COURSE SYLLABUS
COURSE CODE
:
Mathematics in the Modern World Credit Unit /
No. of Hrs / Week
:
3 Unit /
3 Hours a Week Prerequisite to
:
None
Type of Course
:
General Education
Term
:
First Semester
School Year
:
2023-2024
Course Description : This course deals with the nature of Mathematics,
appreciation of its practical, intellectual, and aesthetic dimensions, and
application of mathematical tools in daily life.
The course begins with an introduction to the nature of mathematics as an
exploration of patterns (in nature and the environment) and as an application
of inductive and deductive reasoning. By exploring these topics, students
are encouraged to go beyond the typical understanding of mathematics as
merely a set of formulas but as a source of aesthetics in patterns of nature,
for example and a rich language in itself (and of science governed by logic
and reasoning.
The course then proceeds to survey ways in which mathematics provides a
tool for understanding and dealing with various aspects of present-day
living, such as managing personal finances, making social choices,
appreciating geometric designs, understanding codes used in data
transmission and security, and dividing limited resources fairly. These
aspects will provide opportunities for actually doing mathematics in a broad
range of exercises that bring out the various dimensions of mathematics in a
broad range of exercises that bring out the various dimensions of
mathematics as a way of knowing and test the students’ understanding and
capacity (CMO No. 20, Series of 2013)
● Learning Objectives :
● Knowledge
1. Discuss and argue about the nature of
mathematics, what it is and how it is
expressed.
2. Use different types of reasoning to justify
statements and arguments made about.
3. Discuss the language and symbols of mathematics.
Skills
4. Use variety of statistical tools to process and
manage numerical data
5. Analyze codes and coding schemes used for
identification, privacy and security
6. Use mathematics in other areas such as
finance, voting, health and medicine but
recreation.
Values
1. Appreciate the nature and uses of mathematics in
everyday life.
2. Affirm honesty and integrity in the application
of mathematics to various human.
Learning Outcomes
Topics
1. Identity
Section
1.
The
of
Patterns
in Nature
nature
and Mathematics:
regularities in
● Mathematics
the world.
in our world
(Week 1-2)
2. Articulate the
importance
of
Mathematics
3. Argue about
the nature of
mathematics,
what it is and
how it is
● Core
idea-Mathema
tics is a useful
way to think
about nature
and our world
Methodology
Video
watching Pair
sharing
Journal
writing
Questions:
What
is
Mathematics?
Modeling
Patterns in
the natural
world
Assessment
Evaluation and
Req.
Short
Response/Essa
y writing at the
end of the class
What
role
does
mathematics
play in
your world?
● Pattern
and
Numbers
in
nature
and Many pattern
the world
and
occurrences
exist in nature
● Mathematics
in our world
helps
and in our
organize
life.
pattern
and
the world
Mathematics
is just for the
books,
confined
in
the
classroom.
● Mathematics
Mathematics
helps predict
has no place
behavior
of
in my life
nature
and
phenomena in
the world.
● Mathematics
helps control
Resources
Nature
Number by
Ian Stewart
Days
adventure
in
Math
Wonderland
by Akiyama
& Ruiz
The
students
are unable to
elicit ideas and
concepts from
the reading and
video.
The
students
are able to elicit
ideas
from
readings
and
video and
shows correct
understanding
of these.
The student not
only elicit the
correct
ideas
from readings
and
videos
shows evidence
of internalizing
these,
and
consistently
contributes
additional
thoughts to the
core idea.
4. Express
appreciation
for
mathematics
as a human
endeavor
nature
and
occurences in
the world for
our
own
wnds.
● Mathematics
has numerous
applications in
the
world
making
it
indispensable
5. Discuss
the language,
symbols
and
conventions
of
mathematics.
● The
Nature
of
Mathematics
● Mathematical
Language
and symbols
Individual
or Required
small
group for Instructions:
exercises
Jamison
R
including games.
E
(2000)
Learning
Whole
class discussion the
Language
of
the
comparison
of Mathematics.
between
6. Explain
the
nature
of
mathematics
as a language
7. Perform
Operations
on
mathematical
expressions
correctly.
8. Acknowledge
that
mathematics is
a
useful
language
the English
language and
mathematical
Like any language language.
mathematics has its Compilation
own
symbols, of mathematical
syntax and rules.
symbols
Characteristics
and notations
of
and their
mathematical
symbols
language,
and notations
precise, concise
and their
and powerful.
meanings.
Expressions
Some ideas
vs Sentences
to elicit
Conventions in
and
the mathematical
encourage;
language.
Mathematics is
Four
basic
a
concepts; sets,
language in
functions, relations, itself.
binary
operations.
