PAT Maths

PAT Maths 4th Edition and PAT Maths Adaptive are underpinned by the PAT Maths construct, which allows educators to accurately and efficiently measure students’ abilities in Maths, to diagnose gaps, strengths and weaknesses in student learning, and monitor student progress over time.

The following topics are covered in this article:

• Introduction
• When to assess
• Choosing the right test
• Administering the tests
• Using the results
• About PAT Maths
• Acknowledgements
• Supporting documents
  • Administration instructions
  • Achievement band descriptions
  • Assessment framework
  • Australian norms

Introduction

PAT Maths Adaptive

PAT Maths Adaptive (2021) uses students’ responses to actively determine the content as they progress through the test. Each student sees their own mix of test items as they progress through one of dozens of available testing pathways.

This article about PAT Adaptive provides more detailed information about how the assessment works.

PAT Maths 4th Edition

PAT Maths 4th Edition (2015) comprises test forms ranging from Test 1 to Test 10 and can be administered according to student ability, based on previous scale score and educators' professional judgement. All students in a group respond to the same test items according to which of the ten available test forms they were assigned.

Differences and similarities

Both assessments are suitable for years 1–10, share the same construct and measurement scale, and have some test content in common. All test items are mapped to the Australian Curriculum, Victorian Curriculum and New South Wales Syllabus.

The diagnostic strengths of the adaptive test structure makes PAT Maths Adaptive well-suited to measuring the individual needs of students and providing rich evidence to inform teaching and learning. Comparisons of students' performance based on shared test content is more difficult due to the variety of different test pathways students may follow.

As a conventional, linear, assessment, PAT Maths 4th Edition allows you to administer the same test items to a single group of students. By assessing students on a shared set of items, you can more easily compare student performance on a single body of content.

When to assess

As a school, you should be clear on your purpose for using PAT assessments and carefully plan your assessment approach, especially when monitoring student learning progress over time.

Most schools administer their PAT assessments towards the end of each school year to identify the skills students have attained, to identify specific areas where students need support in their learning and to measure growth from the previous year. This also corresponds with the time of year that the Australian norm or reference group data are typically collected, allowing for more meaningful comparisons.

Some schools choose to use PAT at the beginning of the year, placing a greater emphasis on teachers acting on the diagnostic information. Others use PAT both at the beginning and end of the year in order to maximise the diagnostic information available to monitor growth throughout the year.

Monitoring progress

For the purpose of monitoring student progress, a gap of 9 to 12 months between PAT testing sessions is recommended. Learning progress may not be reflected in a student's PAT scale scores over a shorter period of time. Longitudinal growth should be measured over a minimum of two years of schooling, or three separate testing sessions, in most contexts. This will help account for possible scale score variation, for example where external factors may affect a student's performance on a particular testing occasion.

PAT Adaptive allows you to gather richer diagnostic information about what each student can do in a particular learning area and 'parallel' testlets minimise the chance of students being repeatedly exposed to the same content. For this reason, the PAT Adaptive may be administered at times between those longitudinal measurement points. Scale scores from these interim sittings would not necessarily be considered when monitoring progress over a matter of years.

Choosing the right test

For an assessment to produce valuable information about students’ abilities, it needs to be appropriately targeted to uncover what students can do and understand, as well as what they cannot yet do and understand.

So, when a student responds correctly to approximately 50% of questions, the test is well targeted and provides the maximum information about the skills a student is demonstrating, and those they are still developing.

PAT Maths Adaptive

In some cases, for example, where a student has not previously completed a PAT test, but you know their ability is relatively high or low compared with the 'average' for the year level, you may decide to override the automatically assigned PAT Adaptive entry level:

1. Select the student’s name from the Students page
2. Click Tests
3. Click Edit starting level next to the assigned PAT Adaptive test

For reference, the default PAT Adaptive entry levels for each year level are listed below:

• Level 1: foundation, year 1
• Level 2: year 2
• Level 3: year 3, year 4
• Level 4: year 5, year 6, year 7
• Level 5: year 8, year 9, year 10

PAT Maths 4th Edition

To make decisions about which test is most appropriate for a particular student or group of students, it is essential that you preview the test content:

1. Click Students
2. Click Tests
3. Click Preview

The difficulty of a test and your knowledge of each student should be taken into consideration when selecting an appropriate test form. Curriculum appropriateness and the context of the classroom also need to be taken into account when making this decision.

