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Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

Martelly, Diana I
Fonte: FIU Digital Commons Publicador: FIU Digital Commons
Tipo: Artigo de Revista Científica
Português
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This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition...

Vietnam : Reading and Mathematics Assessment Study, Volume 3

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Economic & Sector Work :: Other Education Study; Economic & Sector Work
Português
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This paper contains three volumes presenting the Vietnam Reading and Mathematics Assessment Study conducted in 2001. The first volume sets the study in its country context, describes its genesis, outlines the methodology, and summarizes the results. The main purpose is to show how the analysis of the study results points to specific policy interventions. The strong link between a teacher's subject knowledge, and the performance of her pupils argues for teacher upgrade programs, while the high variation of pupil performance between schools in the same province calls for local programs that improve school effectiveness. The first volume is followed by a second volume detailing the study results, and a third providing a full description of the study methodology.

Avaliação do Processo de Ensino e Aprendizagem em Matemática: contribuições da teoria histórico-cultural; Evaluation of the Teaching and Learning Process in Mathematics: contributions from historical-cultural theory

MORAES, Silvia Pereira Gonzaga de; MOURA, Manoel Oriosvaldo de
Fonte: UNESP-DEPT MATHEMATICA Publicador: UNESP-DEPT MATHEMATICA
Tipo: Artigo de Revista Científica
Português
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This article presents the results of a study that investigated the meaning of evaluation in mathematics from the historical cultural perspective, focusing on activity theory. In order to develop the investigation, a collaborative group was formed from the Oficina Pedagogica de Matematica de Ribeirao Preto - Sao Paulo (Math Pedagogic Workshop of Ribeirao Preto - OPM/RP), constituted of pre-school teachers and early elementary school teachers, who were participants in this research. The main role of the collaborative group was to offer guided development to the teachers about the teaching of mathematics from the historical-cultural perspective, aiming at collecting data on the process of appropriation of mathematical knowledge by the teachers. The syntheses about the teachers' learning process have contributed to systematize the guiding elements of evaluation in mathematics from the historical-cultural perspective.

O infinito de George Cantor : uma revolução paradigmatica no desenvolvimento da matematica; The George Cantor's infinite : a paradigmatic revolution in the development of mathematics

Eberth Eleuterio dos Santos
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
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Georg Cantor foi um dos mais importantes matemáticos do final do século XIX. A idealização de sua teoria de conjuntos representa um marco no desenvolvimento da matemática. De fato, o aparecimento e o desenvolvimento dessa teoria tiveram profundas conseqüências que não se limitaram ao círculo da matemática. O debate científico que se seguiu a certos resultados como, por exemplo, a apresentação dos números transfinitos, reavivou uma discussão que remonta a antigas disputas ontológicas da filosofia présocrática, exatamente àquelas discussões que se voltavam para a afirmação do Ser como infinito. Essa discussão nasce na Grécia antiga e perpassa toda a história do pensamento ocidental. Conhecemo-la por meio de nomes como Anaximandro, Pitágoras, Parmênides, Platão, Aristóteles. Atravessando os séculos, essas idéias povoaram a mente de personagens como Bruno, Galileu, Leibniz, Kant e muitos outros. Nos séculos XIX e XX, os trabalhos de Cantor reavivaram e deram novo impulso ao tema. Esforçamo-nos em mostrar que estes trabalhos são absolutamente revolucionários. Motivados pelo filósofo da ciência Thomas Kuhn, concluímos que o aparecimento da Teoria de Conjuntos de Cantor representa a revisão de um antigo paradigma filosófico-matemático. Paradigma este que teve sua primeira elaboração lógica e filosófica com Aristóteles e que se desenvolveu como a maneira dominante de pensar a idéia de infinito. Destacamos que alguns dos aspectos apontados por Kuhn como sintomáticos de uma revolução científica estão presentes no trabalho de Cantor e que há...

A matemática moderna e o Ginásio Estadual Vocacional Oswaldo Aranha : sobre caminhos e encontros; Modern mathematics and the Oswaldo Aranha State Vocational High School : on paths and encounters

Mário Eduardo Marques Fernandes
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
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O Colegio Tecnico de Limeira e o Movimento da Matematica Moderna : uma paisagem; The Limeira Technical School and the Modern Mathematics Movement : a view

Murilo França Tabosa
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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O Colégio Técnico de Limeira (Cotil), da Universidade Estadual de Campinas, foi instalado em 1967, na cidade Limeira - SP, então grande pólo industrial na área de mecânica e metalurgia. Nesse mesmo período, de vigência do projeto político-econômico desenvolvimentista do regime militar e dos acordos MECUSAID, temos em nosso país o fortalecimento de um movimento internacional para introdução de projetos inovadores do ensino de Matemática denominado "Movimento da Matemática Moderna". Este trabalho tem como objetivo analisar como um grupo de professores que lecionaram no COTIL, nos primeiros vinte anos de seu funcionamento, percebeu os processos de transformação da instituição e se posicionou em relação ao Movimento de Matemática Moderna. Utilizando a História Oral como metodologia central da investigação, constituímos documentos escritos, a partir dos relatos orais, que foram complementados por outros documentos, tais como: atas de reuniões, diários de professores, planos de disciplina, livros didáticos, legislações educacionais, fotografias.; The Technical College of Limeira (Cotil) as part of State University of Campinas started the activities in 1967 in Limeira -SP , at the time one of the greatest industrial areas for Mechanics and Metallurgy industry. At the same period that the country was under political and economic military regime bringing the incentives for strengthening of international movement for introduction of innovative projects in Mathematics teaching denominated as "Movement of Modern Mathematics". This work has the objective to describe how a group of math teachers realized the transformation process at Cotil during the primary years and how these teachers had positioned themselves into the Movement of Modern Mathematics. To perform the analyzes...

