2hiphima

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HOLY ANGEL UNIVERSITY School of Education

Angeles City

HAU MISSION AND VISION

We, the academic community of Holy Angel University, declare ourselves to be a Catholic University. We dedicate ourselves to our core purpose, which is to provide accessible quality education that transforms students into persons of conscience, competence, and compassion.

We commit ourselves to our vision of the University as a role--‐model catalyst for countryside development and one of the most influential, best--‐managed Catholic universities in the Asia--‐Pacific region.

We will be guided by our core values of Christ--‐ centeredness, integrity, excellence, community, and societal responsibility. All these we shall do for the greater glory of God. LAUS DEO SEMPER!

School of Education Vision

The leading Catholic institution of teacher education in the region that serves as a benchmark for quality instruction, research and other best teaching learning practices.

Mission

To provide quality education that enables students to be critical thinkers, mindful of their responsibilities to society and equipped with holistic education catering to the heart and soul as well as to the body and mind.

Goals

To offer programs and projects that promote Christ centeredness, integrity, excellence, community and societal responsibility, leadership, scholarship, lifelong learning, effective communication, innovation, gender sensitivity and technological integration

Objectives

1. To provide students with the opportunities and exposure to develop them and become highly competent educators, leaders and experts who continuously work for the advancement of educational thinking and practice

2. To instill in the students the spirit of community involvement through relevant programs/projects and become more responsive to the challenges of a progressive and dynamic society

3. To continuously hire academically and professionally qualified and competent faculty equipped with expertise and exposure needed in the practice of the profession

4. To serve as a benchmark for quality instruction, research and best teaching learning practices

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Teacher Education Program Outcomes

1. Have the basic and higher level literacy, communication, numeracy, critical thinking, learning skills needed for higher learning

2. Have a deep and principled understanding of the learning processes and the role of the teacher in facilitating these processes in their students 3. Have a deep and principled understanding of how educational processes relate to a larger historical, social, cultural, and political processes 4. Have a meaningful and comprehensive knowledge of the subject matter they will teach

5. Can apply a wide range of teaching process skills ( including curriculum development, lesson planning, materials development, educational assessment, and teaching approaches)

6. Have direct experience in the field/classroom ( e.g. classroom observation, teaching assistant, practice teaching) 7. Can demonstrate and practice the professional and ethical requirements of the teaching profession

8. Can facilitate learning of diverse types of learners, in diverse types of learning environments, using a wide range of teaching knowledge and skills

9. Can reflect on the relationships among the teaching process skills, the learning processing in the students, the nature of the content/subject matter, and the broader social forces encumbering the school and educational process in order to constantly improve their teaching

knowledge, skills, and practices

10. Can be creative and cooperative in thinking of alternative teaching approaches, take informed risks in trying out these innovative approaches, and evaluate the effectiveness of such approaches in improving student learning ; and

11. Are willing and capable to continue learning in order to better fulfill their mission as teachers.

COURSE SYLLABUS IN

HISTORY AND PHILOSOPHY OF MATHEMATICS (2HIPHIMA)

Faculty: GIL V. TIONGCO

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Course Title:HISTORY AND PHILOSOPHY OF MATHEMATICS Course Code: 2HIPHIMA

Number of Units:3 UNITS

Contact Hours Per Week:3 HOURS Pre-requisite subject/s: NONE COURSE DESCRIPTION

The three-unit course, which explores the humanistic aspects of Mathematics, provides the historical contexts and approaches developed which led to the present understanding of the mathematical concepts. It discusses the history of Mathematics by chronological period from the ancient civilization to the modern times. It also attempts to uncover the philosophical nature of Mathematics.

COURSE LEARNING OUTCOMES

At the end of the course, the students are expected to:

1. Demonstrate a working knowledge and selected techniques and procedures from history of Mathematics.

2. Demonstrate a critical analysis on the kind of Mathematics they are dealing with.

3. Associate the history of Mathematics with the history of human civilization in general 4. State reasons for studying Mathematics.