There is often a wide range of ability within the classroom, so it is not necessary to provide all students in a class with the same test. Instead, the focus should always be on each student’s ability at the time of the assessment, not where they are expected to be.

Administering the tests

The Test Administration Instructions linked at the bottom of this page provide further detail, including teacher scripts and troubleshooting tips.

Preparation

The following steps need to be completed ahead of time:

• Check the technical requirements and run the browser exam from a student device to identify any potential technical issues.
• Schedule your testing date and time. It is best to administer tests in the morning and not immediately before or after an exciting school event.
• Ensure that all students are listed within your school's online assessment account and have been assigned the necessary tests.
• Review and assign appropriate test levels to all students according to their ability (non-Adaptive tests only).
• Download or print a list of your students' login details.
• Make note of your school's online assessment login page, or make sure that the URL is saved on student devices, or available to your students as a link. The address will be similar to https://oars.acer.edu.au/your-school-name.

Instructions

• Tests should be administered under standard testing conditions with invigilation.
• Students' screens should be monitored as part of test invigilation.
• Students are permitted to use pen/pencil and paper to make notes during the test.

If you determine that some students require changed testing conditions due to specific learning needs, these changes should be recorded for future reference. The process for determining and implementing any changes to test conditions should be consistent between classes and across the school.

Delivery

• Students will not be automatically locked out of the tests after the allowed time passes. You must monitor and manage the time, including accommodating toilet breaks or other interruptions that may occur.
• Student responses are automatically saved each time they navigate to another question.
• If technical problems cause the need to postpone the completion of the tests, students may close the browser without losing their progress.
• iPads and tablet devices must be held in landscape orientation.

Calculators

Computer Algebra System (CAS) calculators should not be used in any PAT Maths tests.

For PAT Maths Adaptive:

• Students completing PAT Maths Adaptive should not bring their own calculator.
• For a select number of items at levels 4 to 6, an online calculator tool within the test can be used by students, if they choose. The mathematical processes involved in these questions can be completed without the use of a calculator, but students who already feel confident using a calculator may benefit from using one as it will enable them to concentrate on the more complex cognitive aspects of the question.
• At upper levels, PAT Maths Adaptive assesses the application of more advanced and complex mathematical processes for which the use of a calculator is appropriate and may in fact be required. The online calculator tool is available for all questions at levels 7 to 10.

For PAT Maths 4th Edition:

• Tests 1 and 2: calculators should not be used
• Tests 3–7: the decision to allow standard or scientific calculators should be determined and implemented school wide. Students may not use a calculator for the last four questions.
• Tests 8–10: A calculator will be required for some items in these tests.

PAT Maths Adaptive

• The nature of adaptive assessment means that students will likely see different items (questions), and different numbers of items, in their tests. To reduce student anxiety, it is important to explain that there will be differences between students' tests and to assure them that they will all have enough time to attempt their questions.
• All students will see at least 30 items in their PAT Maths Adaptive test. The most is 42 items.
• The multi-stage structure of PAT Maths Adaptive is not obvious to students, so students should simply be discouraged from skipping items without reading them.
• Students must view (not necessarily respond to) at least half of the items in Stage 3 of their test in order to receive a scale score.
  Tests submitted prematurely will be flagged as 'Invalid: insufficient items viewed' and excluded from the reporting. These tests may be re-opened to allow students to complete them.

Using the results

The information provided by the PAT reports is intended to assist you in understanding students' abilities in the learning area, diagnosing gaps, strengths and weaknesses in students' learning, and measuring learning progress over time.

• Read more about online reports available in the ACER Data Explorer.
• Read more about PAT scales and achievement bands

Scale score

A scale score is a numerical value given to a student whose achievement has been measured by completing an assessment. A student's scale score lies at a point somewhere on the achievement scale, and it indicates that student's level of achievement in that particular learning area — the higher the scale score, the more able the student.

Regardless of the test level or items administered to students, they will be placed on the same scale for the learning area. This makes it possible to directly compare students' achievement and to observe students' progress within a learning area by comparing their scale scores from multiple testing periods over time.

