Reservoir West Primary School

MATHEMATICS

RESPONSIBILITY: Mrs Lorraine Wollmer

This domain is taught by classroom teachers assisted by support teachers

• Near-ability groupings across year levels
• Support teachers and intervention programs
• Extension programs

Mathematics is a human endeavour that has developed by practice and theory from the dawn of civilisation to the present day. Many societies and cultures have contributed to the growth of mathematics, often in times of scientific, technological, artistic and philosophical change and development. Complementary to this broad perspective of mathematics are the various mathematical practices that take place day to day in communities around the world.

Mathematics can be described in terms of its objects, what they are and how they came to be; its established body of knowledge and why this is held to be true; its’ effective application in science, technology and other domains; and the practice and activities of mathematicians past and present. Aims for essential learning in school mathematics are for students to:

• demonstrate useful mathematical and numeracy skills for successful general employment and functioning in society
• solve practical problems with mathematics, especially industry and work-based problems
• develop specialist knowledge in mathematics that provides for further study in the discipline
• see mathematical connections and be able to apply mathematical concepts, skills and processes in posing and solving mathematical problems
• be confident in one's personal knowledge of mathematics, to feel able both to apply it, and to acquire new knowledge and skills when needed
• be empowered through knowledge of mathematics as a numerate citizen, able to apply this knowledge critically in societal and political contexts
• develop understanding of the role of mathematics in life, society and work; the role of mathematics in history; and mathematics as a discipline – its big ideas, history, aesthetics and philosophy.

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Mathematical reasoning and thinking underpins all aspects of school mathematics, including problem posing, problem solving, investigation and modelling. It encompasses the development of algorithms for computation, formulation of problems, making and testing conjectures, and the development of abstractions for further investigation.

The Mathematics domain is organised into six sections, one for each level of achievement from Level 1 to Level 6. Each level includes a learning focus statement and a set of standards organised by dimension. A glossary is included which provides definitions of or additional information about underlined terms.

In Mathematics, standards for assessing and reporting on student achievement apply from Level 1. Standards for Structure are introduced from Level 3.

Standards in the Mathematics domain are organised in five dimensions:

• number
• space
• measurement, chance and data
• working mathematically
• structure.

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Number

The Number dimension focuses on developing students’ understanding of counting, magnitude and order. The natural (counting) numbers with zero extend to positive and negative signed whole numbers and through part-whole relations and proportions of whole numbers to the rational numbers.

Principal operations for computation with number include various algorithms for addition (aggregation), subtraction (disaggregation) and the related operations of multiplication division and exponentiation carried out mentally, by hand using written algorithms, and using calculators, spreadsheets or other numeric processors for calculation.

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Space

The Space dimension focuses on developing students’ understanding of shape and location. These are connected through forms of representation of two- and three-dimensional objects and the ways in which the shapes of these objects and their ideal representations can be moved or combined through transformations. Students learn about key spatial concepts including continuity, edge, surface, region, boundary, connectedness, symmetry, invariance, congruence and similarity.

Principal operations for computation with space include identification and representation, construction and transformation by hand using drawing instruments, and also by using dynamic geometry technology.

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Measurement, Chance and Data

The Measurement, chance and data dimension focuses on developing students’ understanding of unit, measure and error, chance and likelihood and inference. Measure is based on the notion of unit (informal, formal and standard) and relates number and natural language to measuring characteristics or attributes of objects and/or events. Various technologies are used to measure, and all measurement involves error.

Students learn important common measures relating to money, length, mass, time and temperature, and probability – the measure of the chance or likelihood of an event. Other measures include area, volume and capacity, weight, angle and derived rates such as density, concentration and speed.

Principal operations for computation with measurement include the use of formulas for evaluating measures, the use of technology such as data loggers for direct and indirect measurement and related technologies for the subsequent analysis of data, and estimation of measures using comparison with prior knowledge and experience, and spatial and numerical manipulations.

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Structure

The Structure dimension focuses on developing students’ understanding of set, logic, function and algebra. It is fundamental to the concise and precise nature of mathematics and the generality of its results. Key elements of mathematical structure found in each of the dimensions of Mathematics are membership, operation, closure, identity, inverse and the commutative, associative and distributive properties as well as other notions such as recursion and periodic behaviour.

While each of these can be considered in its own right, it is in their natural combination as applied to elements of number, space, function, algebra and logic with their characteristic operations that they give rise to the mathematical systems and structures that are embodied in each of these dimensions.

Principal operations for computation with structure include mental, by hand and technology-assisted calculation and symbolic manipulation by calculators, spreadsheets or computer algebra systems, with sets, logic, functions and algebra.

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Working Mathematically

Working mathematically focuses on developing students’ sense of mathematical inquiry: problem posing and problem solving, modelling and investigation. It involves students in the application of principled reasoning in mathematics, in natural and symbolic language, through the mathematical processes of conjecture, formulation, solution and communication; and also engages them in the aesthetic aspects of mathematics.

In this dimension the nature, purpose and scope of individual work is connected to that of the broader mathematical community, and the historical heritage of mathematics through the discourse of working mathematically. Mental, by hand and technology-assisted methods provide complementary approaches to working mathematically.

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Relationships between the Dimensions

Number is related to the other dimensions through the aspects of counting, magnitude and order. It has logical and natural connections with Measurement, chance and data, and Space. Number systems provide the basis for the development of algebraic relationships in Structure and the contexts and explorations used in Working mathematically.

Space is related to the Number and Measurement, chance and data dimensions through the aspects of shape and location. The properties of patterns, transformations, and symmetry provide links to Structure and Working mathematically.

Measurement, chance and data is related to the Number and Space dimensions through the aspects of units, error, approximation, likelihood, angle, and the properties of two- and three-dimensional shapes. The application of measurement formulas and functions provide a link to Structure. A varied collection of practical contexts for generating and testing conjectures provides links to Working mathematically.

Structure is related to the Number, Space and Measurement, chance and data dimensions through the use of algorithms, patterns and functions. It is linked to Working mathematically through the key elements of mathematical language, concepts and relationships used in modelling and investigations.

Working mathematically is related to the Number, Space and Measurement, chance and data dimensions through the exploration of algorithms, patterns and functions, shapes and dimensions. It provides the processes for the development of inferences and deductions and for the exploration and proof of conjectures related to the Structure dimension.

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VICTORIAN ESSENTIAL LEARNING STANDARDS

This table outlines where a student is expected to be at a particular time in his/her educational journey. Most students will achieve the expected standard. Some will achieve to a higher standard. Some may not reach the expected standard.

Click to view a description of the behaviours that a student should display at each progression point in Mathematics at Levels 1, 2, 3 and 4.

A student’s achievement is reported to parents at June and December. Click for an explanation of the Report Card.

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