Republic of the Philippines

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES

STA. MARIA BULACAN, CAMPUS
Bachelor of Secondary Education major in Mathematics

COURSE TITLE HISTORY OF MATHEMATICS

COURSE CODE SEMA 30013
CREDIT UNITS 3 Units
COURSE PREREQUISITE None
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. It contains the works of some famous mathematicians like Pythagoras,
Euclid, Descartes, Newton, etc.

Institutional Learning Outcomes Program Outcomes Course Outcomes

1. Creative and Critical Thinking
Graduates use their imaginative as well as a
rational thinking ability to life situations in 1. Demonstrate basic and higher-level  Develop students’ skills and capabilities to acquire a broad knowledge on how
order push boundaries, realize possibilities, literacy, communication, necessary to critically analyze and present information using varied instructional
and deepen their interdisciplinary and general critical thinking, and learning skills resources.
understanding of the world. needed for higher learning  Determine the benefits and limitations of various instructional media utilized in
2. Effective Communication 2. Apply research skills acquired in the teaching – learning process.
Graduates are proficient in the four macro various subjects  Demonstrate proficiency in the utilization of instructional media resources to
skills in communication (reading, writing, 3. Execute a wide-range of teaching improve the quality of learning and increase teaching efficiency.
listening, and speaking) and are able to use process skills (including curriculum  Incorporate technology used by students, citizens and the workforce into the
these skills in solving problems. Making development, lesson planning, school curriculum.
decisions, and articulating thoughts when materials development, educational  Utilize appropriate instructional technology resources efficiently and effectively.
engaging with people in various assessment and teaching approaches)  Create rich, learning environments that build students’ competencies and
circumstances. applicable in various contexts independence.
3. Strong Service Orientation (community, nation, and world) and life-
 Practice and advocate ethical use of technology in both personal and
Graduates exemplify the potentialities of an long learning.
professional levels.
efficient, well-rounded and responsible 4. Exhibit employable skills,
 Create usable Instructional Materials such as diorama, collage, three-
professional deeply committed to service competencies, and work attitudes that
dimensional and visual aid materials.
excellence. will meet manpower requirements of
4. Community Engagement educational institutions and businesses  Present exhibit via electronic media platform such as youtube, facebook and
Graduates take an active role in the for social and economic development. other social media tools.
promotion and fulfillment of various 5. Share expertise in literacy, numeracy,
advocacies (educational, social and and livelihood technology to the
environmental) for the advancement of adopted community.
community welfare. 6. Keep abreast with technological
5. Adeptness in the Responsible Use of changes affecting lifestyle and
 Technology workplaces to be globally competitive
Graduates demonstrate optimized use of 7. Develop skills in integrating information
digital learning abilities, including technical and technology into the general and
and numerical skills. professional education subjects.
6. Passion to Lifelong Learning 8. Master the use of new methods,
Graduates are enabled to perform and techniques and tools in teaching and
function in the society by taking responsibility learning IT courses.
in their quest to know more about the world 9. Apply different tools and methodologies
through lifelong learning. in the engagement, development of IT
7. High Level of Leadership and services.
Organizational Skills 10. Display high level of leadership
Graduates are developed to become the best and organizational skills in school and
professionals in their respective disciplines by classroom management
manifesting the appropriate skills and 11. Practice the professional and
leaderships qualities. ethical requirements of the teaching
8. Sense of Personal and Professional profession
Ethics
Graduates show desirable attitudes and
behavior either in their personal and
professional circumstances.
9. Sense of National and Global
Responsiveness
Graduates’ deep sense of national
compliments the need to live in a global village
where one’s culture and other people culture
are respected.
Course Plan

Week Topic Learning Methodology Resources Assessment

Outcomes
(Synchronous) Cultivate the Orientation Course Syllabus Statements of Students’
Week 1 Introduction of the course interest and Setting of Rubrics Expectations
objectives, course initiative to acquire Expectations Presentation Slides
contents, activities and necessary Reviewing/ Discussing
requirements. knowledge, skills, the syllabus
and attitudes to Give some handouts
Assigned specialized become effective and linkages on some
topic (Research pre-service topics
Purposes) teachers in their Inform them on the
respective areas of required text and
specialization. some references to
consider
Week 2 (Asynchronous) Combine different Collaborative Activities MSTeam
Group Collaboration research Summary Reports
Creating Research information and Conducting group The History of Mathematics An Introduction by David M.
Material and employ in generate summary meeting Burton (Seventh Edition), A History of Mathematics by Uta Collaborative meeting
Producing personalized reports of given C. Merzbach and Carl B. Boyer (Third Edition), An Records
Instructional materials. particular topic in Research Activities Episodic History of Mathematics (Mathematical Culture
relation to History Through Problem Solving) by Steven G. Krantz Research Paper
Preparation for the Major of Mathematics Employing MS Word
Requirements such as and MS Powerpoint
Exhibits and Media Generalized facts application in
Presentation. and information developing research
based on the material.
research and
established
appropriate
materials in sharing
information about
the topic assigned.

