Six teachers within the P-2 level were studied in depth in an effort to identify features of effective teaching of mathematics. In the discussion of data these teachers are referred to as Ms Prep, Ms NESB (Prep); Ms Prep/1, Ms Grade 1, Ms Grade 1/2, and Ms Grade 2.
The presentation of the characteristics and practices of effective teachers of mathematics at the P-2 level begins with an introduction and synopsis of results for each teacher using the "nutshell statements" developed by the lesson observer/researchers. On reading through these statements it will become apparent to the reader that although the observers used the same lesson observation and analysis guide, different aspects of teaching became more apparent for each teacher. In this way the Early Years Numeracy Research Project (ENRP) observations allowed the individuality of teachers to emerge.
In the lessons observed, Ms Prep's teaching followed a consistent structure of warm up activities, clear introductions, activities for individuals or groups, and comprehensive reviews. There was limited direct instruction and active use of incidental teaching opportunities.
Ms Prep was able to articulate her goals and had a strong sense of the curriculum content evident both in her language and thinking. The activities matched her stated goals and the experiences were characterised by variety, student engagement, and high expectations for effort and achievement.
Ms Prep showed great interest in the individual children and her actions indicated that she respected them as learners. She listened intently to each child and communicated with them as individuals. She focused on the positive aspects of their contributions. Ms Prep encouraged the children to contribute to class activities and discussions and for them to listen to and respect each other.
Ms NESB created a physically and mentally interesting classroom. Her class was small in size because the whole school recognised that the Prep children come to school without English language backgrounds. Ms NESB was keenly aware of each individual child's social, emotional and mathematical needs. She worked hard to involve each child in mathematical reasoning. She created a warm, supportive, respectful, yet no-nonsense atmosphere in her mathematics classroom. Children were expected to concentrate, examine ideas and help each other to do mathematics. Ms NESB placed greatest emphasis on the domains involving number as the foundation of children's mathematical understandings. Her lessons were composed of tasks that focused on developing a concept through a range of activities. She used games and manipulatives repeatedly to help children to remember and to connect, then to build their knowledge.
Ms NESB was gentle yet demanding. She communicated her belief in children's capabilities. She probed patiently and praised good thinking and acknowledged effort.
Ms Prep/1 prepared carefully for teaching. She targeted a topic for several weeks. As she worked through the topic with her children she monitored their performance closely by collecting and checking their work daily and by making detailed anecdotal notes. Ms Prep/1 then modified the next day's lesson to fit the children's needs.
Mathematics lessons occurred four days a week. The teacher described the Friday integrated lesson as literacy/mathematics but she seemed to integrate other studies such as science also. Ms Prep/1 generally used a whole class/ small group/ whole class structure for mathematics. Children were grouped in various ways; sometimes according to perceived ability, but sometimes in mixed ability and sometimes paired for tutoring. The teacher had a targeted teaching group each day, but this could change if she saw children with "on the spot" needs.
Ms Prep/1 chose tasks that engaged children: mostly games and hands on activities. She used a lot of stories that had some mathematics content. She had a very natural way of relating mathematics to everyday life for children, for example relating two digit numbers to ages of people. There was a mix of open and closed tasks and children usually recorded their group mathematics in some way. The children were on task throughout the lessons and the classroom tone was brisk and businesslike.
Ms Prep/1 thought the project had made her more confident to see what children can already do and immerse them in more challenging mathematics.
Ms Grade 1
Ms Grade 1's teaching of mathematics was characterised by the "family-like" atmosphere she had developed in her classroom. Ms Grade 1 clearly cared about the children as people, and cared about their holistic development. The children explored, investigated and discussed mathematical ideas as they arose, and interacted freely with each other and with Ms Grade 1. It is clear that children's ideas and efforts were valued by the teacher, and she encouraged and celebrated their efforts. Ms Grade 1 had a clear idea of the mathematical ideas she was to explore with the children in each lesson, and planned sequences of activities that would build their understanding. These activities were often open in nature. The activities were presented for the whole class to explore, with the children often working in pairs. A significant amount of each lesson was spent discussing with the children the strategies they used to solve problems, and in focusing on important mathematical ideas. Ms Grade 1 used a range of questions to probe children's understanding and reasoning. She asked many 'Why' and 'How' questions to build children's relational understanding. Ms Grade 1 roved amongst the children as they worked on tasks to support their efforts and probe their understanding. She used her observations to assess the children and plan the next appropriate learning experience for them. Ms Grade 1 used her knowledge of the ENRP Growth Points reached by children to focus her planning.
Ms Grade 1 was a highly reflective teacher, and was always searching for more effective ways to build children's mathematical understanding.
Ms Grade 1/2
Ms Grade 1/2 was a caring teacher, who listened carefully to children and their strategies in solving problems in the situation where the tasks were open and lent themselves to a variety of strategies. In more closed tasks, her focus was more on children carrying out instructions. Ms Grade 1/2 endeavoured to find out where the children were at, and to extend and challenge them appropriately. She regarded her focus group time as the major teaching opportunity. She worked to build engagement, peer responsibility and respect, most evident when the children were working directly with her. Topics were decided with other Grade 1/2 teachers, but lesson by lesson planning was undertaken individually, with occasional sharing of successful lessons or ideas. Open tasks and closed tasks were used, with opportunities for student choice of method.
Ms Grade 1/2 believed that her major change in teaching as a result of the ENRP was in gaining more information about what children know, and working to extend them as far as they were able, moving beyond curriculum guidelines as necessary.
Ms Grade 2
Ms Grade 2's classroom was a place where learning mathematics was taken seriously. It was also infused with enjoyment, success and appreciation. Expectations were very high in terms of both content and mathematical behaviours. Learning opportunities were carefully and thoughtfully structured for Ms Grade 2's children. Fundamentally each child was required to engage with a specific mathematical concept in a lesson and given some flexibility, choice or options within which to work. It was very clear that mathematics was to be done and what was expected within each task. Ms Grade 2 emphasised mathematical thinking, reasoning and justification as well as asking her children to reflect on their learning. The mathematics was substantial and highly focused. Children appeared confident and were capable.
Ms Grade 2 communicated with children in a highly personalised way and knew about the thinking of individuals. She created a no-nonsense, intensely positive environment for learning mathematics and everyone was justifiably proud of the results they achieved separately and together.