Methods to Access and Retrieve Mathematical Content in ActiveMath

2006 ◽  
pp. 331-342 ◽  
Author(s):  
Paul Libbrecht ◽  
Erica Melis
Keyword(s):  
Mathematical Content

scholarly journals Changing the Order of Factors Does Not Change the Product but Does Affect Students’ Answers, Especially Girls’ Answers

2021 ◽  
Vol 11 (5) ◽  
pp. 201
Author(s):  
Clelia Cascella ◽  
Chiara Giberti ◽  
Giorgio Bolondi
Keyword(s):  
Experimental Design ◽  
Rasch Model ◽  
Achievement Tests ◽  
Mathematical Content ◽  
Probability Sample ◽  
Decimal Numbers ◽  
Common Items ◽  
The Rasch Model ◽  
Grade 8

This study is aimed at exploring how different formulations of the same mathematical item may influence students’ answers, and whether or not boys and girls are equally affected by differences in presentation. An experimental design was employed: the same stem-items (i.e., items with the same mathematical content and question intent) were formulated differently and administered to a probability sample of 1647 students (grade 8). All the achievement tests were anchored via a set of common items. Students’ answers, equated and then analysed using the Rasch model, confirmed that different formulations affect students’ performances and thus the psychometric functionality of items, with discernible differences according to gender. In particular, we explored students’ sensitivity to the effect of a typical misconception about multiplication with decimal numbers (often called “multiplication makes bigger”) and tested the hypothesis that girls are more prone than boys to be negatively affected by misconception.

scholarly journals Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

Pythagoras ◽  
2008 ◽  
Vol 0 (68) ◽  
Author(s):  
Michael De Villiers
Keyword(s):  
History Of Mathematics ◽  
Genetic Approach ◽  
Mathematical Content ◽  
Euler Line ◽  
History Of ◽  
Mathematics For Teaching ◽  
The Creation ◽  
Reasoning By Analogy

This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.

scholarly journals Using Student-Centered Projects To Teach Mathematics Content Standards

2006 ◽  
Vol 3 (4) ◽  
Author(s):  
Carryn Bellomo
Keyword(s):  
Middle School ◽  
School District ◽  
Teaching And Learning ◽  
Academic Community ◽  
School Level ◽  
Content Standards ◽  
College Level ◽  
Mathematical Content ◽  
Clark County ◽  
Clark County School District

Teaching and learning standards across the country are becoming more content driven, especially in mathematics.  As such, it is essential to develop substantive college level math courses for pre-service and in-service teachers.  These courses should deliver mathematical content in a relevant way.  Teachers must not only be proficient in their subject, but also recognize how to apply content meaningfully to student’s lives.  As part of a grant funded through the Department of Education in coordination with the Clark County School District, I have designed two college level courses that will deliver mathematical content standards to middle school teachers.  These courses will help prepare teachers at the middle school level by focusing on mathematical content, making connections within the curriculum, using technology, and enhancing the role of mathematics in everyday life and problem solving. The primary purpose of this paper is to share with the academic community the projects used to develop content understanding in mathematics topics such as:  mathematical notation, proportion, computation, estimation, linear regression, reflections, translations, finding relationships, and analyzing data.  This paper will present these projects, and tie them to mathematics standards outlined in the Clark County School District (and Nevada State) Standards.

scholarly journals Developing Primary Pre-service Teachers' Mathematical Content Knowledge During Practicum Teaching

2016 ◽  
Vol 41 (2) ◽  
pp. 152-173 ◽  
Author(s):  
Sharyn Livy ◽  
◽  
Colleen Vale ◽  
Sandra Herbert ◽  
◽  
...  
Keyword(s):  
Content Knowledge ◽  
Mathematical Content Knowledge ◽  
Mathematical Content

scholarly journals O que dizem as pesquisas sobre a Resolução de Problemas na formação inicial de professores de Matemática: um olhar sobre as fragilidades metodológicasWhat research on problem solving in the initial teacher education of mathematics says: a look into the methodological weaknesses