Mathematics as
Elementary logic, a language is
connectives
clear
and
negation variables. objective
Core Idea
●
●
●
●
●
●
Language
conventions are
necessary
in mathematics
for it to be
understood
by
all.
Mathematics is
not a language
but a useless set
of formal rules
and
alien
symbols.
Mathematics
confuses
the
communication
of concept and
ideas.
Language and
Learning across
the disciplines.
Required
for Students:
The Language of
Mathematics
(from
One
Mathematical
Cat,
Language and
Grammar
of Mathematics
(both attached)
Mathematics is
full
off
unnecessary
symbol rules
9. Use different
types
of reasoning
to
justify
statements
and
arguments
made
about
mathematical
concept.
tools
to
process
and manage
numerical
data
● The
nature
of
mathematics
● Problem
solving and
reasoning
● Inductive
and
deductive
reasoning.
10. White clear
and logical
proof
11. Solve
problems
involving
pattern
and
recreational
problems
following
Polya’s
four steps.
12. Organize
one’s method
and
approaches
for
proving
and
solving
problems.
13. Use a variety
of statistical
● Institution,
proof and
certainly
● Polya’s for
steps in
solving
problems
● Recreation
al Problem
solving
● Mathematics
as a tool
Activities:
1. Reading and
writing proofs
2. Small group
problem
solving
3. Whole class
discussion of
key problems
and solutions
Mathematics
requires not only
facilities
with
numbers but also
the
ability
to
critically
think
through situation, to
reason and argue
logically
and
creatively
solve
problems.
Mathematics is an
active
human
endeavor.
● Problem
solving
strategies
Mathematics is for
everyone
● Mathematical
Problems
involving
patterns.
Mathematical
solving
problem
takes time.
There may be be
more than one
mathematical
approach
Activities to do:
Lecture
and conventions.
Evaluation
Requirement:
Required:
Mathematical
Excursions by
R. Aufman et al.
What
is
mathematics really?
Recommended:
Mathematics, A
Practical Odyssey
by
Johnsons and
Mowry
The
number
Devil
by
Enzensberger
Proffesor Stewart’s
cabinet
of
mathematical
curiosities
by Ian
Stewart
One take
home problem set
Quiz on
proving using
deductive or
inductive
reasoning
Standard/Basis for
grading to use
0- Students
did
not
make any
attempt to
solve
the
problem set
or prove to
any
statement
1- The
students
attempted
to
solve 50%
of the
problem
in the
problem set
or
displayed
2- The
student
attempted
to solve the
problem set
or
displayed.
3- The
student is
able
to
completely
solve
50%
of
the
problem
4- The
student is
able
to
completely
solve
75%
of
the
problem set
14. Use
the
methods
of linear
regression
and
correlation
to predict
the value
15. Advovate
the use
of
statistical
data
● Statistical tools
derived
from
mathematics
are useful
in
processing
and managing
numerical data
in order to
described a
phenomenon
and
predict values.
in
the
problem.
Work
with
appropriate
computer
statistical
approach
in
making
important
decisions.
16. Apply
Geometric
concept
especially
isometrics
in
describing
and
creating
designs.
● Mathematics
as a tool.
Activities to do:
Required:
Evaluation:
Small group or
class sharing of
various
indigenous
designs
Geometry
Shapes,
Pattern and
Design a
chapter for a
New edition
of the Math
12 Textbook
for Ateneo
De Manila
University
Requirements:
a. 1
Proble
m set
b. 1 long test
c. Class
exhibit of
created
collected
indigenou
s
design.
17. Contribute
to the
enrichment
of the
Filipino
culture
and
arts using
concepts in
geometry
Geometric
Designs
Core Idea:
Geometry can help
enhance one’s artistic
prowess as well as
enrich one’s own
culture.
● Recognizing
and analyzing
geometric
shapes
● Transformation
Activities:
1. Role
Playing
2. Lectures
3. Written
Exercises
4. Compu
ter
Exercis
es
● Patterns
and
diagram
● Designs, Arts
and Culture
18. Use
Linear Programming
Activities:
Mathematic
al concepts
● Linear
1. Lectures
Inequalities
and tools in
2. Role
other areas
● Geometry
Playing
3. Written
of Linear
such as in
Excercises
● Simplex Method
finance,
voting,
logic,
business
networks
and system
Required:
For all
practical
purposes,
Introduction
to
Contemporar
y
Mathematics
2nd Edition by
COMAP, Inc.
A
student’s
Guide to
Coding and
Information
Theory by
Moser and
Chen
Evaluation
requirement:
3 quizzes
1 long test
Standard basis
off
grading
Numerical
Scores
Evaluation:
1. Probl
em
Set
2. An
integratin
g Project
Ex. Create a
poster aimed
and recruiting
students
to join a club that
promotes
mathematics as
an important tool
in
everyday life.