Inquiry pedagogy to promote emerging proportional reasoning in primary students

Proportional reasoning as the capacity to compare situations in relative (multiplicative) rather than absolute (additive) terms is an important outcome of primary school mathematics. Research suggests that students tend to see comparative situations in additive rather than multiplicative terms and this thinking can influence their capacity for proportional reasoning in later years. In this paper, excerpts from a classroom case study of a fourth-grade classroom (students aged 9) are presented as they address an inquiry problem that required proportional reasoning. As the inquiry unfolded, students' additive strategies were progressively seen to shift to proportional thinking to enable them to answer the question that guided their inquiry. In wrestling with the challenges they encountered, their emerging proportional reasoning was supported by the inquiry model used to provide a structure, a classroom culture of inquiry and argumentation, and the proportionality embedded in the problem context

A Five-Dimensional Model of Creativity and its Assessment in Schools.

Creativity is increasingly valued as an important outcome of schooling,\ud frequently as part of so-called “21st century skills.” This article offers a\ud model of creativity based on five Creative Habits of Mind (CHoM) and\ud trialed with teachers in England by the Centre for Real-World Learning\ud (CRL) at the University of Winchester. It explores the defining and tracking\ud of creativity’s development in school students from a perspective of formative\ud assessment. Two benefits are identified: (a) When teachers understand\ud creativity they are, consequently, more effective in cultivating it in\ud learners; (b) When students have a better understanding of what creativity\ud is, they are better able to develop and to track the development of their\ud own CHoM. Consequently, the Organisation for Economic Co-operation and\ud Development has initiated a multicountry study stimulated by CRL’s\ud approach. In Australia work to apply CRL’s thinking on the educational\ud assessment of creative and critical thinking is underway

Learning from learning logs: A case study of metacognition in the primary school classroom

Structured thinking activities (STAs) are pedagogical tools used to support metacognition in classrooms. Despite their popularity, little is known about how pupils use STAs as platforms to think about and manage their own thinking (i.e. as metacognitive tools). This case study investigated pupils’ use of STAs in relation to metacognition throughout a school year. We focus on two 8‐year‐old pupils, Amy and Laura, as they completed two specific STAs through weekly class meets and termly achievement logs. Data were triangulated through participant observation, qualitative interviews and analysis of written texts. We found clear differences between Laura's and Amy's written STAs, however observation and interviews revealed that engagement with STAs was similar beyond that suggested by the written evidence alone. Whereas Amy used easily spelt ‘stock’ responses, Laura used ‘bare minimum’ responses to meet teacher expectations. As such, neither Amy nor Laura used STAs as metacognitive tools, however in negotiating STAs, both exhibited strategic regulatory skills indicative of metacognition. Whilst our findings highlight that pupils may still be developing explicit metacognitive knowledge necessary to take full advantage of STAs, we highlight the clear value of persistent approaches to using STAs as tools to support developing metacognition, particularly in association with teacher–pupil interactions

Uncovering students’ thinking about thinking using concept maps

Abstract A method for uncovering students' thinking about thinking, specifically their meta-strategic knowledge, is explored within the context of an ongoing, multi-year intervention designed to promote the development of students' thinking dispositions. The development of a concept-map instrument that classroom teachers can use and an analytic framework for interpreting students' responses is presented. In a preliminary study, the concept map instrument is piloted to evaluate changes in students' conceptions of thinking after a year's participation in classrooms where their teachers actively sought to make thinking more visible by noticing and naming the thinking observed as well as introducing and using thinking routines (Ritchhart and Perkins. Educational Leadership, 65(5), 57-61 2008). Concept maps from 239 students from grades 3 through 11 were analyzed. Results suggest that students' conceptions of thinking do improve with age but also can be substantially developed through a classroom culture where thinking is modeled and rich opportunities for thinking are present. The concept map instrument itself proved to be a robust instrument for uncovering students' thinking about thinking. Keywords Metacognitive assessment . Program evaluation . Concept maps . Metacognitive development . Thinking dispositions . Meta-strategic knowledge In the Cultures of Thinking Project, we seek to develop students' dispositions toward thinking by working with teachers to create classrooms where thinking is valued, visible, and actively promoted as part of the regular, day-to-day experience of all students. Because we believe that thinking dispositions are not so much learned as they are enculturated over time, our project focuses on helping teachers to understand the culture of their classrooms Metacognitio