A General Educa1on Course in Mathema1cs
Marian P. Roque
University of the Philippines Diliman
2015 MSP Annual Conven1on Plaza del Norte Hotel and Conven1on Center
Laoag City, Ilocos Norte
General Educa1on Curriculum:
Holis1c Understanding, Intellectual and Civic
Competencies
CHED MEMO No. 20 (2013)
CHED MEMO No. 20 (2013)
§ Framework and ra1onale of the revised GE program
§ Set of minimum standards for the G.E.
component of all degree programs
§ Goals
§ Outcomes and competencies
§ Capacity building
G.E. Curriculum
§ Exposes students to various domains of knowledge, ways of understanding social and natural reali1es
§ Develops
§ intellectual competencies such as cri1cal analy1cal, crea1ve thinking and mul1ple forms of expression
§ Personal and civic responsibili1es demanded of membership in the community, country, and the world
§ Prac1cal skills
§ Lays the groundwork for the development of a professionally competent, humane and moral Filipino in the 21st century
CHED MEMO No. 20 (2013)
8 Core Courses
§ Understanding the self
§ Readings in Philippine History
§ The Contemporary World
§ Mathema1cs in the Modern World
§ Purposive Communica1on
§ Art Apprecia1on
§ Science, Technology and Society
§ Ethics
Mathema1cs in the Modern World
• Nature of mathema1cs,
• apprecia1on of its prac1cal, intellectual, and aesthe1c dimensions, and
• applica1on of mathema1cal tools in daily life.
The UP Liberal Educa1on Program
1925 – 70’s
• provide students with a broader outlook on God, man, and events
• develop their acumen and quickness of mind
• scholars characterized by open mindedness and strong habits of mental discipline
• Cultural and spiritual emphasis anchored on customs, tradi1ons, virtues
• Know not only the works of masters but also various disciplines and approaches used
• expose the students to the achievements not only of the Philippines, but also of those of its Asian neighbours
• academic and intellectual freedom, na1onalism, and search for truth
The G.E. Programs
(mul1disciplinary and interdisciplinary)
• E. Angara (80’s) : bridging the arts and sciences, infuse passion for learning with a high sense of moral and intellectual integrity
• F. Nemenzo (2000) : Revitalized G.E. Program
• Broaden students’ intellectual horizons, balance na1onalism with interna1onalism, develop an awareness of various ways of knowing/disciplines, and teach integra1on of knowledge and skills.
• E. Roman (2012) : Hybrid R.G.E.P.
• Communica1on, History, Math G.E. required
• In light of the implementa1on of the K12 that will incorporate the skills courses in the various disciplines, par1cularly in the last two years of basic educa1on, eight courses that provide broader and integra1ve perspec1ves would sufficiently
complement the basic educa1on of students. As an answer to the problem of excessive specializa1on of disciplines and the high demand for technical skills, the new program emphasizes an interdisciplinary approach, one which will link the sciences, social sciences, mathema1cs, and the humani1es. This integra1ve approach of the GE program, complemented by the areas of specializa1on will ensure that UP educa1on fulfils its mission as an engine of progress in na1on building.
UP’s New G.E. Program (2018)
• ins1ll a passion for learning and reading, and an understanding of the nature of art, science, philosophy, and culture;
• develop cri1cal, dialec1cal, and integra1ve thinking necessary for examining ideas and values and making sound judgments;
• inculcate the value of respect for self, others, and the environment;
• nurture love for country based on our unique historical experience as the inner
• source of our strength and the basis for our cultural mooring and na1onal iden1ty;
• mo1vate and challenge the student to serve the na1on with utmost dedica1on and integrity;
• enkindle an ac1vism strongly founded on moral convic1on where one’s ac1on, whether as leader or team-‐player, is ra1onal and responsible;
and
• foster an aspira1on to be a peace-‐loving ci1zen of our country and of the world, tolerant, compassionate, and judicious in behavior, speech, and ac1on;
Mul$, Inter, Transdisciplinary
UP’s New G.E. Program
• To ins1ll a passion for life-‐long learning and reading
• To broaden intellectual & cultural horizons
• To foster na1onalism balanced with interna1onalism
• To deepen the capacity for the integra1on of knowledges & of skills
• Methods of Inquiry
• Empirical & Deduc1ve Forms of Reasoning
• Interpre1ve & Aesthe1c Approaches
• Ethical Reasoning
• Competencies and Values
• Communica1on (Oral, Visual, Wrigen, Digital & Performa1ve)
• Independent, Crea1ve, Cri1cal, Dialec1cal and Integra1ve Thinking
• Integrity, honor, and excellence
Our Present G.E. Math Courses
• Math 1 (General Mathema1cs)
o The development of mathema1cal literacy &
apprecia1on through a synop1c view of the different branches of mathema1cs with historical notes & applica1ons.