5. Identify various societal pressures that influence the development of mathematics.

6. Discuss the different philosophical schools of mathematical thought.

7. Demonstrate creative and critical thinking skills.

8. Appreciate human participation in the development of mathematics by associating the names and accomplishments of particular individuals with respective events in mathematics.

9. Demonstrate the values of patience, perseverance and hardworking as what themathematicians had exemplified.

10. Construct line of the history of Mathematics COURSE CONTENT:

Timetable (Hours)

Desired Learning Outcomes Course Content/Subject Matter Teaching and Learning Activities

Assessment Task/Student Output

Evaluation Tool Resource Materials

1

Discuss the importance of a well-managed and organized classroom environment that is conducive to learning.

Classroom administration and management

Interactive Lecture Course outline seen

and signed by student

Student Handbook

Katz, Victor. A

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3

2

Discuss the significance of Ancient mathematics. Give the reasons for studying the history of Mathematics.

Show a working knowledge and selected techniques and

procedures from the ancient Mathematics.

Explain The significance of Greek Mathematics

Give and discuss the

contributions of Phythagoras and Plato

Discuss the contributions of Euclid, Archimedes and Apollonius

Discuss the contributions of Erasthoshenes, Sieve, Heron, Diophantus and Pappus

Identify other Greek Mathematicians.

Give and discuss the

contributions of other Greek Mathematicians

I. ANCIENT MATHEMATICS A. Counting

B. Arithmetic Computation C. Numeration Systems D. Elementary Geometry E. Babylonian & Egyptian Mathematics

II. GREEK MATHEMATICS a. The earliest Greek

Mathematics

b. Phytagoras& his school c. Plato

d. Euclid and the Elements e. Archimedes Physics,

Numerical calculations and Geometry

f. Apollonius and Conics g. Erasthosthenes and the Sieve h. Heron

i. Diophantus j. Pappus

k. Other Greek Mathematicians

Interactive

Lecture/Powerpoint Presentation

Internet Resource List Cooperative Learning Demonstration

Interactive Lecture/

Discussion Peer Exchange (Students swap their work, motivating them to think more about the material and discuss it among themselves.

Interactive

Lecture/Discussion Demonstration

Interactive Lecture/

Discussion

Demonstration Puzzles

Engaged Recitation Group work

Exercise/Drills

Reading assignment Cooperative Learning Cooperative Learning Quiz

Mathematicians Disc (student are required to make instructional materials that can be used in

presenting lesson) Quiz

Quiz

Only One Correct Answer

Rubric for group work

Seatwork/Group

Must attain at least 60 % passing rate

Rubric for

Mathematicians Disc

History of Mathematics: An Introduction, New York: Harper Collins, 1993

Swetz Frank J.

and Vistro-Yu Catherine. The History of Mathematics. A Study Guide, Ateneo de Manila University: Office of Research and Publication. Quezon City 1999.

Katz, Victor. A History of Mathematics: An Introduction, New York: Harper Collins, 1993

Swetz Frank J.

and Vistro-Yu Catherine. The History of Mathematics. A Study Guide, Ateneo de Manila University: Office of Research and Publication.

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2

Discuss human participation in the development of Hindu and Arabian Mathematics

Compare Greek and Hindu Mathematics

Explain the Mathematics of Islam.

Identify various societal pressures that influence the development of the

Mathematics of Islam.

III. HINDU AND ARABIAN MATHEMATICS

a. Number computing b. Arithmetic and Algebra c. Comparison of Greek and

Hindu Mathematics d.

e. The Mathematics of Islam f. Arithmetic and Algebra g. Geometry and Trigonometry

Interactive

Lecture/Discussion thru powerpoint

presentation

Behavioral modeling (An instructional activity that

demonstrates how to perform an action or set of actions in a specific environment

InteractiveLecture/

Discussion thru Powerpoint Presentation

Cooperative Learning

Practice Drills/Cooperative Learning

Must attain at least 60

% passing rate

Quezon City 1999.

Katz, Victor. A History of Mathematics: An Introduction, New York: Harper Collins, 1993

Swetz Frank J.

and Vistro-Yu Catherine. The History of Mathematics. A Study Guide, Ateneo de Manila University: Office of Research and Publication. Quezon City 1999.

