Assessment

The students’ level of achievement in Units 1 and 2 is a matter for school decision. Assessments of levels of achievement for these units will not be reported to the VCAA. Schools may choose to report levels of achievement using grades, descriptive statements or other indicators.

In each VCE study at Units 1 and 2, teachers determine the assessment tasks to be used for each outcome in accordance with the study design.

Teachers should select a variety of assessment tasks for their program to reflect the content and key knowledge and key skills being assessed and to provide for different learning styles. Tasks do not have to be lengthy to make a decision about student demonstration of achievement of an outcome.

A number of options are provided to encourage use of a range of assessment activities. Teachers can exercise flexibility when devising assessment tasks at this level, within the parameters of the study design.

Note that more than one assessment task can be used to assess satisfactory completion of each outcome in the units, and that an assessment task can typically be used to assess more than one outcome.

There is no requirement to teach the areas of study in the order in which they appear in the units in the study design. In mathematics an activity or task will often draw on content from one or more areas of study in natural combination, and involve key knowledge and skills form all three outcomes for the study.

In VCE Foundation Units 3 and 4, the student’s level of achievement will be determined by School-assessed Coursework and two end-of-year examinations. The VCAA will report the student’s level of performance as a grade from A+ to E or UG (ungraded) for each of three Graded Assessment components: Unit 3 School-assessed Coursework, Unit 4 School-assessed Coursework and the end-of-year examination.

In Units 3 and 4, school-based assessment provides the VCAA with two judgments:

S (satisfactory) or N (not satisfactory) for each outcome and for the unit; and levels of achievement determined through the specified assessment tasks in relation to all three outcomes for the study. School-assessed Coursework provides teachers with the opportunity to:

1. use the designated tasks in the study design
2. develop and administer their own assessment program for their students
3. monitor the progress and work of their students
4. provide important feedback to the student
5. gather information about the teaching program.

Teachers should design an assessment task that is representative of the content from the areas of study as applicable, addresses the outcomes and the key knowledge and key skills in accordance with the weightings provided in the study design, and allows students the opportunity to demonstrate the highest level of performance. It is important that students know what is expected of them in an assessment task. This means providing students with advice about relevant content from the areas of study, and the key knowledge and key skills to be assessed in relation to the outcomes. Students should know in advance how and when they are going to be assessed and the conditions under which they will be assessed.

Assessment tasks should be part of the teaching and learning program. For each assessment task students should be provided with the:

• type of assessment task as listed in the study design and approximate date for completion
• time allowed for the task
• nature of the assessment used to measure the level of student achievement
• nature of any materials they can utilise when completing the task
• information about the relationship between the task and learning activities, as appropriate.

Following an assessment task:

• teachers can use the performance of their students to evaluate the teaching and learning program
• a topic may need to be carefully revised prior to the end of the unit to ensure students fully understand content from the areas of study and key knowledge and key skills for the outcomes
• feedback provides students with important advice about which aspect or aspects of the key knowledge they need to learn and in which key skills they need more practice.

Authentication

• The teacher must consider the authentication strategies relevant for each assessment task. Information regarding VCAA authentication rules can be found in the VCE and VCAL Administrative Handbook section: Scored assessment: School-based Assessment.

Identifying the context for the investigation

Consider real-life contexts that students can relate to or have applicability to the students’ own lives and / or communities. The contexts may also be vocational, such as trade or industry based, and relate to the students’ interests, VET studies or school-based apprenticeships.

Once the context has been selected, teachers should ensure that the context has scope to cover the mathematical content from two or more areas of study.

Identification of the areas of study: key knowledge and key skills selected for the investigation should be addressed in the planning phase by the teacher.

The expectation when designing tasks for investigations is that the assessment will be of 4–6 hours’ duration over a period of 1–2 weeks.