• Math 2 (Prac1cal Mathema1cs)
o basic mathema1cs skills & applica1ons in everyday life
Math 1 : G.E. Math (1987)
Math Apprecia1on
• Mathema1cal Statements
• Sets
• Numbers
• Modular Systems
• Mathema1cal Systems
• Geometry
• Sta1s1cs and Probability
• Calculus
Math 2 : Prac1cal Math (2001)
• Percentage
• Mathema1cs behind a restaurant bill
• Mathema1cs in sport
• Compound interest
• Credit card
• Geometric progressions
• Step func1ons, Socialized pricing
• Alloca1on problems
• Fair division mathema1cs
• Prac1cal geometry problems.
Math 1 : G.E. Math (2012)
• Math as a Language
• Math as a crea1ve ac1vity
• Math as a tool
Nature of Math Math is everywhere
Math as a Language
•
Symbols, Opera1ons, Rela1ons
•
Mathema1cal Statements
•
Sets
•
Numbers
•
Proper1es of Opera1ons, Rela1ons
Numbers
•
Methods of Numera1on
•
Ancient Numera1on Systems
•
Base Numerals
•
Real Numbers and its Subsets
•
Clock Arithme1c and Modular Systems
•
Cardinality of the Set of Real Numbers
Math as a Crea1ve Ac1vity
• Logic
• Pagerns
• Axioma1c Systems
• Geometry
• Euclidean
• Non-‐Euclidean
• Projec1ve
• Finite Geometries
• Transforma1ons
Math as a tool Math is everywhere
• Math in the Sciences (natural, physical,
medicine)
• Math in the Arts
• Math in the Social Sciences
• Math in Business
• Math in Economics
• Etcetera
Sample topics
• Marks that represent the object being counted
• Early forms: scratches on the ground or cave walls, notches on pieces of bone or wood, knots on ropes or vines, piles of pebbles or s1cks
More Efficient Methods of Numera1on
• Simple Grouping: Symbols are
introduced to represent bigger numbers
• Mul1plica1ve Grouping: Mul1pliers are used to minimize repe11ons
• Posi1onal System: The posi1on of a
numeral represents a value
ILLUSTRATION: 99
u Tally Marks :
llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllll
u Simple Grouping:
1 – l, 5 – V , 25 – N, 125 – M 625 –
§ 99 = NNNVVVVllll u Mul1plica1ve Grouping Mul1pliers: o, −, =, Δ, ☐
§ 99 = ΔN ☐V ☐l u Posi1onal System
§ 99 = Δ ☐☐
Intro to groups
• Clock arithme1c
• Modular Systems
+ I R A L
I I R A L
R A
A I
L
Intro to groups
• Clock arithme1c
• Modular Systems
+ I R A L
I I R A L
R R A L I
A A L I R
L L I R A
Some Ac1vi1es
• Crea1ng own numera1on system
• Crea1ng art based on modular systems, transforma1ons
• Reports
• Essays
Who can teach G.E. courses?
• Experienced, broad and deep knowledge of subject mager
• Have awareness of other disciplines and can relate math to these disciplines
• Wide reader
• Innova1ve, crea1ve
• Good communica1on skills, pa1ent, sense of humor
• No terror teachers, please!
Who can take these courses?
• Before 2012
• Math 1 cannot be taken by those taking College Algebra, Calculus, and Sta1s1cs
• Math 2 can be taken by everyone
• 2012
• Math 1 can be taken by all students except B.S.
