Exploring Young Students' Functional Thinking

The Early Years Generalising Project (EYGP) involves Australian Years 1-4 (age 5-9) students and investigates how they grasp and express generalisations. This paper focuses on data collected from six Year 1 students in an exploratory study within a clinical interview setting that required students to identify function rules. Preliminary findings suggest that the use of gestures (both by students and interviewers), self-talk (by students), and concrete acting out, assisted students to reach generalisations and to begin to express these generalities. It also appears that as students become aware of the structure, their use of gestures and self- talk tended to decrease

Young Australian Indigenous students' growing pattern generalisations :The role of gesture when generalising

This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns. This paper presents a hypothesised cultural learning semiotic model that was a result of the interactions that occurred between the non-Indigenous researcher, the Indigenous students and the Indigenous Education Officers

Young Indigenous students' engagement with growing pattern tasks: A semiotic perspective

The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns

Serving Two Masters : A Study of Quantitative Literacy at Small Colleges and Universities

The past twenty years have seen a growing interest in promoting quantitative literacy (QL) courses at the college level. At small institutions, financial realities impose limitations on faculty size and therefore the variety of courses that may be offered. This study examined course offerings below calculus at four hundred twenty-eight small colleges to gain a thorough understanding of the approaches to developing QL among the general population of undergraduate students. Using a three-phase model of examining progressively narrower subsets of QL programs at small institutions, document-based data from college catalogs and communication with mathematics program chairs were studied to summarize the most common approaches to QL, and to provide narrative descriptions of courses and programs most consistent with the recommendations of the Mathematical Association of America. The analysis of the data includes information on actual curricula and enrollments, and uses qualitative techniques to provide descriptions of successful courses and programs. Through this analysis, variables important in developing effective QL courses and programs at the undergraduate level were identified. The support of both the mathematics department and an institution’s administration were determined to be necessary factors in successful QL programs. Other factors contributing to program or course success were the individual efforts of faculty members in teaching QL courses, and the development of print-based materials conducive to effective QL instruction. Finally, the study provides recommendations for developing resources to support instruction and suggests future research to promote the development of the growing body of knowledge surrounding efforts to teach quantitative reasoning within the general education curriculum

Enriching the professional learning of early years teachers in disadvantaged contexts: The impact of quality resources and quality professional learning

Studies indicate that very few teachers entering disadvantaged contexts feel prepared academically or professionally to teach effectively. This study focuses on the impact of a model for professional learning, the RoleM Professional Learning model (RPL), situated in a disadvantaged context over a three-year period. The participating teachers (n = 12) in this study taught in the first three years of school (Foundation to Year 2). To ascertain the effectiveness of RPL, teachers were interviewed three times a year and students’ pre and post-test scores were also considered. The results indicate that quality teaching is related to the establishment of quality resources and quality professional learning. Additionally, students demonstrated significant gains between the pre and post-test scores. Furthermore, as teachers move towards exhibiting the characteristics of expert teachers they progress through five stages and it takes at least two years for this progression to occur

An exploration into growing patterns with young Australian Indigenous students

This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students’ understandings of growing patterns. Indigenous students in Year 2 and 3 (n=16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced

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

Exploring excellence in Indigenous education in Queensland secondary schools

In the national and international landscape, there is very limited exploration of cultural constructs of excellence, in particular, in Indigenous contexts. This pilot study aimed to centre the voices of Indigenous people in conceptualising excellence in Indigenous education, as well as to share understandings between Indigenous and non-Indigenous practitioners. Qualitative data collection methods were used including collaborative yarning, storying, and semi-structured interviews. Data were analysed using cross-case analysis to examine the views of educators across three school sites. Indigenous participants highlighted the importance of nurturing culture and identity; building up young people; and, building a culture of inclusivity and belonging. Supportive leadership was also identified as an enabler for enacting excellence in schools. A direct outcome of this project was a whole-school policy that builds on a strengths perspective and forefronts the embedding of Indigenous knowledges and perspectives, supporting the wellbeing of Indigenous students, affirming the identities of Indigenous students and having specific strategies to engage with local Indigenous communities