Chapter 3
Mathematics Education
Mathematics is the art and science of discovering patterns and explaining them. These patterns
are all around us, in nature, in technology, and in the motion of the earth, sun, moon, and stars.
There is Mathematics in everything that we do and see, from shopping and cooking, to throwing
a ball and playing games, to solar eclipses and climate patterns. Mathematics thus gives us the
foundational concepts and capacities required to think about the world around us and the world
beyond us. But most of all, when taught well, Mathematics is truly enjoyable and can become a
lifelong passion. The goal of Mathematics Education is to bring to life these aspects of Mathematics.
Mathematics, including Computational Thinking, has never been more important globally, for
machine learning, data science, climate modelling, infrastructure development, and the numerous
communicating clearly and precisely — through content areas such as arithmetic, algebra,
geometry, probability, statistics, trigonometry, and calculus.
268
, National Curriculum Framework for School Education
Section 3.1
Aims
Mathematics helps students develop not only basic arithmetic skills, but also the crucial capacities
of logical reasoning, creative problem solving, and clear and precise communication (both oral
and written). Mathematical knowledge also plays a crucial role in understanding concepts in
other school subjects, such as Science and Social Science, and even Art, Physical Education, and
Vocational Education. Learning Mathematics can also contribute to the development of capacities
for making informed choices and decisions. Understanding numbers and quantitative arguments
is necessary for effective and meaningful democratic and economic participation.
Mathematics thus has an important role to play in achieving the overall Aims of School Education.
a. Basic Numeracy.
quantifying and performing calculating is essential for basic daily interactions, such as
shopping and banking. Mathematics Education in schools should ensure that all students
space and measurement.
b. Mathematical Thinking. Mathematical thinking involves systematic and logical ways to
think about and interpret the world. The capacities for identifying patterns, explaining
patterns, quantifying and measuring, using deductive reasoning, working with abstractions,
and communicating clearly and precisely are some illustrations of mathematical thinking.
Mathematics Education in schools should aim for developing such mathematical thinking in
all students.
c. Problem Solving.
through mathematical thinking is an important aspect of learning Mathematics. Clear and
precise formulation of problems and puzzles, knowing the appropriate mathematical
concepts and techniques that can model the problems, and possessing the techniques and
the creativity to solve the problems are core aspects of problem solving. Mathematics
Education in schools should aim for developing such problem-solving capacities in all
students. Problem solving also develops the capacities of perseverance, curiosity,
d. Mathematical Intuition. Developing an intuition for what should or should not be true in
working out precise answers, and engaging in informal argumentation before carrying out
rigorous proofs are all effective ways of developing such mathematical intuition in students.
Developing such mathematical intuition in all students should be one of the aims of
Mathematics Education in schools.
269
, National Curriculum Framework for School Education
e. Joy, curiosity, and wonder. Discovering, understanding, and appreciating patterns and
other mathematical concepts, ideas, and models can require great creativity and often
generates great wonder and joy. To see Mathematics as merely calculations and mechanical
procedures is very limiting. Mathematics Education in schools should nurture this sense of
joy, curiosity, aesthetics, creativity, and wonder in all students.
Section 3.2
Nature of Knowledge
words, once assumptions (sometimes called axioms) are agreed upon, and a mathematical truth
is established based on those assumptions through logical and rigorous reasoning (sometimes
called proof), then that truth cannot be refuted or debated and is true for all time. On occasion,
truth, and this too is considered a breakthrough; this is because Mathematics is not just a
collection of truths, but is also a framework of methods, tools, and arguments used to arrive at
these truths.
Over thousands of years, the mathematical truths that are known to humans have grown in
knowledge, is cumulative — new concepts that are learned often build on those learned
previously.
truths), and then verifying/refuting those conjectures through logical and rigorous reasoning
creativity, sense of aesthetics, and elegance. Often, there are many different ways to arrive at the
reason that mathematicians often refer to their own subject as more of an art than a science.
Mathematics often uses a formal, stylised, and symbolic language for communication — in order
reason that developing intuition is described as an important aspect of learning and doing
Mathematics.
