Formação de professores de matemática da educação superior e as tecnologias digitais: aspectos do conhecimento revelados no contexto de uma comunidade de prática online

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Programação no ensino de matemática utilizando Processing 2: Um estudo das relações formalizadas por alunos do ensino fundamental com baixo rendimento em matemática

Pós-graduação em Educação para a Ciência - FC

O uso de elementos da criptografia como estímulo matemático na sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma análise dos livros de André Perez Y Marin: um momento da história da matemática escolar brasileira no início do século XX

Pós-graduação em Educação Matemática - IGCE

Creating Meaningful Homework and Implementing Homework Presentations to Aid in Mathematics Instruction

In this action research study of sixth grade mathematics, I investigated the use of meaningful homework and the implementation of presentations and its effect on students’ comprehension of mathematical concepts. I collected data to determine whether the creating of meaningful homework and the implementation of homework presentations would have a positive impact on the students’ understanding of the concepts being taught in class and the reasoning behind assigning homework. The homework was based on the lesson taught during class time. It was grade-level appropriate and contained problems similar to those students completed in class. A pre-research and post-research survey based on homework perceptions and my teaching practices was given, student interviews were conducted throughout the research period, weekly teacher journals were kept that pertained to my teaching practices and the involvement of the students that particular week, and homework assignments were collected to gauge the students’ understanding of the mathematics lessons. Most students’ perceptions on homework were positive and most understood the reasoning for homework assignments.

Improving Communication about Mathematics through Vocabulary and Writing

In this action research study, where the subjects were my 6th grade mathematics students, I investigated the impact of direct vocabulary instruction on their communication and achievement. I strategically implemented the addition of vocabulary study into each lesson over a four-month time period. The students practiced using vocabulary in verbal discussions, review activities, and in mathematical problem explanations. I discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data I collected. I also found that in general, students felt that knowing the definition of mathematical words was important and that it increased their achievement when they understood the words. In addition, students were more exact in their communication after receiving vocabulary instruction. As a result of this research, I plan to continue to implement vocabulary into daily lessons and keep vocabulary and communication as a focus of my 6th grade mathematics class.

Summarization in Math Class

This action research study of twenty students in my sixth grade mathematics classroom examines the implementation of summarization strategies. Students were taught how to summarize concepts and how to explain their thinking in different ways to the teacher and their peers. Through analysis of students’ summaries of concepts from lessons that I taught, tests scores, and student journals and interviews, I discovered that summarizing mathematical concepts offers students an engaging opportunity to better understand those concepts and render that understanding more visible to the teacher. This analysis suggests that non-traditional summarization, such as verbal and written strategies, and strategies involving movement and discussions, can be useful in mathematics classrooms to improve student understanding, engagement in learning tasks, and as a form of formative assessment.

Here is the Plan: So What is the Question?

In this action research study of my classroom of 5th grade mathematics students, I investigated their understanding of the mathematical operations by having them write problems to match given equations. I discovered that writing a story to match an equation does provide insight into a student’s understanding of mathematical concepts, however, reading comprehension is a factor in the understanding. Readers who struggle with comprehension do struggle with understanding and writing math story problems. The discussion that follows the writing of a math story problem and the solving of the written problems helps to strengthen the students’ mathematical abilities as well as their communication skills and confidence levels. Through my study, students learned that it was alright to make mistakes because the learning from those mistakes is what is important. As a result of this research, I plan to continue to have students write stories to match given equations as a source of information about student understanding. I will continue to give opportunities to revisit those written problems as a tool to increase students’ comprehension and communication skills, as well as their confidence.

Cooperative Learning Groups in the Eighth Grade Math Classroom

In this action research study of my classroom of 8th grade mathematics students, I investigated whether cooperative learning would lead to a better understanding of the mathematical concepts and thus more success for the students. I used my three eighth grade classes with two using cooperative groups and the third not. I discovered that the students who wanted to work in cooperative groups were more successful than they had been. I also discovered that the grouping itself has a great effect on how the group works together. The wrong grouping of students can lead to disaster and many headaches for the teacher. Overall the two classes that used cooperative groups did better grade wise than the one class that was taught using the traditional way of not using cooperative groups. As a result of this research, I plan to continue using cooperative groups but will be more aware of the students who are grouped together.