2020 ◽  
Vol 22 (2) ◽  
pp. 721-750
Author(s):  
Luiz Otavio Rodrigues Mendes ◽  
Ana Lucia Pereira ◽  
Marcelo Carlos de Proença
Keyword(s):  
Teacher Education ◽  
Problem Solving ◽  
Teaching And Learning ◽  
Basic Education ◽  
Initial Teacher Education ◽  
Future Research ◽  
Point Problem ◽  
Mathematical Content ◽  
Revisión Sistemática ◽  
Starting Point

ResumoA resolução de problemas, quando trabalhada com o problema como ponto de partida, tem apresentado profícuas possibilidades no ensino superior. No entanto, quais as possíveis fragilidades quando se trabalha com esta abordagem nesta perspectiva? À vista disso, este artigo apresenta o resultado de uma pesquisa que tem como objetivo desvelar as fragilidades que se evidenciam a partir do desenvolvimento da abordagem de resolução de problemas, em que se tem o problema como ponto de partida na formação inicial de professores de Matemática, apresentadas em teses e dissertações. A partir de uma revisão sistemática da literatura, encontramos 12 pesquisas que constituíram o corpus de dados, para serem analisadas seguindo as técnicas de Análise de Conteúdo, de onde foi possível identificarmos quatro categorias. Os principais resultados revelam que as fragilidades se relacionam com: I) dificuldades quanto à falta de conhecimento sobre o conteúdo matemático da educação básica pelos licenciandos; II) dificuldades apresentadas pelos licenciandos em comunicar suas ideias a respeito do conteúdo matemático trabalhado; III) dificuldade no entendimento dos problemas pelos estudantes; e, IV) dificuldades relativas ao tempo, referentes à realização das atividades pelos licenciandos e ao desenvolvimento da abordagem de ensino. Tais apontamentos podem contribuir com pesquisas futuras que desejem traçar este caminho, aprimorando-as e contribuindo com o processo de ensino e aprendizagem da Matemática.Palavras-chave: Solução de problemas, Formação inicial de professores, Matemática.AbstractWhen working with the problem as a starting point, problem-solving has presented fruitful possibilities in Higher Education. However, what are the possible weaknesses when working with this approach from this perspective? In view of this, this article presents the result of research that aims to unveil the fragilities that are evident from the development of the problem-solving approach, in which the problem is taken as a starting point in the initial training of mathematics teachers, presented in theses and dissertations. From a systematic review of the literature, we found 12 surveys that constituted the corpus of data, to be analyzed following the Content Analysis techniques, from which it was possible to identify four categories. The main results reveal that the weaknesses are related to I) difficulties related to the students’ lack of knowledge about the mathematical content of basic education; II) students’ difficulties to communicate their ideas about the mathematical content worked; III) students’ difficulty in understanding the problems; and, IV) difficulties related to time, concerning the students’ activity performance and the development of the teaching approach. Such notes can contribute to future research that wishes to follow this path, improving them and contributing to the process of teaching and learning Mathematics.Keywords: Problem-solving, Initial teacher education, Mathematics.ResumenLa resolución de problemas cuando se trabaja con el problema como punto de partida, ha presentado posibilidades fructíferas en la educación superior. Sin embargo, ¿cuáles son las posibles debilidades de entender y trabajar con este enfoque en esta perspectiva? En vista de esto, este artículo presenta el resultado de una investigación que tiene como objetivo develar las debilidades que se evidencian a partir del desarrollo del enfoque de resolución de problemas, en el que el problema se toma como punto de partida en la formación inicial de docentes de Matemáticas, presentadas en tesis y disertaciones. A partir de una revisión sistemática de la literatura, se encontraron 12 investigaciones que constituían el corpus de datos, para ser analizadas siguiendo las técnicas de Análisis de Contenido de manera cualitativa. Los principales resultados revelan que las debilidades están relacionadas con I) dificultades relacionadas con la falta de conocimiento sobre el contenido matemático de la Educación Básica por parte de los estudiantes de docencia, II) dificultades presentadas por los estudiantes de docencia para comunicar sus ideas sobre el contenido matemático trabajado, III) dificultad presentada por los alumnos para comprender problemas y IV) dificultad relacionada con el tiempo para desarrollar actividades y aplicar el enfoque. Tales notas pueden contribuir a futuras investigaciones que deseen trazar este camino, mejorarlas y contribuir al proceso de enseñanza y aprendizaje de las Matemáticas.Palabras clave: Resolución de problemas, Formación inicial de profesores, Matemáticas