Section 3.3
Current Challenges
Our current education system has faced multiple challenges with respect to Mathematics
learning.
a.
learning in Mathematics and excludes them from effective economic and democratic
270
Mathematics Education
Mathematics is the art and science of discovering patterns and explaining them. These patterns
are all around us, in nature, in technology, and in the motion of the earth, sun, moon, and stars.
There is Mathematics in everything that we do and see, from shopping and cooking, to throwing
a ball and playing games, to solar eclipses and climate patterns. Mathematics thus gives us the
foundational concepts and capacities required to think about the world around us and the world
beyond us. But most of all, when taught well, Mathematics is truly enjoyable and can become a
lifelong passion. The goal of Mathematics Education is to bring to life these aspects of Mathematics.
Mathematics, including Computational Thinking, has never been more important globally, for
machine learning, data science, climate modelling, infrastructure development, and the numerous
communicating clearly and precisely — through content areas such as arithmetic, algebra,
geometry, probability, statistics, trigonometry, and calculus.
268
, National Curriculum Framework for School Education
Section 3.1
Aims
Mathematics helps students develop not only basic arithmetic skills, but also the crucial capacities
of logical reasoning, creative problem solving, and clear and precise communication (both oral
and written). Mathematical knowledge also plays a crucial role in understanding concepts in
other school subjects, such as Science and Social Science, and even Art, Physical Education, and
Vocational Education. Learning Mathematics can also contribute to the development of capacities
for making informed choices and decisions. Understanding numbers and quantitative arguments
is necessary for effective and meaningful democratic and economic participation.
Mathematics thus has an important role to play in achieving the overall Aims of School Education.
a. Basic Numeracy.
quantifying and performing calculating is essential for basic daily interactions, such as
shopping and banking. Mathematics Education in schools should ensure that all students
space and measurement.
b. Mathematical Thinking. Mathematical thinking involves systematic and logical ways to
think about and interpret the world. The capacities for identifying patterns, explaining
patterns, quantifying and measuring, using deductive reasoning, working with abstractions,
and communicating clearly and precisely are some illustrations of mathematical thinking.
Mathematics Education in schools should aim for developing such mathematical thinking in
all students.
c. Problem Solving.
through mathematical thinking is an important aspect of learning Mathematics. Clear and
precise formulation of problems and puzzles, knowing the appropriate mathematical
concepts and techniques that can model the problems, and possessing the techniques and
the creativity to solve the problems are core aspects of problem solving. Mathematics
Education in schools should aim for developing such problem-solving capacities in all
students. Problem solving also develops the capacities of perseverance, curiosity,
d. Mathematical Intuition. Developing an intuition for what should or should not be true in
working out precise answers, and engaging in informal argumentation before carrying out
rigorous proofs are all effective ways of developing such mathematical intuition in students.
Developing such mathematical intuition in all students should be one of the aims of
Mathematics Education in schools.
269
, National Curriculum Framework for School Education
e. Joy, curiosity, and wonder. Discovering, understanding, and appreciating patterns and
other mathematical concepts, ideas, and models can require great creativity and often
generates great wonder and joy. To see Mathematics as merely calculations and mechanical
procedures is very limiting. Mathematics Education in schools should nurture this sense of
joy, curiosity, aesthetics, creativity, and wonder in all students.
Section 3.2
Nature of Knowledge
words, once assumptions (sometimes called axioms) are agreed upon, and a mathematical truth
is established based on those assumptions through logical and rigorous reasoning (sometimes
called proof), then that truth cannot be refuted or debated and is true for all time. On occasion,
truth, and this too is considered a breakthrough; this is because Mathematics is not just a
collection of truths, but is also a framework of methods, tools, and arguments used to arrive at
these truths.
Over thousands of years, the mathematical truths that are known to humans have grown in
knowledge, is cumulative — new concepts that are learned often build on those learned
previously.
truths), and then verifying/refuting those conjectures through logical and rigorous reasoning
creativity, sense of aesthetics, and elegance. Often, there are many different ways to arrive at the
reason that mathematicians often refer to their own subject as more of an art than a science.
Mathematics often uses a formal, stylised, and symbolic language for communication — in order
reason that developing intuition is described as an important aspect of learning and doing
Mathematics.
Section 3.3
Current Challenges
Our current education system has faced multiple challenges with respect to Mathematics
learning.
a.
learning in Mathematics and excludes them from effective economic and democratic
270
