Pre-University Students\u27 Perceptual Flexibility with Mathematical Elements

Do students see things the same as what mathematics teachers have anticipated? In a light-hearted and inquisitive mode, two fundamental mathematical tasks were administered to 147 pre-university students who newly joined a private college for enrolment into various programs. One task simply required the participants to state the variables in a linear equation and the other attempted to elicit what the participants would naturally perceive from a diagram featuring a straight line crossing the coordinate axes. This study aimed to examine the participants’ perceptual flexibility with mathematical elements without explicit hints. The emergent textual responses were qualitatively classified and the frequencies of the various types of response evaluated. While the two tasks appear to be drearily ordinary to arouse excitement, the data startlingly revealed a wide range of valid and invalid responses from the participants, and some mathematical elements appeared to be more visually implicit or explicit than others to the participants. Specifically, few participants perceived composite functions embedded in the linear equation as variables and even fewer participants noticed a right-angled triangle emerging from the straight line crossing the coordinate axes. The results are discussed from the perceptual perspective of Gestalt psychology, which suggests the participants’ lack of flexibility in mentally reconfiguring perceptual elements. The potential implications for mathematics learning associated with perceptual flexibility are discussed and the instructional efforts that may enhance students’ perceptual flexibility recommended. In particular, we argue that a problem-solving process may require flexible perception of mathematical elements in order to gain access to learned concepts and hence particular solution choices

Theorising the take-up of ICT : can Valsiner's three zones framework make a contribution?

This paper explores the contribution of theory to understanding the take-up of ICT and, in particular, it describes how Valsiner’s three zones framework came to be used in a study of lecturers in Saudi higher education institutions. The paper describes the value of theory and, in the process, illustrates some of the approaches taken in the literature on teachers’ use of ICT. The challenges faced in theorising are also covered. The paper then gives the background to a study of ICT use among university lecturers before moving to a discussion of methodology and presentation of key findings. Next, attention shifts to explaining key aspects of Valsiner’s zones framework and showing how this framework was applied to explain the modest but differentiated use of ICT across eight institutions. Finally, the paper discusses the strengths and limitations of the zones framework and highlights some of the wider challenges which theorisation pose

Innovation dialogue - Being strategic in the face of complexity - Conference report

The Innovation Dialogue on Being Strategic in the Face of Complexity was held in Wageningen on 31 November and 1 December 2009. The event is part of a growing dialogue in the international development sector about the complexities of social, economic and political change. It builds on two previous events hosted the Innovation Dialogue on Navigating Complexity (May 2009) and the Seminar on Institutions, Theories of Change and Capacity Development (December 2008). Over 120 people attended the event coming from a range of Dutch and international development organizations. The event was aimed at bridging practitioner, policy and academic interests. It brought together people working on sustainable business strategies, social entrepreneurship and international development. Leading thinkers and practitioners offered their insights on what it means to "be strategic in complex times". The Dialogue was organized and hosted by the Wageningen UR Centre for Development Innovation working with the Chair Groups of Communication & Innovation Studies, Disaster Studies, Education & Competence Studies and Public Administration & Policy as co; organisers. The theme of the Dialogue aligns closely with Wageningen UR’s interest in linking technological and institutional innovation in ways that enable ‘science for impact’

Understanding teaching practice in support of Non-English-Speaking-Background (NESB) students’ mathematics learning

Research is needed that gives special attention to the experiences of mathematics teachers of Non-English-Speaking-Background (NESB) students. This need prompted me to investigate four of my tertiary mathematics classes that included a number of NESB students, through practitioner research. The main data collection methods for the study were audio-taping classroom discussions, journaling of my experiences, and student group interviews. The data were analysed around three main domains: classroom social norms, sociomathematical norms and classroom mathematical practices. The first key finding was that NESB students can shift from being less-active to more active participants in mathematical activity when the teacher works with them to jointly constitute classroom social norms that attach importance to, make it safe to and encourage student participation. In this study, these were volunteering to share ideas, explaining and justifying contributions, and asking questions. Establishing these social norms occurs gradually, and NESB students can adopt them over time. The second key finding indicates that changes can occur in strategies NESB students use to solve mathematics problems that are embedded in everyday contexts, if they are involved in the joint construction of sociomathematical norms that value the negotiation of mathematical meaning. Over time, and with support, students can develop the ability to support their thinking, and come to understand what counts as mathematical problem-analysis, explaining and justifying mathematically, and communicating mathematically. The authority to evaluate the authenticity of mathematical contributions can be distributed among NESB students and between students and the teacher, if students are positioned as creators and evaluators of mathematical knowledge. The third key finding is that the specific ways of acting and reasoning that are appropriate for a particular mathematics topic evolve when the teacher and NESB students discuss problems and solutions related to that specific mathematical idea. Instead of relying on memorized procedures for solving problems, students progressively rely on their conceptual understanding of specific mathematical ideas and practices. The findings challenge the general view that NESB students will necessarily be passive and prefer to learn by memorising information. They indicate that NESB students can develop as active learners, embracing expectations and obligations that they will contribute ideas and negotiate meaning, rather than follow what the teacher says. Over time, a number of my NESB students developed autonomy in mathematical problem solving and their ability to solve mathematics problems and contribute to class discussion improved. In light of the findings, I propose that NESB students’ mathematics learning may be enhanced by a focus on initiating and guiding joint constitution of classroom social norms that value and encourage student participation in the social construction of knowledge and sociomathematical norms that promote conceptual understanding through negotiation of mathematical meaning. I further propose that NESB students’ mathematics learning may be supported by guiding collective construction of classroom mathematical practices concerned with the specific ways of reasoning and acting needed in particular mathematics topics. The findings of this study have relevance and offer fresh insights for mathematics teachers, researchers and tertiary institutions into how NESB students can be supported to learn mathematics. Further research in this area could examine practices of other mathematics teachers involved with NESB students