1 PRELIMINARY EXAMINATION

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3

2

3

2

Enumerate the human

participation in the development of European Mathematics.

Discuss European Mathematics

-Discuss The Fourteenth Century, The Early Arithmetic

And The Beginning of Algebraic Symbolism

Identify the contributions of Viete and other Mathematicians

Discuss The Dawn of Modern Mathematics,

The Seventeenth Century and Logarithms

Give and explain the contributions of Galileo , Kepler

and Pascal

Discuss Analytic Geometry and Other Pre-calculus Development.

Enumerate and discuss the contributions of Rene Descartes

Give and discuss the contributions of Pierre de Fermat

And Other Seventeenth Century Mathematicians

Discuss Calculus and related concepts

Compare The Beginnings of Differentiation from

The Beginnings of Integration Give and explain the contributions

IV. EUROPEAN MATHEMATICS

a. The Dark Ages

b. The Period of Transmission c. The Thirteenth Century and

Fibonacci

d. The Fourteenth Century e. The Early Arithmetic f. The Beginning of Algebraic

Symbolism

g. Francois Viete and other Mathematicians

V. THE DAWN OF MODERN

MATHEMATICS

a. a.The Seventeenth Century b. b.Logarithms

c. c.Galileo and Kepler d. d.D. Pascal

VI. ANALYTIC GEOMETRY AND OTHER PRE-CALCULUS

DEVELOPMENT

A. Analytic Geometry B. Rene Descartes C. Pierre de

D. Other Seventeenth Century Mathematicians

VII. THE CALCULUS AND RELATED CONCEPTS

a. The Beginnings of Differentiation b. The Beginnings of

Integration

c. Wallis and Barrow

Interactive

Lecture/Discussion using illustrative examples

Interactive

Lecture/Discussion using illustrative examples Demonstration

Interactive

Lecture/Discussion Demonstration

Lecture/Discussion using illustrative examples Demonstration

Interactive

Lecture/Discussion using illustrative examples Open Discussion Peer Exchange

Practice Drills/Seatwork

Cooperative Learning Engaged Recitation Group work Quiz

Learning

Engaged Recitation Group work Quiz

Cooperative Learning Cooperative Learning Engaged Recitation Group work Quiz

Rubric on Group Output/Presentatio n

Rubric on Group Presentation

College Algebra 3^rd Edition by Bautista

Katz, Victor. A History of Mathematics: An Introduction, New York: Harper Collins, 1993 Swetz Frank J. and Vistro-Yu

Catherine. The History of Mathematics. A Study Guide, Ateneo de Manila

University: Office of Research and Publication.

Quezon City 1999.

History of Mathematics: An Introduction, New York: Harper Collins, 1993 Swetz Frank J. and Vistro-Yu

University: Office of Research and

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3

of Wallis and Barrow

Give and discuss the contributions of Newton , Leibniz, Other Mathematicians

d. Newton e. Leibniz

f. Other Mathematicians

Group Presentation Publication.

Quezon City 1999.

1 MIDTERM EXAMINATION

4

3

4

Discuss human participation during the transition to the twentieth Century

Enumerate the significant events of the nineteenth century

Explain the Bernoulli Family Give and explain the contributions of Laplace, Legendre and Gauss

Identify the other Mathematicians during the transition to the twentieth century

Discuss the philosophy of Mathematics

Identify the philosophical schools of Mathematical thought

VIII. TRANSITION TO THE TWENTIETH

a. Significant Events of the Nineteenth Century b. The Bernoulli Family c. Laplace, Legendre, Gauss IX. IX. SEARCH FOR

CERTAINTY: INTO THE TWENTIETH CENTURY X. PHILOSOPHY OF

MATHEMATICS a. Logicism b. Intuitionism c. Formalism d. Constructivism

Interactive

Lecture/Discussion using illustrative examples Open Discussion

Interactive

Lecture/Discussion using illustrative examples Open Discussion Peer exchange

Quiz

Katz, Victor. A History of Mathematics: An Introduction, New York: Harper Collins, 1993 Swetz Frank J. and Vistro-Yu

University: Office of Research and Publication.

