General Content Outline Goals and Guidelines After completing and understanding Year 3 well, students should then move onto Year 4. In this stage, students now begin to think abstractly rather than relying on visual perception or concrete experiences, although these aids will enhance the learning of new mathematical concepts. With the increased ability to think abstractly there is an improved capacity to think hypothetically and reason logically. Students value mathematics the more the learning experiences provided recognise their interests.The development of an ownership of their own problems and the solutions will occur if the problems attract and involve the students.
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The teaching of processes is necessary to develop independent problem solvers.Therefore, for students to acquire concepts, skills and factual knowledge, opportunities need to be provided in settings that foster positive attitudes to mathematics.The Curriculum Programs Branch, Ministry of Education, 1989, publication Learning Mathematics: Pre-Primary to Stage Seven Mathematics Syllabus Handbook (page 4) lists the following processes as part of the learning of mathematics. These processes are not tied to one particular aspect of content but are used across a range of areas:
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Students should be encouraged to persist with problems and ask questions. They are also more able to think of concepts as mathematical objects in their own right. With teaching emphasising the investigation of mathematical ideas and relationships, students should also be learning to make speculations and test them by thinking hypothetically and reasoning logically.
1. comprehension of mathematical information given in oral and/or written forms;
© R. I . C.Publ i cat i ons •f orr evi ew pur posesonl y• 2. selection of appropriate strategies; 3. purposeful use of materials;
4. selection of appropriate operations to solve problems; 5. reflection in actions to formulate ideas;
6. expression of mathematical ideas in words, pictures and symbols; 7. construction of lists, tables and graphs;
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9. identification of patterns and relationships; 10. classification, ordering and comparing; 11. analysis and interpretation of information; 12. formulation of hypotheses; and
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8. estimation of number and measurement activities;
o c . che e r o t r s super 13. justification of conclusions and inferences.
Understanding, skills and knowledge relationships make up the content that builds up conceptual structures. In the New Wave Maths series the following areas of mathematical content are included:
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1. Working Mathematically – develops mathematical thinking processes through conceptualising, investigating, applying and verifying and reasoning mathematically.
2. Space – describes and analyses the features of objects, environments and movements through location, shape, transformations and geometric reasoning.
3. Measurement – using direct and indirect measurement and estimation skills in length, area, mass, volume and capacity and time.
4. Chance and Data – using knowledge of chance and data processes to collect and organise data, summarise and represent data, interpret data and understand chance.
New Wave Maths Book D – Teachers Guide • 5 •