Education Commons^™

Reframing Mathematical Futures Ii Project: Development Of A Draft Learning Progression For Algebraic Reasoning, L Day, M Horne, M Stephens

Education Conference Papers

Curriculum documents make a clear distinction between algebraic skills and algebraic reasoning, where the development of the former is far more readily articulated than the latter. While there are many studies of algebraic reasoning, these are usually topic specific and/or highly contextual. What are the big ideas of algebraic reasoning and is it possible to map their learning trajectory? This paper reports on the preliminary phase of a large national study in Australia which is designed to move beyond the hypothetical and to provide an evidence-based foundation for a learning progression. Using rich assessment tasks designed for middle years students …

Generalisation Through Noticing Structure In Algebraic Reasoning, L Day

Education Conference Papers

“Mathematicians see generalising as lying at the very heart of mathematics” (Mason, Graham & Johnston-Wilder, 2005, p.283). The Australian Curriculum: Mathematics develops number and algebra together as they complement each other. Developing number and algebra together provides opportunities for searching for patterns, conjecturing and generalising mathematical relationships. Further, it allows the focus to be on the process of mathematics and noticing the structure of arithmetic and our number system, rather than the product of arriving at a correct answer.

Developing Learning Progressions To Support Mathematical Reasoning In The Middle Years - Algebraic Reasoning, L Day, M Stephens, M Horne

Education Conference Papers

As part of the Reframing Mathematical Futures II Project on Mathematical Reasoning, algebraic reasoning was identified as one of the three areas to be investigated. This involved developing a hypothetical learning progression for algebra to inform the design of assessment tasks to test the progression. The assessment forms were then sent to trial schools and the data was analysed using Rasch analysis. This paper reports on the analysis of preliminary data received and outlines some implications for teaching.

Exploring Reasons Why Australian Senior Secondary Students Do Not Enrol In Higher-Level Mathematics Courses, G Hine

Education Conference Papers

In this research paper, I present the reasons why senior secondary students elect not to enrol in a higher mathematics course. All Year 11 and Year 12 mathematics students within Western Australian secondary schools were invited to participate in an online survey comprised chiefly of qualitative items. The key reasons espoused by students include an expressed dissatisfaction with mathematics, the opinion that there are other more viable courses of study to pursue, and that the Australian Tertiary Admissions Ranking (ATAR) can be maximised by taking a lower mathematics course. In addition, student testimony suggests that there are few incentives offered …

Child's Play The Developmental Benefits Of The Play Choices Of Modern Children: Implications For School Curricula, Doireann O'Connor, Tracy Treasure, Christine Robinson, M Mccormack, V O'Rourke

Education Conference Papers

This paper presents data from the Irish Neighbourhood Play Study. The Irish Neighbourhood Play Study explored the play choices of children from 0 to 15 years of age. This paper reports the findings on the play choices of children and these are presented alongside the levels of engagement within each play type. Construction Play, Motor Play, Fantasy (Imaginative) Play and Social Play are all applied as broad categories with detailed data presented that drills down into what elements of play children are choosing within each category. The developmental benefits of each play type are then explored and discussed. These findings …

Proof By Mathematical Induction: Professional Practice For Secondary Teachers, G Hine

Education Conference Papers

Mathematical induction is a proof technique that can be applied to establish the veracity of mathematical statements. This professional practice paper offers insight into mathematical induction as it pertains to the Australian Curriculum: Mathematics (ACMSM065, ACMSM066) and implications for how secondary teachers might approach this technique with students. In particular, literature on proof—and specifically, mathematical induction—will be presented, and several worked examples will outline the key steps involved in solving problems. After various teaching and learning caveats have been explored, the paper will conclude with some mathematical induction example problems that can be used in the secondary classroom.

Boys And Girls Come Out To Play: Gender Differences In Children's Play Patterns, D O'Connor, M Mccormack, C Robinson, V O'Rourke

Education Conference Papers

This paper presents findings from The Irish Neighbourhood Play Study; a national, cross-border research project which recorded children’s play patterns in Ireland during 2012. The study incorporated 1688 families across 240 communities. This study recorded the play patterns of children in Ireland aged birth-14 years. The findings of the study are discussed here in the context of gendered patterns. Particular emphasis is placed on the skill differences developed through various play choices. These differences are explored within the context of established literature on the learning strengths of boys and girls. Established bodies of literature on children’s learning across gender lines …

The Age Of Imagination: Imagining Play And Invention: Implications For Creative Development, D O'Connor, M Mccormack, C Robinson, V O'Rourke

Education Conference Papers

This paper presents findings from The Irish Neighbourhood Play Study; a national, cross-border research project which recorded children’s play patterns in Ireland during 2012. The study incorporated 1688 families across 240 communities. Data was established on the play choices of children aged from birth to 14 years. Multiple differentials were explored including socio-economic and geographical environments.

This paper focuses on the findings within imaginary play patterns for the full cohort. As such, it presents the play patterns for imaginary play in children aged birth-14 years. The findings are discussed in the context of developmental patterns with particular emphasis on the …

The Influences Of Opportunity. Differences In Children's Play Choices Across Diverse Communities In Ireland, D O'Connor, V O'Rourke, C Robinson Mcgunnigle, M Mccormack

Education Conference Papers

This paper presents findings from The Irish Neighbourhood Play Project; a research study initiated by IT Sligo and Early Childhood Ireland in 2012. The focus of this paper is on the data section which highlights children’s play choices and opportunities across socio-economic communities. The study incorporated almost 1800 families across 240 communities. Data was collected within disadvantaged communities, middle class communities and affluent communities. Where and what children are playing was investigated. The choices children and families make within play have a direct effect on the developing brain of the young child (Acar & Torquati, 2015). This, in turn, affects …

Is It Time For The Risky Classroom? Dealing With Risk And Uncertainty Is A Natural Part Of Adult Life. Yet Modern Children Are Shielded From Risk At Every Opportunity. A Pedagogical Shift Is Required, D O'Connor, V O'Rourke, C Robinson Mcgunnigle, M Mccormack

Education Conference Papers

Risk within learning environments is a much debated topic within early childhood education. The sector sees and understands the benefits of risk but often remain risk adverse. No –one wishes for children to experience injury and as such safety measures are essential. However, risk has also been shown to be essential for holistic development and learning in the early years (Lights, 2014). It is very important in the formation of many important skills and contributes greatly to children’s holistic health (Brussoni, Olsen, Pike & Sleet, 2012). Contemporary research and the most up-to-date wisdom requires educators to embrace risk and risky …

Is Play Disappearing? Instances Of No-Play In Children's Neighbourhoods: Implications For Learning, Development And Curriculum, Doireann O'Connor, Tracy Treasure, Christine Robinson, M Mccormack, V O'Rourke

Education Conference Papers

This paper presents data from the Irish Neighbourhood Play Study that explored children’s engagement in play. The data raises concerns around recorded instances of no-play in play environments. The instances of no-play were recorded during peak play time periods including weekend and afterschool hours. This data raises the critical question: Are today’s children being afforded sufficient time to play? Both the quality of opportunity to play and the quantity of time afforded to children to engage in play are important factors in children’s learning and development (Fisher, Hirsh-Pasek, Golinkoff, Singer & Berk, 2011; Whitebread, 2012). The data from the Irish …