For example, the teacher may choose to conduct a statistical investigation into Australia's take up of home solar energy systems. The broad theme is addressing home energy usage in Australia, with a sub-theme of solar energy. Such a statistical investigation will readily cover Area of Study 1: Algebra, number and structure, and Area of Study 3: Data analysis, probability and statistics. The teacher should revisit the key knowledge and skills with the students so that they are prepared to use and apply these in their investigation.

Formulate the question or problem to be investigated

The first step in an investigative approach as stipulated in the study design, is to develop the problem through understanding the context and identifying the issues. Teachers may use the problem-solving cycle, brainstorming or conjecturing cycle. In this phase the students should identify what they are going to research and express and plan out the problem using mathematics.

In this example, teachers may help structure and guide students in deciding what they will focus on and writing a set of questions that could be addressed. Different students may choose slightly different sets of questions to investigate. The teacher needs to ensure that the different sets of questions still cover the same set of required areas of study and the three outcomes. 

A useful resource in helping students to develop statistical questions.

In this scenario of solar home usage, a key starting question could include:

• Are Victorian’s installing more solar energy systems in their homes?

Then with more research and discussions about what information might be available to base the research on, and how this question could be answered, students may need to work through a series of further questions (or do a brainstorm or mind map) on more specific questions that they can work through, such as:

• How can we tell if this is true or not?
• What data exists for us to use? How is it categorised? Over what time periods is it available?
• Are there different sorts and types of solar power systems?
• Is cost a factor to be considered?

Then the students can pose a more specific question or set of questions to research, such as:

• What percentage of homes in each local government area (LGA) in Victoria have solar systems installed?
• How has the percentage changed over the last decade?
• Is it possible to predict what it might be in ten years’ time?
• Does it vary across Victoria? How?

Now that the question has been identified, students first should undertake background research identifying sources of data for collection and use. They should undertake to develop a conceptual understanding of rooftop solar and explore the reasons for people choosing to install this energy source.

Students should then decide which variables they need to investigate further. In this instance a student may select the independent variable of percentage of homes, and dependent variable of LGA. They then undertake data collection using secondary sources.

Explore the problem mathematically

Students should test their conjectures or select and use appropriate mathematics to solve the problem or issue using computational thinking where possible. They should demonstrate their proficiency and skills in using the key knowledge and skills as per the area(s) of study. The use of technology should be selected and used to suit the context of the investigation. Where possible the use of technology should mirror the technologies used in real-life so that students are learning and demonstrating technology-based workplace skills.

Students should test their conjectures, examine their results and test the feasibility and accuracy of their mathematical conclusions. Students should then link their mathematical results back to the original context.

Investigations may be open-ended in nature and have a range of results.

In this example, students select the most appropriate forms of data display (column graphs) and the most appropriate measures of central tendency and spread. The statistical analysis must have purpose and relevance to the original question.

Once the students have drawn conclusions from their analysis, they should reflect back on the original question to see if the mathematical results make sense. If the need arises, students should be encouraged to re-adjust or recalculate their results as part of the cycle. Students should be able to justify how their results make sense in relation to the question.

Students may then undertake further calculations linking their results to the broader themes and explore mathematical concepts of probability. In this instance, they might consider the likelihood of power outages due to extreme weather events caused by the changing climate, and then draw links from the maths back to the question.

Communicate the results

Students should be able to explain the results or solution(s) to their investigation using mathematics. The communication must be relevant to the original question(s) and the teacher should expect the results will not be uniform for each student.
The use of statistical language should be demonstrated in their communication of the mathematics and the results. Students should draw inferences and make conclusions.

Teachers should provide opportunities for students to define and explain the limitations and errors or misinterpretations of their study.

Students may wish to present their work in a format that is suitable to the task, for instance in this example students may present their work as a large A2 poster using a free scientific template found online. They might use the clear sub-headings to demonstrate their use of the steps required for the investigation.

Start with identifying the context for the investigation

Teachers should work together with students to identify real-life contexts that students can relate to or find applicable to their own lives and / or communities. The contexts may be vocational, such as trade or industry based, and relate to students’ interests, VET studies, or school-based apprenticeships.

