IfSR - Proportional thinking
The Interview for Student Reasoning - Proportional thinking (IfSR-PT) is the final assessment of a series of on-demand assessments that enables teachers to hear and see how students apply their mathematical understandings of proportional thinking. IfSR-PT is divided into 4 sections:
- Section 1: Early proportional thinking
- Section 2: Fractions, decimals and percentages
- Section 3: Ratios
- Section 4: Rates
More information on each section is available below.
Assessment guide and materials
The Assessment guide and student materials document (PDF 1.02MB) (staff only) supports teachers to administer the assessment.
The first part of the manual outlines:
- the purpose of the assessment
- details on how to prepare for, administer and lodge the assessment
- a summary of related syllabus outcomes and links to the National Numeracy Learning Progression.
The second part of the manual details the materials required for each of the four sections for the assessment. Templates for printable resources are available in separate section documents below.
- A complete paper version of the assessment items (PDF396KB) (staff only) is also available for download if required.
Use the justification and anticipation guide (PDF 877KB) (staff only) alongside the Interview for Student Reasoning: Proportional thinking (IfSR-PT) assessment to suggest possible student responses and anticipated justifications, as well as identifying common errors and misconceptions.
Section 1: Early proportional thinking
Early proportional thinking is characterised by students’ abilities to apply multiplicative strategies such as partitioning to solve simple proportional problems and work meaningfully with multiple representations of proportional relationships. When working towards Stage 2 outcomes and beyond, students need to think multiplicatively to be able to reason proportionally.
Section 2: Fractions, decimals and percentages
Flexible strategies with single-digit numbers are characterised by the development of a range of flexible strategies such as using renaming, doubles and known facts that can be used for mental computation. When working towards Stage 2 outcomes and beyond, students apply a range of mental strategies in various multiplicative situations and represent thinking in a range of ways.
Section 3: Ratios
Ratios are characterised by a relationship between two numbers of the same type of unit of measure and students' abilities to compare two amounts of the same kind of measure. When working towards Stage 4 outcomes and beyond, students need to have consolidated fractional, decimal and percentage knowledge.
Section 4: Rates
Rates involves students being able to compare different types of measures.
When working towards Stage 4 outcomes and beyond, students need to be competent in working with fractions, decimals and percentages, in order to think multiplicatively and proportionally to make comparisons of rates.
Teachers administer the assessment using the online tool for entering student responses. The online tool is available via ALAN.
The ALAN helpdesk has solutions for all ‘How to' questions for administering the assessment
This short preparation video 'How to navigate the online assessment' helps teachers familiarise themselves with the online tool.
The Interview for Student Reasoning – IfSR, is an online on-demand diagnostic numeracy assessment.
The IfSR informs teachers of the way a student reasons and uses their mathematical knowledge.
What is IfSR- Proportional thinking?
IfSR- Proportional thinking or IfSR-PT is an online assessment that enables a teacher to gain insights into how a student reasons and works flexibly with numbers in proportional situations.
From the insights a teacher can establish where students are in their learning in order to target their teaching.
The tool enables a teacher to monitor student progress through the use of PLAN2.
There are 4 sections in IfSR-PT. Each section has items that relate to the section titles.
All items are aligned to the Mathematics K-10 syllabus and the National Numeracy Learning Progression.
Who is IfSR-PT for?
The assessment is designed to be delivered flexibly to assess individuals or groups of students K-10 to identify their reasoning skills in proportional thinking.
You can select students who you would like to gather more information on. It is designed to supplement existing school practices and inform your decision making within the teaching and learning cycle to identify how students construct their mathematical understandings and to help you tailor your teaching more specifically to student needs.
How do I administer the online assessment?
Before you begin the assessment, read the assessment guide, familiarise yourself with the online assessment tool and prepare the necessary materials.
Select the year level, class or group.
The IfSR-PT assessment has been modularised to give you flexibility in assessing sub-skills for targeted teaching.
This allows you to select the starting point when beginning each section.
