Ann Gervasoni

Children’s Mathematical Knowledge Prior to Starting School and Implications for Transition

Research over the past 10 years has established that many children starting school are more mathematically capable than teachers, mathematics curricula and text book writers assume. This issue and implications arising for children’s transition to school are explored in this chapter through examining data for 125 children who participated in the Australian Let’s Count Longitudinal Evaluation Study in 2012, 1438 children who participated in the Australian Early Numeracy Research Project (ENRP) in 2001, and the new Australian Curriculum—Mathematics. The children’s mathematics knowledge was assessed using the Mathematics Assessment Interview. The findings suggest that large numbers of children in both the Let’s Count preschool group and the ENRP Beginning School group met the new Australian Curriculum—Mathematics Foundation Standard prior to beginning school. This suggests that many children may be inadequately challenged by the mathematics tasks and instruction they experience in their first year of school.

Caution: Classroom under observation

In this article, it is argued that there are serious difficulties in observing someone else teach for the purpose of providing evaluation or corrective feedback on their teaching. The article reports on responses from a group of teacher educators who watched a videotaped classroom lesson. Their written critiques were surprisingly contradictory, so much so as to call into question the reliability of lesson critiques. It is suggested that, where observation and critique of classroom teaching are used, summative judgements be avoided, and that a major goal of observations be to stimulate debate about different teaching styles and individual and cooperative reflection. Most importantly, observers must acknowledge the variety of intentions and perspectives of classroom teachers.

Students with ‘Special Rights’ for Mathematics Education

The chapter draws attention to the need for equitable access to quality mathematics education for students with ‘special rights’. These special rights stem from the fact that students who are visually or hearing impaired, or who have Down syndrome or other intellectual or physical impairments, historically have not had access to high-quality mathematics education. Included in this group with special rights are students who underperform in mathematics due to explicit or implicit exclusion from quality mathematics learning and teaching environments. It is argued that it is important for the international mathematics education community to advocate strongly for students with ‘special rights’ in entreating communities and governments to provide the resources for equitable access to quality education so that all children may thrive mathematically. During an era in which boundaries are being continuously broken and citizens are surprised constantly by what is humanly possible given faith, motivation and opportunity, it is more important than ever for all students to reach their mathematical potential, and achieve the level of mathematical literacy required to participate fully in an ever-increasingly complex global society. This is just as true for those with special rights for mathematics education.

Mathematics and Transition to School

1 Mathematics and Transition to School: Theoretical Frameworks and Practical Implications Bob Perry, Amy MacDonald, and Ann Gervasoni Part I The Mathematics Young Children Bring to the First Year of School 2 Swimming Upstream in a Torrent of Assessment Anita M. Wager, M. Elizabeth Graue, and Kelly Harrigan 3 Assessing Young Childrens Mathematical Understanding: Opportunities and Expectations at the Transition to School Barbara Clarke 4 Childrens Mathematical Knowledge Prior to Starting School and Implications for Transition Ann Gervasoni and Bob Perry 5 Transition to School: Prior to School Mathematical Skills and Knowledge of Low-Achieving Children at the End of Grade 1 Andrea Peter-Koop and Sebastian Kollhoff 6 Lets Count: Early Childhood Educators and Families Working in Partnership to Support Young Childrens Transitions in Mathematics Education Amy MacDonald 7 The Role of the Home Environment in Childrens Early Numeracy Development: A Canadian Perspective Sheri-Lynn Skwarchuk and Jo-Anne LeFevre 8 Mathematics Teachers Responding to Childrens Resources to Create Learning for All Jonina Vala Kristinsdottir and Hafdis Gudjonsdottir Part II Continuity of Mathematics Curriculum and/or Pedagogy as Children Begin School 9 The Relationship Between Policy and Practice in the Early Mathematics Curriculum for Reception-Class Children in England Carol Aubrey and D nd Durmaz 10 Scaling Up Early Mathematics Interventions: Transitioning with Trajectories and Technologies Julie Sarama and Douglas H. Clements 11 Partnerships that Support Childrens Mathematics During the Transition to School: Perceptions, Barriers and Opportunities Wendy Goff and Sue Dockett 12 The Culture of the Mathematics Classroom During the First School Years in Finland and Sweden Kirsti Hemmi and Andreas Ryve 13 A New Zealand Perspective: Mathematical Progressions from Early Childhood to School through a Child Centred Curriculum? Shiree Lee and Gregor Lomas 14 The Impact of a Patterns and Early Algebra Program on Childrens Learning in Transition to School in Australian Indigenous Communities Marina M. Papic, Joanne T. Mulligan, Kate Highfield, Judith McKay-Tempest, and Deborah Garrett 15 Preschool Mathematics Learning and School Transition in Hong Kong Sharon Sui Ngan Ng and Jin Sun Part III Informal and Formal Mathematics and the Transition to School 16 Early Mathematics in Play Situations: Continuity of Learning Hedwig Gasteiger 17 Mathematical Conversations that Challenge Childrens Thinking Jill Cheeseman 18 Transition to School: Supporting Childrens Engagement in Mathematical Thinking Processes Liz Dunphy 19 Listening to Childrens Mathematics in School Elizabeth Carruthers

POWERFUL PEDAGOGICAL ACTIONS IN MATHEMATICS EDUCATION

A critical issue for all involved in primary and secondary mathematics education is how to ensure that all students learn mathematics successfully so that at the end of schooling they have the mathematical knowledge, skills, and confidence necessary to fully participate in further learning, employment, community life, and citizenship. This issue focuses attention on pedagogy which is the method or process of teaching, and generally refers to instructional strategies or actions (Ball & Bass, 2000). This chapter provides an overview of Australasian studies that have explored successful pedagogy within the context of mathematics education over the past four years (2008 to 2011). Our purpose is to highlight new insights that contribute to knowledge about what constitutes successful mathematics pedagogy for all students, to note any issues or tensions emerging from the findings, to identify any silences in the research agenda, and to recommend areas for future research.

