Evidence of Young Students' Critical Mathematical Thinking

In this study, the authors investigate the ways in which young students demonstrate their critical mathematical thinking (CMT). Students aged 5-6 who are beginning their first formal year of education participated in the study. Data is presented from individual clinical interviews undertaken with 16 students. These interviews were analysed using the Critical Mathematical Thinking for Young Students (CMTFYS) framework to identify common patterns in the responses. The findings suggest that these young students beginning school, most often rely on providing explanations and more specifically, justifying, to demonstrate their CMT

Conceptualising critical mathematical thinking in young students

International curriculum and policy directions have called to embed critical thinking across discipline areas including mathematics; however, conceptually, this is under-theorised and under-researched in the field of mathematics education. This paper presents the conceptualisation of critical mathematical thinking (CMT) and the application of a literature informed conceptual framework; in particular, it examines what CMT capabilities young students exhibit as they enter formal schooling. We present the findings from one-on-one task-based interviews, undertaken with 16 young students (aged 5–6) as a means to investigate their CMT capabilities and refine the CMT framework. The interview data were analysed using the new critical mathematical thinking conceptual framework. The data confirms the definition and understanding of CMT in young students, indicating a need for curriculum refinement, improved teaching practices, and further research in this area

Critical mathematical thinking in young students

The aims of the study were to investigate critical mathematical thinking in young students, and teaching actions/questions that help these young students exhibit their critical mathematical thinking. A key finding was the conceptualisation of a Critical Mathematical Thinking Framework for Young Students. This framework (a) articulates the key characteristics young students exhibit as they engage in critical mathematical thinking, and (b) can be used by teachers to help them identify critical mathematical thinking within the classroom context. Additionally, specific teacher questions that support young students to exhibit critical mathematical thinking were delineated. The study determined that teachers play a pivotal role in supporting young students to exhibit their critical mathematical thinking

Defining the characteristics of critical mathematical thinking

In this paper, we report on the interim findings of a study that seeks to identify the characteristics of children’s Critical Mathematical Thinking CMT. Characteristics of CMT were initially generated from a synthesis of relevant research literature and then validated using a case study methodology via trials in early childhood classrooms. This paper provides a framework for CMT distilled from the literature and an illustrative case study of one student to provide tentative evidence that young children’s use of CMT capabilities can be identified. The long term aim of this line of research is to explore the potential to promote CMT capabilities in a targeted manner

Early childhood mathematics : Recognise, celebrate and build—Book 2

This book, part of the Research in Practice Series, invites educators to explore mathematical processes and pedagogies. Here we highlight the value of assessment in planning for children’s mathematical learning and the critical role of the teacher as an active agent in the planning cycle for mathematics. The book will support educators to: identify practical strategies to enable mathematical processes in young children’s learning integrate technology into their everyday assessment practices and children’s play-based and intentional experiences document and assess children’s mathematics learning integrate mathematics learning into their intentional teaching and children’s play-based and inquiry-based learning

Practicum Experiences in Special Schools : A Case Study

Initial teacher education programs in New South Wales have included a dedicated special education unit to build the capacity of pre-service teachers to meet the diverse needs of complex learners. Pre-service teachers who have completed these types of units develop a good theoretical understanding of inclusive education, and their professional development can be enhanced through professional experience and practicums in inclusive and special-education settings (e.g., Lancaster and Bain in Int J Disability, Dev Educ 54:245–256, 2007); Tindall et al. in Eur Phys Educ Rev 21:206–221, 2015; Walton and Rusznyak in Teach Teach Educ 36:112–120, 2013). This chapter outlines a pilot project to place pre-service teachers in a School for Specific Purposes. The case study of one pre-service teacher during her 20-day placement and the development of insights about inclusive and special education are discussed

The Hub System : An Effective Work-Integrated Learning Partnership

This chapter explores a partnership between a university and a community of schools to develop profession-ready teachers through work-integrated learning (WIL). Viewed through the lens of the leaders of the partnership, the authors investigated factors to which the success of this program can be attributed. A systems-thinking approach (Senge, The fifth discipline: The art and practice of the learning organization. Doubleday, New York, 2006) was used to analyse the interview data. Evidence emerged that suggested that the leaders of this partnership contributed to its success by developing strong relationships in which multi-dimensional views were valued. The chapter raises practical implications for the sustainability and replication of this partnership model