Cue recognition and cue elaboration in learning from examples.

This paper describes the processes used by students to learn from worked-out examples and by working through problems. Evidence is derived from protocols of students learning secondary school mathematics and physics. The students acquired knowledge from the examples in the form of productions (condition-->action): first discovering conditions under which the actions are appropriate and then elaborating the conditions to enhance efficiency. Students devoted most of their attention to the condition side of the productions. Subsequently, they generalized the productions for broader application and acquired specialized productions for special problem classes.

Características del desarrollo de una mirada profesional en estudiantes para profesor de matemáticas en un contexto b-learning

Esta investigación presenta un estudio cuyo objetivo es identificar aspectos que apoyan el desarrollo de la mirada profesional en estudiantes para profesores de matemáticas en un contexto b-learning. Analizamos las producciones de un grupo de estudiantes para profesores de matemáticas de educación secundaria (documentos escritos y participaciones en un debate on-line) cuando analizaban el razonamiento proporcional de estudiantes de educación secundaria. Los resultados indican que la interacción en el debate en línea permitió a algunos estudiantes para profesor mejorar su capacidad de identificar e interpretar aspectos relevantes del pensamiento matemático de los estudiantes de educación secundaria. Estos resultados indican que el desarrollo de “una mirada profesional” del profesor es un proceso complicado pero que la posibilidad de construir un discurso progresivo en línea es un factor importante para su desarrollo.

¿Cómo estudiantes para profesor de matemáticas comprenden el aprendizaje del límite de una función?

En este estudio presentamos una investigación que tiene como objetivo generar información sobre cómo estudiantes para profesor de educación secundaria (EPS) comprenden el proceso de aprendizaje de las matemáticas. El contexto que hemos utilizado es la actividad de anticipar respuestas de los estudiantes de Bachillerato que reflejen diferentes niveles de desarrollo conceptual de la comprensión del concepto de límite de una función, como una actividad relevante vinculada a la competencia docente. Los resultados muestran dos formas distintas de considerar la comprensión del concepto de límite por parte de los EPS que tienen implicación sobre cómo anticipan las respuestas de los estudiantes y sobre las características de los problemas que plantean para apoyar el aprendizaje de la concepción dinámica de límite de los estudiantes.

Una descomposición genética para el concepto de recta tangente

Presentamos una descomposición genética del concepto de recta tangente vista como una trayectoria hipotética de aprendizaje. Para generar esta descomposición genética se ha realizado un análisis histórico de la génesis del concepto, un análisis de libros de texto de Bachillerato, una síntesis de los resultados de las investigaciones sobre la comprensión de la recta tangente y hemos tenido en cuenta los resultados de un cuestionario respondido por alumnos de Bachillerato. La descomposición genética integra las perspectivas analítica local y geométrica como medio para favorecer la tematización del esquema de recta tangente.

Concepciones de profesores de nivel medio superior sobre el uso de la historia de la matemática

En esta comunicación se presentan resultados de una investigación cuyo objeto fue analizar concepciones de profesores de matemáticas de nivel medio superior sobre la inclusión de la historia de la matemática en su práctica docente. Se usó un método mixto para la recogida y análisis de datos. Para detectar concepciones de los profesores, se elaboraron un cuestionario y una entrevista. Los resultados de su aplicación indican que la mayoría de los profesores del estudio no están habituados a considerar la historia de la matemática en su enseñanza; además sus concepciones sobre incluir este recurso están condicionadas por su visión del sistema educativo.

First course in algebra : student's text : Parts I-II /

Includes indexes.

Education pamphlets

A collection of miscellaneous pamphlets.

Education pamphlets

A collection of miscellaneous pamphlets.

A sociocultural analysis of learning to teach

This paper addresses the question of how teachers learn from experience during their pre-service course and early years of teaching. It outlines a theoretical framework that may help us better understand how teachers' professional identities emerge in practice. The framework adapts Vygotsky's Zone of Proximal Development, and Valsiner's Zone of Free Movement and Zone of Promoted Action, to the field of teacher education. The framework is used to analyse the pre-service and initial professional experiences of a novice secondary mathematics teacher in integrating computer and graphics calculator technologies into his classroom practice. (Contains 1 figure.) [For complete proceedings, see ED496848.]

Building learning communities to support beginning teachers use of technology

This paper reports on the early stages of a three year study that is investigating the impact of a technology-enriched teacher education program on beginning teachers' integration of computers, graphics calculators, and the internet into secondary school mathematics classrooms. Whereas much of the existing research on the role of technology in mathematics learning has been concerned with effects on curriculum content or student learning, less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers' professional learning in the context of specific classroom and school environments. Our research applies sociocultural theories of learning to consider how beginning teachers are initiated into a collaborative professional community featuring both web-based and face to face interaction, and how participation in such a community shapes their pedagogical beliefs and practices. The aim of this paper is to analyse processes through which the emerging community was established and sustained during the first year of the study. We examine features of this community in terms of identity formation, shifts in values and beliefs, and interaction patterns revealed in bulletin board discussion between students and lecturers.