Develop
interpersonal skill in
collaboration of
work.

(Synchronous) Show one’s Lecture/ Discussion The History of Mathematics An Introduction by David M. Screenshot of Class
Week 3 knowledge Peer Teaching Burton (Seventh Edition) Involvement and
Unit 1: Early Number regarding Primitive Discovery approach A History of Mathematics by Uta C. Merzbach and Carl B. Participation
Systems and Symbols Counting, A Sense Collaborative learning Boyer (Third Edition)
of Number An Episodic History of Mathematics (Mathematical Culture Recitation
Ancient Mathematics Explained the Readings and Video Through Problem Solving) by Steven G. Krantz
Ancient Presentation
Popular Mathematician in Mathematicians
https://www.slideshare.net/PEM2309/history-of-
Ancient Time. Contributions
mathematics-egyptian-and-babylonian
Understand the
concept of Number https://www.youtube.com/watch?v=cZH0YnFpjwU
Recording of the
Babylonians,
Deciphering
Cuneiform:
Grotefend and
Rawlinson, Writing
in Ancient China
Week 4 (Asynchronous) Enhancing Collaborative Collaborative Output
Group Collaboration Presentation using Discussion PowerPoint file to be
Media Platforms shared to everyone
Making Media
Presentation (Term Paper Develop
from the Assigned Topic) interpersonal skill in
collaboration of
work

(Synchronous) Know the Rhind Review or Recall The History of Mathematics An Introduction by David M. Short quiz from previous
Week 5 UNIT 2: Papyrus, The Lecture / Discussion Burton (Seventh Edition) Unit 1(10 items)
Mathematics in Early Rosetta Stone Situational analysis
Civilization Understand the Screenshots of Class
Egyptian Arithmetic Involvement and
Egyptians Arithmetic Analyze and Participation
assess the Four
Mesopotamia: Problems from the Recitation
Sexagesimal (base 60 Rhind Papyrus,
Egyptian
Mathematics as

Applied to
Arithmetic
Understand Egyptian
Geometry,
Approximating the Area
of a Circle
Understand Babylonian
Mathematics, A Tablet
of Reciprocals
Plimton, Babylonian
Use of the Pythagorean
Theorem

(Synchronous) Gained knowledge Readings/ The History of Mathematics An Introduction by David M. Short quiz from previous
Week 6 UNIT 3: Mathematics in in Hippocrates and Burton (Seventh Edition) Unit 2(10 items)
Early Civilizations the Quadrature of Instructional Materials An Episodic History of Mathematics (Mathematical Culture
the Circle Through Problem Solving) by Steven G. Krantz Screenshots of Class
Rise of the Watching Video Involvement and
Sophists, Plato’s The History of Mathematics An Introduction by David M. Participation
 Academy Discussion of their Burton (Seventh Edition)
Research A History of Mathematics by Uta C. Merzbach and Carl B. Recitation
Boyer (Third Edition)
Lecture and
Consultation

Peer Review
Small Group
Instructional Diagnosis
KWL
Week (Asynchronous) Develop creativity Collaborative Learning The History of Mathematics An Introduction by David M. Sample Model
7 Making Video Blogs skills in Burton (Seventh Edition), A History of Mathematics by Uta For Education
Planning and presentation Google meeting C. Merzbach and Carl B. Boyer (Third Edition), An Technology Room
Collaboration discussion Episodic History of Mathematics (Mathematical Culture
Lesson Planning Demonstrate Through Problem Solving) by Steven G. Krantz Rubrics:
Creating 3 Dimensional communication Handicraft making For Project presentation
Instructional Materials skills
such as diorama, frames, Model making
mathematical materials, Explain with
sculpture, model etc. mastery the subject Arts/ Drawing activities
assigned through
video blog making.

Employing
Educational
Technology in
learning and
teaching.

