Extending Learners’ Mathematical Thinking: Venues and Ventures

Dear Colleagues,

In recent years, a variety of metaphors have been introduced to characterize mathematics teaching in classrooms that focus on inquiry and development of conceptual understanding amongst learners. Common to all these various characterizations are three specific actions teachers need to do so to optimize both student autonomy, and their mathematical advancement, including eliciting, supporting and extending. Eliciting actions invite students to share their ideas and encourage elaborations on, and comparison of solution methods. Supporting actions attempt to coordinate and manage students’ work. Here, the teacher may suggest strategies, offer interpretations, record and/or re-voice student ideas. Extending actions have been less precisely described and considered to be interventions that move students beyond their initial solutions.

There is evidence that teachers frequently exhibit eliciting actions as they ask students to share ideas and then using them to encourage group discourse. The most prevalent supporting actions reported in the literature include reminding students of task goals, what they already know, re-voicing learners’ ideas and introducing alternative interpretations. Accounts of how teachers extend learners’ mathematical cognition, however, are rarely reported. Indeed, although common practices associated with extending have been conceptualized to include encouraging reasoning, encouraging reflection, and creating a space for development of new mathematical insights—research reports rarely cite evidence of extending actions beyond encouraging reflection or requesting explanations. It remains unclear what form or shape extending actions might take or the potential outcome of these actions relative to learners’ mathematical development. This Special Issue is devoted to disseminating current empirical research as well as theoretical views on the ways in which mathematical thinking of learners are extended through specific teacher questions, tasks, curricular materials and technological tools. Of particular interest is defining specific features of these interventions that lead to the development of deeper and more sophisticated mathematical knowledge. In a general sense, the Special Issue aims to offer an in-depth and current perspective on connections between teaching and learning. Some questions of interest that can inform the preparation of articles include, but are not limited to:

• What theoretical models are used or being developed for capturing growth in mathematical thinking?
• What is the impact of the concept/content under study on the type of extending actions that teachers need to do?
• What types of mathematics-focused professional development models might be put in place to advance teachers’ capacity for extending learners’ mathematical thinking?
• What methodologies are used in capturing moves towards extending learners’ mathematical thinking?
• What theoretical lenses are useful for assessing the growth of learners’ mathematical thinking?

Dear Colleagues,

The Special Issue aims to offer an international perspective on current research on teaching and learning of mathematical thinking in educational settings. The venue chosen focuses on ways that learners’ mathematics is extended through deliberate and strategic interventions along with detailed discussion of short- and long-term outcomes of these interventions.

Prof. Dr. Azita Manouchehri
Guest Editor

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• Mathematical Reasoning
• Extending Thinking
• Teaching Mathematics
• Theory and Practice