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to a problem presented in some contextualised form. In the process of formulating situations
mathematically, individuals determine where they can extract the essential mathematics to
analyse, set up and solve the problem. They translate from a real-world setting to the domain of
mathematics and provide the real-world problem with
mathematical structure, representations and
specificity. They reason about and make sense of constraints and assumptions in the problem.
Specifically, this process of formulating situations mathematically includes activities such as the
following:
selecting an appropriate model from a list;
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identifying the mathematical aspects of a problem situated in a real-world context and
identifying the significant variables;
recognising mathematical structure (including regularities, relationships, and patterns) in
problems or situations;
simplifying a situation or problem in order to make it amenable to mathematical analysis (for
example by decomposing);
identifying constraints and assumptions behind any mathematical modelling and
simplifications gleaned from the context;
representing a situation mathematically, using appropriate variables, symbols, diagrams,
and standard models;
representing a problem in a different way, including organising it according to mathematical
concepts and making appropriate assumptions;
understanding and explaining the relationships between the context-specific language of a
problem and the symbolic and formal language needed to represent it mathematically;
translating a problem into mathematical language or a representation;
recognising aspects of a problem that correspond with known
problems or mathematical
concepts, facts or procedures;
choosing among an array of and employing the most effective computing tool to portray a
mathematical relationship inherent in a contextualised problem; and
creating an ordered series of (step-by-step) instructions for solving problems.
Employing Mathematical Concepts, Facts, Procedures and Reasoning
79. The word
employ in the mathematical literacy definition refers to individuals being able to apply
mathematical concepts, facts, procedures, and reasoning to solve mathematically-formulated
problems to obtain mathematical conclusions. In the process of employing mathematical concepts,
facts, procedures and reasoning to solve
problems, individuals perform the mathematical
procedures needed to derive results and find a mathematical solution (e.g. performing arithmetic
computations, solving equations, making logical deductions from mathematical assumptions,
performing symbolic manipulations, extracting mathematical information from tables and graphs,
representing and manipulating shapes in space, and analysing data). They work on a model of the
problem situation, establish regularities, identify connections between mathematical entities, and
create mathematical arguments. Specifically, this process of employing mathematical concepts,
facts, procedures and reasoning includes activities such as:
performing a simple calculation;
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**
drawing a
simple conclusion; **
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This activity is included in the list to foreground the need for the test items developers to include items that
are accessible to students at the lower end of the performance scale.
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These activities (**) are included in the list to foreground the need for the test items developers to include
items that are accessible to students at the lower end of the performance scale.
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selecting an appropriate strategy from a list; **
devising and implementing strategies for finding mathematical solutions;
using mathematical tools, including technology, to help find exact or approximate solutions;
applying mathematical facts, rules, algorithms, and structures when finding solutions;
manipulating numbers, graphical and statistical data and information, algebraic expressions
and equations, and geometric representations;
making mathematical diagrams, graphs, simulations, and constructions and extracting
mathematical information from them;
using and switching between different representations in the process of finding solutions;
making generalisations and conjectures based on the results of applying mathematical
procedures to find solutions;
reflecting on mathematical arguments and explaining and justifying mathematical results;
and
evaluating the significance of observed (or proposed) patterns and regularities in data.
Interpreting, Applying and Evaluating Mathematical Outcomes
80. The word
interpret (and
evaluate) used in the mathematical literacy definition focuses on the
ability of individuals to reflect upon mathematical solutions, results or conclusions and interpret
them in the context of the real-life problem that initiated the process. This involves translating
mathematical solutions or reasoning back into the context of the problem and determining whether
the results are reasonable and make sense in the context of the problem.
Interpreting, applying
and evaluating mathematical outcomes
encompasses both the ‘interpret’ and ‘evaluate’ elements
of the mathematical modelling cycle. Individuals engaged in this process may be called upon to
construct and communicate explanations and arguments in the context of the problem, reflecting
on both the modelling process and its results. Specifically, this process of interpreting, applying
and evaluating mathematical outcomes includes activities such as:
interpreting information presented in graphical form and/or diagrams;
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**
evaluating a mathematical outcome
in terms of the context; **
interpreting a mathematical result back into the real-world context;
evaluating the reasonableness of a mathematical solution in the context of a real-world
problem;
understanding how the real world impacts the outcomes and calculations of a mathematical
procedure or model in order to make contextual judgments about how the results should be
adjusted or applied;
explaining why a mathematical result or conclusion does, or does not, make sense given
the context of a problem;
understanding the extent and limits of mathematical concepts and mathematical solutions;
critiquing and identifying the limits of the model used to solve a problem; and
using mathematical thinking and computational thinking to make predictions, to provide
evidence for arguments, to test and compare proposed solutions.
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