Supporting Whole-Class Collaborative Inquiry in a Secondary Mathematics Classroom

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.

Family Myths, Beliefs, and Customs as a Research/Educational Tool to Explore Identity Formation

This paper outlines a qualitative research tool designed to explore personal identity formation as described by Erik Erikson and offers self-reflective and anonymous evaluative comments made by college students after completing this task. Subjects compiled a list of 200 myths, customs, fables, rituals, and beliefs from their family of origin and then reflected upon the relevance and meaning of such items. The research and instructional tool described in the paper should be of considerable interest to teachers who work to promote self-reflection amongst adolescents as well as case study researchers and therapists who wish to study identity formation and values.

Empowering Teachers as Leaders: A Hard Sell

Despite emphasis on preparing teachers as leaders, teacher educators realize that the transition of classroom practitioners into school leaders is fraught with many obstacles. This session addresses some of these obstacles, describes strategies and opportunities that we have used in our graduate master’s degree programs for teachers that support professionals as they make this change. The session will present evidence on the results of our efforts in terms of teachers’ performances within their programs and in the field after they graduate.

Learning and Assessing Competencies: New challenges for Mathematics in Engineering Degrees in Spain.

The introduction of new degrees adapted to the European Area of Higher Education (EAHE) has involved a radically different approach to the curriculum. The new programs are structured around competencies that should be acquired. Considering the competencies, teachers must define and develop learning objectives, design teaching methods and establish appropriate evaluation systems. While most Spanish universities have incorporated methodological innovations and evaluation systems different from traditional exams, there is enough confusion about how to teach and assess competencies and learning outcomes, as traditionally the teaching and assessment have focused on knowledge. In this paper we analyze the state-of-the-art in the mathematical courses of the new engineering degrees in some Spanish universities.

Mathematics Game e-Library for Elementary School, study case: Mexico

One of the most relevant subjects for the intellectual formation of elementary school students is Mathematics where its importance goes back to ancient civilizations and which its importance is underestimated nowadays. This phenomenon occurs in Mexico, where 63.1% of the total population of elementary school students between the third and sixth grade have insufficient/elemental level of mathematics knowledge. This has resulted in the need to use a new mechanism to complement student’s classroom learning. With the rapid growth of wireless and mobile technologies, the mobile learning has been gradually considered as a novel and effective form of learning due to it inherits all the advantages of e-learning as well as breaks the limitations of learning time and space occurring in the traditional classroom teaching. This project proposes the use of a Mathematics Game e-Library integrated by a set of games for mobile devices and a distribution/management tool. The games are developed for running on mobile devices and for cover the six competencies related with the mathematics learning approach established in Mexico. The distribution/management tool allows students to reach contents according to their needs; this is achieved through a core engine that infers, from an initial profile, the games that cover the user’s knowledge gaps.

Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

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.

Changes in how prospective teachers anticipate secondary students’ answers

This study focuses on how prospective teachers learn about students’ mathematical thinking when (i) anticipating secondary students’ answers reflecting different characteristics of understanding and (ii) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school teachers enrolled in an initial training programme. The results indicate three changes in how the prospective teachers anticipate secondary students’ answers in relation to the role given to a perceptual or relational perspective of the classification of quadrilaterals. These changes are described considering how prospective teachers grasp the students’ understanding of the inclusive relation among quadrilaterals as a conceptual advance. We argue that prospective teachers’ learning was promoted after participating in a structured environment where they had the opportunity to discuss how to recognize the features of student’s understanding.

Initiatives d’activisme en formation initiale de professeurs: préparer à l’action et à la transformation.

L’action collective raisonnée, connue sous le nom d’activisme, orientée vers la résolution de problèmes de la société, offre des possibilités d'apprentissage tout au long de la vie et permet aux étudiants de développer des connaissances du domaine de la science et de la technologie. Dans une société où les découvertes scientifiques et les progrès technologiques sont constants, les potentialités de cette approche sont également reconnues dans la formation de citoyens responsables, capables d'agir et de résoudre des problèmes, tout en essayant d'influencer d'autres citoyens à prendre des décisions sur les problèmes complexes tels que ceux que présentent les questions socialement vives. Considérant que la formation de jeunes et d’adultes plus responsables et scientifiquement informés est fondamentale, cette recherche-action visait: a) à munir les futurs enseignants de compétences dans la conception, la mise en oeuvre et l'évaluation des activités orientées vers l'action sociopolitique sur les questions socialement vives; b) promouvoir chez les participants les valeurs de citoyenneté et de sensibilisation à l'environnement; c) identifier les difficultés et le potentiel de ces initiatives; d) comprendre l'impact de ce type d'expérience éducative chez les futurs enseignants. Les participants à l'étude étaient des étudiants préparant une licence en éducation élémentaire (futurs professeurs des écoles primaires et maternelles) dans le contexte de la discipline d’Éducation à l’Environnement. L'analyse des narratives produites par les futurs enseignants a permis de constater que tous avaient développé des compétences au niveau de la planification et de l'intervention dans la société, en recourant à différents types d'initiatives. Cette expérience de formation a ainsi permis, aux participants le développement de capacités à l'action et à la transformation sociale et environnementale. Il a également été possible de sensibiliser le public-cible des actions réalisées par les futurs enseignants à agir de façon plus responsable sur l'environnement.

High school mathematics /

Each unit comprises Student's ed. and Teachers' ed., interleaved.

The Mathematics teacher

Mode of access: Internet.

Paper folding for the mathematics class /

Includes bibliographical references (p. iv).

Prairie State Achievement Examination, PSAE : teachers' handbook, 2000 - 2001.

An introductory handbook for teachers that discusses first-time administration of the PSAE, including how the test is constructed and contains information about test-preparation materials, timelines, test-day schedules, and upcoming informational workshops.

On associations of teachers: An address delivered at a meeting held in Dorchester, on Wednesday, 8th of September, for the purpose of forming an Association of Teachers, for Norfolk County. ...

Pages [15]-16 contain the "Constitution of the Norfolk Association of Teachers."

Designing the mathematics classroom.

Mode of access: Internet.