scholarly journals Ações de Docência com Uso de Tecnologias Digitais na Formação Inicial de Professores de Matemática

2020 ◽  
Vol 13 (2) ◽  
pp. 211-221
Author(s):  
Ivanete Fátima Blauth ◽  
Suely Scherer
Keyword(s):  
Teaching Practice ◽  
Basic Education ◽  
Digital Technologies ◽  
Pedagogical Knowledge ◽  
The Other ◽  
Mathematical Content ◽  
Initial Formation ◽  
Practice Teaching ◽  
Teaching Learning ◽  
School Space

ResumoNeste artigo discutimos resultados de uma pesquisa em que se analisou ações propostas em uma disciplina de Prática de Ensino, identificando aquelas que podem ter possibilitado a construção de conhecimentos tecnológicos e pedagógicos de conteúdo, por egressos de um curso de Licenciatura em Matemática. Dentre as ações identificadas, duas são relacionadas à aprendizagem da docência, uma vivenciada na sala de aula da disciplina, em que o acadêmico teve colegas como alunos, e a outra realizada no espaço da escola, em que o acadêmico assumiu a regência de uma aula de matemática em escolas de Educação Básica. O objetivo neste artigo é analisar essas duas ações e possíveis relações com a construção de conhecimentos tecnológicos e pedagógicos de conteúdo matemático. Os dados foram produzidos na pesquisa a partir de entrevistas realizadas com 27 egressos desse curso de Licenciatura em Matemática, que realizaram a disciplina de Prática de Ensino e concluíram o curso, no período de 2010 a 2015. A partir da análise de “falas de egressos”, concluiu se que as duas ações propostas na disciplina de Prática de Ensino, nas quais os professores em formação tiveram a oportunidade de praticar a docência, podem ter oportunizado a construção de conhecimentos tecnológicos e pedagógicos de conteúdo matemático. Nessas ações, esses egressos tiveram que estudar conteúdos matemáticos e tecnologias, de maneira a atender objetivos de aulas e favorecer a aprendizagem de seus alunos.Palavras-chave: Prática de Ensino. Formação Inicial. Matemática. Tecnologias Digitais.AbstractIn this paper we discuss the results of a research in which actions proposed in a Teaching Practice discipline were analyzed, identifying those may have made the construction of technological and pedagogical knowledge, by graduates of a Mathematics Degree. Among the actions identified, two are related to teaching learning, and other experienced in the classroom, in which the students was the academic’s colleagues, and the other was in the school space, in which the academic took over the conduct of a class of mathematics in Basic Education schools. The objective of this article is to analyze these two actions and possible relationships with the construction of technological and pedagogical knowledge of Mathematical content. The data were produced in the research based on interviews with 27 graduates of this Mathematics Degree, who took the Teaching Practice discipline and completed the course, from 2010 to 2015. From the analysis of the “speeches of graduates”, it was concluded that the two actions proposed in the Teaching Practice discipline, in which the teachers in training had the opportunity to practice teaching, may have given rise to the construction of technological and pedagogical knowledge of Mathematical content. In these actions, these graduates had to study Mathematical content and technologies, in order to meet class objectives and favor the learning of their students.Keywords: Teaching Practice. Initial Formation. Mathematics. Digital Technologies.

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