Understanding the number system is the key to teaching and learning mathematics. Here is a framework which shows how children's understanding about the number system becomes more sophisticated as their thinking develops. This framework can help teachers offer appropriate learning experiences in mathematics.
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There is growing pressure for all teachers to become teachers of values. Here are some ways in which mathematics teachers can incorporate values education into their existing mathematics programme without needing to make any major changes to either the content or teaching approaches.
Most children have trouble understanding decimals - they confuse them with whole numbers or with fractions. Here are some concrete suggestions for how children can use their everyday knowledge to overcome the difficulty of realising decimals are a result of division.
Mathematics is more than numbers and measurement. It is a way of thinking which allows concepts to be built up; problems to be explored and solved; conjectures to be made and examined; and complex ideas about the world to be communicated. Developing a problem-solving focus to deal with mathematics requires more than a range of problem-solving strategies.
Analysing the pattern of incorrect answers to Assessment Resource Bank items is providing valuable diagnostic information. This can enable teachers to identify roadblocks to student understanding and learning, and develop appropriate strategies to remedy them. ARB data also enables a broad range of curriculum outcomes to be assessed.
The integrated learning system SuccessMaker is in many New Zealand schools. However, the author’s review of these systems concludes that few have proven effective in producing substantial gains in reading and language; gains in certain areas of maths do not appear to be transferred to other tasks; and system-generated progress data requires validation. Autonomous learning is not viable for many students, and curriculum integration is also an issue.
In-class modelling of teaching practices in mathematics enables the facilitator to take an active role when working with teachers. By situating aspects of this professional development in classrooms, teachers are able to see how they can incorporate the new practices into their existing teaching approaches.
Cognitively Guided Instruction provides a basis for understanding why a child is able to solve certain problems and not able to solve others. Within a problem-solving environment, interactive processes, involving students’ explanations and justifications of their thinking, support mathematical sense-making and meaning construction. Decisions about what to teach and when to teach it are based on teachers’ knowledge of their students’ understandings.
The evaluation of the Numeracy Exploratory Study at Year 9 in secondary schools in 2001 showed that a programme for assessing, teaching, and reassessing numeracy was both necessary and effective for this older age group. Students had unexpected difficulties with multiplicative concepts in particular. After a carefully graded assessment, related to specific teaching suggestions for meeting students’ needs, teachers took different steps to address these needs.
Research into children’s understanding of number over the last decade suggests that there are identifiable progressions in how children develop number concepts. The Early Numeracy Project included a diagnostic tool designed to give teachers quality information about the mathematical knowledge and strategies of their students. This article discusses the results.