Quezon City 1999.

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1 FINAL EXAMINATION

COURSE REQUIREMENTS

Class Standing: quizzes, drills/exercises, written and oral report, learning paper, projects, lesson demonstration Major Exams: Prelim, Midterm, Finals

Grading System:

CSP- Class Standing in the Prelim Period Transmutation Table For the Average*

CSM- Class Standing in the Midterm Period Average Point-Grade Equivalent

CSF- Class Standing in the Final Period 97-100 1.00

P - Prelim Exam 94-96 1.25

M - Midterm Exam 91-93 1.50

F - Final Exam 88-90 1.75

85-87 2.00

Midterm Average= 70%( Class Standing)+ 30%(Major Exam. Ave.) 82-84 2.25 Class Standing=

2 CSM CSP

79-81 2.50

Major Exam Ave.=

2 M P

76-78 2.75

Final Average= 70%(Class Standing) +30% (Major Exam. Ave.) 75 3.00 Class Standing=

3

CSF CSM

CSP 

BELOW 75 5.00

Major Exam Ave.=

3 F M P 

*Manual input for the computerized class record program Note: Raw scores will be transmuted using the department’s transmutation table.

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Passing Score: 60%

CLASSROOM POLICIES

1. Attendance and Punctuality.

The student is expected to come to class regularly and on time. For absences, please refer to Policy on Absences below.

2. Active class participation/Group Activity. The student is expected to participate actively in class recitations, discussions, and other activities as the case maybe.

The student is also expected to work harmoniously with her group mates and contribute to the preparation of their group work.

3. Projects and Other Requirements. The student is expected to submit all projects and other requirements on time.

4. Lesson Demonstration/Lesson Presentation The student is expected to prepare and present the assigned topic/lesson on the scheduled date.

5. Electronic Devices. Students are not permitted to use any electronic devices with the exception of approved calculators anytime during class.

This includes the wearing of headsets and cellular telephone earpieces as well as laptop computers.

All electronic devices other than those approved must be in the OFF position during exams and quizzes.

EXPECTATIONS FROM STUDENTS

The student’s responsibility is to come to each class prepared. She is also expected to take all examinations on the date scheduled. She is expected to attend to each class and participate actively in the discussions.

ACADEMIC DISHONESTY

All college students are expected to be academically honest. Cheating, lying and other immoral and unethical behavior will not be tolerated.

Any student found guilty of cheating in examination or plagiarism in submitted course requirements will (at a minimum0 receive an F or failure in the course requirement or in the course. Plagiarism and cheating refer to the use of unauthorized books, notes or otherwise securing help in a test, assignments, reports or term papers; representing the work of another person as one’s own; collaborating without authority, with another student during an examination or in preparing academic work; signing another students name on an attendance sheet; or otherwise practicing scholastic dishonesty.

POLICY ON ABSENCES

The allowed number of absences for students enrolled in a one-hour class is a maximum of ten (10) absences and seven (7) absences for a 1- 1/2 hour-class-based on student handbook. Request for excused absences or waiver of absences must be presented upon reporting back to class.

Special examinations will be allowedonly in special cases, such as prolonged illness. It is the responsibility of the student to monitor his/her own tardy incidents and absences that might be accumulated leading to a grade of “FA”. It is also her responsibility to consult with the teacher, chair or dean should her case be of special nature.

COURSE REFERENCES

Eves, Howard. An Introduction to the History of Mathematics, 6th ed. Philadelphia: Saunders, College Publishing, 1990.

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(Textbook)

Burton, David. The History of Mathematics: An Introduction, 2nd ed. Dubuque, I A: William c.

Brown, 1991

Katz, Victor. A History of Mathematics: An Introduction, New York: Harper Collins, 1993 Swetz Frank J. and Vistro-Yu Catherine.The History of Mathematics. A Study Guide, Ateneo de Manila University: Office of Research and Publication. Quezon City 1999.

CONSULTATION HOURS:

Days Time Room

MW 2-5 PM/ 9-12/ 1-5PM CASED CONSULTATION ROOM