Mathematics – Relationships with other domains

Introduction

The advice for this section focuses on the relationships between the domains to provide students with multi domain learning opportunities that will help support their deeper understanding of the essential knowledge and skills.

The Arts

The Arts and Mathematics involve student understanding of relationships between time and space, rhythm and line through the experience of these abstract concepts in various arts forms and mathematical ideas. Mathematics provides notions of scale, shape, pattern, proportion and orientation to the visual arts. In the Performing Arts, Mathematics has links with aspects ranging from the frequency of musical notes through to the use of Fibonacci and other sequences in musical compositions. Mathematically related aesthetic considerations, such as the golden ratio, are used across visual, performing and multi-modal arts forms.

Construction in the Arts requires the use and understanding of measurement in the manipulation of space, time and form. Creating patterns in the Arts involves counting, measurement and design in different ways across the various arts forms. The Arts also support the development of critical numeracy skills, by engaging students in the deconstruction of media texts. This can include a consideration of how statistics can be used to analyse hypotheses.

Civics and Citizenship

The concepts developed in the study of Mathematics are applicable to a range of Civic and Citizenship understandings. Mathematical structure and working play essential roles in key aspects of our society as well as key civics concepts. Particular aspects of Civics and Citizenship require mathematical understanding, including concepts of majority rule, absolute majority, one vote one value, representation based on electorates of equal sizes, and the preferential and proportional voting systems. Mathematical understanding also supports the development of community research and the presentation of findings, for example, the use of data and statistics, and including the analysis and presentation of information in charts and diagrams. The recognition and understanding of this mathematical basis to many social structures and processes is integral to the development of informed and active citizens.

Communication

Mathematical structure and Working mathematically play essential roles in understanding natural and human worlds. In communicating about these worlds, students use a combination of everyday language and mathematical symbols involving numerals, operations, connectives, variables and relations.

Development of the language of Mathematics is crucial to its practical application. Students learn to use the language and concepts of Mathematics both within the discipline itself, and also its applications to modelling and problem solving across the other domains. In this process they employ a range of Communication tools for illustrating relationships and displaying results such as venn diagrams and tree diagrams.

Design, Creativity and Technology

In Design, Creativity and Technology students apply numbers to everyday situations; they explain and use mental and written algorithms for addition, subtraction, multiplication and division. Students carry out arithmetic computations and choose mathematical models and procedures to apply in the process of designing and making products and systems.

When designing, students use drawing tools, accurately drawing two-dimensional and three-dimensional representations. They represent depth in their drawings and describe what can and cannot be seen in simple objects and drawings. They use a variety of forms of representation including oblique, isometric and perspective to visually represent objects and use computer drawing packages and computer aided design/computer-aided manufacturing (CAD/CAM) for two- and three-dimensional representations and analysis of design.

In the process of investigating, designing, making and testing products and systems students measure length, perimeter, area, surface area, angle and time for familiar products. They recognise and use different units of measurement for appropriate contexts and use suitable instruments to measure length, angle, volume and time. They select and use suitable procedures to measure, estimate and calculate for instance length, area, volume and angle. In the process they learn to use formulae as appropriate. Students investigate situations and solve problems set in a wide range of practical contexts, for example, the design and construction for packaging involving the use of nets for three dimensional shapes.

English

The use of logical and analytical thinking in Mathematics, including the use of conjectures and proof, has clear links to the development of structured and coherent argument in speaking and writing. Mathematical structure is strongly related to semantics, syntax and language, and to the use of propositions and quantifiers embedded in principled argument in natural language.

The development of skills for critical analysis of literary, everyday and media texts in English empowers individuals to participate effectively in society. This is complemented by the fundamental role that Mathematics plays in cultural, social and technological advances and in empowering individuals as critical citizens in contemporary society and for the future.

Number, space and measurement, chance and data, are common aspects of people’s experience in everyday personal, study and work situations, and are naturally embedded in activities related to the English dimensions of reading, writing, speaking and listening.

Health and Physical Education

In Health and Physical Education, Mathematics provides tools and procedures which can be used to model situations and solve problems in areas such as:

scoring different sporting events involving time, distance, weight and number as variables
combinatorial problems related to developing competition draws and ladders
calculating percentage improvement in results from data collected through fitness testing or performance in physical activities
collecting, recording, interpreting and presenting health, skill or fitness related data in a range of formats such as graphs and tables
predicting trends in key indicators of health status in Australia.

The Humanities – Economics

The Economics and Mathematics are related through the use of mathematics to model a broad range of economic, political and social phenomena. Examples include the use of statistical modelling and analysis in a census, sampling populations to predict election outcomes, and modelling and forecasting economic indicators such as the Consumer Price Index (CPI) and business confidence.

The application of mathematical skills plays a key role in financial literacy, in particular the use of ratio, proportion and percentage in related calculations such as percentage increase or decrease in price of a commodity or personal income.