The Impact on Learning When Families and Educators Act Together to Assist Young Children to Notice, Explore and Discuss Mathematics

Let’s Count is a new Australian early mathematics initiative that aims to promote positive mathematical experiences for young children (3–5 years) as part of families’ everyday activities. The 154 children who experienced Let’s Count in 2013 demonstrated noteworthy growth in their mathematical knowledge from the beginning of their preschool year to its end. On almost every measure, the Let’s Count cohort bettered the performance of the comparison groups, with some measures showing statistically significant differences. This suggests that educators and families working in partnership to assist young children to notice, explore and discuss the mathematics they encounter during everyday experiences had a positive effect on children’s construction of mathematics.

Mathematics and Transition to School: Theoretical Frameworks and Practical Implications

This edited book brings together for the first time an international collection of work built around two important components of any young child’s life—learning mathematics and starting (primary or elementary) school. The chapters take a variety of perspectives, and integrate these two components in sometimes explicit and sometimes more subtle ways. This chapter provides a theoretical framework for transition to school and investigates possible places for mathematics in that transition. It stresses the importance of considering the strengths of all involved in the transition to school and how these strengths can be used to assist children learn increasingly sophisticated mathematics. The chapter concludes with an analysis of each of the book chapters in terms of their links into the theoretical framework for transition to school and young children’s mathematics learning.

Rattling the Cage: Moving beyond ethical standards to ethical praxis in self-study research

The ethical practice underpinning self-study research has been addressed extensively in the literature of self-study of teacher education practices. Less attention has been paid to how researchers deal with ethical tensions and dilemmas when they arise unexpectedly during self-study research. In this article, we examine how the extrapolation and examination of one critical incident in the process of conducting self-study research challenged our ethics as researchers and led us to new understanding and knowledge. Our focus is on the initial acknowledgment of what we considered to be an ethical dilemma as it had rattled our cage. We were uncomfortable, disturbed, and challenged. We analyzed the data using critical incident analysis and discussed the outcomes in relation to being ethically responsive as researchers. Our responsiveness has led us to ethical praxis, whereby we now routinely and intentionally incorporate ethical dilemma identification and data analysis into our research designs. This study also highlights that our responsibilities as researchers are both private and public. By distilling the essence of a single critical incident, we can contribute new knowledge to the conversation about ethical practice.

How to Teach and Assess Whole Number Arithmetic: Some International Perspectives

This chapter focusses on the diverse theoretical and methodical frameworks that capture the complex relationship between whole number arithmetic (WNA) learning, teaching and assessment. Its aim is to bring these diverse perspectives into conversation. It comprises seven sections. The introduction is followed by a narrative of a Macao primary school lesson on addition calculations with two-digit numbers, and this sets the context for the subsequent three sections that focus on the development of students’ mathematical and metacognitive strategies during their learning of WNA. Apart from examining the impact of teachers’ knowledge of pedagogy, learning trajectories, mathematics and students on children’s learning of WNA, learning theories are also drawn on to interpret the lesson in the Macao Primary School. Two interpretations of the variation theory (VT), an indigenous one and a Western perspective, provide much needed lenses for readers to make sense of the lesson. In addition, the theory of didactical situations (TDS) is also applied to the lesson. The chapter also includes a reflection on possible classroom assessment and the role of textbooks, both of which were less apparent in the lesson, for the teaching and learning of WNA.

Bringing families and preschool educators together to support young children's learning through noticing, exploring and talking about mathematics

This chapter draws on findings from the longitudinal evaluation of the Australian initiative Let’s Count (Perry and Gervasoni 2012) to consider how the process of bringing families and pre-school educators together, with a focus on mathematics, enhanced young children’s mathematics learning. The data examined is parent and educator interview data that explores the effectiveness of the Let’s Count approach. The findings, sustained over two separate data collection periods over 2 years, provide clear evidence that Let’s Count is at least as successful as other mathematics learning programs in terms of children’s mathematical knowledge and skills outcomes, and suggest in respect to some mathematical concepts that Let’s Count may be a superior approach. Themes emerging from interviews with parents highlight that the parents valued the educators talking to them about ideas and suggestions regarding the type of activities that are rich sources of mathematics learning. It many ways these discussions provided parents with prompts, inspiration, encouragement and confidence. The interview data also highlight that sustaining communication between the parents and educators across the year was challenging for some. Recommendations arising from the Let’s Count Longitudinal Evaluation for future initiatives include: encouraging parents to support their children to notice, explore and discuss the mathematics that is part of everyday experiences; enabling sustained communication opportunities for parents to discuss the mathematics they notice their child using and exploring; and providing suggestions about how to extend this learning.