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Processes of mathematical inquiry in kindergarten

Svanhild Breive at the Department of Mathematical Sciences at the Faculty of Engineering and Science has submitted her thesis entitled «Processes of mathematical inquiry in kindergarten» and will defend the thesis for the PhD-degree Wednesday 5 June 2019.

The results show that mathematical inquiry, which challenges children to argue for and explain their ideas, may, I hold, lay the ground for children to become critical and autonomous thinkers and problem solvers.

Svanhild Breive

PhD-Candidate and Assistant Professor

Svanhild Breive at the Department of Mathematical Sciences at the Faculty of Engineering and Science has submitted her thesis entitled «Processes of mathematical inquiry in kindergarten» and will defend the thesis for the PhD-degree Wednesday 5 June 2019.

She has followed the PhD-programme at the Faculty of Engineering and Science with Specialisation in Mathematics Education.

The study is situated within a research and development project called the Agder Project (in Norwegian only) - a cooperation between the University of Stavanger and the University of Agder. The Agder Project are funded by the Research Council of Norway (NFR no. 237973), The Sørlandet Knowledge Foundation, Aust-Agder utviklings- og kompetansefond, (in Norwegian Only), Aust-Agder County and Vest-Agder County.

Summary of the thesis by Svanhild Breive:

Processes of mathematical inquiry in kindergarten - abstract

The thesis reports from a research study which investigates the processes that unfolds when kindergarten children (age 5-years-old), together with their kindergarten teachers and peers inquire into and solve mathematical problems.

The study is situated within a research and development project called the Agder Project, which aims to investigate the effects of a preschool intervention programme in Norway that focuses on four sets of competences: social-emotional, self-regulation, language, and mathematics. This research study uses a case study design where five kindergarten teachers and their groups of 5-year-old children, who were part of the focus group of the Agder Project, were chosen as participants.

Interactions between kindergarten teachers and children

The study examines in depth the interactions between kindergarten teachers and children, and amongst the children themselves, when they work together to solve mathematical problems.

Through mathematical inquiry children and adults not only co-create and acquire knew knowledge but they also ‘become themselves’ in the encounter with each other and the environment. When kindergarten children and adults inquire into and solve mathematical problems together, they continuously position themselves in a manner which is ethical through and through. Ethical principles like mutual respect, trust and responsibility lay the foundation for mathematical inquiry and problem solving to occur, and therefore, mathematical inquiry in kindergarten may be seen as an ‘ethical process’.

The study also proposes that mathematical inquiry in kindergarten is a multimodal and dialectical process. It is multimodal, in that it involves gesture, bodily movements, facial expressions, tone of voice and artefacts as well as verbal language. Children’s mathematical reasoning (explanations and argumentations) is to a great extent materialised through gestures and other bodily actions, in combination with words.

Moreover, kindergarten teachers engage children in mathematical activities by their multimodal participation. For example, instead of asking a lot of verbal questions they guide children by their bodily actions and tone of voice towards the aim of the activity and consequently give children a space of freedom to contribute.

Moreover, mathematical inquiry is a dialectical process, in that it involves a symmetrical interplay between children and adults where all have equally important roles in shaping interaction and each other’s learning. The kindergarten teachers play significant roles for introducing children to cultural ways of thinking mathematically, and to cultural ways of collaborating. However, the results show how children also take responsibility for moving the mathematical activities forward and how they guide kindergarten teachers in mathematical inquiry activities. Both kindergarten teachers and children are mutually dependent on each other to carry out mathematical inquiry activities, and thus both are teachers and learners of each other.

Kindergarten Teachers must facilitate children’s opportunities

The implications that can be drawn from the study are that it is important that KTs facilitate children’s opportunities to solve mathematical problems together with others in a variety of settings and with a variety of available artefacts.

It is also important that kindergarten teachers pay attention to children’s contributions (verbal and non-verbal) and try to understand their perspectives, that is, position themselves as learners and let the children guide them in the activities. This may promote children to contribute with their ideas and explanations and to take responsibility for carrying out the mathematical learning activities.

Moreover, the study emphasises that kindergarten teachers may benefit from being consciously aware of the affect their bodily actions have on children’s mathematical reasoning and for engaging them in mathematical discourse without having to ‘teach’ (i.e., tell) them mathematical concepts and relations.

Mathematical inquiry processes may prepare children for school

The research study further suggests that engaging 5-year-old kindergarten children in mathematical inquiry processes may prepare them for school.

The results show that mathematical inquiry, which challenges children to argue for and explain their ideas, may, I hold, lay the ground for children to become critical and autonomous thinkers and problem solvers.

Through mathematical inquiry children can learn to collaborate, which includes respecting each other, trusting each other and working together to accomplish a task, and may therefore help children to adjust to the new school context.

Dispution facts:

The Candidate: Svanhild Breive (1981, Breive, Hovden in Setesdal), BA in mathematics and physics, UiA (2009), Masters degree in mathematics Education, UiA (2014). Now employed as an Assistant Professor in Mathematics Education at USN - University og South-Eastern Norway.

The trial lecture and the public defence will take place at Gabriel Scotts auditorium – B1-001, Campus Kristiansand.

Assistent head of Department of Mathematical Sciences Elna Svege, will chair the disputation.

Trial lecture at 10:30 a.m.

Public defense at 12:30 p.m.

Given topic for trial lecture: “Tension between free and structured play, agency and constraint, inquiry and teaching: Conceptions of the child in early childhood education

Thesis title«Processes of mathematical inquiry in kindergarten».

Search for the thesis in AURA - Agder University Research Archive, a digital archive of scientific papers, theses and dissertations from the academic staff and students at the University of Agder. The thesis will also be available at the University Library, and some copies will also be available for loan at the auditorium where the disputation takes place.

Opponents:

First opponent: Professor Luis Radford, Université Laurentienne Sudbury, Canada

Second opponent: Professor Merrilyn Goos, University of Limerick, Ireland

Professor Simon Goodchild, UiA, is appointed as the administrator for the assessment commitee.

Supervisors were Associate Professor Ingvald Erfjord (main supervisor) and Professor Martin Carlsen, Associate Professor Per Sigurd Hundeland and Professor John Monaghan (co-supervisors)