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46. The ability to reason logically and to present arguments in honest and convincing ways is a skill
that is becoming increasingly important in today’s world. Mathematics is a science about well-
defined objects and notions which can be analysed and transformed in different ways using
‘mathematical reasoning’ to obtain conclusions about which we are certain. Through mathematics,
students learn that using appropriate reasoning they can reach results and conclusions which they
can trust to be true. Further, those conclusions are logical and objective, and hence impartial,
without any need for validation by an external authority. This kind of reasoning which is useful far
beyond mathematics, can be learned and practiced most effectively within mathematics.
47. Two aspects of m
athematical reasoning are especially important in today’s world and in
defining the PISA items. One is deduction from clear assumptions (deductive reasoning), which is
a characteristic feature of mathematical process. The usefulness of this ability has already been
stressed. The second important dimension is statistical and probabilistic (inductive) reasoning. At
the logical level, there is these days frequent confusion in the minds of individuals between the
possible and the probable, leading many to fall prey to conspiracy theories or fake news. From a
technical perspective, today’s world is increasingly complex and its multiple dimensions are
represented by terabytes of data. Making sense of these data is one of the biggest challenges that
humanity will face in the future. Our students should be familiarised with the nature of such data
and making informed decisions in the context of variation and uncertainty.
48. Mathematical reasoning (both deductive and inductive), enabled by some key understandings
that undergird school mathematics, is the core of mathematical literacy. Included among these key
understandings are:
Understanding quantity, number systems and their algebraic properties;
Appreciating the power of abstraction and symbolic representation;
Seeing mathematical structures and their regularities;
Recognising functional relationships between quantities;
Using mathematical modelling as a lens onto the real world (e.g. those arising in the
physical, biological, social, economic, and behavioural sciences); and
Understanding variation as the heart of statistics.
The description of each of these that follows provides an overview of the understanding and how it
supports reasoning. While the descriptions may appear abstract, the intention is not for them to be
treated in an abstract way in the PISA assessment. The message that the descriptions should
convey is how these ideas surface throughout school mathematics and how, by reinforcing their
occurrence in teaching we support students to realise how they can be applied in new and different
contexts.
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