MODULE II
MATHEMATICAL LANGUAGE
AND SYMBOLS
Lesson 1 Variables
Lesson 2 The Language of Sets
Lesson 3 The Language of Relations
and Functions
, 2
MODULE II
Mathematical Language and Symbols
INTRODUCTION
There are over 4,000 languages and dialects in the world, and all of
them share one thing in common: they have a category for words
representing nouns, or objects, and a category for words representing verbs,
or actions. Taking this commonality as a starting point provides an
interesting way of looking at the mathematical world and its language. All
human languages have grammatical structures that distinguish between
nouns and verbs; these structures express the distinction between the
objects themselves and the actions carried out by or on the objects.
A model first proposed by the Balanced Assessment Program at the
Harvard Graduate School of Education (Schwartz & Kenney, 1995) suggests
that we think about mathematical nouns, or objects, as being numbers,
measurements, shapes, spaces, functions, patterns, data, and
arrangements—items that comfortably map onto commonly accepted
mathematics content strands. Mathematical verbs may be regarded as the
four predominant actions that we ascribe to problem-solving and reasoning:
• Modeling and formulating. Creating appropriate representations and
relationships to mathematize the original problem.
• Transforming and manipulating. Changing the mathematical form in
which a problem is originally expressed to equivalent forms that
represent solutions.
• Inferring. Applying derived results to the original problem situation,
and interpreting and generalizing the results in that light.
• Communicating. Reporting what has been learned about a problem to
a specified audience.
Taken as a whole, these four actions represent the process that we go
through to solve a problem. Taken individually, they represent actions that
students can develop and on which they can be assessed.
In addition, vocabulary may also be confusing because the words
mean different things in mathematics and non-mathematics contexts,
because two different words sound the same, or because more than one
word is used to describe the same concept. Symbols may be confusing either
because they look alike (e.g., the division and square root symbols) or
because different representations may be used to describe the same process
(e.g., •, *, and × for multiplication).
In this module, we look at how some of the ways in which language
plays a vital role in mathematics learning.
Module II includes the discussion of the following:
Lesson 1 Variables
Lesson 2 The Language of Sets
Lesson 3 The Language of Relations and Functions
Mathematics in the Modern World - Module II -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Discuss the language, symbols, and conventions of mathematics.
2. Explain the nature of mathematics as a language.
3. Perform operations on mathematical expressions correctly.
4. Acknowledge that mathematics is a useful language.
DIRECTIONS/ MODULE ORGANIZER
1. Module II consists of three (3) lessons. Take time to read all these
three (3) lessons, so you can have a better understanding and
appreciate about the language of mathematics and symbols.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module II -
MATHEMATICAL LANGUAGE
AND SYMBOLS
Lesson 1 Variables
Lesson 2 The Language of Sets
Lesson 3 The Language of Relations
and Functions
, 2
MODULE II
Mathematical Language and Symbols
INTRODUCTION
There are over 4,000 languages and dialects in the world, and all of
them share one thing in common: they have a category for words
representing nouns, or objects, and a category for words representing verbs,
or actions. Taking this commonality as a starting point provides an
interesting way of looking at the mathematical world and its language. All
human languages have grammatical structures that distinguish between
nouns and verbs; these structures express the distinction between the
objects themselves and the actions carried out by or on the objects.
A model first proposed by the Balanced Assessment Program at the
Harvard Graduate School of Education (Schwartz & Kenney, 1995) suggests
that we think about mathematical nouns, or objects, as being numbers,
measurements, shapes, spaces, functions, patterns, data, and
arrangements—items that comfortably map onto commonly accepted
mathematics content strands. Mathematical verbs may be regarded as the
four predominant actions that we ascribe to problem-solving and reasoning:
• Modeling and formulating. Creating appropriate representations and
relationships to mathematize the original problem.
• Transforming and manipulating. Changing the mathematical form in
which a problem is originally expressed to equivalent forms that
represent solutions.
• Inferring. Applying derived results to the original problem situation,
and interpreting and generalizing the results in that light.
• Communicating. Reporting what has been learned about a problem to
a specified audience.
Taken as a whole, these four actions represent the process that we go
through to solve a problem. Taken individually, they represent actions that
students can develop and on which they can be assessed.
In addition, vocabulary may also be confusing because the words
mean different things in mathematics and non-mathematics contexts,
because two different words sound the same, or because more than one
word is used to describe the same concept. Symbols may be confusing either
because they look alike (e.g., the division and square root symbols) or
because different representations may be used to describe the same process
(e.g., •, *, and × for multiplication).
In this module, we look at how some of the ways in which language
plays a vital role in mathematics learning.
Module II includes the discussion of the following:
Lesson 1 Variables
Lesson 2 The Language of Sets
Lesson 3 The Language of Relations and Functions
Mathematics in the Modern World - Module II -
, 3
OBJECTIVES
After studying the module you should be able to:
1. Discuss the language, symbols, and conventions of mathematics.
2. Explain the nature of mathematics as a language.
3. Perform operations on mathematical expressions correctly.
4. Acknowledge that mathematics is a useful language.
DIRECTIONS/ MODULE ORGANIZER
1. Module II consists of three (3) lessons. Take time to read all these
three (3) lessons, so you can have a better understanding and
appreciate about the language of mathematics and symbols.
2. Accomplish all the learning activities and submit them to your tutor
in the next face-to-face meeting.
3. For difficulties, try to contact the curriculum adviser or your
tutor/professor.
Mathematics in the Modern World - Module II -