Teaching and learning mathematics using moodle

Lopes, Ana Paula Ferreira Fernandes; Babo, Rosalina; Azevedo, José Manuel Monteiro Lopes
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This paper summarizes a project that is contributing to a change in the way of teaching and learning Mathematics. Mathematics is a subject of the Accounting and Administration course. In this subject we teach: Functions and Algebra. The aim is that the student understand the basic concepts and is able to apply them in other issues, when possible, establishing a bridge between the issues that they have studied and their application in Accounting. As from this year, the Accounting course falls under in Bologna Process. The teacher and the student roles have changed. The time for theoretical and practical classes has been reduced, so it was necessary to modify the way of teaching and learning. In the theoretical classes we use systems of multimedia projection to present the concepts, and in the practical classes we solve exercises. We also use the Excel and the mathematical open source software wxMaxima. To supplement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio Online (Online Support Project). With the creation of this new project we wanted to take advantage already obtained results with the previous experiences, giving to the students opportunities to complement their study in Mathematics. One of the great objectives is to motivate students...

Symmetry and rotation skills of prospective elementary mathematics teachers

Turgut,Melih; Yenilmez,Kürşat; Anapa,Pınar
Tipo: Artigo de Revista Científica Formato: text/html
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The aim of this study was to investigate the skills and deficiencies of senior university students enrolled in a mathematics education program with the concepts of symmetry and rotation of geometric figures. The study was conducted with 32 prospective teachers in the Department of Education at a public university located in Western Turkey. This descriptive study was designed with a case study. A structured interview technique was used for data collection. A measurement tool consisting of 12 drawing problems testing symmetry (5 problems) and rotation (7 problems) ability was used in the study. Descriptive statistical methods were used for data analysis. The drawings were analyzed individually, and the students' mistakes and deficiencies were categorized. According to the results of the study, prospective elementary mathematics teachers did not have difficulty in drawing the symmetry of an object or in determining the symmetry axis. However, while they could rotate the figure when a rotation axis was provided, they failed to rotate it in the absence of an axis. In addition, prospective elementary mathematics teachers generally failed to find the center of the given rotated figures. The results of the present study were consistent with results in the literature.

Students' views and attitudes towards mathematics teaching and learning: A case study of a curriculum experience

Ponte, João Pedro da; Matos, João Filipe; Leal, Leonor; Guimarães, Henrique Manuel; Canavarro, Ana Paula
Tipo: Conferência ou Objeto de Conferência
Relevância na Pesquisa
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This paper describes a qualitative case study dealing with the views about mathematics teaching and learning held by students of a school involved in a experience of new curricula, stressing active methodologies and groupwork. At grade 7, the students noticed important differences in the mathematics classes and welcomed them. At grade 10, students had a general positive attitude towards mathematics but did not perceive major chnages. However, they were very concerned with the implications of this experience for their academic progression.

Recursion and Combinatorial Mathematics in Chandashaastra

Kulkarni, Amba
Tipo: Artigo de Revista Científica
Português
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Contribution of Indian Mathematics since Vedic Period has been recognised by the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text related to the description and analysis of meters in poetic work, describes algorithms which deal with the Combinatorial Mathematics. These algorithms essentially deal with the conversion of Binary numbers to Decimal numbers and vice versa, finding the value of 'n choose r', evaluating 2^n, etc. All these algorithms are recursive in nature. There are also evidences of making use of stack variables to stack the intermediate results for later use. Interestingly later work by Kedar Bhatt (around 800 AD) has only iterative algorithms for the same problems. We describe both the recursive as well as iterative algorithms in this paper.; Comment: 25 pages

On the transition period of implementing new mathematics curriculum for Foundation Engineering students

Karjanto, N.; Osman, R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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An overview on several mathematics modules in the transition period of introducing a new curriculum for the Foundation programme in Engineering at the University of Nottingham Malaysia Campus is discussed in this paper. In order to progress to Undergraduate programmes in Engineering, previously the students must complete three mathematics modules of 40 credit points in total, for which one of them was a year-long module with 20 credit points. Currently under the new curriculum, the students are required to complete five mathematics modules with 10 credit points each. The new curriculum gives positive impacts for both the lecturers and the students in terms of material organization, fully utilizing textbooks and a new arrangement for tutorial sessions. The new curriculum also provides the students with stronger mathematical background in critical thinking and problem solving skills to equip them to embark the Undergraduate programmes in Engineering.; Comment: 17 pages

Mathematics and language

Tipo: Artigo de Revista Científica
Português
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This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well.

