Mathematical Education Research Papers - Academia.edu (original) (raw)

An increasing number of studies are evidencing relationships between physical activity and the mathematical performance of early school students. This is not surprising due to the fact that children grow in all areas simultaneously and their motor and intellectual development determine each other. Nevertheless, such an approach of combining mathematics education with physical exercises, in addition through play, which is the basis of children's activity and the preferred way of spending time, it is still rare at schools. In response to this problem "Eduball" has been created, which are educational balls with printed letters, numbers and other signs, used for team mini-games. Surprisingly, despite the studies on general usefulness of Eduball in preschool and early-school education and the effects of physical exercise classes carried out using these balls, still little is known about their impact on mathematical development. Here we investigate the relationships between the use of Eduball and the acquisition of mathematical knowledge and skills by children. We used a quantitative approach in the form of an experiment in natural settings in which seven-year-old students (first grade) took part (N=25). For the purposes of this experiment we created scenarios of physical exercise classes integrated with mathematical contents that used Eduball. Mathematical knowledge and skills were assessed by one of the commonly used tests. The results were compared with the data from the control group of traditional physical education classes (N=22). As assumed, after a one-year experiment students from both groups improved their results, but we found a greater progress in terms of mathematical knowledge and skills in the experimental class compared to the control one. Eduball particularly affected competences related to such mathematical categories as: sets and their elements, multiplication and division, geometric shapes and measuring length, measuring volume and mass. In sum, our results show that physical exercise classes that used Eduball stimulate the acquisition of mathematical competences by students, and, consequently, confirm that there is a strong relation of physical and mathematical development. Therefore, there is a need to review children's educational models, as well as primary school curricula, to combine physical and cognitive activities.

- by Agnieszka Kruszwicka and +2
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- Education, Mathematics Education, Physical Activity, Neuroeducation

Mathematics is a discipline much feared by most students in schools. Handing out strategies to demystify this discipline through interdisciplinarity, that is, to show how mathematics can be used in other branches of knowledge is our goal. Thinking about this issue, we developed the POEMATHICS Project as an alternative L. S. Carreiro (B) 655 656 L. S. Carreiro et al. activity for the teaching of mathematics allied to the Portuguese language teaching. This initiative consists of relating the mathematics with the written language. Students should develop poems, poetry, texts, stories, music, etc., using mathematical terms and ideas. To promote this activity is necessary the participation of teachers of a language (this work deals with English examples and a workshop done in Por-tuguese) and Mathematics so that students can be accompanied and together awaken the pleasure of learning as well as improving math and linguistic skills.

- by Navid Razmjooy and +1
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- Semiotics, Semantics, Cognition, Neurolinguistics
- by Valsa Koshy
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- Technology, Mathematics Education, Policy Development, Science and Technology
- by mdnor bakar
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- Everyday Life, Mathematical Education, Curriculum and Pedagogy
- by Peter Radonich
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- Model-Eliciting Activities, Mathematical Education
- by Marietjie Potgieter
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- Calculus, Life Sciences, Pure Mathematics, Sciences

Le Indicazioni Nazionali (I.N.) per i licei scientifici sottolineano l'importanza del percorso scolastico che ha il fine di fornire allo studente «gli strumenti culturali e metodologici per una comprensione approfondita della realtà, affinché egli si ponga, con atteggiamento razionale, creativo, progettuale e critico, di fronte alle situazioni, ai fenomeni e ai problemi». Di conseguenza anche l'Esame di Stato assume note-vole importanza, quale verifica della preparazione complessiva conseguita, sulla base delle conoscenze, abilità e competenze acquisite, che devono essere adeguate sia al «proseguimento degli studi di ordine superiore, all'inserimento nella vita sociale e nel mondo del lavoro, sia coerenti con le capacità e le scelte personali». Per i docenti non è un compito facile quello di costruire dei percorsi didattici idonei a far maturare le competenze proprie dell'istruzione liceale. I contenuti da affrontare sono infatti molto vasti ed il tempo è ristretto per gestirli con serenità e con il giusto sviluppo; è poi fondamentale fornire non solo una visione concettuale dei singoli argomenti, ma anche esempi concreti di applicazione. Oltre alle I.N., sono i vecchi temi delle maturità a condizionare in modo determinante le scelte didattiche, ed è proprio per questo motivo che è importante che la seconda prova contenga, oltre ai problemi «standard», anche qualcosa di nuovo: problemi senza troppe descrizioni e senza guide prestabilite, che abbiano la funzione di disorientare un po' lo studente medio, per cercare di valutare le effettive competenze matematiche acquisite. È necessario quindi indirizzare lo studente verso una «consapevolezza»: non deve agire per modelli prefissati, monolitici, ricalcando schemi già visti e rivisti; al contrario, deve conoscere gli aspetti teorici e applicativi degli oggetti matematici affrontati e, tra di essi, scegliere quello più adatto alla risoluzione del problema in gioco. Nel seguito vengono proposti dei nuovi esempi di problemi «non standard»-anche di livello elevato, per valorizzare gli studenti più brillanti.

