1.2 The ACER Assessment Framework: Contexts, Processes, and Performance Bands

Structure of the ACER LANTITE Assessment Framework (2024 Edition)

The ACER LANTITE Assessment Framework (2024 edition) defines personal numeracy as "interpreting and communicating important non-technical mathematical information and using such information to solve relevant real-world problems to participate in an education community, to achieve one's goals, and to develop one's knowledge and potential as a teacher." Rather than testing abstract symbol manipulation, every question is classified on four design dimensions:

1. Mathematical Content Area (Strand) — what mathematical concepts are required.
2. Numeracy Process — what cognitive action the candidate must perform.
3. Context Domain — what real-world setting frames the stimulus.
4. Calculator Availability — whether the item appears in Section 1 (calculator available) or Section 2 (calculator not available). The framework targets $75\text{–}85\%$ of items for the calculator section and $15\text{–}25\%$ for the no-calculator section; the current form uses 52 and 13 questions ($80\%$ and $20\%$).

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Dimension 1: Three Mathematical Content Areas (Strands)

1. Number and Algebra (40–50% of Test | ~26–33 Questions)

Number and Algebra is the single largest content strand on the test, accounting for nearly half of all questions. It assesses fluency with:

• Proportional Reasoning, Ratios, and Rates: Scaling recipes or classroom supplies, simplifying and dividing quantities in a given ratio, enforcing mandatory teacher-to-student supervision ratios, and working with compound rates such as speed ($\text{km/h}$), fuel consumption ($\text{L/100 km}$), and hourly pay rates (in $ per hour).
• Percentages, Decimals, and Fractions: Converting fluently among fractions, decimals, and percentages; computing percentage increases, discounts, markups, and percentage change; and calculating Australia's 10% Goods and Services Tax (GST) (where a GST-inclusive price equals $1.10$ times the pre-GST price, so dividing a GST-inclusive total by $11$ isolates the exact GST component).
• Financial Mathematics: Analysing household, personal, and school excursion budgets; comparing unit prices and multi-buy retail offers; calculating gross pay, overtime rates, income tax brackets, and superannuation contributions; and evaluating simple interest ($I = Prt$) and step-by-step compound interest schedules.
• Algebraic Formulas and Relationships: Substituting numerical values into word formulas or symbolic rules, solving linear relationships, and interpreting step functions such as progressive shipping or venue-hire fee tables.

2. Statistics and Probability (25–35% of Test | ~16–23 Questions)

Statistics and Probability is the second largest content strand and reflects the heavy data-literacy demands of contemporary Australian schools:

• Data Representation and Extraction: Reading and cross-referencing two-way frequency tables, stacked and grouped bar charts, line graphs, dual-axis charts, pie charts, scatter plots (including trend lines and outliers), histograms, stem-and-leaf plots, and box-and-whisker plots.
• Summary Statistics and Educational Scales: Calculating and comparing measures of centre (mean, median, and mode) and measures of spread (range and interquartile range [IQR]); calculating weighted averages across assessment tasks; and interpreting quartiles, percentiles, five-number summaries, and standardized school reporting scales such as NAPLAN proficiency bands.
• Chance and Probability: Determining single-event, complementary ($P(\text{not } A) = 1 - P(A)$), and compound probabilities using fractions, decimals, and percentages; conditional frequency probabilities from two-way tables; and expected frequencies over repeated trials.

3. Measurement and Geometry (20–30% of Test | ~13–20 Questions)

Measurement and Geometry evaluates practical spatial, temporal, and metric reasoning:

• Metric Conversions and Derived Units: Converting accurately across metric prefixes for length ($\text{mm}, \text{cm}, \text{m}, \text{km}$), mass ($\text{mg}, \text{g}, \text{kg}, \text{t}$), and capacity/volume ($\text{mL}, \text{L}, \text{kL}, \text{cm}^3, \text{m}^3$), where $1\text{ cm}^3 = 1\text{ mL}$ and $1\text{ m}^3 = 1{,}000\text{ L}$.
• Time, Timetables, and Time Zones: Calculating elapsed time across 12-hour ($\text{am/pm}$) and 24-hour clocks, reading bus/train/flight schedules and school bell timetables, and converting across Australian and international time zones (including Australian Eastern, Central, and Western Standard and Daylight Saving Times, where Central time uses a $30$-minute offset).
• Mensuration, Scale, and Navigation: Computing perimeter, area of rectangles, triangles, circles, and composite classroom floor plans; surface area and volume of rectangular prisms and cylinders; reading map ratios (such as $1 : 25{,}000$), grid references, and 8-point or 360-degree true bearings.