A score on a Reading scale, for example, has no meaning on the Maths scale. In fact, the units of the scale will have different meanings for each scale. This is because these units are calculated based on the range of student levels of achievement, which vary widely between learning areas.

Achievement bands

Students in the same achievement band are operating at approximately the same achievement level within a learning area regardless of their school year level.

Viewing student achievement in terms of achievement bands may assist you to group students of similar abilities. By referencing the achievement band descriptions, you can understand the types of skills typical of students according to their band.

Item difficulty

Item difficulty is a measure of the extent of skills and knowledge required to be successful on the item. This makes it possible to allocate each test item a score on the same scale used to measure student achievement. An item with a high scale score is more difficult for students to answer correctly than a question with a low scale score. It could generally be expected that a student is able to successfully respond to more items located below their scale score than above.

Item difficulties are estimated based on the performance of individuals with a range of abilities who respond to that item, first at the item trial stage and later verified in real test results. The concept being assessed in the item is one aspect of item difficulty. Other factors may combine to make an item more or less complex. For example, the level of abstraction, the number of steps required, whether the question involves problem-solving or computation, the question context, the required precision of response, cognitive load, etc. An item assessing a concept that is introduced earlier in the curriculum may still be quite complex. Conversely, an item assessing a concept introduced later may be simpler.

By referencing the difficulty of an item, or a group of items, and the proportion of correct responses by a student or within a group, it may be possible to identify particular items, or types of items, that have challenged students.

Australian norms

Norm data that represents the achievement of students across Australia is available as a reference sample against which student achievement can be compared.

The comparison between a student's scale score achievement and the Australian norm sample can be expressed as a percentile rank.

The percentile rank of a score is the percentage of students who achieve less than that score. For example, a student with a percentile rank of 75th compared to the Year 3 norm sample has a scale score that is higher than 75% of Australian Year 3 students.

About PAT Maths

PAT Maths aims to measure mathematical ability. It conceives of ability in mathematics as being more than just remembering mathematical facts and procedures. Students must be able to use their mathematical knowledge to solve problems, interpret data, and support or refute claims. To be able to do so, students must have a solid foundation in the basic skills and so must be able to quickly and accurately perform routine calculations.

The PAT Maths construct is the organising principle of the assessments; it is used to guide test development and structure the PAT reports. This structure is also part of the Progressive Achievement approach because the knowledge, skills and understanding represented in the tests are designed to support educators in identifying student needs.

Three overarching elements guide assessment development:

• Strands
• Proficiencies
• Contexts

The PAT Maths Assessment Framework document linked at the bottom of this page provides further detail about these components.

In both PAT Maths and the Australian Curriculum: Mathematics F–10, there are three strands used:

• Number and algebra
• Measurement and geometry
• Statistics and probability

These are also the basis of the sub-strands in PAT Maths. There are eight sub-strands in PAT Maths:

• Whole number operations
• Fractions and decimals
• Money and financial maths
• Patterns and algebra
• Measurement
• Geometry
• Statistics
• Probability

PAT Maths also addresses the mathematical proficiencies. These proficiencies are not discrete and an individual item will likely call on more than one of the four:

• Understanding
• Fluency
• Problem solving
• Reasoning

Test items are each associated with a different context. A context is the situation within which the details of a test item or task are located, or the situation that generated the stimulus material for the task:

• Abstract
• Practical
  • Individual
  • Interactive
  • External

Acknowledgements

PAT Maths Adaptive is the most recently developed assessment to use the PAT Maths construct and builds on the earlier PAT Maths 4th Edition assessment. Katherine McGill was the lead test developer. Ammar Aldaoud, Andrew Mannion, Pam Munro-Smith, Ray Philpot, James Spithill, Geoffrey Tobin and Stravroula Zoumboulis all made valuable contributions to the development of the test content. Siek Toon Khoo and Ling Tan led the psychometrics and methodology work. Steve Kambouris worked on PAT Adaptive design and item banking, Liang-Cheng Zhang on trial analysis, Fuchun Huang on trial analysis and testlet selection, and Clare Ozolins on PAT Adaptive norming. Other staff members who made valuable contributions include Penny Pearson and Kathy He.

Supporting documents