MTHddd 111 - HISTORY OF MATHEMATICS.docx

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1. History of Mathematics

UNIVERSIDAD DE MANILA
Revision Date: September 4, 2023
College of Education
First Semester
Bachelor of Secondary Education major
Mathematics
S.Y. 2023-2024
University Vision
A leading Higher Education Institution that prepares visionary and ethical leaders who shall create a
positive impact in the society
University Core Values
E – Ethics and Integrity
Q – Quality and Excellence
U – Unity and Collaboration
A – Achievement and Passion
L – Leadership and Innovation
University Mission
Universidad De Manila is committed to provide equal opportunities by developing the learners’
knowledge, skills, and values, through quality education and technology-driven systems, in a diverse
yet inclusive environment for learning, research, and community engagement
College of Education Vision
A local-rooted yet globally competitive college with a bold vision to become a true Center of
Excellence in Teacher Education, dedicated to nurturing visionary and ethical professionals who
excel in an inclusive and diverse learning environment.
College Core Values
E - Empowered
D – Diverse and Globally Competitive
U – Upholding Ethical and Moral Standards
C – Committed to Unwavering Excellence
A – Adaptive and Resilient
R – Rigorously Research and Extension-Driven
E – Education Rooted in Compassion
We EDUcate, we CARE
College of Education Mission
To cultivate a lifelong gender-sensitive environment that champions quality education of
the highest standard, benefiting the city, country, and global community
Program Outcomes
Common to the Teacher Education
1.Articulate the rootedness of education in philosophical, social, cultural, historical, psychological, and political contexts.

2. 2.Demonstrate master of subject matter/discipline.
3.Facilitate learning and delivery modes appropriate to specific learners and their environments.
4.Develop innovative curricula, instructional plans, teaching approaches, resources for diverse learners.
5.Apply skills in the development and utilization of ICT to promote quality, relevant, and sustainable educational practices.
6.Demonstrate a variety of thinking skills in planning, monitoring, assessing, and reporting learning processes and outcomes.
7.Practice professional and ethical teaching standards sensitive to the changing local, national and global realities.
8.Pursue lifelong learning for personal and professional growth through varied experiential and field-based opportunities.
Specific to Bachelor of Secondary Education major in Mathematics
1.Exhibit competence in mathematical concepts and procedures.
2.Exhibit proficiency in relating mathematics to other curricular areas.
3.Manifest meaningful and comprehensive pedagogical content knowledge (PCK) of mathematics
4.Demonstrate competence in designing, constructing, and utilizing different forms of assessment in mathematics.
5.Demonstrate proficiency in problem solving by solving and creating routine and non-routine problems with different levels of complexity.
6.Use effectively appropriate approaches, methods, and techniques in teaching mathematics including technological tools.
7.Appreciate mathematics as an opportunity for creative work, moments of enlightenment, discovery and gaining insights of the world.
Grading System
Final Grade = 30% preliminary + 30% midterm + 40% pre-final
Preliminary Grade (Weight = 30%)
• Class Standing = 60%
• Prelim Examination = 40%
Preliminary Grade = 100%
Mid-Term Grade (Weight = 30%)
• Class Standing = 60%
• Mid-Term Examination = 40%
Mid-term Grade = 100%
Pre-Final Grade (Weight = 40%)
• Class Standing = 60%
• Final Examination = 40%
Pre-final Grade =100%
Course Code Course Name History of Mathematics
Pre-requisite Subject Course Credit 3 units, 3 hrs./wk. (18 weeks, 54 hrs.
total)

3. Course Description
The course presents the humanistic aspects of mathematics which provides the historical context and timeline that led to the
present understanding and applications of the different branches of mathematics Topics included in this course are not very technical
and rigid aspects of mathematics; rather they are early, interesting, and light developments of the field. They are intended to enrich the
background of the students in the hope that the students find value and inspiration in the historical approach to the mathematical
concepts.
Course Learning Outcomes
At the end of the course, the pre-service teachers should be able to:
A.Demonstrate knowledge and understanding of the historical facts and landmarks that led to the development of the
different branches and schools of thought in mathematics;
B.Show critical and creative thinking in analyzing popular problems involving foundational concepts in mathematics; and
C.Manifest appreciation for mathematics as a dynamic field through sharing of personal experiences of enlightenment
relative to the evolution of the different branches of mathematics.