(Synchronous) Know Euclid and Lecture/Discussion The History of Mathematics An Introduction by David M. Short quiz from previous
Week 7 UNIT 4: The Beginnings the Elements, Small Group Burton (Seventh Edition) Unit 3(10 items)
of Greek Mathematics Euclid’s Life and Instructional Diagnosis
Writings Group Activity
The Alexandrian School: Euclid’s Foundation Drills and Exercises
Euclid for Geometry, Higher Order Results
Euclid’s Proof of Questioning Class Involvement and
the Pythagorean Participation
Theorem Drills and Exercises
Understand
Euclid’s Number
Theory, The
Algorithm of Euclid
 Eratosthenes, the
Wisa Man of
Alexandria, The
Sieve of
Eratosthenes,
Measurement of
the Earth
Know Archimedes,
Estimating the
Value of Pi

The Decline of
Alexandrian
Mathematics, The
Spread of
Christianity
(Synchronous) Be versed in The Review past lessons The History of Mathematics An Introduction by David M. Short quiz from previous
Week 8 Unit 5: The Twilight of Arithmetica, Peer Review Burton (Seventh Edition) Unit 4(10 items)
Greek Mathematics: Diophantus’s Peer Teaching A History of Mathematics by Uta C. Merzbach and Carl B.
Diophantus Number Theory Collaborative Boyer (Third Edition) Drills and Exercises
Understand Discussion A History of Mathematics by Uta C. Merzbach and Carl B. Results
Diophantine Small Group Boyer (Third Edition) Class Involvement and
Equations in Instructional Diagnosis Participation
Greece, India, and
China, Early Readings
Mathematics in
India, The Chinese Watching Video
Hundred Fowl’s
Problem
The Mathematical
Collection of
Pappus, Hypatia,
the First Woman
Mathematician,
Roman
Mathematics:
Boethius and
Cassiodorus
Analyze The
Algebra of al-
Khowarizmi, Omar
Khayyam, The
 Astronomers al-
Tusi and al-Kashi,
The Ancient
Chinese Nine
Chapters
Week 9 (Synchronous) Develop Critical Online Quiz Long Test 1
Long test 1 and Analytic Skills Multiple Choice type of
Platform Test
www.joinmyquiz.com Employ Platform:
Coverage: From Unit 1- mathematical www.joinmyquiz.com
Unit 5 techniques in
solving
mathematical
problem.

Remembering
information
necessary in
mastery of
mathematical
terms.

(Asynchronous) Explain the decline and Readings The History of Mathematics an Introduction by David M. Recorded Video
Week 10 UNIT 6: The First revival of learning, and Burton (Seventh Edition) MSTeam
Awakening: Fibonacci transmission of Arabic Watching Video
Learning to the West https://www.youtube.com/watch?v=SjSHVDfXHQ4
Exercises and Drills
Analyze the Hindu-
https://www.youtube.com/watch?v=9DV0u7encA4
Arabic Numerals, and
Shooting Videos
the Works of Jordanus
https://www.youtube.com/watch?v=S27k_gGjoHE
de Nemore
Demonstration Video
Demonstrate the blogs
Fibonacci Sequence
Discover the
Shooting and Video Pythagorean Number
Capturing (Video Blog Triples
making) for the assigned
topic Demonstrate
mastery of the topic
assigned.
 (Synchronous) Appreciate the Europe Question and Answer The History of Mathematics An Introduction by David M. Short quiz from previous
Week 11 UNIT 7: in the Fourteenth and approach of learning Burton (Seventh Edition) Unit 6(10 items)
The Renaissance of Fifteenth Centuries, The from previous lesson,
Mathematics: Cardan and Class Involvement and
Italian Renaissance,
Tartaglia Lecture/Discussion Participation
Artificial Writing: The Rubrics
Mathematics in Europe invention of Printing Peer Teaching
Applying and restoring
the Algebraic tradition: Situational analysis
Robert Recorde, The
Italian Algebraists:
Pacioli, del Ferro, and
Tartaglia
Explain the Cardan’s
Ars Magna, Bombelli
and Imaginary Roots of
the Cubic
Analyze Ferrari’s
Solution of the
Quadratic Equation,
The Story of the Quintic
Equation, Ruffini, Abel,
and Galois

