This paper builds from a prior study into the teaching and learning of basic number facts in New Zealand. It reports the changes in practice of one teacher that were brought about by her reflection on the effectiveness of her teaching and learning programme. It details how this teacher created a process which helped make the learning of basic facts more relevant and meaningful to her and her Year 6 students.

<p>A difference between the beliefs and practices about mathematics learning and teaching held by teachers in kindergartens and teachers in new entrant classrooms may lead to problems as teachers and children manage the transition from kindergarten to school. The New Zealand education system is governed by various curriculum documents underpinned by similar philosophies to support teacher practice. These documents are based on an expectation that teachers build from children’s existing knowledge and experiences. The system is based on expectations relating to knowledge that are loosely linked to the year level and age of children. Evidence about teachers’ practices and beliefs was gathered using a case study approach. Five primary schools and their neighbouring kindergartens were purposively selected for this study. Fourteen kindergarten and five new entrant teachers were observed and interviewed and completed questionnaires about their beliefs and practices in mathematics teaching and learning over a two year period. Mathematical events were analysed to document teachers’ practices. Kindergarten teachers’ practice most commonly mirrored their stated beliefs about how children best learned mathematics. New entrant teachers, although possessing similar stated beliefs to kindergarten teachers, did not necessarily follow these beliefs in their classroom practice. The beliefs of kindergarten and new entrant teachers in mathematics teaching and learning were similar, but their practices differed in several dimensions. Kindergarten teachers believed children best learned mathematics through free play and exploration of the world around them. These teachers encouraged children to follow their own interests and supported children as they developed their ideas and became active problem solvers. These beliefs arose from teachers’ personal experiences combined with the primarily sociocultural focus of the early childhood curriculum, Te Whariki. New entrant teachers’ beliefs about mathematics learning and teaching were similar to those of kindergarten teachers – children learned through having fun, solving problems, and doing things in a real-life context. However, new entrant teachers also had clear expectations of the skills five-year-olds needed to know on their entry to school. When children did not appear to possess these skills, teachers focused on remediation of the perceived deficits. In practice, new entrant teachers directed children’s learning based on their beliefs about what children needed to know to be successful at school. This approach lead to structured and managed environments with little regard for children’s prior-to-school knowledge and experiences. These inconsistencies in mathematics teaching and learning between schools and kindergartens could be minimised with professional development for teachers that focused on developing the relationships between teachers in both settings.</p>

<p>A difference between the beliefs and practices about mathematics learning and teaching held by teachers in kindergartens and teachers in new entrant classrooms may lead to problems as teachers and children manage the transition from kindergarten to school. The New Zealand education system is governed by various curriculum documents underpinned by similar philosophies to support teacher practice. These documents are based on an expectation that teachers build from children’s existing knowledge and experiences. The system is based on expectations relating to knowledge that are loosely linked to the year level and age of children. Evidence about teachers’ practices and beliefs was gathered using a case study approach. Five primary schools and their neighbouring kindergartens were purposively selected for this study. Fourteen kindergarten and five new entrant teachers were observed and interviewed and completed questionnaires about their beliefs and practices in mathematics teaching and learning over a two year period. Mathematical events were analysed to document teachers’ practices. Kindergarten teachers’ practice most commonly mirrored their stated beliefs about how children best learned mathematics. New entrant teachers, although possessing similar stated beliefs to kindergarten teachers, did not necessarily follow these beliefs in their classroom practice. The beliefs of kindergarten and new entrant teachers in mathematics teaching and learning were similar, but their practices differed in several dimensions. Kindergarten teachers believed children best learned mathematics through free play and exploration of the world around them. These teachers encouraged children to follow their own interests and supported children as they developed their ideas and became active problem solvers. These beliefs arose from teachers’ personal experiences combined with the primarily sociocultural focus of the early childhood curriculum, Te Whariki. New entrant teachers’ beliefs about mathematics learning and teaching were similar to those of kindergarten teachers – children learned through having fun, solving problems, and doing things in a real-life context. However, new entrant teachers also had clear expectations of the skills five-year-olds needed to know on their entry to school. When children did not appear to possess these skills, teachers focused on remediation of the perceived deficits. In practice, new entrant teachers directed children’s learning based on their beliefs about what children needed to know to be successful at school. This approach lead to structured and managed environments with little regard for children’s prior-to-school knowledge and experiences. These inconsistencies in mathematics teaching and learning between schools and kindergartens could be minimised with professional development for teachers that focused on developing the relationships between teachers in both settings.</p>