Fractions
Fractions are more difficult to understand than whole numbers because they are relational numbers. A sound understanding of fractions is essential to progress in mathematics learning.
Geometric reasoning
Geometry is the branch of mathematics which involves the exploration of location, and the shape, size and properties of objects.
Mental computation
The importance of mental computation has been identified by a considerable body of research.It has been found that nearly 80% of all calculations by adults are carried out mentally, and that frequently estimation is sufficient.Approaches to calculation in school should reflect the demands of everyday life, as explained in the article on the AAMT website.Research also indicates that an emphasis on mental computation can improve students' development of number, while an early introduction to formal written methods can harm it.The includes mental strategies as well as written and technology-based methods.Mental strategies provide an important window into students' understanding of number.
Reasoning
Mathematics is reasoning.It was created by reasoning and depends on reasoning for its further development as well as its usefulness.Reasoning is one of the four proficiencies in the national curriculum, which describes it as a capacity for logical thought and actions. Reasoning develops throughout the curriculum and there are identifiable milestones. You can download a summary of .Mathematics content knowledge is important, but it should be taught and learned in a way that emphasises the process skills, or proficiencies. Then students will not only gain content knowledge but will also learn to think as young mathematicians. They will be well prepared for future learning as well as very competent in using mathematical processes in everyday life.Reasoning is not problem solving.You can download which is a summary drawn from the Australian Curriculum: Mathematics showing how reasoning is different from problem solving.
Statistics
Students today are constantly bombarded with information from various media, much of it based on data. Statistical literacy skills are critical if students are to make socially responsible decisions.These skills are developed through the Statistics and Probability content strand of the Australian Curriculum: Mathematics, in conjunction with the proficiency strands – Understanding, Fluency, Problem solving and Reasoning. Numeracy, a cross-curriculum general capability, links statistical literacy to most other disciplines in the curriculum.Statistics involves investigating meaningful, context-based questions using data. An investigation usually follows a pathway – the question, data collection, data representation, summarising of the data and ultimately a conclusion.Problem-solving experiences that exemplify these investigative stages help build understanding of the fundamental big ideas that underpin statistics. Students should develop fluency with these skills, as well as reasoning for decision-making. Students can use statistical literacy skills in other school subjects and in aspects of their lives outside school.