Application of multivariate splines to discrete mathematics

Xu, Zhiqiang
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and give a simple proof for the volume formula for the Pitman-Stanley polytope. Third, an explicit formula for the Ehrhart quasi-polynomial is presented.; Comment: Box splines; Number of integer points in polytopes; Pitman-Stanley polytope

Hypothesis of the Functional Semantic Constructions and Mathematics in the Functional Semantic Aspect

Semenov, Y.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This essay contains three parts. The first part of essay focuses on the hypothesis of the functional semantic constructions (FSC-Hypothesis). This hypothesis explains that a language, a number, a money are the functional semantic constructions. In the second part the author considers the Mathematics with respect to the FSC-Hypothesis. Author turns in the solution for the following problems: Ontology of Mathematics, Objects of Mathematics, Number, Classification of the numbers. Last part contains the critical remarks to the axiomatic allocation of the real numbers to the linear point continuum and to the countability / uncountability of the set of rational and of the set of real numbers.

Topical Bias in Generalist Mathematics Journals

Grcar, Joseph F.
Tipo: Artigo de Revista Científica
Português
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Generalist mathematics journals exhibit bias toward the branches of mathematics by publishing articles about some subjects in quantities far disproportionate to the production of papers in those areas within all of mathematics.; Comment: 8 pages, 3 figures

Klein's double discontinuity revisited: what use is university mathematics to high school calculus?

Winsløw, Carl; Grønbæk, Niels
Tipo: Artigo de Revista Científica
Português
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Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in the form of calculus courses. We have several studies of bridging measures, success rates and many other aspects of these entrance transition problems. In this paper, we consider the inverse transition, experienced by university students as they revisit core parts of high school mathematics (in particular, calculus) after completing the mandatory undergraduate mathematics courses. To what extent does the advanced experience enable them to approach the high school calculus in a deeper and more autonomous way? To what extent can capstone courses support such an approach? How could it be hindered by deficiencies in the students' advanced experience? In this paper, we present a theoretical framework for an analysis of these questions, as well as a number of critical observations and reflections on how they appear in our own institutional context.; Comment: Will appear in "Recherches en Didactique des Math\'ematiques" vol. 34 no. 1

Responses to Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics'', by A. Jaffe and F. Quinn

Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunder; Mandelbrot, Benoit B.; Ruelle, David; Schwarz, Albert; Uhlenbeck, Karen; Thom, René; Witten, Edward; Zeeman, Christopher
Tipo: Artigo de Revista Científica
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This article is a collection of letters solicited by the editors of the Bulletin in response to a previous article by Jaffe and Quinn [math.HO/9307227]. The authors discuss the role of rigor in mathematics and the relation between mathematics and theoretical physics.; Comment: 30 pages. Abstract added in migration.

Reforms of the university mathematics education for non-mathematical specialties

Xiao, Shutie
Tipo: Artigo de Revista Científica
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This article is a part of the report for the research project Reform of the Course System and Teaching Content of Higher Mathematics (For Non-Mathematical Specialties)'' in 1995, supported by the National Ministry of Education. There are thirteen universities participated in this project. The Report not only reflects results of our participants, but also includes valuable opinions of many colleagues in the mathematical education circles. In this article, after a brief description on the history and reform situation of the higher mathematics education in China, attention concentrates to three aspects. They are: main problems in this field existing; the functions of mathematics accomplishment for college students; these concern course system, teaching and learning philosophy, such as overemphasized specialty education, overlooking to arouse rational thinking and aesthetic conceptions, etc. The last aspect contains a discussion on several important relationships, such as: knowledge impartment and quality cultivation, inherence and modernization of the mathematical knowledge, teacher's guidance and students' initiative, mathematical basic training and mathematical application consciousness and ability cultivation, etc.

The strength of the tree theorem for pairs in reverse mathematics

Patey, Ludovic
Tipo: Artigo de Revista Científica
Português
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No natural principle is currently known to be strictly between the arithmetic comprehension axiom (ACA) and Ramsey's theorem for pairs (RT^2_2) in reverse mathematics. The tree theorem for pairs (TT^2_2) is however a good candidate. The tree theorem states that for every finite coloring over tuples of comparable nodes in the full binary tree, there is a monochromatic subtree isomorphic to the full tree. The principle TT^2_2 is known to lie between ACA and RT^2_2 over RCA, but its exact strength remains open. In this paper, we prove that RT^2_2 together with weak K\"onig's lemma (WKL) does not imply TT^2_2, thereby answering a question of Montalban. This separation is a case in point of the method of Lerman, Solomon and Towsner for designing a computability-theoretic property which discriminates between two statements in reverse mathematics. We therefore put the emphasis on the different steps leading to this separation in order to serve as a tutorial for separating principles in reverse mathematics.; Comment: 16 pages

Patel, Mukul