Fang, Yanping

Situated learning perspective and the principal of authenticity has guided design of the video cases which were derived from authentic problems of a classroom teacher and his unit of lessons (see more detail in the abstract of the second paper). Informed by literature on mathematics problem solving (such as Stacey & MacGregor, 1999) and the model method (such as Ng & Lee, 2009), three video cases were developed to highlight the following pedagogical themes: 1) understanding the case teacher's rationale and approaches to bridging; 2) understanding the cognitive challenges in bridging; and 3) understanding students' feedback and initial Algebra learning outcome. Interviews with the case teacher provided a first-person narration of his rationale for planning, teaching and assessing student learning. To support teachers’ viewing and reflection, scaffolds (prompts) were designed in the form of viewing questions to stimulate critical analysis of a case lesson on the content, instructional goals and facilitation of student understanding. In the mean time, we anchored teacher learning in the Macrocontexts of video-based problem solving for repeated viewing and responses to questions in the personal blogs called, My Workplace, which is merged together with an online Discussion Forum to generate multiple perspectives (Cognition & Technology Group at Vanderbilt, 1993). Our Microcontext includes identifying ‘critical incidents’ according to what they think as important, difficult, and hinge points in a case lesson (Paine, Fang & Wilson, 2003) and discussion supported by e-facilitation in the Forum platform (Wang, 2008). Building of the Online PLC was piloted in the case teacher’s school for almost a year (Feb – Nov 2010), which started from a group of mathematics teacher leaders and later extended to 70 English-medium teachers of the school (see more detail in the abstract of the third paper). The teachers’ feedback in piloting stage has informed several rounds of iterative design and continuous improvements of the design and use (Stephens & Hartman, 2004). Research is going on to draw out implications for scaling up the use in diverse school contexts and learning platforms (such as lesson study)

This report highlights the major findings of a two-year CRPP-funded intervention project in which researchers worked closely with a primary school to introduce Lesson Study as a tool for teacher learning and community building. The findings are presented through a survey study of teachers' perception of Lesson Study; two case studies of the knowledge construction and community building processes in two sampled Lesson Study teams, one in English Language and one in Mathematics and a methodological exploration that attempted to represent the instructional improvement in four mathematics research lessons from both quantitative and qualitative perspectives. A video case intended to be used as a tool to support teacher development was developed to document the learning of a mathematics topic through the experience of a Lesson Study team. Its components and development process are also illustrated.

Video cases have been shown as effective tools to support teacher learning and teacher development. This study aims to design web-based video cases to support teachers in mathematical problem solving. Two video cases were built by drawing on data from a three-year funded project in Singapore. The first case is built on two Grade 5 teachers’ different pedagogy in conducting problem solving activities while the second case draws on different challenges that two pairs of Grade 5 students experienced in the process of solving problems. The framing includes case commentary, guiding questions, and discussion forum to help users reflect on their practices and initiate peer-sharing and -learning among users. The long-term goal of the design is to build a virtual community of practice.

A project on lesson study carried out in 2006 and 2007 aimed to find out how it can be used to bring about enhanced teacher learning and instructional improvements. This two-year intensive collaboration between researchers and a local primary school involved planning, teaching and observing research lessons together, as well as studying the processes of school-based curriculum development and teacher learning. The challenges of implementing lesson study in the Singapore context and its evolving local adaptations were carefully documented and analysed. We found that with strong school support, lesson study could bring about continual instructional improvement and a sense of community among the teachers, even though its time-consuming nature may pose numerous challenges for the teachers and schools.

Students’ limited view of mathematics and their strong orientation on numbers have been major hindrances in developing students’ capacity in problem solving. Our study aims to understand students’ challenges in reasoning quantitatively and gain insights on how they overcome these challenges. To this end, seven pairs of Grade 5 students and eight pairs Grade 7 were observed and videotaped when they solved one routine task and one nonroutine task. Their processes in solving these two tasks were analyzed using the method of conceptual analysis (Glasersfeld, 1995). Findings suggest that there were two major areas of difficulties that they experienced in reasoning quantitatively. Some of the major challenges behind those difficulties were the lack of quantitative understanding in whole numbers and fractions, the stronger focus on the magnitudes of quantities than the quantities themselves, and the stronger reliance on visually-perceived relationships in the model representation of situation than the quantitative relationships. A case of a Grade 7 pair is presented to discuss a context of pair collaboration that fosters the overcoming challenges in reasoning quantitatively that suggests a practical implication of using collaborative learning to support students’ development of quantitative reasoning capacity.