Bharath Sriraman
The Mathematics Enthusiast
If straight edge and compass constructions are the so-called “atoms” of Euclidean geometry, if sequences are the “atoms” of Analysis, then what are the “atoms” (if any) of mathematics education? Arguably mathematics education is a much wider field than Euclidean Geometry or Elementary Analysis, however there are several fundamental things that the field purports to study, chief among which is mathematical thinking or more generally “thinking”. The book under review, though it appears in a Cambridge University Press series entitled Learning in Doing: Social, Cognitive, and Computational Perspectives, is in my view situated at the intersection of Consciousness Studies, …
Intuitions Of "Infinite Numbers": Infinite Magnitude Vs. Infinite Representation, Ami Mamolo
Intuitions Of "Infinite Numbers": Infinite Magnitude Vs. Infinite Representation, Ami Mamolo
The Mathematics Enthusiast
This study examines undergraduate students’ emerging conceptions of infinity as manifested in their engagement with geometric tasks. Students’ attempts to reduce the level of abstraction of infinity and properties of infinite quantities are described. Their arguments revealed they perceive infinity as an ongoing process, rather than a completed one, and fail to notice conflicting ideas. In particular, confusion between the infinite magnitude of points on a line segment and the infinite representation of real numbers was observed. Furthermore, students struggled to draw a connection between real numbers and their representation on a number line.
Two Applications Of Art To Geometry, Viktor Blåsjö
Two Applications Of Art To Geometry, Viktor Blåsjö
The Mathematics Enthusiast
Geometry and art exploit the same source of human pleasure: the exercise of our spatial intuition. It is not surprising, then, that interconnections between them abound. Applications of geometry to art, of which we shall indicate a few, go back at least to Alberti’s De Pictura (1435). But although geometry started out, as it so often does, as a most courteous suitor in its relationship with art, it was soon to be affectionately rewarded. We shall study two of these rewards.
A Conceptual Framework For Cross-Curricular Teaching, Astrid Beckmann
A Conceptual Framework For Cross-Curricular Teaching, Astrid Beckmann
The Mathematics Enthusiast
The Montana Mathematics Enthusiast is pleased to present a special supplemental issue this year focused on the issue of interdisciplinarity in the curriculum and classroom. This book is based on the longitudinal research carried out by Prof. Astrid Beckmann of the University of Education, Schwäbisch Gmünd- Germany, who is one of the co-founders of the Mathematics and its Connections to the Arts and Sciences international group (MACAS).
Statistics Teaching In An Agricultural University: A Motivation Problem, Klara Lokos Toth
Statistics Teaching In An Agricultural University: A Motivation Problem, Klara Lokos Toth
The Mathematics Enthusiast
There are many teaching methods and there are various teaching materials even in one university, not to mention different universities specialising in different disciplines. So I cannot talk about Hungarian method in general, but about my experience in teaching statistics. I teach statistics on several levels (BSc, MSc, PhD) and in different faculties (Agriculture and environmental Sciences, Economic and Social Sciences) and in different forms. I find different problems according to the faculties and forms. In this paper I focus on only one of them, which is the most important for me.
For The Rest Of Your Life, Mike Fletcher
For The Rest Of Your Life, Mike Fletcher
The Mathematics Enthusiast
‘For the Rest of Your Life’ is a new TV game show. Contestants play to win money every month. This can be for as little as one month or, if every one of their guesses is correct, for the rest of their lives.