- by Francesco Daddi
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- Mathematics, Matematica, Mathematical Education, Didattica Della Matematica

The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors’ visions about their texts and approaches they choose when new concepts are introduced. Authors’ responses are discussed in relation to results about students’ difficulties with approaching calculus reported by previous research. A questionnaire has been designed and sent to seven authors of the most used calculus textbooks in Norway and four authors have responded. The responses show that the authors mainly view teaching in terms of transmission so they focus mainly on getting the mathematical content correct and ‘clear’. The dominant view is that the textbook is intended to help the students to learn by explaining and clarifying. The authors prefer the approach to introduce new concepts based on the traditional way of perceiving mathematics as a system of definitions, examples and exercises. The results of this study may enhance our understanding of the role of the textbook at tertiary level. They may also form a foundation for further research.

- by Mira Randahl
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- Mathematics, Calculus, Mathematics Education, Questionnaires

Nella maggior parte dei libri di testo in adozione nei licei scientifici, le trasformazioni affini vengono trattate come un argomento a sé stante e ne viene confinata l'applicazione esclusivamente a limitate tipologie di problemi.[...] Questo articolo ha lo scopo di estendere, mediante alcuni esempi opportunamente scelti, il campo di applicabilità delle affinità al caso delle coniche. Reputo fondamentale proporre in classe alcuni di questi problemi, per mostrare come le trasformazioni del piano possano proficuamente "entrare in campo" in situazioni, a priori, del tutto sconnesse con il loro ambito tradizionale.

- by Francesco Daddi
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- Mathematics, Mathematics Education, Geometry, Matematica
- by Angel Plaza
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- Mathematical Education, Curriculum and Pedagogy, Fibonacci Number

Este libro está basado en decenas de estudios, todos con el afán de comprender cómo la educación puede fomentar las habilidades adecuadas para las sociedades innovadoras.
Se enfoca en la educación matemática, una materia destacada a nivel mundial, pero que aún se le considera un obstáculo para el aprendizaje entre muchos estudiantes. Y si bien existe un consenso casi absoluto de que los problemas matemáticos adecuados para el siglo XXI deben ser complejos, desconocidos y no rutinarios (CUN, por sus siglas en inglés), la mayoría de libros de texto sólo incluyen problemas rutinarios basados en la aplicación de algoritmos prefabricados. El reto se podrá hacer mayor conforme el desarrollo de la habilidad matemática llegue a ser un objetivo clave en los currículos escolares. Es indudable la necesidad de introducir métodos didácticos innovadores para mejorar la educación matemática, y en particular la habilidad de los estudiantes para resolver tareas complejas y no rutinarias. Éstas requieren de la aplicación de procesos metacognitivos, tales como la planeación, el control y la reflexión.
Será fundamental capacitar a los estudiantes a “pensar en su pensamiento” durante el proceso
de aprendizaje.

In the article considered the issue of improving the quality of mathematical preparation of students at
technical universities, as an integrating basic component in the development of special and technical
disciplines. For the formation of the mathematical competence of students of technical universities
through professional orientation of teaching mathematics and the use of professionally-oriented tasks
necessary to ensure the implementation of the integrative connections of mathematics and special
disciplines of technical profile.

- by Viktoriya Golovachyova
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- Mathematical Education

In this paper we explore how the naturalistic perspective in philosophy of mathematics and the situative perspective in mathematics education, while on one level are at odds, might be reconciled by paying attention to actual mathematical practice and activity. We begin by examining how each approaches mathematical knowledge, and then how mathematical practice manifest itself in these distinct research areas and gives rise to apparently contrary perspectives. Finally we argue for a deeper agreement and a reconciliation in the perspectives based on the different projects of justification and explanation in mathematics.