Once the context has been selected, teachers should ensure that the context has scope to cover content from two or more areas of study.

Identification of the areas of study: key knowledge and key skills selected for the investigation should be addressed in the planning phase by the teacher.

A useful guide for the design of the assessment is that it be of 4–6 hours’ duration over a period of 1–2 weeks, providing students with the opportunity for sustained problem-solving.

Generally, young people are shunning car ownership in favour of greener transport options. You might identify that students are thinking about a range of transport options beyond school, from catching public transport to a car subscription to buying a car. Knowing the sorts of financial problems and decisions students are thinking about provides good scope for an investigation drawing on knowledge and skills from Areas of Study 1 and 3. The teacher should revisit the key knowledge and skills with the students so that they are prepared to use these in their investigation.

Formulate the question or problem to be investigated

The first step in an investigative approach as stipulated in the study design, is to develop the problem through understanding the context and identifying the issues. Teachers may use the problem-solving cycle or conjecturing cycle. In this phase the students should express the problem using mathematics.

In this example, teachers may guide students in writing a question to be addressed such as, ‘What is the best transport option for my personal circumstances?’ In this question, ‘best’ might reflect personal values to minimise one’s environmental impact, what is most practical or convenient, and what is cost-effective.

Now that the question has been identified, students first should undertake background research identifying a range of possible options, and the costs, terms and conditions associated with each online. Possible websites to visit include:

Public Transport Victoria
Commercial car subscription services
RACV’s guide to buying a car

Students will need to establish assumptions or guidelines about their transport usage, considering where they travel, how long their journey takes, how frequently they’re moving about, and at what times of day. They should undertake to develop a conceptual understanding of public transport ticket options and pricing, the typical cost structure of a car subscription service, and the upfront and ongoing costs associated with second-hand car ownership.

Explore the problem mathematically

Students should test their conjectures or select and use appropriate mathematics to solve the problem or issue using computational thinking where possible. They should demonstrate their proficiency and skills in using the key knowledge and skills as per the area(s) of study. The use of technology should be selected and used to suit the context of the investigation. Where possible the use of technology should mirror the technologies used in real-life so that students are learning and demonstrating technology-based workplace skills.

Students should test their conjectures, examine their results and test the feasibility and accuracy of their mathematical conclusions. Students should then link their mathematical results back to the original context.

Investigations may be open-ended in nature and have a range of results.

In this example, students might have a general sense or preference for one option over others. Collecting available information and compiling it into a suitable format (such as a comparison table) is preparation for testing this conjecture. It may be necessary to use mathematics to ensure that figures are in a consistent format for easy comparison (i.e. making sure all costs are expressed as monthly).

Once the students have drawn conclusions from their analysis of the mathematics, they should reflect back on the original question to see if the mathematical results make sense. If the need arises, students should be encouraged to re-adjust or recalculate their results as part of the cycle. Students should be able to justify how their results make sense in relation to the question.

Students may then undertake further calculations and mathematical statements as they seek to generalise their results.

Communicate the results

Students should be able to explain the results or solution(s) to their investigation using mathematics. The communication must be relevant to the original question(s) and the teacher should expect the results will not be uniform for each student.

The use of mathematical language should be demonstrated in their communication of the mathematics and the results. Students should draw inferences and make conclusions.

Teachers should provide opportunities for students to define and explain the limitations and errors or misinterpretations of their study.

Students may wish to present their work in a format that is suitable to the task, for instance in this example students may present their work as an infographic or website. Such formats make it easy to identify and argue that public transport is a greener transport option at around one fifth of the cost of maintaining a second-hand car. However, catching public transport adds significantly to travel time, making it a less convenient option.

• Units 3 and 4, Outcome 1
  
• Units 3 and 4, Outcome 2
  
• Units 3 and 4, Outcome 3