Math in the Modern World - Module 1 (Sequences)
1.1 Mathematics in our World
(A Study of Patterns)
Overview
Welcome to the first module of GE 1 (Mathematics in the Modern World)!
This course begins with an introduction to the nature of mathematics as an exploration of unseen
patterns in nature and environment, a rich language in itself governed by logic and reasoning, and
an application of inductive and deductive reasoning.
Section 1 is composed of the following: 1.1 Mathematics in our World; 1.2 Mathematics Language
and Symbols; and 1.3 Problem Solving and Reasoning. These topics will allow students to go
beyond the typical understanding of mathematics as purely a bunch of memorized formulas and
duplicated mathematical computations, but as a powerful tool used to understand better the
world around us. Moreover, we will discuss and argue about the nature of mathematics, what it is,
and how it is expressed, represented, and used. We will study mathematics as a language in order
to read and write mathematical texts and communicate ideas with precision and conciseness. We
will also justify statements and arguments made about mathematics and mathematical concepts
using different methods of reasoning.
Mathematics has always been perceived as a study of numbers, symbols, and rules. It is an art of
geometric shapes and patterns, a tool in decision-making and problem solving. It has a language
that differs from the ordinary speech. It is done with curiosity, with a penchant for seeking
patterns and generalities, with the desire to know the truth, with trial and error, and without the
fear of facing more questions and problems to solve. The following diagram shows the very nature
of mathematics.
study of
patterns
art language
Mathematics
is a/an …
set of process of
problem- thinking
solving tools
Nocon, R. & Nocon, E.
In this module, we will focus on Lesson 1.1 - Mathematics in our World (A Study of Patterns). The
lesson is anchored by the following core idea: Mathematics is a useful way to think about nature
and the world. Our intention is to observe things, in both in nature and the world, through pattern-
,seeking, understand the substantial interconnection and relationship of the mathematics and the
world, and appreciate mathematics as a discipline full of essence and beauty
Learning Outcomes
After working on this module, you will be able to:
1. identify patterns in nature and irregularities;
2. articulate the importance in mathematics in one’s life;
3. argue about mathematics, what it is, how it is expressed, represented, and
used; and
4. express appreciation for mathematics as a human endeavor.
Activities To Do
1.) Watch the video “Nature by Numbers” by Cristóbal Vila
(link:
https://vimeo.com/9953368) and write one (1) sentence that describes your impression
after watching the video.
2.) Identify pattern/s observed in the pictures.
(a) ( b)
(c)
, (d)
(e)
Questions To Ponder
The video and the pictures leave us questions to think about.
• What are the different kinds and forms of patterns you have seen in the video
and/or pictures?
• How does these patterns help us understand the connection between our world
and mathematics?
Patterns and Numbers in Nature and the World
When we buy clothes, accessories, furniture, house decorations, and other similar objects, we
tend to look for beautiful geometric designs or patterns. We appreciate the patterns seen in the
colorful wings of butterflies, the arrangement of flowers and leaves, the reflection of the mountain
tops to the clear waters of lakes, the different shapes of clouds in the skies, and other patterns seen
in the nature. In the busy streets of the cities, we are impressed by the intricate but well-designed
modern homes and high-rise buildings. We are wowed by nature and man-made creations because
of these repeated designs of geometric visuals.
Repeated ways or occurrences that happens or was done are also considered as patterns. For
example, the cycle of the moon, the changing seasons, and even the transmission pattern of the
COVID 19 pandemic.
Patterns surround us. It is everywhere and are in every people’s task or activity.
Mathematics, developed by human mind and culture, is a formal system of thought for
recognizing, classifying, and exploiting patterns. (Stewart, I.). Mathematics is indeed a study of
patterns. Results in mathematics are brought by the generalizations of patterns. The study of
patterns allows us to observe and identify relationships, discover logical connections, and make
generalizations. Moreover, the use and study of patterns allows us to be logical thinkers and better
problem solvers.