(Asynchronous) Appreciate the Dawn of The History of Mathematics An Introduction by David M. Short quiz from previous
Week 12 UNIT 8: Modern Mathematics, Collaborative learning Burton (Seventh Edition) Unit 7(10 items)
The Mechanical World: Galileo’s Telescopic Technology A History of Mathematics by Uta C. Merzbach and Carl B.
Descartes and Newton Integration Boyer (Third Edition) Assignment. Applying
Observations, Francois
basic calculus
History of Calculus Vieta, the decimal Watching Videos procedure.
invention of Simon
Stevin, Napier’s Readings Problem Set
Invention of Logarithms, Exercises
and the Astronomical Drills and Exercises
Discoveries of Brahe
and Kepler
Relate to the works of
Descartes: The
Discours de la Methode,
 The algebraic Aspect of
La Geometrie,
Perspective Geometry:
Desargues and
Poncelet
Illustrates the works of
Newton: The Principia
Mathematica, The
Textbooks of Oughtred
and Harriot, Walli’s
Arithmetica Infinitorum,
The Lucasian
Professorship: Barrow
and Newton,

Summarize the
Gottfried Leibniz: The
Calculus Controversy,
Maria Agnesi and Emilie
du Chatelet

(Synchronous) Generalize the Origins Question and Answer The History of Mathematics An Introduction by David M. Short quiz from previous
Week 13 UNIT 9: The of Probability Theory, from the previous topic Burton (Seventh Edition) Unit 8(10 items)
Development of Graunt’s Bills of
Probability Theory: Moratility Lecture/ Discussion Problem Set
Pascal, Bernoulli, and Apply the Pascal and Activity
Laplace the Cycloid, Introducing Argument Class Involvement and
Mathematical Induction and Case study Participation
Appreciate the Bernoulli
Brothers: John and
James, Laplace, Daniel
Bernoulli, Poisson, and
Chebyshev

(Asynchronous) Identify the Marin Collaborative learning The History of Mathematics An Introduction by David M. Problem Set
Week 14 UNIT 10: The Revival of Mersenne and the Technology Burton (Seventh Edition) Activity
Number Theory: Fermat, Search for Perfect Integration A History of Mathematics by Uta C. Merzbach and Carl B. Screen shots of Class
Euler and Gauss Boyer (Third Edition) Involvement and
Watching Videos Participation
 Numbers
Employ the Famous Readings
Last Theorem of
Creating Video blogs
Fermat, Maclaurin’s
proper
Teatise on Fluxions

Explain the Prince of

Finalizing video editing Mathematicians: Carl
(Blog Making) Friedrich Gauss,
Lagrange, Monge, and
Carnot, The Legacy of
Gauss, Dirichlet and
Jacobi

(Synchronous) Attempts to Prove the Discussion of previous The History of Mathematics An Introduction by David M. Short quiz from previous
Week 15 UNIT 11: Nineteenth- Parallel Postulate, The problem set Burton (Seventh Edition) Unit 9-10(10 items)
Century Contributions: Efforts of Proclus, A History of Mathematics by Uta C. Merzbach and Carl B.
Lobachevsky to Hilbert Lecture and Boyer (Third Edition) Class Involvement and
Playfair, and Wallis,
Discussion An Episodic History of Mathematics (Mathematical Culture Participation
Saccheri Quadrilaterals, Through Problem Solving) by Steven G. Krantz Rubrics
The Accomplishment of
Legendre
Know The Founders of
Non-Euclidean
Geometry, Gauss’s
Attempt at a new
Geometry, The Struggle
of John Bolyai,
Lobachevsky Models of
the New Geometry:
Riemann, Beltrami, and
Klein, Grace Chisholm
Young
Understand the works
of D’ Alembert and
Cauchy on Limits,
Fourier’s Series, The
Father of Modern
Analysis, Weierstrass
 Sonya Kovalevsky, The
Axiomatic Movement:
Pasch and Hilbert

Understand the works

of Babbage and the
Analytical Engine,
Peacock’s Treatise on
Algebra, Hamilton’s
Discovery of
Quaternions, Matrix
Algebra: Cayley and
Sylvester

(Asynchronous) Differentiate Hardy and Discussion of their The History of Mathematics An Introduction by David M.
Week 16 UNIT 12: Extensions and Ramanujan, The previous Problem Set Burton (Seventh Edition) Screen Shots Class
Generalizations: Hardy, Rejuvenation of English An Episodic History of Mathematics (Mathematical Culture Involvement and
Hausdorff and Noether Readings Through Problem Solving) by Steven G. Krantz Participation
Mathematics, A Unique
Collaboration: Hardy Watching Videos
and Littlewood, India’s
Prodigy Ramanujan
Explain The Beginnings
of Point-Set Topology,
Frechet’s Metric
Spaces, The
Neighborhood Spaces
of Hausdorff, Banach
and Normed Linear
Spaces
Understand the works
of Emmy Noether’s
Theory of Rings, Von
Neumann and the
Computer, Women in
Modern Mathematics

(Synchronous) Develop Critical Online Quiz Long Test 2

 Week 17 Long Test 2 and Analytic Skills Multiple Choice type of
Platform Test
www.joinmyquiz.com Employ Platform:
Coverage: From Unit 6- mathematical www.joinmyquiz.com
Unit 12 techniques in
solving
mathematical
problem.