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in indefinite integration, inverse Laplace transforms and linear ordinary differential

- by Yiu Man
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- Algebra, Problem Solving, Computation, Mathematical Education

W rozdziale tym przedstawiono tradycyjne metody kształtowania kompetencji matematycznych dzieci, takie jak metoda samodzielnych doświadczeń, kierowania aktywnością, zadań i ćwiczeń; metody oparte na pokazie, przykładzie, udostępnianiu sztuki, rozmowie, opowiadaniu, zagadce, objaśnieniu, instrukcji, wierszu i piosence, czy też metody żywego słowa. Omówiono także alternatywne strategie, takie jak: metody bazujące na koncepcji pedagogicznej Montessori, Froebla, Steinera, Domana czy Friedrich, de Galgóczy i Schindelhauer, a także Naglaka, Rokity i Rzepy. Pokazano również nowe, oparte na technologiach informacyjno-komunikacyjnych, przestrzenie aktywności matematycznych: środowisko rzeczywistości wirtualnej i cyberparków. Odniesiono się ponadto do uczniów ze specjalnymi potrzebami matematycznymi, którzy wymagają jeszcze innych metod pracy. W tym kontekście wyjaśniono różnice między takimi problemami z matematyką jak akalkulia, dyskalkulia czy specyficzne trudności matematyczne. Wreszcie ukazano to, jak rozpoznać w klasie uczniów uzdolnionych matematycznie, jak z nimi pracować oraz wyróżniono kompetencje zawodowe, które powinien posiadać nauczyciel takich uczniów. Rozdział kończy krótkie podsumowanie zachęcające do refleksji nad procesem nauczania matematyki.

- by Michal Klichowski and +1
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- Mathematics Education, Rudolf Steiner, Early Childhood Education, Math Education in Early Childhood Education
- by Liaqat Khan
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- Mathematical Education, Curriculum and Pedagogy
- by Anwar H Joarder
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- Statistics, Probability, Sampling, Teaching Methods

The purpose of this study was to determine the efficiency of 4MAT method of instruction in which learning style and cerebral hemispheres are taken into account in teaching the binary operation and its properties in mathematics. The sample of this study comprised 58 ninth grade students in two separate classes in a high school. One of the classes was selected as the experimental group in which 4MAT method of instruction was used; and the other class was selected as the control group in which the traditional teaching was given, and this selection was performed randomly. The data have been obtained primarily from three scales, namely ‘mathematical knowledge test’, ‘mathematical attitude scale’ and ‘knowledge test on binary operation and its properties’. It has been determined that 4MAT method of instruction was more efficient than the traditional method in teaching of the binary operation subject in mathematics.

- by Enver Tatar
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- Mathematics, Mathematics Education, Cognitive Style, Learning Style
- by Chanakya Wijeratne and +1
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- Calculus, Infinity, Mathematical Education, Curriculum and Pedagogy
- by Eleni Tsolaki
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- Teaching and Learning, Action Research, Student Engagement, Curriculum Development
- by Abujiya Mu'azu
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- Mathematics, Statistics, Statistical Analysis, Mathematical Logic
- by Temple Fay
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- Undergraduate Research, Linear Model, Mathematical Education, Curriculum and Pedagogy
- by Ansie Harding
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- Numerical Method, Look Ahead, Mathematical Education, Curriculum and Pedagogy

Todo surge a partir de la idea de hacer más sencillo el estudio y análisis de funciones elementales de la matemática, funciones como: cuadrática, cúbica, lineal, constante, valor absoluto, raíz cuadrada, trigonométricas (seno, coseno y tangente), logarítmica entre otras, que son base en temas de cálculo integral y diferencial así como de matemáticas en general. Primeramente partimos del hecho de que una función en matemáticas la podemos entender como una relación entre dos conjuntos (pueden existir relaciones entre más conjuntos) donde a cada elemento del primero conjunto le corresponde uno y solo un elemento del segundo conjunto formando así parejas ordenadas como (a, b) donde 'a' y 'b' pertenecen a los Números Reales. La función es entonces una asociación o regla de correspondencia en donde al primer conjunto suele llamarse conjunto de partida...

- by John Mason
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- Higher Education, Teaching Methods, Story Telling, Mathematical Education
- by Qiaoping Zhang
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- Mathematical Education
- by Balarabe Yushau
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- Mathematical Education, Curriculum and Pedagogy
- by Temple Fay
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- Mathematical Education, Curriculum and Pedagogy, Fourier Series
- by Boris Koichu
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- Problem Solving, Mathematical Education, Curriculum and Pedagogy, University Student

È interessante vedere come l'algebra lineare permetta di trovare formule esplicite per il generico termine di successioni definite in modo ricorsivo mediante espressioni lineari. In questo articolo viene affrontato il caso della... more

- by Francesco Daddi
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- Mathematics, Algebra, Linear Algebra, Mathematical Education
- by Sergio Falcon
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- Mathematical Education, Curriculum and Pedagogy, Fibonacci Number

The purpose of this study is to reveal how math anxiety changes according to the variables of grade/age and gender. The study was carried out with a total of 1247 individuals consisting of 10 different grades from 3rd-grade to 12th-grade students studying in schools selected from different socio-economic environments in a province of Turkey. The Math Anxiety Scale (MAS) was used as a data collection tool. As a result of the analysis, evidence was found that math anxiety is significantly higher in female students than male students. It was also determined that math anxiety was classified in ascending order for the 5th, 3rd, 6th, 4th, 8th, 11th, 12th, 7th, 9th, 10th graders, respectively. Another result is that participants’ math anxiety averages were less in comparison with the previous research results. Based on this important result, it can be said that math anxiety is decreasing over the years as a result of the constructivist education.