Select the student, then choose to ‘ASSESS’ or continue the assessment for the student you are working with.
Confirm the student and section by selecting the ‘Start with task....’ or ‘Continue progress’ button, to start or resume the assessment.
When administering each question you will see: the section being assessed, any materials that may be required, and instructions for the task.
Read the questions to the student that are marked with a speech bubble icon.
The progress bar displays the count of completed tasks out of the total number of tasks for that section.
Move to a specific task by selecting ‘Go to’.
Record student responses by selecting an option from the response panel.
You can record a comment, noting the student’s behaviour.
This will assist you when analysing the results.
Select the ‘Flag’ button to mark and draw your attention to particular tasks.
Select ‘Next’ to move to the next question.
Responses will be saved automatically.
How do I review individual student progress in the IfSR tool?
View the number of questions in the sub-section and navigate to a specific question if needed in the progress bar. Select “go to”, answered questions will be displayed in blue, not answered in white, and flagged with a black triangle in the top left corner.
Select the x to return to the assessment
To pause the interview without completion, select the ‘Exit’ button in the top right corner.
This will save your progress and close the assessment screen.
How do I finalise responses and lodge the assessment?
To lodge the assessment select ‘Finish Interview’.
Lodgement will not be possible until all tasks have been responded to.
Navigate to any unanswered tasks, or mark all unanswered tasks remaining as ‘Not given’, noting a reason and any additional comments.
You can also ‘Save and exit’ to lodge responses at a later time or finalise student responses by selecting ‘Lodge’ once all responses have been recorded.
Once lodged, student responses cannot be modified.
How do I access student assessment analysis and responses?
View the status of an assessment and access a student analysis for each section assessed from the main page of the online tool.
Here you can continue, re-assess or begin a new assessment.
Re-assessment of a section can occur at any time.
A Student Assessment Analysis can be downloaded in the online tool for each section assessed by selecting the Analysis button.
The analysis can assist in making decisions about the next steps in learning to meet the needs of individual students.
Where else can I analyse student responses?
IfSR-PT maps student responses to the National Numeracy Learning Progression in PLAN2.
Direct links to class observations and cohort snapshot are available via the 'Class analysis' button.
The Area of focus template in PLAN2 is aligned with IfSR-PT to enable you to target your teaching.
For further information on the Interview for Student Reasoning diagnostic numeracy assessment, please visit the IfSR webpage.
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Fractions and proportional reasoning (primary)
This professional learning course supporting teachers to understand and implement evidence-based teaching strategies for fractions and proportional reasoning (primary) and access, adapt and implement universal resources to support effective teaching practice.
Access Fractions and proportional reasoning (primary) via MyPL (course code NR31680)
Fractions and proportional reasoning (secondary)
This professional learning course supporting teachers to understand and implement evidence-based teaching strategies for fractions and proportional reasoning (secondary) and access, adapt and implement universal resources to support effective teaching practice.
Access Fractions and proportional reasoning (secondary) via MyPL (course code NR31681)
Additional professional learning supporting IfSR-PT will be available during 2023.
Proportional thinking strategies (in 4 parts).
- Part 1: Early proportional thinking
- Part 2: Fractions, decimals and percentages
- Part 3: Ratios
- Part 4: Rates
The tasks and activities in each resource support proportional thinking. Used together, the resources support a connected network of critical mathematical concepts, skills and understanding. This 4 part series will be updated to reflect the new 3-10 Mathematics syllabus (released in 2024).
Resources supporting the evidence-based teaching of numeracy more broadly are available via the Universal Resources Hub (staff only)
Visit the Interview for Student Reasoning web page for information on the purpose of the assessment.
Visit the Literacy and numeracy professional learning web page for more professional learning opportunities in the practical application of evidence-based teaching of numeracy.
Visit the ALAN helpdesk for solutions relating to administering the assessment.
