Reporting on mathematics
In the NSW Mathematics K–10 Syllabus, the Working mathematically outcome describes the thinking and doing of mathematics. In doing so, the outcome indicates the breadth of mathematical actions that teachers need to emphasise.
Students learn to work mathematically by using these processes in an interconnected way. The coordinated development of these processes results in students becoming mathematically proficient.
The Working mathematically processes are:
- communicating
- understanding and fluency
- reasoning
- problem solving.
To highlight how these processes are interrelated, there is one overarching Working mathematically outcome in Mathematics K–10.
MAO-WM-01 – develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly.
For further information on Working mathematically see ‘Elaborating on Working mathematically K-10 (NESA Teaching and Learning Support Documents)'
Considerations for reporting on Working mathematically
Working mathematically is an outcome within the Mathematics K–10 Syllabus. For teaching, assessing and reporting purposes, it should be embedded within the focus areas. This provides the mathematical concepts and context for the application of the Working mathematically processes.
The Working mathematically outcome does not have specific content groups or content points as it is not a focus area. As such, the Working mathematically outcome should not be reported on in isolation.
All outcomes within the syllabus must be assessed but there is no requirement that they will all be reported on in the biannual reports. The number of outcomes to be reported in each subject/course is not mandated. This is a school-based decision.
Suggested examples
These samples represent one way of designing reporting templates for biannual reports for parents and carers. These are examples for reporting on mathematics for K-2. Schools will need to determine the outcomes and content that they will report on each semester.
The Mathematics K-10 Syllabus affords a refreshed approach to mathematics teaching and therefore reporting. Sample reports include value-added features that support this approach.
These examples illustrate the Working mathematically outcome within the content and within the personalised comment for the student. The Working mathematically processes are highlighted for teachers to clearly identify where the Working mathematically processes are embedded. It is not recommended that these be highlighted in the parent facing report templates.
Schools are encouraged to choose an approach that best suits their school context and community needs.
As new information is released from NESA and if the department’s Curriculum planning and programming, assessing and reporting to parents K-12 policy (CPPAR) is updated, these sample reports will be reviewed.
Curriculum area |
Working towards expected level |
At expected level |
Above expected level |
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Number and AlgebraRepresenting numbers as quantities to at least 20 using objects (such as fingers), number words and numerals |
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Using concrete materials or fingers to model and solve addition and subtraction questions |
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Copy, continue and create repeating patterns using shapes, objects, images or pictures |
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Measurement and SpaceUse comparative language to describe length, such as ‘longer than’, ‘shorter than’, ‘the same as’ |
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Sort shapes according to features such as size and shape |
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Statistics and probabilityInterpret information presented in a data display to answer questions |
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Overall achievement |
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Raphael is an enthusiastic learner in mathematics and has shown growth in all focus areas this semester. He has demonstrated Working mathematically when he identifies and extends patterns, as well as creating and explaining his own patterns using materials.
Future directions for Raphael include:
- identifying the number before and the number after a given number
- grouping and sharing materials by distributing objects one by one or using another method
- sorting three-dimensional objects and identify the attribute used to sort them
Note: The text in bold demonstrates an example of how the Working mathematically processes are embedded within the mathematics content.
Curriculum area |
Working towards expected level |
At expected level |
Above expected level |
|---|---|---|---|
Number and AlgebraCounts forwards to at least 30 |
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Reads numerals to at least 20, including zero |
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Separates and take away objects to model subtraction |
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Measurement and SpaceGives and follows simple direction |
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Compares lengths by placing objects side by side and aligning the ends |
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Describes shapes, including circles, squares, triangles and rectangles |
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Statistics and probabilityAsks questions to collect information from their peers |
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Arranges objects according to a characteristic to form a data display |
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Overall achievement |
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Note: The text in bold demonstrates an example of how the Working mathematically processes are embedded within the mathematics content.
