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effect sets up a two way table and the student is asked to demonstrate an understanding of the
different probability estimates that the two-way table provides
106. Identifying conditional decisions making as a focal point of the uncertainty and data content
category signals that students should be expected to appreciate how the formulation of the
analysis in a model impacts the conclusions that can be dawn and that different
assumptions/relationships may well result in different conclusions.
Content Topics for Guiding the Assessment of Mathematical Literacy of 15-year-old Students
107. To effectively understand and solve contextualised problems involving change and
relationships; space and shape; quantity; and uncertainty and data requires drawing upon a variety
of mathematical concepts, procedures, facts, and tools at an appropriate level of depth and
sophistication. As an assessment of mathematical literacy, PISA strives to assess the levels and
types of mathematics that are appropriate for 15-year-old students on a trajectory to become
constructive, engaged and reflective 21st century citizens able to make well-founded judgments
and decisions. It is also the case that PISA, while not designed or intended to be a curriculum-
driven assessment, strives to reflect the mathematics that students have likely had the opportunity
to learn by the time they are 15 years old.
108. In the development of the PISA 2012 mathematical literacy framework, with an eye toward
developing an assessment that is both forward-thinking yet reflective of the mathematics that 15-
year-old students have likely had the opportunity to learn, analyses were conducted of a sample of
desired learning outcomes from eleven countries to determine both what is being taught to
students in classrooms around the world and what countries deem realistic and important
preparation for students as they approach entry into the workplace or admission
into a higher
education institution. Based on commonalities identified in these analyses, coupled with the
judgment of mathematics experts, content deemed appropriate for inclusion in the assessment of
mathematical literacy of 15-year-old students on PISA 2012, and continued for PISA 2021, is
described below.
109. For PISA 2021 four additional focus topics have been added to the list. The resulting lists is
intended to be illustrative of the content topics included in PISA 2021 and not an exhaustive listing:
Growth phenomena: Different types of linear and non-linear growth
Geometric approximation: Approximating the attributes and properties of irregular or
unfamiliar shapes and objects by breaking these shapes and objects up into more familiar
shapes and objects for which there are formulae and tools.
Computer simulations: Exploring situations (that may include budgeting, planning,
population distribution, disease spread, experimental probability, reaction time modelling
etc.) in terms of the variables and the impact that these have on the outcome.
Conditional decision making: Using basic principles of combinatorics and an understanding
of interrelationships between variables to interpret situations and make predictions.
Functions: The concept of function, emphasising but not limited to linear functions, their
properties, and a variety of descriptions and representations of them. Commonly used
representations are verbal, symbolic, tabular and graphical.
Algebraic expressions: Verbal interpretation of and manipulation with algebraic
expressions, involving numbers, symbols, arithmetic
operations, powers and simple roots.
Equations and inequalities: Linear and related equations and inequalities, simple second-
degree equations, and analytic and non-analytic solution methods.
Co-ordinate systems: Representation and description of data, position and relationships.
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Relationships within and among geometrical objects in two and three dimensions: Static
relationships such as algebraic connections among elements of figures (e.g. the
Pythagorean theorem as defining the relationship between the lengths of the sides of a
right triangle), relative position, similarity and congruence, and dynamic relationships
involving transformation and motion of objects, as well as correspondences between two-
and three-dimensional objects.
Measurement: Quantification of features of and among shapes and objects, such
as angle
measures, distance, length, perimeter, circumference, area and volume.
Numbers and units: Concepts, representations of numbers and number systems (including
converting between number systems), including properties of integer and rational numbers,
as well as quantities and units referring to phenomena such as time, money, weight,
temperature, distance, area and volume, and derived quantities and their numerical
description.
Arithmetic operations: The nature and properties of these operations and related notational
conventions.
Percents, ratios and proportions: Numerical description of relative magnitude and the
application of proportions and proportional reasoning to solve problems.
Counting principles: Simple combinations.
Estimation: Purpose-driven approximation of quantities and numerical expressions,
including significant digits and rounding.
Data collection, representation and interpretation: Nature, genesis and collection of various
types of data, and the different ways to analyse, represent and interpret them.
Data variability and its description: Concepts such as variability, distribution and central
tendency of data sets, and ways to describe and interpret these in quantitative and
graphical terms.
Samples and sampling: Concepts of sampling and
sampling from data populations,
including simple inferences based on properties of samples including accuracy and
precision.
Chance and probability: Notion of random events, random variation and its representation,
chance and frequency of events, and basic aspects of the concept of probability and
conditional probability.
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