O uso de elementos da criptografia como estímulo matemático na sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma análise dos livros de André Perez Y Marin: um momento da história da matemática escolar brasileira no início do século XX

Pós-graduação em Educação Matemática - IGCE

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Especificaciones eMathTeacher, creación del Modelo Granular Lingüístico de la evaluación del aprendizaje humano, y diseño de sistemas que implementan estos conceptos

El concepto de algoritmo es básico en informática, por lo que es crucial que los alumnos profundicen en él desde el inicio de su formación. Por tanto, contar con una herramienta que guíe a los estudiantes en su aprendizaje puede suponer una gran ayuda en su formación. La mayoría de los autores coinciden en que, para determinar la eficacia de una herramienta de visualización de algoritmos, es esencial cómo se utiliza. Así, los estudiantes que participan activamente en la visualización superan claramente a los que la contemplan de forma pasiva. Por ello, pensamos que uno de los mejores ejercicios para un alumno consiste en simular la ejecución del algoritmo que desea aprender mediante el uso de una herramienta de visualización, i. e. consiste en realizar una simulación visual de dicho algoritmo. La primera parte de esta tesis presenta los resultados de una profunda investigación sobre las características que debe reunir una herramienta de ayuda al aprendizaje de algoritmos y conceptos matemáticos para optimizar su efectividad: el conjunto de especificaciones eMathTeacher, además de un entorno de aprendizaje que integra herramientas que las cumplen: GRAPHs. Hemos estudiado cuáles son las cualidades esenciales para potenciar la eficacia de un sistema e-learning de este tipo. Esto nos ha llevado a la definición del concepto eMathTeacher, que se ha materializado en el conjunto de especificaciones eMathTeacher. Una herramienta e-learning cumple las especificaciones eMathTeacher si actúa como un profesor virtual de matemáticas, i. e. si es una herramienta de autoevaluación que ayuda a los alumnos a aprender de forma activa y autónoma conceptos o algoritmos matemáticos, corrigiendo sus errores y proporcionando pistas para encontrar la respuesta correcta, pero sin dársela explícitamente. En estas herramientas, la simulación del algoritmo no continúa hasta que el usuario introduce la respuesta correcta. Para poder reunir en un único entorno una colección de herramientas que cumplan las especificaciones eMathTeacher hemos creado GRAPHs, un entorno ampliable, basado en simulación visual, diseñado para el aprendizaje activo e independiente de los algoritmos de grafos y creado para que en él se integren simuladores de diferentes algoritmos. Además de las opciones de creación y edición del grafo y la visualización de los cambios producidos en él durante la simulación, el entorno incluye corrección paso a paso, animación del pseudocódigo del algoritmo, preguntas emergentes, manejo de las estructuras de datos del algoritmo y creación de un log de interacción en XML. Otro problema que nos planteamos en este trabajo, por su importancia en el proceso de aprendizaje, es el de la evaluación formativa. El uso de ciertos entornos e-learning genera gran cantidad de datos que deben ser interpretados para llegar a una evaluación que no se limite a un recuento de errores. Esto incluye el establecimiento de relaciones entre los datos disponibles y la generación de descripciones lingüísticas que informen al alumno sobre la evolución de su aprendizaje. Hasta ahora sólo un experto humano era capaz de hacer este tipo de evaluación. Nuestro objetivo ha sido crear un modelo computacional que simule el razonamiento del profesor y genere un informe sobre la evolución del aprendizaje que especifique el nivel de logro de cada uno de los objetivos definidos por el profesor. Como resultado del trabajo realizado, la segunda parte de esta tesis presenta el modelo granular lingüístico de la evaluación del aprendizaje, capaz de modelizar la evaluación y generar automáticamente informes de evaluación formativa. Este modelo es una particularización del modelo granular lingüístico de un fenómeno (GLMP), en cuyo desarrollo y formalización colaboramos, basado en la lógica borrosa y en la teoría computacional de las percepciones. Esta técnica, que utiliza sistemas de inferencia basados en reglas lingüísticas y es capaz de implementar criterios de evaluación complejos, se ha aplicado a dos casos: la evaluación, basada en criterios, de logs de interacción generados por GRAPHs y de cuestionarios de Moodle. Como consecuencia, se han implementado, probado y utilizado en el aula sistemas expertos que evalúan ambos tipos de ejercicios. Además de la calificación numérica, los sistemas