What Makes A “Good” Statistics Student And A “Good” Statistics Teacher In Service Courses?, Sue Gordon, Peter Petocz, Anna Reid
What Makes A “Good” Statistics Student And A “Good” Statistics Teacher In Service Courses?, Sue Gordon, Peter Petocz, Anna Reid
The Mathematics Enthusiast
Statistics is taught within a diverse array of disciplines and degree programs at university. In recent research we investigated international educators’ ideas about teaching and learning ‘service’ statistics. This paper investigates what these educators think are important attributes, knowledge and skills for learners and teachers of statistics. Results show that educators are in agreement about qualities of ‘good’ statistics students, such as curiosity and critical thinking. An emerging issue was the role mathematics plays in learning statistics as a service subject with some academics postulating mathematics as the basis of statistical learning, others proposing it has limited or little importance …
To Publish Or Not To Publish?- That Is The (Editorial) Question, Bharath Sriraman
To Publish Or Not To Publish?- That Is The (Editorial) Question, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Students’ Conceptions About Probability And Accuracy, Ignacio Nemirovsky, Mónica Giuliano, Silvia Pérez, Sonia Concari, Aldo Sacerdoti, Marcelo Alvarez
Students’ Conceptions About Probability And Accuracy, Ignacio Nemirovsky, Mónica Giuliano, Silvia Pérez, Sonia Concari, Aldo Sacerdoti, Marcelo Alvarez
The Mathematics Enthusiast
College students’ conceptions about probability and accuracy were explored. Both qualitative and quantitative analyses were done by means of two tests applied at two different moments. We show the results referring to the beliefs and conceptions about probability, margin for error, accuracy, certainty, truth and validity. Previous misconceptions about science may cause difficulties in the interpretation of scientific models. So, to find out students’ beliefs about science and technology, a Likert scale type test was made and presented to part of the sample. Although most of the people who answered the survey accredited the incidence of probability in the results …
Undergraduate Student Difficulties With Independent And Mutually Exclusive Events Concepts, Adriana D'Amelio
Undergraduate Student Difficulties With Independent And Mutually Exclusive Events Concepts, Adriana D'Amelio
The Mathematics Enthusiast
The concepts of disjunctive events and independent events are didactical ideas that are used widely in the classroom. Previous observations of attitudes in assessments given to students at university level who attended the introductory Statistics course helped to detect the confusion between disjunctive and independent events, and indicate the spontaneous ideas that students tend to elaborate about both concepts in different situations in which these appear. However the didactical relation between these ideas and their formal definitions is not known in detail. In this work, we analyze students’ misconceptions, their persistence, and the process by which the student confronts his …
Teaching Statistics Must Be Adapted To Changing Circumstances: A Case Study From Hungarian Higher Education, Andras Komaromi
Teaching Statistics Must Be Adapted To Changing Circumstances: A Case Study From Hungarian Higher Education, Andras Komaromi
The Mathematics Enthusiast
Teaching statistics can bring up difficulties of various types for the teacher. Some of these are independent of the environment, i.e. they could occur at any place and time; some are specifically conditional on the surrounding circumstances. This paper presents an example for both of these kinds from the practice of two Hungarian teachers.
If A.B = 0 Then A = 0 Or B = 0?, Cristina Ochoviet, Asuman Oktaç
If A.B = 0 Then A = 0 Or B = 0?, Cristina Ochoviet, Asuman Oktaç
The Mathematics Enthusiast
We present a study carried out in Uruguay, with secondary school students and tertiary level mathematics students, concerning the zero-product property. In our research we observed that when early secondary and late secondary school students have to solve equations of the form (ax + b)(cx + d) = 0, they do not always apply the property, even when it is the only available tool and have received specific instruction on its application to the resolution of equations of this type. We also detected an error that students make when they have to verify the solutions of this type of equations. …
Calculating Dependent Probabilities, Mike Fletcher
Calculating Dependent Probabilities, Mike Fletcher
The Mathematics Enthusiast
In the 2004 European soccer competition France were one of the favourites to win the World Cup and Thierry Henry, their star forward, was one of the favourites to be top goal scorer. Bookkeepers were offering odds of 4 :1 on France winning the competition and odds of 8: 1 on Thierry Henry being the top scorer. A large number of punters went into betting shops in the United Kingdom and made a single bet that France would win the competition and that Thierry Henry would be top scorer. The counter clerks in the betting shops accepted the bets and …
Teacher Knowledge And Statistics: What Types Of Knowledge Are Used In The Primary Classroom?, Tim Burgess
Teacher Knowledge And Statistics: What Types Of Knowledge Are Used In The Primary Classroom?, Tim Burgess
The Mathematics Enthusiast
School curricula are increasingly advocating for statistics to be taught through investigations. Although the importance of teacher knowledge is acknowledged, little is known about what types of teacher knowledge are needed for teaching statistics at the primary school level. In this paper, a framework is described that can account for teacher knowledge in relation to statistical thinking. This framework was applied in a study that was conducted in the classrooms of four second-year teachers, and was used to explore the teacher knowledge used in teaching statistics through investigations. As a consequence, descriptions of teacher knowledge are provided and give further …
The Impact Of Undergraduate Mathematics Courses On College Student’S Geometric Reasoning Stages, Nuh Aydin, Erdogan Halat
The Impact Of Undergraduate Mathematics Courses On College Student’S Geometric Reasoning Stages, Nuh Aydin, Erdogan Halat
The Mathematics Enthusiast
The purpose of this study is to investigate possible effects of different college level mathematics courses on college students’ van Hiele levels of geometric understanding. Particularly, since logical reasoning is an important aspect of geometric understanding, it would be interesting to see whether there are differences in van Hiele levels of students who have taken non-geometry courses that emphasize or focus on logic and proofs (Category I) and those that don’t (Category II). We compared geometric reasoning stages of students from the two categories. One hundred and forty nine college students taking various courses from the two categories have been …