Elizabeth Warren - Academia.edu (original) (raw)

Papers by Elizabeth Warren

Mathematics Education Research Journal

International curriculum and policy directions have called to embed critical thinking across disc... more 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.

Advances in Mathematics Education, 2013

Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um a... more Na Austrália, os alunos provenientes de meios socialmente desfavorecidos continuam a revelar um atraso de um ou dois anos relativamente aos colegas oriundos de outros meios no que se refere a testes de numeracia, tanto nacionais como internacionais. Os resultados da investigação indicam claramente que a qualidade dos professores faz a diferença. Este estudo foca-se no impacto de um modelo de aprendizagem profissional, o modelo RoleM (RPL), numa escola, ao longo de três anos. Os professores participantes (n = 12) lecionavam os primeiros três anos de escolaridade (desde a Educação Pré-escolar ao segundo ano; alunos de 4/5 a 8 anos de idade). Para avaliar a eficácia do RPL, os professores foram entrevistados três vezes por ano. Os resultados indicam que um ensino de qualidade se relaciona com a disponibilização de recursos de qualidade e com uma aprendizagem profissional igualmente de qualidade. À medida que os professores evoluem no sentido de manifestarem características de professor...

This paper presents the results from an initial lesson in a series of design experiments focusing... more 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 twofold role in the lessons and communication of the mathematics experienced.

… of the 34th Annual Conference of …, 2011

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explo... more The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focussing on the identification, prediction and justification of function rules. It reports on students attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

Contemporary Issues in Early Childhood, 2005

Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching e... more Sixty-five Year 2 children with ages ranging from six to seven years participated in a teaching experiment to introduce functional thinking. The results show that young children are capable of generalising, can provide examples of relations and functions, can describe the inverse of such relationships and give valid reasons for how they found the inverse relationships. They also indicate that specific features of instruction assist this process, particularly abstracting underlying mathematical relationships, notably the materials used by the teacher and the children, the types of activities and the questions asked by the teacher. This leads to specific implications for the teaching of arithmetic in the early years.

This paper reports on the preliminary findings from the researchers' thesis exploring how young A... more This paper reports on the preliminary findings from the researchers' thesis exploring how young Australian Indigenous students engage in mathematical generalisation tasks. Six students (8.5 years) were purposely selected to participate in one on one Piagetian clinical interview to explore how they engage and express generalisations with growing patterns. Initial findings of the study suggest that these young students can generalise contextual growing patterns. Representing the patterns with concrete materials and kinaesthetically engaging with tasks enhanced their ability to reach generalisations. In addition, using patterns where the relationship between the two variables was visually explicit assisted students to express this relationship in general terms. Interestingly, cultural gestures (both verbal and non-verbal) were apparent throughout the interviews. These gave insight into how Indigenous students engage in one-on-one settings in contrast to whole class interactions.

PNA. Revista de Investigación en Didáctica de la Matemática, 2013

The Early Years Generalizing Project (EYGP) involves Australian years 1 to 4 (age 5 to 9) student... more The Early Years Generalizing Project (EYGP) involves Australian years 1 to 4 (age 5 to 9) students and investigates how they grasp and express generalizations. This paper focuses on data collected from 6 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 generalizations and to begin to express these generalities. It also appears that as students became aware of the structure, their use of gestures and selftalk tended to decrease.Exploración del pensamiento funcional de estudiantes jóvenesEl Early Years Generalizing Project (EYGP) implica a estudiantes de primer a cuarto curso de la educación primaria australiana (de 5 a 9 años) e investiga cómo comprenden y expresan las generalizaciones. Este artículo se centra en los datos recogidos de 6 estu...

merga.net.au

L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedin... more L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. Fremantle: MERGA. ... Indigenous Children's Ability to Pattern as They Enter

The implementation of a new mathematics syllabus in the elementary context is problematic, especi... more The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was grounded in theories related to a community of practice (Lave & Wenger, 1991), a socio-constructivist perspective (Vygotsky,1962/1934) and effective models of professional development (Clarke & Hollingsworth, 2002; Guskey, 1986). This paper focuses on the effectiveness of the model as six Year 1 teachers worked in pairs developing and implementing learning experiences for three differing aspects of the Patterns and Algebra strand. The results indicate the model offered positive professional learning experiences for the six teachers and assisted them in becoming experts in their own right, especially with regard to content and pedagogical knowle...

This paper examines teacher actions that support young children to consider repeating pattens as ... more This paper examines teacher actions that support young children to consider repeating pattens as co-variational (functional) relationships, to use this understanding to predict uncountable steps in the relationships, to express these relationships in general terms, and use repeating patterns to introduce proportional thinking. A teaching experiment was conducted in two classrooms, comprising of a total of 45 children whose average age was 9 years and 6 months. This experiment focused on exploring teacher actions (including the use of concrete materials, recording of data, and questions asked) that supported young children’s development of co-variational reasoning. The results indicated that explicit instruction assisted children to find patterns across the table as well as down the table, to find the relationships between the number of tiles and an uncountable number of repeats. Also the results indicate that young children are capable of not only thinking about the form. Mathematic...

Contemporary Issues in Early Childhood, 2005

This paper presents the results from an initial lesson in a series of design experiments focusing... more 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.

Australasian Journal of Early Childhood

The Australian Journal of Indigenous Education

This paper explores the role of oral language and representations in negotiating mathematical und... more This paper explores the role of oral language and representations in negotiating mathematical understanding. The data were gathered from two Indigenous Australian classrooms in Northern Queensland. The first classroom, a Year 6/7 consisted of 15 students whose ages range from 10 years to 12 years with eight being Aboriginal, six from Torres Strait and one from Papua New Guinea. The second classroom, a Years 4/5/6 classroom consisted of 14 Year 3/4/5 students, with eight being Aboriginal and six of Torres Strait Island origin. Both teachers had been working in this context for up to five years and were perceived by both the school community and local educational consultants as exemplary teachers of Indigenous Australian students. Data were gathered from conversations with the two teachers, and from videos of their lessons especially designed to illuminate issues they negotiate on a day-to-day basis when teaching mathematics. The results indicate that explicit consideration needs to b...

The Australian Journal of Indigenous Education, 2004

This study examined teachers’ perceptions of the role of teacher aides in mathematics classrooms ... more This study examined teachers’ perceptions of the role of teacher aides in mathematics classrooms in rural and remote Indigenous communities. Twelve teachers from three schools in rural and remote Queensland participated in the study. The results from the first year of the project indicated that there were differences in how these teachers worked with their teacher aides, particularly the specific roles assigned to them in the mathematics classroom, with non-Indigenous teacher aides being given greater responsibilities for student learning and Indigenous teacher aides for behavioural management. As a result of teacher aide in-service on mathematics learning, teachers’ perception of the Indigenous teacher aides changed, resulting in each being given greater responsibility for student learning.

Mathematics Teacher Education and Development, Mar 28, 2013

Mathematics Education Research Journal

Advances in Mathematics Education, 2013

… of the 34th Annual Conference of …, 2011

Contemporary Issues in Early Childhood, 2005

PNA. Revista de Investigación en Didáctica de la Matemática, 2013

merga.net.au

Contemporary Issues in Early Childhood, 2005

This paper presents the results from an initial lesson in a series of design experiments focusing... more 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.

Australasian Journal of Early Childhood

The Australian Journal of Indigenous Education

The Australian Journal of Indigenous Education, 2004

Mathematics Teacher Education and Development, Mar 28, 2013