generan informes de evaluación, en lenguaje natural, sobre los niveles de competencia alcanzados, usando sólo datos objetivos de respuestas correctas e incorrectas. Además, se han desarrollado dos aplicaciones capaces de ser configuradas para implementar los sistemas expertos mencionados. Una procesa los archivos producidos por GRAPHs y la otra, integrable en Moodle, evalúa basándose en los resultados de los cuestionarios. ABSTRACT The concept of algorithm is one of the core subjects in computer science. It is extremely important, then, for students to get a good grasp of this concept from the very start of their training. In this respect, having a tool that helps and shepherds students through the process of learning this concept can make a huge difference to their instruction. Much has been written about how helpful algorithm visualization tools can be. Most authors agree that the most important part of the learning process is how students use the visualization tool. Learners who are actively involved in visualization consistently outperform other learners who view the algorithms passively. Therefore we think that one of the best exercises to learn an algorithm is for the user to simulate the algorithm execution while using a visualization tool, thus performing a visual algorithm simulation. The first part of this thesis presents the eMathTeacher set of requirements together with an eMathTeacher-compliant tool called GRAPHs. For some years, we have been developing a theory about what the key features of an effective e-learning system for teaching mathematical concepts and algorithms are. This led to the definition of eMathTeacher concept, which has materialized in the eMathTeacher set of requirements. An e-learning tool is eMathTeacher compliant if it works as a virtual math trainer. In other words, it has to be an on-line self-assessment tool that helps students to actively and autonomously learn math concepts or algorithms, correcting their mistakes and providing them with clues to find the right answer. In an eMathTeacher-compliant tool, algorithm simulation does not continue until the user enters the correct answer. GRAPHs is an extendible environment designed for active and independent visual simulation-based learning of graph algorithms, set up to integrate tools to help the user simulate the execution of different algorithms. Apart from the options of creating and editing the graph, and visualizing the changes made to the graph during simulation, the environment also includes step-by-step correction, algorithm pseudo-code animation, pop-up questions, data structure handling and XML-based interaction log creation features. On the other hand, assessment is a key part of any learning process. Through the use of e-learning environments huge amounts of data can be output about this process. Nevertheless, this information has to be interpreted and represented in a practical way to arrive at a sound assessment that is not confined to merely counting mistakes. This includes establishing relationships between the available data and also providing instructive linguistic descriptions about learning evolution. Additionally, formative assessment should specify the level of attainment of the learning goals defined by the instructor. Till now, only human experts were capable of making such assessments. While facing this problem, our goal has been to create a computational model that simulates the instructor’s reasoning and generates an enlightening learning evolution report in natural language. The second part of this thesis presents the granular linguistic model of learning assessment to model the assessment of the learning process and implement the automated generation of a formative assessment report. The model is a particularization of the granular linguistic model of a phenomenon (GLMP) paradigm, based on fuzzy logic and the computational theory of perceptions, to the assessment phenomenon. This technique, useful for implementing complex assessment criteria using inference systems based on linguistic rules, has been applied to two particular cases: the assessment of the interaction logs generated by GRAPHs and the criterion-based assessment of Moodle quizzes. As a consequence, several expert systems to assess different algorithm simulations and Moodle quizzes have been implemented, tested and used in the classroom. Apart from the grade, the designed expert systems also generate natural language progress reports on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. In addition, two applications, capable of being configured to implement the expert systems, have been developed. One is geared up to process the files output by GRAPHs and the other one is a Moodle plug-in set up to perform the assessment based on the quizzes results.

