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This study focuses on the challenge of promoting significant mathematical discourse among preservice teachers. The study was conducted as part of an academic course that accompanies their practical training. Twenty-three math preservice teachers' learning process was examined as a result of using an analytic model designed for discourse protocols' analysis. Findings revealed that an active and dynamic process occurred, modifying teacher practice and developing critical reflective thinking among preservice teachers. The change occurred in two "ripples of influence": (1) improving discourse to one promoting learning by demonstrating hypothetical scenarios and (2) perception of the role of teachers and class management.

This study focuses on the interactions between students, their peers, their teacher, and digital game-based multiple supports provided by a rich learning environment designed in order to promote meaningful mathematics among low-achieving students. Attempting to identify which aspects of the setting facilitated meaningful learning and which were ineffectual or even detrimental to it, the authors traced the knowledge building processes of 11 fifth grade LAS over eight weeks in which they studied subtraction of decimal numbers. Pre- and post-program data were also collected through diagnostic interviews. Microanalysis of lesson transcripts, videotaped computer activities, and individual worksheets revealed differences in tool-use and in interactions among supports, which led to different learning results. The results suggest that digital game-based learning environments may be a key to promote meaningful learning in terms of mathematical strategy building. At the same time, it highlights the complexity of each tool in the environment as well as interactions among tools.

This study explores milestones in the process of becoming a teacher-leader, in a way by which their teachers’ professional identity expands into an all-encompassing identity. This implies into a ‘hyphenated identity’ where each of the ‘teacher’ and ‘leader’ labels has a unique meaning and power. Data have been collected for 2 years from 46 leading teachers in elementary and high schools, using a phenomenological approach. The findings present a process of professional identity expansion, characterised by developmental movement, a shifting movement between spaces, as well as between one identity and another. Therefore, a model with the following six key milestones was designed: a) the transition from ‘identify’ to ‘identification’; b) the process of shaping and expanding identity consciousness; c) expansion of the sense of self-efficacy into practice; d) the ability to ‘move aside’; e) enhancement of pedagogical knowledge and (f) establishment of a spiral return to teachers; definition as leaders. [ABSTRACT FROM AUTHOR]

The study set out to discover what characterizes the meaningful learning of mathematics among low-achieving students (LAS) and to highlight the challenges their characteristics pose for scaffolding, in particular for its adaptive core: contingent teaching. The setting was an extracurricular program for teaching meaningful mathematics to LAS through a combination of learning in context, interactive computerized activities, and contingent teaching. Using microgenetic analysis of lesson transcripts, videotaped computer activities and worksheets, and data from teachers' and students' pre- and post-program interviews, we traced the learning processes of 11 fifth grade LAS over 2 months in which they studied the subtraction of decimal numbers. Our findings reveal that nine of the LAS showed evidence of meaningful strategy construction and use. However, their learning processes were inconsistent and difficult to predict, and were characterized by progressions and regressions, as demonstrated in two case studies. Theoretical and pedagogical implications related to scaffolding are discussed.

In this paper, we present a computerized tool developed specifically for a study that examined the development of creative thinking among third and fourth graders, following multidisciplinary instruction that combined mathematics and music. The computerized tool included closed and open questions. The closed questions allowed the students to perform separated mathematical and musical tasks by typing a specific melody, rhythm, pattern, or mathematical form; The open questions required the students to respond freely and creatively using the computer keyboard or a virtual piano keyboard. The programming was written in Max/MSP environment using BACH package that enables generating, modifying, and playing musical scores either with a mouse or keyboard. The software was built in a modular way by using math and music units, which makes it possible in the future to expand the number of tasks as needed. The article reviews the necessity of developing a technological tool for the research, the deliberations that accompanied the development of the technological tool, the technology's contribution to monitoring creative thinking process and drawing conclusions for further research. [ABSTRACT FROM AUTHOR]

The question of how to enhance the learning of low-achieving students in mathematics presents an important challenge to researchers and teachers alike. We investigated whether and how the use of a contextual story presented in a video clip facilitated low-achieving students' understanding of the meaning of fraction expansion. To this end, we (a) videotaped one group of three such students during a guided interaction session, (b) interviewed students and teachers about their first impressions of the use of the video clip, and (c) conducted pre-post-tests to examine the discourse students choose to employ to discuss expansion. Despite the interviewees' impression that the use of the video clips makes it easier to remember the story, the analysis of the guided interaction session revealed that the students did not use it spontaneously when asked to explain why a fraction and its expanded form are equivalent. Rather, their explanations revolved around the expansion procedure. It was the tutor's careful interventions in the discourse, building on the students' recall of the story, which led to a synergy effect that facilitated the students' understanding and articulation of the meaning of fraction expansion. This combination proved to be a potentially successful strategy in effectively promoting low-achieving students' understanding in mathematics, as demonstrated in the students' discourse and post-test performance. At the same time, our results highlight the delicate scaffolding required to achieve a beneficial effect.