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Dimension 2: Three Cognitive Numeracy Processes

Every question is also classified by the primary cognitive process required:

1. Identifying Mathematical Information and Meaning in Activities and Texts (20–30%): Extracting relevant numerical values, rules, thresholds, and conditions embedded inside written policies, fee schedules, timetables, or charts while filtering out distractor figures.
2. Using and Applying Mathematical Knowledge and Problem-Solving Processes (45–55%): Selecting the correct mathematical method, formulating a single-step or multi-step calculation sequence, and executing the arithmetic, proportional, or algebraic procedure accurately.
3. Interpreting, Evaluating, Communicating, and Representing Mathematics (20–30%): Assessing whether a numerical claim or statistical conclusion is supported by the data, comparing competing options against constraints, and judging the reasonableness of results.

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Dimension 3: Three Real-World Context Domains

Stimulus materials are drawn from three authentic context areas relevant to pre-service and practising teachers:

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What Is In Scope: Non-Technical Mathematics, Item Formats, and Difficulty

The framework limits the test to non-technical mathematics: the everyday uses of mathematics that numerate adults meet, as opposed to procedures reserved for the study of mathematics itself. ACER gives two boundary examples:

So spend your preparation on proportional reasoning, measurement, data displays and given formulas rather than on algebraic manipulation or trigonometry.

Scored Items, Trial Items, and Response Formats

Each numeracy test has 60 scored items (48 calculator-available and 12 calculator-not-available) plus 5 unscored trial items. Items use three automatically scored formats:

• Simple multiple choice: usually four options, one best answer.
• Complex multiple choice: several statements, each answered with one of two or more responses such as Yes/No or True/False.
• Constructed numeric response: you type a number into an answer box.

Target Difficulty Against the ACSF

ACER concentrates items around the benchmark and deliberately includes easier items so that it can describe what candidates below the standard can do:

Because roughly half the items are targeted at Level 3 or below, a well-prepared candidate should find many questions routine. The numeracy benchmark itself sits within Level 4, so the items near the pass line typically involve multi-step proportional reasoning, less familiar data displays, and measurement problems that combine rates, scales, and time.

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The National Benchmark, Psychometric Equating, and Achievement Bands

The Top 30% Adult Population Standard

The LANTITE standard is established at the minimum level of personal literacy and numeracy expected of graduating teachers entering the Australian classroom. The benchmark is broadly equivalent to the top 30 per cent of the Australian adult population. ACER's 2013 numeracy expert panel set an indicative range in the middle to upper part of Australian Core Skills Framework (ACSF) Level 4. A 2017 equating study against the OECD Programme for the International Assessment of Adult Competencies (PIAAC) located the top-30% point at a numeracy scale score of 110, and that standard has applied since Test Window 3 in 2017.

Why ACER Does Not Publish a Fixed Raw Pass Mark

Candidates often search for a single raw cutoff—such as "45 out of 65" or "70%". ACER does not use a fixed raw score because multiple secure test forms are administered across different days and test windows to preserve test security. Even when constructed to identical specifications, two test forms can differ slightly in average item difficulty. Through psychometric analysis, ACER places every question's difficulty on a common proficiency scale, and results are released only after that analysis and quality assurance are complete. A candidate sitting a marginally harder test form requires slightly fewer raw correct answers to reach the benchmark scale score than a candidate sitting a marginally easier form, guaranteeing that the standard remains identical for every candidate.

Statement of Test Results and Three Achievement Bands

When results are released, candidates receive an official Statement of Test Results reporting their overall outcome in one of three Achievement Bands:

• Band 1: The candidate's score is below the test standard (the candidate has not yet met the national numeracy requirement).
• Band 2: The candidate's score is at and above the test standard (the candidate has met the national numeracy requirement).
• Band 3: The candidate's score is clearly above the test standard (the candidate has met the national numeracy requirement with a wide margin of proficiency).