Análisis de la modulación de voz ocasionada por el temblor vocal

La realización de este proyecto está basado en el estudio realizado por Jean Schoentgen en el cual el autor caracterizó el micro temblor vocal por medio del índice y la frecuencia de modulación. En este proyecto se utilizará la herramienta Matlab para el cálculo de estos parámetros y al finalizar se analizarán los datos obtenidos. El proyecto se ha dividido en tres grandes partes. En la primera de ellas se ha explicado brevemente los conceptos básicos de la voz y conceptos importantes tales como el temblor fisiológico, el patológico y el Jitter vocal entre otros, también se han detallado conceptos matemáticos utilizados en el desarrollo del código. Esto se realizó con el fin que el lector tenga claros algunos conceptos importantes antes del desarrollo del código y así pueda entender con más facilidad el estudio realizado en este proyecto, en esta parte no se ha realizado una explicación muy extensa de cada concepto, entendiendo que el lector posee unos conocimientos básicos de ingeniería, por otra parte existen innumerables libros que explican de una manera más precisa cada uno de estos conceptos. En la segunda parte se llevó a cabo el desarrollo del código. Como se mencionó anteriormente se ha utilizado la herramienta Matlab que es muy utilizada en la mayoría de las asignaturas de la carrera obteniendo así un buen dominio de esta, además posee unos toolbox muy útiles que facilitan los cálculos matemáticos. En esta parte se ilustra paso a paso cada etapa de elaboración del código y algunas graficas de la señal de voz a medida que pasa por cada etapa del código. En la última parte se obtienen los datos de todos los cálculos de los registros de voz y se analiza cada uno de ellos a la vez que se comparan con los del estudio de Jean Schoentgen y se analizan las posibles diferencias. ABSTRACT. The Project is based on the search made by Jean Schoentgen, whose research the micro tremor vocal can be established by frequency modulation and modulation index. This project has been carried out in Matlab to calculate the aforementioned parameters and finally, the results were contrasted with the results from Jean Shoetngen’s research. This project consists of three parts: The first of all, to be able to understand this project to future readers .It was explained different basic concepts about the voice such as physiologic tremor, pathological tremor and Jitter. Furthermore, mathematical concepts were explained in detail, due to these were used in the software development. Then, it was focused on software development such as the elaboration of code and different voice signals that were processed. This part was made with Matlab, which is mathematical software with high-level language for numerical computation, visualization, collaborate across disciplines including signal and image processing and application development. At finally, the acquired calculations were contrasted with the results from Jean Schoentgen’s research.

A reference architecture for instructional educational software

Our extensive research has indicated that high-school teachers are reluctant to make use of existing instructional educational software (Pollard, 2005). Even software developed in a partnership between a teacher and a software engineer is unlikely to be adopted by teachers outside the partnership (Pollard, 2005). In this paper we address these issues directly by adopting a reusable architectural design for instructional educational software which allows easy customisation of software to meet the specific needs of individual teachers. By doing this we will facilitate more teachers regularly using instructional technology within their classrooms. Our domain-specific software architecture, Interface-Activities-Model, was designed specifically to facilitate individual customisation by redefining and restructuring what constitutes an object so that they can be readily reused or extended as required. The key to this architecture is the way in which the software is broken into small generic encapsulated components with minimal domain specific behaviour. The domain specific behaviour is decoupled from the interface and encapsulated in objects which relate to the instructional material through tasks and activities. The domain model is also broken into two distinct models - Application State Model and Domainspecific Data Model. This decoupling and distribution of control gives the software designer enormous flexibility in modifying components without affecting other sections of the design. This paper sets the context of this architecture, describes it in detail, and applies it to an actual application developed to teach high-school mathematical concepts.