The Humanities – Geography

Geography and Mathematics are related through the use of Mathematics to model a broad range of economic, political and social phenomena. Examples include the use of statistical modelling and analysis in a census, sampling populations to predict election outcomes, and modelling and forecasting economic indicators such as the Consumer Price Index (CPI) and business confidence.

Mathematics provides the basis of measurement, scale and spatial representation used in maps and plans. Geography also uses the concepts of direction, length, angle and bearing, gradient and contour and area.

The Humanities – History

The study of History includes the analysis and interpretation of a range of historical information including population charts and diagrams and other statistical information. The concepts and skills developed in Mathematics support student understanding and interpretation of a range of history sources and their presentation as evidence in demonstrating historical understanding.

Information and Communications Technology

In Mathematics, extensive use is made of Information and Communications Technology (ICT), with applications specified at all levels in the standards. From Students make use of increasingly sophisticated calculators to check estimations, perform computations and investigate number, function and algebraic properties. Computer software includes the use of spreadsheets, dynamic geometry packages, statistical and graphing tools and computer algebra systems. Mathematical investigations on the Internet require effective, efficient and discriminatory use of search engines.

Interpersonal Development

In working mathematically students will engage with others to formulate and test conjectures, gather, analyse and interpret data and apply mathematics to solve real life problems. These activities are often carried out in teams that require students to collaborate and cooperate, share and discuss, and these behaviours are central in working towards the standards in Interpersonal Development.

Language Other Than English (LOTE)

Common and central to both domains is consideration in language of semantic (meaning of key concepts, ideas, terms) and syntactic (structural relationships in natural and symbolic language) elements and features.

This involves acquiring knowledge of words, symbols, terms and definitions, understanding and application of concepts, and the use of related technical skills. Students develop thinking processes of analysis and synthesis, involving relationships between simple and complex ideas and expressions.

These developments involve the use of Mathematics in everyday activities such as number systems in counting, buying and selling, measuring, designing and building, and estimating and describing chance events using different written and spoken languages in a range of social and cultural contexts.

Personal Learning

The mathematical processes of inquiry, investigation, problem-solving, modelling and the use of technology give rise to opportunities and challenges for Personal Learning. These mathematical processes provide contexts within which students can acquire self knowledge and dispositions that support learning. Opportunities also occur for students to learn with their peers including seeking and responding appropriately to feedback. Establishing values in which individual differences are respected and appreciated encourages unique and varied approaches to working mathematically. As students see mathematical connections and are able to apply mathematical concepts, skills and processes in posing and solving problems, they become confident in their personal knowledge of Mathematics. They increasingly manage their own learning and growth through the setting of goals and managing resources. The strategies of planning, monitoring, revising, reflecting and if needs be modifying enable students to develop resilience and become adaptive learners. Students will become progressively empowered through knowledge of mathematics and as numerate citizens they will be able to apply this knowledge critically, in societal and political contexts.

Science

The knowledge and skills students engage with in the various dimensions of Mathematics support students in their studies of all aspects of Science. In Science, students use measurement and number concepts, particularly in data collection, estimation of error, analysis and modes of reporting. The Mathematics domain supports students in developing number handling skills. In Science, students observe, describe and measure aspects of the world around them, using more sophisticated and accurate measuring tools and instruments as they progress through their schooling. They collect, record, interpret and display data appropriately, looking for patterns, drawing conclusions and making generalisations. Students justify their choice of instruments and the accuracy of their measurements, commenting on the reliability of the procedures, the measurements used, and the conclusions drawn against the hypothesis being tested. Predictions for further investigations, extrapolations and interpolations may be made from their own experimental results or from reliable second-hand data. The understandings, tools and techniques of Mathematics help students to understand measurement and magnitude; to process and analyse data collected in their own experimental investigations and those of others. Mathematical conventions used in graphing, conversions of units, calculations and manipulation of formulae, the use of spreadsheets to facilitate computations and generation of graphs, the use of scientific calculator functions, the manipulation of very small and very large numbers, direct and indirect variation and the implication of limitations in instrumental measurement are essential in conducting and reporting on scientific investigations. Mathematical modelling is used extensively in the natural sciences, physics and in bioinformatics, and by computer scientists.

Thinking Processes

The study of Mathematics exemplifies important thinking processes within its own discipline and also provides a context within which these and other thinking processes can be developed and refined. 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. Computation and proof are essential and complementary aspects of Mathematics that enable students to develop thinking skills directed toward explaining, understanding and using mathematical concepts, structures and objects.

Thinking strategies and tools are used extensively in Mathematics. As students progress in their learning they move from using concrete thinking skills to applying higher order processes to their learning. Students are encouraged to take managed risks in developing possible alternate approaches to problems and tasks. Curiosity has an important role to play in stimulating mathematical inquiry, while reflection and metacognition are important components of the problem solving process in which new and often creative approaches are required to find solutions.