About this resource
Advice on use
IfSR - Proportional thinking (IfSR-PT) is part of a suite of teacher-led online numeracy assessments administered by the classroom teacher to individual students through one-to-one interviews. They can be administered at any point in time to reveal what a student knows, ways a student reasons with and thinks about mathematical tasks, and as a tool to investigate the gaps in a student’s mathematical knowledge.
- The assessment is modularised to give teachers flexibility in assessing sub-skills for targeted teaching.
- The administration is flexible and adaptable to enable teachers to gather information on a student's conceptual knowledge in numeracy.
- IfSR - PT does not need to be administered within a specific timeframe or from beginning to end.
- Teachers tailor the administration of the assessment to suit the needs of individual students by selecting either a section, sub-section or specific tasks. For example, a teacher may select to administer only a small group of tasks in one section.
- The teacher decides on tasks and/or sections by reviewing existing assessment such as classroom observations and/or teacher judgement.
This resource may be used across the curriculum where it supports the teaching and learning of numeracy skills aligned to syllabus outcomes.
For further advice on use, please see the IfSR-PT assessment guide.
When using these resources in the classroom, it is important for teachers to consider the needs of all students, including Aboriginal and EAL/D learners.
EAL/D learners will require explicit language support and scaffolding, informed by the Enhanced EAL/D enhanced teaching and learning cycle and the student’s phase on the EAL/D Learning Progressions. For further information visit the English as an additional language or dialect education webpage.
Learning adjustments enable students with disability and additional learning and support needs to access syllabus outcomes and content on the same basis as their peers. Teachers can use a range of adjustments to ensure a personalised approach to student learning.
A range of tools to identify, assess and challenge high potential and gifted learners are available to support teachers in the classroom. Identifying contributors to achievement helps teachers identify and target areas for students’ growth and improvement. A differentiation adjustment tool can be used to plan effective teaching strategies.
Alignment to system priorities and/or needs
These resources reflect the following existing frameworks:
- Mathematics K-2 Syllabus (2022)
- Mathematics 3-10 Syllabus (2012)
- National Numeracy Learning Progressions (Version 3)
- Australian Professional Standards for Teachers
- Literacy and Numeracy Five Priorities
Alignment to School Excellence Framework
These resources support the School Excellence Framework and clearly align to the following domains and themes:
- Assessment: Formative Assessment, Summative Assessment
- Student Performance Measures: Internal and external measures against syllabus standards
- Effective classroom practice: Lesson planning, Explicit teaching, Feedback
- Data Skills and Use: Data Analysis, Data Use in Teaching
- Learning and development: Expertise and innovation
Centre for Education Statistics and Evaluation (2020). What works best: 2020 Update, CESE website
Clarke D, Clarke B and Roche A. (2011) ‘Building Teachers’ Expertise in Understanding, assessing and developing children’s mathematical thinking: the power of task based, one-to-one assessment interviews’, ZDM Mathematics Education 43:901-913
Department of Education and Training, Victoria (n.d.) Assessments for Common Misunderstandings, DET Victoria website
Hurst C and Hurrell D (2016) Assessing Children’s Multiplicative Thinking Mathematics Education Research Group of Australasia
Lamon, S (1999) Teaching Fractions and Ratios for Understanding – Essential content knowledge and instructional strategies for teachers. Mahwah, NJ: Lawrence Erlbaum and Assoc
Siemon D, Beswick K, Brady K, Clark J, Faragher R, and Warren E (2019) Teaching Mathematics: Foundations to middle years. Oxford University Press
Booker G, Bond D, Sparrow L and Swan P (2014). Teaching primary mathematics. Frenchs Forest, NSW: Pearson Australia
Vale C, Bragg L A, Widjaja W, Herbert S, and Loong E Y-K (2017). ‘Children's mathematical reasoning: opportunities for developing understanding and creative thinking’, Australian Primary Mathematics Classroom, 22(1), 3
Comments and feedback to contribute to evaluation and support ongoing resource development can be provided via Literacy and Numeracy resource feedback form.
Reviewed by: Literacy and Numeracy team
Last updated: January 2023
Anticipated resource review date: January 2024