Resisting the desire for the unambiguous: productive gaps in researcher, teacher and student interpretations of a number story task

This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of that recasting. This question is situated within a two-pronged task design challenge as to emerging gaps between the task designer’s intentions and teacher’s actions and secondly between the teachers’ intentions and students’ actions. Through analysing two teachers and their respective Grade R students’ interpretations of a worksheet task, provided to teachers in the project, we illuminate the way explicit constraints, in the form of task specifications, can be both enabling and constraining of learning. In so doing we recast this ‘double gap’ as enabling productive learning spaces for teacher educators, teachers and students

The Use of Polls to Enhance Formative Assessment Processes in Mathematics Classroom Discussions

This contribution addresses the theme of technology for formative assessment in the mathematics classroom and in particular the ways connected classroom technology may support formative assessment strategies in whole class activities. Design experiments have been developed through the use of a connected classroom technology by which students may share their productions, opinions, and reflections with their classmates and the teacher during or at the end of a mathematical activity. With this technology the teacher may create polls, submit them to the students, gather their answers and show the results in real time. The paper discusses how polls can be used during classroom activities to foster the activation of formative assessment strategies. As a result of the design-based research, a classification of polls according to their contents and aims is proposed. Different ways of structuring classroom discussions and patterns of formative assessment strategies, which are developed from the different types of polls, are discussed