4. Time
Allotment
Intended Learning Outcomes (ILOs) Content Suggested Teaching Learning
Activities
Suggested Assessment
Week 1-3At the end of the week, the pre-
service teacher (PST) should be able
to:
Discuss the development of
mathematics in the ancient
period
Show the evolution of
numeration systems in
ancient times
Recognize the symbols and
notations used
Perform the mathematical
operations used in this
period.
Unit 1. The Development of
mathematics: ancient period
a.Origins of Mathematics:
Egypt and Babylonia
b.Mathematics of Ancient
Greece
c.Islamic, Hindu and
Chinese Mathematics
1.Content Focus / Discussion
2.Library work
3.Book reports
Formative Assessment:
1.Pen and Paper quiz
2.Seatwork
3.Class participation
Week 4-6At the end of the week, the pre-
service teacher (PST) should be able
to:
Discuss the development of
mathematics in the medieval
and renaissance period
Discuss the birth of the
calculus: Newton and Leibniz
Identify the giants of
mathematics in this period
and discuss their
contributions.
Unit 2. The Development of
mathematics: a historical
overview: Medieval Period
a.Medieval period and
the Renaissance
b.Birth of the Calculus
c.Euler, Fermat and
Descartes
1.Content Focus / Discussion
2.Library work
3.Book reports
Formative Assessment:
1.Pen and Paper quiz
2.Seatwork
3.Class participation

5. Week
7-10
At the end of the week, the pre-
service teacher (PST) should be able
to:
Discuss the origin of non-
Euclidean geometries
Identify the personalities
associated with non-
Euclidean geometries
Present a timeline of these
geometries from the time of
their conception
Examine the origins of
modern algebra and number
theory and set theory
Identify the personalities
associated with these
branches of mathematics
Discuss the problems in the
foundations of mathematics
Unit 3. The Development of
mathematics: a historical
overview: Modern Period
a.Non-Euclidean
Geometries
b.Modern algebra and
number theory
c.Birth of set theory and
problems in the
foundations of
mathematics
1.Content Focus / Discussion
2.Individual / Group Drill and
Practice
3.Library work
4.Book reports
Formative Assessment:
1.Pen and Paper quiz
2.Seatwork
3.Class participation
Week
11-13
At the end of the week, the pre-
service teacher (PST) should be able
to:
Discuss what is mathematics
from a variety of points of
view
Discuss and describe what
mathematicians do.
Discuss and debate the origin
of mathematics
Unit 4. The Nature of
Mathematics
a.What is mathematics?
b.What do
mathematicians do
c.Is mathematics
invented or created?
1.Content Focus / Discussion
2.Individual / Group Drill and
Practice
3.Problem Solving
Formative Assessment:
1.Pen and Paper quiz
2.Seatwork
3.Class participation

6. Week
14-18
At the end of the week, the pre-
service teacher (PST) should be able
to:
Discuss the foundations and
formalism of mathematics
Discuss the relationship
between mathematics and
emergence of technology
UNIT 5. Issues and Aspects
a.The concepts and role
of the proof
b.Infallibility and certainty
in mathematics
c.Mathematics and
technology: the role of
computers
1.Content Focus / Discussion
2.Individual / Group Drill and
Practice
3.Individual/Group
demonstrations
Formative Assessment:
1.Pen and Paper quiz
2.Seatwork
3.Class participation
References
Burton, D. M. (2010). The history of mathematics: An introduction (7th ed). McGraw-Hill Education
Davis, P., Hersh, R., & Marchisotto, E. A. (2011). The mathematical experience. Springer Science & Business
Media. Dunham, W. (1991). Journey through genius: The great theorems of mathematics. Wiley.
Hodgkin, L. (2005). A history of mathematics: from Mesopotamia to modernity. Oxford University Press on
Demand. Katz, V. J. (2009). The History of Mathematics: An (3rd ed). Pearson Addison-Wesley.
Consultation Hours:
Monday – Friday: 1:00 – 4:00 PM
Prepared and revised by:
Ronnie F. Sta. Maria
Checked By:
Dr. Amalfi B. Tabin Jr.
Approved by
Dr. Ronald A. Herrera