Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, “How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?” The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers’ progressive development of classroom norms of mathematical inquiry and how they facilitate learning

Inferring to a model: using inquiry-based argumentation to challenge young children's expectations of equally likely outcomes

Children’s informal reasoning about uncertainty can be considered a product of their beliefs, language, and experiences, much of which is formed outside of formal schooling. As a result, students can adopt informal intuitions that are incompatible with formal reasoning. Although the creation of cognitive conflict has been considered as one means of challenging students’ understandings, prior research in probability suggests that students may simultaneously hold multiple, incompatible understandings without conflict arising. Design-based methodology was adopted to investigate young (7–8 years old) students’ inferential reasoning under uncertainty, using an inquiry-based unit developed around addition bingo. This paper selectively reports on students’ inferences that initially suggested they were tacitly working from a uniform distribution (equiprobability bias), but shifted as students collected empirical data (from a discrete symmetric triangular distribution). Their inferences were challenged using an argumentation framework, with particular emphasis on the need for defensible evidence. Initial findings suggest potential for argumentation and inferential approaches that make students’ conceptions explicit through ‘visibilizing’ their knowledge

Exploring the classroom practices that may enable a compassionate approach to financial literacy education

From an early age, children are faced with financial dilemmas and are expected to make effective financial decisions about money. In this paper, we explore the classroom practices that may enable a compassionate approach to financial literacy education. We observed an inquiry-based mathematics lesson in a Year 4 primary school classroom. The financial maths task asked students to decide on the best fundraising option for the school. We used the theory of practice architectures to analyse the interactions in the classroom in order to understand what may have enabled and constrained classroom practices. We found that classroom practices such as engaging with peers through positive and collaborative learning opportunities, making ethical, social and mathematical connections of the task, and considering the impact of financial decisions on others may enable a compassionate approach to financial literacy education

Using expectancy-value theory to explore aspects of motivation in inquiry based learning in primary mathematics

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and Wigfield 2002) provides a framework through which children’s beliefs about their mathematical competency and their expectation of success are able to be examined and interpreted, alongside students’ perceptions of task value. In this paper, Eccles and Wigfield’s expectancy-value model has been adopted as a lens to examine a complete unit of mathematical inquiry as undertaken with a class of 9–10-year-old students. Data were sourced from a unit (∼10 lessons) based on geometry and geometrical reasoning. The units were videotaped in full, transcribed, and along with field notes and student work samples, subjected to theoretical coding using the dimensions of Eccles and Wigfield’s model. The findings provide insight into aspects of IBL that may impact student motivation and engagement. The study is limited to a single unit; however, the results provide a depth of insight into IBL in practice while identifying features of IBL that may be instrumental in bringing about increased motivation and engagement of students in mathematics. Identifying potentially motivating aspects of IBL enable these to be integrated and more closely studied in IBL practises

Young children's explorations of average through informal inferential reasoning

This study situates children's early notions of average within an inquiry classroom to investigate the rich inferential reasoning that young children drew on to make sense of the questions: Is there a typical height for a student in year 3? If so, what is it? Based on their deliberations over several lessons, students' ideas about average and typicality evolved as meaning reasonable, contrary to atypical, most common (value or interval), middle, normative, and representative of the population. The case study reported here documents a new direction for the development of children's conceptions of average in a classroom designed to elicit their informal inferential reasoning about data

The pedagogy of mathematics inquiry

Most problems given to children in school mathematics are clearly stated, take only a few minutes to answer, include little or no use of context and have a single correct answer. In mathematical inquiry, often problems are riddled with ambiguity, can require days or even weeks to address, necessitate an indepth understanding of the surrounding contextual issues and have no single correct answer. Because of this, the pedagogical practices that underpin an inquiry-based approach in mathematics are quite different than those in more conventional classrooms. This chapter explains the key elements that distinguish mathematical inquiry from more conventional mathematical tasks and what this means for teachers. Four phases of inquiry (Discover, Devise, Devdop, Defend) are used to outline the complexity and diversity of practices that teachers need to embed into their pedagogical practices. To illustrate inquiry-based teaching in practice, a case study is used from a teacher's classroom of Year 617 students (ages 10-13 years). The case study comes from a longitudinal study aimed at understanding the evolving pedagogics and experiences of primary teachers as they adapted their teaching practices to incorporate mathematical inquiry. In the case study, two consecutive units with similar mathematical structures and learning goals are provided along with interviews from the teacher following each unit to highlight many of the unique challenges and opportunities that emerged for her pedagogically in teaching mathematical inquiry. Finally, the chapter uses Hare! and Koichu's (2010) principles of operationalising learning to summarise three overarching elements and their implications for adapting to a pedagogy of mathematical inquiry

Teaching primary teachers to teach statistical inquiry: The uniqueness of initial experiences

Experience with statistical inquiry has been advocated in statistics education as vital for learners’ understandings of statistical processes. Research has suggested, however, that practices at the school level have focused almost solely on graphs and procedures. While important, these skills do not develop learners’ abilities to cope with the decisions that arise in the face of uncertainties and ambiguities that accompany statistical investigations. A longitudinal study in Australia researched experienced primary teachers’ evolving experiences in teaching statistical inquiry. This paper will report on the uniqueness of teachers’ early experiences in teaching statistical inquiry, an issue that emerged in the first three years of the study. Critical skills that teachers need to develop to teach statistical investigations that are often neglected in teacher professional development are discussed, including implications for research and teacher education