Curriculum area |
A | B | C | D | E |
|---|---|---|---|---|---|
Number and AlgebraSequences numbers and arranges them on a line by considering the order and size of those numbers |
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Creates, recalls and recognises combinations of two numbers that add up to numbers less than 10 |
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Uses concrete materials to model a half of a collection and shows the relation between the half and the whole |
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Measurement and SpaceDescribes the path from one location to another on drawings and diagrams |
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Recognises and explains the relationship between the size of a unit and the number of units needed |
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Explores, manipulates and describes features of polygons |
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Statistics and probabilityInterprets a data display and identifies the biggest or smallest values |
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Compares familiar activities and events and describes them as being more or less likely to happen |
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Overall achievement |
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Angela enjoys mathematics and with support, has shown improvement this semester. She has demonstrated Working mathematically when she explains her strategies for solving addition and subtraction problems and uses concrete materials to show her understanding.
Future directions for Angela include:
- identifying the number before and after a given three-digit number
- creating, recording and recognising combinations of two numbers that add to numbers from 11 up to and including 20
- selecting and naming a shape from a description of its features.
Note: The text in bold demonstrates an example of how the Working mathematically processes are embedded within the mathematics content.
Curriculum area |
A | B | C | D | E |
|---|---|---|---|---|---|
Number and AlgebraEstimates the number of objects in a collection and checks by counting in tens |
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Solves addition and subtraction problems involving one- and two-digit numbers |
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Describes how the missing number in a number pattern was determined |
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Measurement and SpaceMeasures the lengths of objects using uniform informal units |
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Recognises and classifies shapes using obvious features |
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Tells time to the half-hour |
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Statistics and probabilityIdentifies and describes activities that involve chance |
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Asks questions and gathers data |
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Creates data displays and interprets them |
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Overall achievement |
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Jose has a positive attitude towards mathematics and has made progress in all focus areas this semester. He can explain how he uses counting on and counting back strategies to add and subtract one- and two-digit numbers. Jose uses materials to model sharing into equal groups. A future goal is to learn to skip count by 2s, 5s and 10s to find the total number in the groups. He shows confidence creating and explaining repeating patterns. An area of future learning is telling the time to the half-hour. Jose is developing his reasoning skills and is beginning to use mathematical vocabulary to communicate his ideas in measurement activities.
Note: The text in bold demonstrates an example of how the Working mathematically processes are embedded within the mathematics content.
Curriculum area |
Limited |
Basic |
Sound |
High |
Outstanding |
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Number and AlgebraContinues and creates number patterns |
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Recognises, recalls and records combinations of two numbers that add up form 10 |
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Models and uses equal groups of objects to represent multiplication |
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Measurement and SpaceFollows directions to familiar locations |
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Measures areas using uniform informal units |
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Statistics and probabilityCreates displays of data and interpret them |
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Overall achievement |
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James applied himself consistently in mathematics this semester and has made growth in all focus areas. He can fluently skip count by 2s, 5s and 10s and describes the missing number in a pattern. James has an excellent understanding of numbers that add up to 10 and applies this understanding in problem solving tasks.
He is confident in describing and communicating directions between one location and another and reflects this understanding in drawings. James can measure area by selecting and using appropriate units. Future directions for James include adding and subtracting two-digit numbers and using place value knowledge to partition and rename three-digit numbers.
Note: The text in bold demonstrates an example of how the Working mathematically processes are embedded within the mathematics content.
How to assess Working mathematically
The Working mathematically processes should be embedded within the concepts being taught, assessed and reported on. Embedding Working mathematically ensures students are able to fluently understand concepts and make connections to other focus areas. The mathematics focus area outcomes and content provide the knowledge and skills for students to 'reason about', and contexts for problem solving. The overarching Working mathematically outcome is taught and assessed in conjunction with the mathematics content outcomes.
The sophistication of Working mathematically processes develops through each stage of learning and can be observed in relation to the increase in complexity of the mathematics outcomes and content. A student's level of competence in Working mathematically can be monitored over time, for example, within Additive Relations by the choice of strategy appropriate to the task, and the use of efficient strategy for the stage of learning the student is working at’ (Mathematics K-10 Syllabus, 2022).