- by Open Access Publishing Group
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- Gender Studies, Teaching and Learning, Education, Teacher Education
- by Edgar Reyes
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- Mathematics Education, Mathematical Logic, Geometry, Models
- by Mian Adnan
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- Range, Mathematical Education, Curriculum and Pedagogy

In this report some mathematical relations between the normal probability functions (probability density and cumulative probability) and other transcendental functions (including the exponential, error, trigonometric, gamma, beta, and hypergeometric functions). The mathematical expressions are accompanied by historical remarks and anecdotes, showing that Mathematics and History are a rich source of relations, some of them unexpected. The normal bell, normal single-wave, and normal exponential transcendental functions are also introduced.

- by David Tall
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- Mathematical Education, Curriculum and Pedagogy, Diagnostic Test

Marcus du Sautoy's book "Finding Moonshine" is a rich exploration of the topic of groups, referred to throughout the book as "symmetries". Writing for a general audience, du Sautoy proceeds, chapter by chapter, to record what he does, month by month, in a year of his life as a professional research mathematician. In doing so, he reflects on earlier moments in his life that led to him becoming a mathematician, and on events and people who contributed to the mathematical development of the theory of groups. Most simply, groups can be understood through the example of the mathematical properties of symmetry found in mirror-reflections of 2-dimensional objects, and other symmetries observed in rotating some 2-dimensional objects, such as squares, rectangles, triangles, and pentagons. The "Moonshine" de Sautoy searches for and finds is the mysterious connection between the "Monster", the biggest possible finite group that first exists in a mathematical universe of 196,883 dimensions, and the Fourier expansion of the related Modular function (whose first coefficient is 196,884). This is a brilliant, lucid story!

- by John Gough
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- Mathematics, Philosophy of Science, History of Mathematics, Philosophy Of Mathematics

Due to the changing nature of learning and teaching in universities, there is a growing need for professional development for lecturers and tutors teaching in disciplines in the mathematical sciences. Mathematics teaching staff receive some training in learning and teaching but many of the courses running at university level are not tailored to the mathematical sciences. This article reports on

- by Diane Donovan and +3
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- Higher Education, Learning and Teaching, Professional Development, University Teaching
- by Ami Mamolo
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- Mathematical Education, Curriculum and Pedagogy

Este artículo comparte los resultados de una investigación que exploró el uso de la consola de juego Xbox360-Kinect y del videojuego Body and Brain Connection en un entorno educativo en México para fomentar el desarrollo de las habilidades de suma y resta en alumnos de 2º grado. La investigación siguió un enfoque cuantitativo con un diseño cuasi experimental, en el que los participantes en el grupo experimental recibieron un tratamiento que consistió en cuatro distintas modalidades de juego del videojuego Body and Brain Connection para la consola de juego Xbox360-Kinect; en contraste, el grupo de control no fue expuesto al videojuego. El impacto del tratamiento experimental sobre las habilidades básicas de los alumnos se valoró mediante la aplicación de las sub-pruebas de suma y resta de la prueba Comprehensive Mathematical Abilities Test (CMAT). Los datos recolectados mostraron un impacto positivo, en diferente magnitud y grado, a la luz del género de los participantes como variable de análisis. Además, los alumnos con los menores puntajes en los pre-tests de suma y resta resultaron ser los más beneficiados por el tratamiento experimental. Se concluye que el uso de esta tecnología educativa promueve el desarrollo de las habilidades de suma y resta, constituyéndose como una herramienta formativa, activa, innovadora y significativa para la mejora de las habilidades matemáticas básicas de los alumnos.

ABSTRACT In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the basic concepts of limits, but had room for further improvement in those that required them to explain their answers. An analysis of the students’ performances in the tests by using the APOS (i.e. action-process-object-schema) theory framework is reported. Reflections and suggestions on how to teach the topic more effectively are provided. This article can be assessed via the link: http://www.tandfonline.com/doi/pdf/10.1080/0020739X.2013.822577

- by Yiu Man
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- Mathematics, Calculus, Mathematical Logic, Teaching Methods