Level 9 to 10

Financial Planning

Numeracy Focus: Developing number sense; Using proportional reasoning

Learning area: The Humanities: Economics and Business, Victorian Curriculum: Mathematics

Setting numeracy learning goals must be based on students’ needs and challenge their thinking to support learning. Students know what is expected of them and how to achieve the learning goals. Expectations are high, but achievable. Assessment provides evidence of prior learning and supplies the teacher with information to set appropriate future goals. Students use learning goals to monitor their own progress.

In this lesson the teacher demonstrates setting goals for the students by providing clear learning intentions with numeracy goals, numeracy specific language and a realistic context. The purpose for learning is made explicit by linking a specific numeracy-focused activity to the learning goals. The lesson focuses on the numeracy skills needed for financial literacy in addition to linking to exponential functions thus providing clear links between mathematics and economics and business.

The students are observed using the learning intentions as they self-monitor their progress in the classroom and understand how the task relates to both the learning goal and the context.

MoneySmart: Financial literacy

Numeracy Focus: Developing number sense; Using proportional reasoning

Learning area: The Humanities: Economics and Business, Victorian Curriculum: Mathematics

The MoneySmart First car — wheels and deals lesson plan offers examples of teacher planning for learning underpinned by explicitly identified numeracy learning goals. Clear instructions, scaffolding strategies, questioning and assessment suggestions are described. The resource develops proportional reasoning and number sense by encouraging students to consider the range of costs and helping them to save money by making informed and responsible choices when buying a car.

In structuring a numeracy lesson or unit, teachers consider the sequence and pace of each lesson. Structured lessons reinforce routines and scaffold student learning with an effectively planned sequence of activities. Effective inclusion of numeracy requires teachers to consider explicit numeracy learning goals for students when structuring lessons.

Wootube

Numeracy focus: All

Learning Area: Victorian Curriculum: Mathematics

Explicit numeracy teaching involves teachers modelling and demonstrating mathematical concepts using materials, representations, problems, and open-ended questions to support students’ independent exploration of mathematical concepts that underpin numeracy. Explicit teaching is not prescriptive teaching of processes and algorithms.

Eddie Woo, Australia’s 2018 Local Hero, describes his explicit teaching lessons and explains the reasoning behind why he chose to record his mathematics classroom. He discusses the value in explicit teaching, highlighting that students viewing the video receive the benefit of teachable moments and feel involved in classroom discussion. These teachable moments are considered opportunity for active and further learning of numeracy. You will notice that he does not restrict classroom discussion, rather, student input is actively encouraged. He references the approach of explicit teaching in short bursts. This approach is current with the shortened form of bit size media that today’s learners are exposed.

Eddie Woo’s classroom practice illustrates that the learning intentions are shared with the students at the beginning of the lesson and continue to be unpacked as the lesson progresses. Woo models the application of numeracy knowledge and skill as he introduces new content and connects with prior numeracy knowledge. He provides opportunity for student input while using a teacher-led model to incorporate the success criteria. Woo checks for understanding through feedback loops at the end of the lesson, ties it together, and provides opportunity for further questioning.

Design Your Own Database

Numeracy Focus: Developing number sense; Using proportional reasoning; Exploring chance and data 

Learning area: Technologies: Digital technologies, The Humanities: History, Victorian Curriculum: Mathematics

Worked examples demonstrate the steps required to complete a task, enable teachers to explicitly model effective problem-solving strategies, and to scaffold student learning to reduce students’ cognitive load. Teachers use the worked examples in the Everything you wanted to know resource to clarify the learning objectives, demonstrate the creation and use of databases, the monitor student learning, and support students to move towards independent practice.

