The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Gender bias in the Trends in Mathematics and Science Study 2003 (TIMMS) for Canadian students /

This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Dyscalculia : action plans for successful learning in mathematics.

Recurso basado en observaciones de niños con dificultades matemáticas y en métodos probados para ayudarlos. Pone ejemplos de problemas que los niños pueden encontrar con la manipulación de los números. Proporciona a los profesores orientación sobre cómo evitar la confusión de los alumnos y cómo guiarlos a través del currículo de matemáticas más complejas.

First aid in mathematics.

Recurso que ofrece a los estudiantes de matemáticas toda la ayuda, el apoyo y la práctica necesaria para el aprendizaje y la revisión de esta asignatura. El contenido está planificado para dar cobertura a temas de matemáticas básicas. Los ejercicios y las pruebas de revisión ayudan al alumno a consolidar su conocimiento y lograr el mejor resultado.

Children's errors in mathematics : understanding common misconceptions in primary schools.

Manual diseñado para ayudar a los profesores de primaria a identificar en los niños sus conceptos erróneos en matemáticas. Considera tres perspectivas diferentes: el nivel del plan de estudios, el nivel del aula y el nivel de cada alumno. La comprensión de cómo los niños construyen su conocimiento matemático y los errores que cometen, permite identificar y explicar por qué ocurre el error. También permite adelantarse a conceptos erróneos habituales y a planificar las lecciones. Tiene un índice con referencias cruzadas para el programa nacional británico.

Answers to first aid in mathematics.

Folleto con las soluciones a todos los ejercicios y pruebas de revisión del recurso con el título 'First aid in mathematics'.

Achieving TABE Success in Mathematics: Level D.

Este libro ayuda a los estudiantes a preparar el examen de matemáticas TABE. Los estudiantes desarrollarán un entendimiento de conceptos matemáticos, aprenderán estrategias para resolver problemas. Los temas del libro son: operaciones con números, cálculo con números enteros, ratio, proporción y porcentaje, análisis de datos, funciones, álgebra, estadísticas y probabilidad (interpretando información en tablas, usando tablas para hacer comparaciones), geometría (reconociendo tipos de ángulos, identificando polígonos, reconociendo tipos de triángulos, identificando partes de un círculo, trabajando con figuras de tres dimensiones) , medidas, decimales (sumando, restando, multiplicando y dividiendo decimales), fracciones , integrales (sumando, restando, multiplicando y dividiendo integrales).

Adecuación curricular del diagnóstico y la evaluación en matemáticas = Curricular validity of assessment and evaluation instruments in mathematics.

Resumen basado en el del autor

Discourses of power in Mathematics Education research : concepts and possibilities for action. 'Discursos sobre el poder en la investigación en Educación Matemática : conceptos y posibilidades para la acción'.

Resumen basado en el de la publicación

Conceptualizing professional development in mathematics : elements of a model. 'Conceptualización del desarrollo profesional en matemáticas : elementos de un modelo'.

Resumen basado en el de la publicación