Remembering
information
necessary in
mastery of
mathematical
terms.

Week 18 FINAL EXAM Rubrics:

Creativity and Design-
Uploading the Electronic 25%
Exhibits (Video Blogs) Content Completeness
and Clarity of Information
Share to the file using FB –
platform and gain atleast 25%
500 likes Goal oriented and
Originality of Media
materials-
25%
Overall Impact and
Popularity
- 25%

Reading and References

The History of Mathematics An Introduction by David M. Burton (Seventh Edition), A History of Mathematics by Uta C. Merzbach and Carl B. Boyer (Third Edition), An Episodic
History of Mathematics (Mathematical Culture Through Problem Solving) by Steven G. Krantz
https://jontalle.web.engr.illinois.edu/uploads/298/HistoryMath-Burton.85.pdf
https://www.youtube.com/watch?v=cZH0YnFpjwU
https://www.youtube.com/watch?v=DVngFvtZwAU
https://www.storyofmathematics.com/greek.html#:~:text=To%20some%20extent%2C%20however%2C%20the,that%20which%20is%20learned%E2%80%9C).
https://www.youtube.com/watch?v=p5gn2hj51hs
https://www.math.uh.edu/~shanyuji/History/h-13a.pdf
https://www.youtube.com/watch?v=FjliV5u2IVw
https://www.youtube.com/results?search_query=fibonacci+theory+explained
https://mathshistory.st-andrews.ac.uk/Education/renaissance/
https://www.math.tamu.edu/~dallen/history/renaissc/renassc.html#:~:text=The%20general%20cultural%20movement%20of,the%20mathematics%20of%20the%20time.&text=The%20Italian
%20merchants%20of%20the,little%20by%20way%20of%20mathematics.
https://www.youtube.com/watch?v=fI1OeMmwYjU
https://www.cs.virginia.edu/~asb/teaching/cs202-spring07/slides/11-permutations-and-combinations.ppt
https://www.youtube.com/watch?v=pS6bQviSHrA
https://www.youtube.com/watch?v=D_qujUbNXHw&list=PLU3TaPgchJtTf-bN1OIn0XEmrO1unrl7O
https://www.youtube.com/watch?v=D_qujUbNXHw&list=PLU3TaPgchJtTf-bN1OIn0XEmrO1unrl7O
https://www.youtube.com/watch?v=SjSHVDfXHQ4

https://www.youtube.com/watch?v=9DV0u7encA4

https://www.youtube.com/watch?v=S27k_gGjoHE

Course Grading System

Class Standing 70%

 Shot Quiz / Long Tests - 30%

 Projects/Assignments/Output/Research Work – 30%
 Class Participation/ Collaboration Involvement Recitation- 10%

Midterm Examination(Final Exam Equivalent / Final Examinations 30%

100%

Midterm Grade + Final Term Grade = FINAL GRADE

2
Classroom Policy
 Suggest students for their own suggestions on the best ways to keep in touch.
 Help our students feel included in the process of rethinking education for a challenging time.
 Extend a sense of care to our students and try to build community that’s going to be able to work together to get through the learning challenges that we have
 Collect work or activity via email, save into folders.
 Students are expected to be academically honest. cheating, lying, and other form of immoral and unethical behavior will not be tolerated.
 Cheating during the examination or quiz, the student will get a grade of 5.0 in that particular exam or quiz or failure in the course.
 Absences, during Synchronous meeting due to connection problem, work related, personal matters must inform instructor ahead of time as much as possible for
monitoring purposes.

Consultation Time
Schedule of meeting with the teacher to discuss a particular problem with a student in order to provide advice.( M-F 8:00 AM – 5:00 PM Only Via FB Messenger)

Prepared by: Reviewed by:

Jay-R A. Manamtam, MOM Dr. Katherine Joyce M. Castro

Academic Head, PUP Santa, Maria, Bulacan Campus

Modified by:

Leonardo G. Correa MATh

Faculty Member, PUP SMB Campus

Noted by:

Assoc. Prof. Marilyn F. Isip, MBE

Campus Director, PUP Santa Maria, Bulacan Campus

Approved by:

Emmanuel C. De Guzman PhD

Vice President for Academic Affair
Revised October 2022