In this resource the teacher demonstrates the steps required to perform an effective search, ensuring students concentrate on the data collection and analysis and the acquisition of appropriate numeracy skills. Students maintain a numeracy focus throughout the digital technology unit as they present statistical information and use databases to gather information from secondary sources. The Learning Demo (see link in left margin) component of this activity illustrates how the worked example strategy can be utilised whenever a process or series of steps is required. In this case the process required was an effective search, enabling students to apply numeracy skills to data sets.

Complex Instruction: Sharing Responsibility for Learning

Numeracy Focus: All

Learning Area: Victorian Curriculum: Mathematics 

Professor Jo Boaler discusses complex instruction as one method of embedding collaboration in a numeracy environment. Boaler’s presentation details student roles and the significance of planning a collaborative learning environment. She describes how such approaches can be especially helpful in mathematics and numeracy, for example in logical reasoning; explaining and justifying answers; and posing questions. Students suggest that working in groups has helped them develop multiple approaches to solving problems.

Collaborative learning occurs when students work in small groups to cooperatively solve problems. When students are introduced to the concept of collaborative learning teachers use strategies to establish ground rules to promote an atmosphere of cooperation and collaboration. Assigning set roles within groups helps to establish good working relationships and allows students to take responsibility for different areas of a task.   

A geographical focus on Choose your own statistics

Numeracy Focus: Exploring chance and data; Using proportional reasoning

Learning area:  The Humanities: Geography, Victorian Curriculum: Mathematics, Health and Physical Education

Multiple exposures of numeracy are incorporated through practising new knowledge spaced over time or alternatively through the use of different activities to vary the interaction. Effective teachers identify a numeracy focus which students can encounter and engage with over a variety of subjects, thus encouraging cross-curricula multiple exposures.

In this example geography, mathematics, and health and physical education are incorporated to develop students’ numeracy understanding as they interpret and represent data comparing global population statistics and life expectancy. Students consolidate their learning through engaging with data and re-engaging with new content over a period of time. The unit uses a variety of learning and assessment tasks that provide timely feedback and vary students’ interactions with numeracy knowledge and skills, and support transfer of learning. The Numeracy Learning Progressions are evident as students becomes increasingly able to recognise and use visual and numerical displays to describe data associated with statistical investigations, and to critically evaluate investigations by others.

Posing Open Questions for Science Inquiry

Numeracy Focus: All

Learning area: Victorian Curriculum: Mathematics, Science

Questioning is a powerful tool to engage students and stimulate interest and curiosity in fostering numeracy. Effective open-ended questioning enhances and extends students’ numeracy development though probing students’ numeracy thinking, invoking curiosity, stimulating interest and reasoning. Questions to provoke inquiry should link to students’ lives and interests. Students need to feel free to ask questions to clarify their understanding and respectfully challenge others’ ideas

This resource models teacher questioning to facilitate students to pose questions for themselves in choosing and planning a science inquiry. Numeracy is at the forefront of science inquiry, as students measure, perform calculations, apply rates and ratio and records statistics throughout their projects. The teacher in the video-clip poses open questions, such as, “How does this happen?” or “Why does this happen?” to provide reasoning opportunities for students to analyse, justify, generalise, and express alternative points of view. In this video, students choose an science inquiry question that appeals to them. They conduct experiments, evaluate their findings, and communicate their results and analysis.

Numeracy forms an essential part of this science inquiry as students use mathematics to investigate and support their findings. Examples shown in the video include graphical and other forms of data display, measurement  calculations for volume using graduated measuring cylinders and proportional reasoning and measurement for titration calculations.

Interview with MAV Education consultants: Unpacking Feedback HITS

Numeracy Focus: Developing number sense; Exploring patterns and relationships

Learning area: Victorian Curriculum: Mathematics

Feedback to students should be precise, timely, specific, accurate and actionable. If feedback is provided in the form of a marked assessment the numeracy skill should be identifiable, suggestions for areas of improvement specific and accessible by the individual, and presented in a timely manner. Feedback should make students feel supported and confident about learning new numeracy skills. Feedback is most effective when individuals can consolidate their learning through opportunities that engage and re-engage them with new content over a period of time.