1.1 Mathematics in our World
(A Study of Patterns)
Overview
Welcome to the first module of GE 1 (Mathematics in the Modern World)!
This course begins with an introduction to the nature of mathematics as an exploration of unseen
patterns in nature and environment, a rich language in itself governed by logic and reasoning, and
an application of inductive and deductive reasoning.
Section 1 is composed of the following: 1.1 Mathematics in our World; 1.2 Mathematics Language
and Symbols; and 1.3 Problem Solving and Reasoning. These topics will allow students to go
beyond the typical understanding of mathematics as purely a bunch of memorized formulas and
duplicated mathematical computations, but as a powerful tool used to understand better the
world around us. Moreover, we will discuss and argue about the nature of mathematics, what it is,
and how it is expressed, represented, and used. We will study mathematics as a language in order
to read and write mathematical texts and communicate ideas with precision and conciseness. We
will also justify statements and arguments made about mathematics and mathematical concepts
using different methods of reasoning.
Mathematics has always been perceived as a study of numbers, symbols, and rules. It is an art of
geometric shapes and patterns, a tool in decision-making and problem solving. It has a language
that differs from the ordinary speech. It is done with curiosity, with a penchant for seeking
patterns and generalities, with the desire to know the truth, with trial and error, and without the
fear of facing more questions and problems to solve. The following diagram shows the very nature
of mathematics.
study of
patterns
art language
Mathematics
is a/an …
set of process of
problem- thinking
solving tools
Nocon, R. & Nocon, E.
In this module, we will focus on Lesson 1.1 - Mathematics in our World (A Study of Patterns). The
lesson is anchored by the following core idea: Mathematics is a useful way to think about nature
and the world. Our intention is to observe things, in both in nature and the world, through pattern-
,seeking, understand the substantial interconnection and relationship of the mathematics and the
world, and appreciate mathematics as a discipline full of essence and beauty
Learning Outcomes
After working on this module, you will be able to:
1. identify patterns in nature and irregularities;
2. articulate the importance in mathematics in one’s life;
3. argue about mathematics, what it is, how it is expressed, represented, and
used; and
4. express appreciation for mathematics as a human endeavor.
Activities To Do
1.) Watch the video “Nature by Numbers” by Cristóbal Vila
(link:
https://vimeo.com/9953368) and write one (1) sentence that describes your impression
after watching the video.
2.) Identify pattern/s observed in the pictures.
(a) ( b)
(c)
, (d)
(e)
Questions To Ponder
The video and the pictures leave us questions to think about.
• What are the different kinds and forms of patterns you have seen in the video
and/or pictures?
• How does these patterns help us understand the connection between our world
and mathematics?
Patterns and Numbers in Nature and the World
When we buy clothes, accessories, furniture, house decorations, and other similar objects, we
tend to look for beautiful geometric designs or patterns. We appreciate the patterns seen in the
colorful wings of butterflies, the arrangement of flowers and leaves, the reflection of the mountain
tops to the clear waters of lakes, the different shapes of clouds in the skies, and other patterns seen
in the nature. In the busy streets of the cities, we are impressed by the intricate but well-designed
modern homes and high-rise buildings. We are wowed by nature and man-made creations because
of these repeated designs of geometric visuals.
Repeated ways or occurrences that happens or was done are also considered as patterns. For
example, the cycle of the moon, the changing seasons, and even the transmission pattern of the
COVID 19 pandemic.
Patterns surround us. It is everywhere and are in every people’s task or activity.
Mathematics, developed by human mind and culture, is a formal system of thought for
recognizing, classifying, and exploiting patterns. (Stewart, I.). Mathematics is indeed a study of
patterns. Results in mathematics are brought by the generalizations of patterns. The study of
patterns allows us to observe and identify relationships, discover logical connections, and make
generalizations. Moreover, the use and study of patterns allows us to be logical thinkers and better
problem solvers.
