A More Sophisticated Treatment of Collisions

An improved argument about collisions in gas phase kinetics is elaborated upon, based on textbook arguments which oversimplify the concepts.

Undergraduate Engineering Students' Understanding of Heat, Temperature, and Radiation

Difficulty understanding heat and temperature concepts has been recognized in engineering education. Confusion has been shown to persist after instruction. The purpose of this study was to determine whether undergraduate engineering students’ knowledge of four heat transfer concept areas significantly changed with instruction and whether this varied by major and GPA. Two hundred twenty-eight undergraduate engineering students from six institutions were assessed prior to and after instruction. Results showed significant improvement in most concept areas but mean scores were below mastery. Previously documented misconceptions persisted after instruction. Significant differences were found by major and GPA. Suggestions for future research provided.

Constructed Response Answers in a Multiple-Choice Universe

A scheme is introduced which allows computer readable multiple choice forms used in traditional examinations to be employed for constructed response items.

Orchestrating Whole Group Discourse to Mediate Mathematical Meaning

The most common pattern of classroom discourse follows a three-part exchange of teacher initiation, student response, and teacher evaluation or follow-up (IRE/IRF) (Cazden, 2001). Although sometimes described as encouraging illusory understanding (Lemke, 1990), triadic exchanges can mediate meaning (Nassaji & Wells, 2000). This paper focuses on one case from a study of discursive practices of seven middle grades teachers identified for their expertise in mathematics instruction. The central result of the study was the development of a model to explain how teachers use discourse to mediate mathematical meaning in whole group instruction. Drawing on the model for analysis, thick descriptions of one teacher’s skillful orchestration of triadic exchanges that enhance student understanding of mathematics are presented.

The Effect of Direct Instruction versus Discovery Learning on the Understanding of Science Lessons by Second Grade Students

This study examined the effectiveness of discovery learning and direct instruction in a diverse second grade classroom. An assessment test and transfer task were given to students to examine which method of instruction enabled the students to grasp the content of a science lesson to a greater extent. Results demonstrated that students in the direct instruction group scored higher on the assessment test and completed the transfer task at a faster pace; however, this was not statistically significant. Results also suggest that a mixture of instructional styles would serve to effectively disseminate information, as well as motivate students to learn.

Improving Automaticity with Basic Addition Facts: Do Taped Problems Work Faster Than Cover, Copy, Compare?

This small pilot study compared the effectiveness of two interventions to improve automaticity with basic addition facts: Taped Problems (TP) and Cover, Copy, Compare (CCC), in students aged 6-10. Automaticity was measured using Mathematics Curriculum-Based Measurement (M-CBM) at pretest, after 10 days, and after 20 days of intervention. Our hypothesis was that the TP group will gain higher levels of automaticity more quickly than the CCC and control groups. However, when gain scores were compared, no significant differences were found between groups. Limitations to the study include low treatment integrity and a short duration of intervention.

Could it be possible to replace DERIVE with MAXIMA?

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative software product, and considering the possibility of using a public-domain software such as MAXIMA. Here we make a comparative study of DERIVE and MAXIMA as support tools for a Calculus course for first year Engineering students.

An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

EDUCAÇÃO MATEMÁTICA E AS TECNOLOGIAS: POR UMA APRENDIZAGEM SIGNIFICATIVA

presente trabalho tem por finalidade refletir a educação matemática inserida em um momento em que emerge um novo paradigma que valoriza uma educação transdisciplinar. Tem como foco o educando em todos os seus aspectos: corporal, emocional, racional e espiritual. Partindo do princípio que se vive em um mundo globalizado, onde as informações processam-se no dia-a-dia com mais velocidade e que um dos responsáveis, por este acúmulo de informações, o computador, valoriza-se neste estudo esta tecnologia como estratégia para uma educação inovadora na aprendizagem matemática. Pesquisando-se a real necessidade, por parte dos alunos, em utilizar a informática dentro do ambiente escolar, questionase o fundamento da dificuldade e/ou resistência de educadores de uma escola pública da rede estadual do Estado de São Paulo em utilizar estas inovações tecnológicas, efetivamente o computador, como ferramenta importante na busca de uma educação significativa.(AU)

EDUCAÇÃO MATEMÁTICA E AS TECNOLOGIAS: POR UMA APRENDIZAGEM SIGNIFICATIVA

presente trabalho tem por finalidade refletir a educação matemática inserida em um momento em que emerge um novo paradigma que valoriza uma educação transdisciplinar. Tem como foco o educando em todos os seus aspectos: corporal, emocional, racional e espiritual. Partindo do princípio que se vive em um mundo globalizado, onde as informações processam-se no dia-a-dia com mais velocidade e que um dos responsáveis, por este acúmulo de informações, o computador, valoriza-se neste estudo esta tecnologia como estratégia para uma educação inovadora na aprendizagem matemática. Pesquisando-se a real necessidade, por parte dos alunos, em utilizar a informática dentro do ambiente escolar, questionase o fundamento da dificuldade e/ou resistência de educadores de uma escola pública da rede estadual do Estado de São Paulo em utilizar estas inovações tecnológicas, efetivamente o computador, como ferramenta importante na busca de uma educação significativa.(AU)

Tareas matemáticas en la formación de maestros: caracterizando perspectivas

El diseño de tareas en los programas de formación de maestros se vincula al desarrollo del conocimiento necesario para realizar diferentes tareas profesionales- organizar el contenido matemático, interpretar el aprendizaje, gestionar la enseñanza. Se ejemplifica esta perspectiva en el caso del diseño de tareas matemáticas considerando la tarea profesional del maestro de analizar libros de texto.

Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

Construcción de conocimiento y desarrollo de una mirada profesional para la práctica de enseñar matemáticas en entornos en entornos en línea

Este trabajo sintetiza en tres ámbitos algunos de los resultados de las investigaciones sobre la construcción del conocimiento de la enseñanza de las matemáticas en entornos de aprendizaje multimedia que integran espacios de interacción social en contextos b-learning. Estos ámbitos son (i) el papel de la interacción y la negociación de significados en la construcción del conocimiento; (ii) el proceso de instrumentalización del conocimiento de Didáctica de la Matemática en procesos de formación; y (iii) las características de las estructuras argumentativas en los procesos de aprender a conceptualizar la enseñanza de las matemáticas. Finalmente, se identifican nuevas cuestiones de investigación que emergen desde estas investigaciones.

Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.