The example shared in this audio clip highlights multiple aspects of providing numeracy feedback within a mathematical context. Effective feedback starts with setting clear goals at the beginning of a unit or assessment, which teachers can use as a focus when providing feedback on tasks. They suggest a rubric containing criteria specific to numeracy should be provided early on. The rubric supports both teacher and student self-assessment during a task and as final feedback, which clearly demonstrates to students where they met numeracy specific criteria and details areas of improvement. In-task feedback should be continual, both informal (e.g., questioning or verbal) and formal (e.g., written response) in nature.

Low stakes self-assessment quizzes provide instant feedback to students and prompt self-reflection. The example highlights how feedback about students’ numeracy gathered within a mathematical context might be shared across other curriculum areas.

Numeracy data provides feedback on student learning and numeracy outcomes. Teachers utilise external sources to collect data or internal testing platforms to gather student data using pre and post-testing to provide student or class progression feedback.

These data are used to inform teachers of areas of need within a class, and provide insights into how best to structure teaching and learning to enable all students to progress in the area of numeracy.

Visible Thinking Routines

Numeracy Focus: Using proportional reasoning; Exploring chance and data

Learning area:  Victorian Curriculum: Mathematics, Science

Metacognitive strategies teach children to think about their thinking. Activities to promote metacognitive strategies in numeracy include planning how to approach a learning task; evaluating progress; monitoring comprehension, and reflection. Learning visual thinking routines skills equips students with powerful reflective questions for approaching any numeracy challenge.

The resource, Visible thinking routines illustrates how educators can encourage students to focus on the process and not simply the solution. These metacognitive strategies can be used extensively within the numeracy context to encourage students to demonstrate their thinking and collaborate with others to share ideas. Explicitly presenting multiple strategies provides students with a repertoire of learning approaches which they can select from in different learning situations.

This secondary school science class begins a unit with ‘Question Starts’ to pose some big questions. The mathematical language used in the questions helps maintain a numeracy focus, in this case related to using proportional reasoning and exploring chance and data. The teacher can support the numeracy focus by modelling appropriate mathematical language.

The ‘Question starts’ routine featured in the resource encourages students to pose their own questions to promote reasoning and to help develop authentic solutions. Reasoning is a key mathematical proficiency. Students are shown the benefit of questioning their learning and provides opportunities to focus on numeracy throughout the unit. This approach helps student maintain control over, and take responsibility for, their learning. The self-selected nature of the questions and the accessible and intriguing content helps to motivate students.

Mechanical linkages

Numeracy Focus: Using proportional reasoning; Understanding and using geometric properties and spatial reasoning

Learning area:  Victorian Curriculum: Mathematics, Digital Technologies, Science

Differentiated teaching in a numeracy environment involves a provision of open-ended, challenging tasks with high expectations of all students. Tasks are adjusted continually by teachers to ensure all students’ needs are met. These adjustments are based on ongoing assessment to provide realistic, challenging goals for each student. When adjustments are consistently applied students build meaningful learning. Assessment of progress to fulfil each student’s learning goals is based on comparison with previous achievement rather than a comparison with other students.

The reSolve: Maths by Inquiry project provides numeracy focused classroom resources that are accessible to all students. This form of differentiated teaching provides opportunity for all students to experience challenge, success and improvement in their numeracy. Notice that each task caters for all learners, allowing individuals or groups to work at different levels, supporting a range of abilities and methods of thinking and learning.

Mechanical Linkages includes three lessons where students see and manipulate physical models and apply numeracy skills to solve problems. They construct physical models out of plastic strips or light card and have the opportunity to use a prepared dynamic geometry computer simulation.

Students use language associated with geometry as they visualise, describe and analyse shapes and angles in their environment. The lesson has cross-curricular links to science and digital technologies as it utilises machines, hands-on manipulatives, and computing components.