Percent in a Nutshell …

Ironically, the “learning of percent” is one of the most problematic aspects of school mathematics. In our view, these difficulties are not associated with the arithmetic aspects of the “percent problems”, but mostly with two methodological issues: firstly, providing students with a simple and accurate understanding of the rationale behind the use of percent, and secondly - overcoming the psychological complexities of the fluent and comprehensive understanding by the students of the sometimes specific wordings of “percent problems”. Before we talk about percent, it is necessary to acquaint students with a much more fundamental and important (regrettably, not covered by the school syllabus) classical concepts of quantitative and qualitative comparison of values, to give students the opportunity to learn the relevant standard terminology and become accustomed to conventional turns of speech. Further, it makes sense to briefly touch on the issue (important in its own right) of different representations of numbers. Percent is just one of the technical, but common forms of data representation: p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2 "Percent problems” are involved in just two cases: I. The ratio of a variation m to the standard M II. The relative deviation of a variation m from the standard M The hardest and most essential in each specific "percent problem” is not the routine arithmetic actions involved, but the ability to figure out, to clearly understand which of the variables involved in the problem instructions is the standard and which is the variation. And in the first place, this is what teachers need to patiently and persistently teach their students. As a matter of fact, most primary school pupils are not yet quite ready for the lexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of each problem ... Schoolchildren must firmly understand that a comparison of objects is only meaningful when we speak about properties which can be objectively expressed in terms of actual numerical characteristics. In our opinion, an adequate acquisition of the teaching unit on percent cannot be achieved in primary school due to objective psychological specificities related to this age and because of the level of general training of students. Yet, if we want to make this topic truly accessible and practically useful, it should be taught in high school. A final question to the reader (quickly, please): What is greater: % of e or e% of Pi

The relationship between selected standardized test scores and performance in advanced placement math and science exams: Analyzing the differential effectiveness of scores for course identification and placement

There is a national need to increase the STEM-related workforce. Among factors leading towards STEM careers include the number of advanced high school mathematics and science courses students complete. Florida's enrollment patterns in STEM-related Advanced Placement (AP) courses, however, reveal that only a small percentage of students enroll into these classes. Therefore, screening tools are needed to find more students for these courses, who are academically ready, yet have not been identified. The purpose of this study was to investigate the extent to which scores from a national standardized test, Preliminary Scholastic Assessment Test/ National Merit Qualifying Test (PSAT/NMSQT), in conjunction with and compared to a state-mandated standardized test, Florida Comprehensive Assessment Test (FCAT), are related to selected AP exam performance in Seminole County Public Schools. An ex post facto correlational study was conducted using 6,189 student records from the 2010 - 2012 academic years. Multiple regression analyses using simultaneous Full Model testing showed differential moderate to strong relationships between scores in eight of the nine AP courses (i.e., Biology, Environmental Science, Chemistry, Physics B, Physics C Electrical, Physics C Mechanical, Statistics, Calculus AB and BC) examined. For example, the significant unique contribution to overall variance in AP scores was a linear combination of PSAT Math (M), Critical Reading (CR) and FCAT Reading (R) for Biology and Environmental Science. Moderate relationships for Chemistry included a linear combination of PSAT M, W (Writing) and FCAT M; a combination of FCAT M and PSAT M was most significantly associated with Calculus AB performance. These findings have implications for both research and practice. FCAT scores, in conjunction with PSAT scores, can potentially be used for specific STEM-related AP courses, as part of a systematic approach towards AP course identification and placement. For courses with moderate to strong relationships, validation studies and development of expectancy tables, which estimate the probability of successful performance on these AP exams, are recommended. Also, findings established a need to examine other related research issues including, but not limited to, extensive longitudinal studies and analyses of other available or prospective standardized test scores.

Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

Matematik Öğretmeni Adaylarının Dörtgenleri Sınıflandırma Becerilerinin İncelenmesi

This study aimed to explore prospective teachers’ performance on recognizing quadrilaterals with their special cases and constructing a hierarchical classification of them. The participants consisted of 44 freshmen studying at a public university’s elementary school mathematics education department. Data was collected with a question form containing two questions at the first day of the geometry course taught in the second term of the first year. For quantifying the data of the first question, while students who identify the prototypes of quadrilaterals and their special cases were given 1 and 2 points for each correct answer respectively, -1 point was given for each incorrect answer. The similarity index was employed to quantify students’ concept maps. We investigated that students could detect the prototypes of the quadrilaterals but not their special cases. Additionally, the similarity index between majority of freshmen’ concept maps and the referent map was found as low or moderate.