Math students
• Math 2 can only be taken by students of degree programs not requiring a service Math course
A New G.E. Math:(2018) Math, Culture, and Society
• UP Baguio
• UP Cebu
• UP Diliman
• UP Los Banos
• UP Manila
• UP Mindanao
• UP Visayas
Course Descrip1on
• Apprecia1on of the beauty and power of mathema1cs through the examina1on of its nature, development, u1lity, and rela1onship with culture and society.
Course Goals
• ins1ll in the student an apprecia1on of
mathema1cs, par1cularly the significant role that mathema1cs plays in society, both past and present. For this to occur, students must come to understand
• the nature of math,
• its historical and contemporary role,
• place the discipline properly in the context of other human intellectual achievements.
Course Objec1ves
o explain the nature of mathema1cs as an intellectual and crea1ve discipline;
o recognize the importance of mathema1cs in various human ac1vi1es;
o relate the concepts of mathema1cs to his or her field/s of interest;
o discuss the interplay of mathema1cs and society;
o produce crea1ve work inspired by mathema1cal ideas;
and
o discuss local and global issues and trends in mathema1cs.
Course Outline
• Introduc1on (overview of the course)
• Nature of Math
• Math as a Language, Way of thinking, Crea1ve Ac1vity, and tool
• U1lity and Ubiquity of Mathema1cs
• Math in different disciplines
• Issues and Trends in Mathema1cs
• Math and Gender
• State of Math and Math Educa1on in the Philippines
• Ethnomathema1cs
• Great Problems: Solved and Unsolved
• Math and the Nobel Prize. Etc.
COURSE OUTLINE LEARNING OUTCOMES SUGGESTED ACTIVITIES
I. Introduc$on A. Overview of the
course
B. Student and public aptudes and percep1ons of math C. Preliminary
reflec1ons on the nature and prac1ce of math
• Ar1culate individual percep1ons of math.
• Relate percep1ons to actual experiences in math.
• Essay on student’s personal percep1on on Math
• Short film or audio-‐visual presenta1on
COURSE OUTLINE LEARNING
OUTCOMES SUGGESTED ACTIVITIES
II. Nature of Math
A. Logic, Reasoning B. Axioma1c Systems C. Numbers
D. Shapes E. Func1ons
(mathema1cal modelling, calculus) F. Math as the
Science of Pagerns
1. Explain the nature of mathema1cs as an intellectual and crea1ve discipline.
• Create own numera1on system
• Crea1ve project using modular systems
• Essay/Debate: Is math created or discovered?
COURSE OUTLINE LEARNING OUTCOMES SUGGESTED ACTIVITIES
III. U$lity and Ubiquity of Math
A. Arts and Humani1es B. Social Sciences C. Science,
Technology, Engineering
• Recognize importance of math in various human ac1vi1es.
• Relate math concenpts to student’s field/s of interest.
• Produce crea1ve work inspired by mathema1cal ideas.
• Create own numera1on system
• Crea1ve project using modular systems
• Essay/Debate: Is math created or discovered?
COURSE OUTLINE LEARNING OUTCOMES SUGGESTED ACTIVITIES
IV. Issues and Trends
A. Math and Gender B. State of Math
and Math Educa1on C. Ethnomath D. Great
Problems:
Solved and Unsolved
• Discuss the interplay of mathema1cs and society.
• Discuss local and global issues and trends in mathema1cs.
• Produce crea1ve work inspired by mathema1cal ideas.
• Play a game: Male
“versus” Female
• Visit a cockpit and study the math of
“kristos”
• Report/Discuss role of math in history and society and role of history and society in the development of math (cause or effect)
Some lessons learned…
• Mathema1cs Apprecia1on Courses: The Report of a CUPM Panel, The American Mathema1cal Monthly,
Vol 90, No. 1, Jan 1983
Things to emphasize
• Math and culture
• Math and history
• Math and other disciplines
• Math is dynamic
• Doing Math/Mathema1cal inves1ga1ons/Problem Solving to learn and appreciate math
• Aptude affects performance
• Read!!!
Things to avoid
• Emphasizing skills/ drill or rigor exercises
• Remedial topics
• Overemphasize history
• Topics not interes1ng to teacher
• Topics students cannot really relate to
• Make course too easy, condescending
• Make Math more difficult to understand
• Inflexible syllabus, evalua1on
In conclusion:
• Math apprecia1on course plays a role in changing the aptude/opinion of students
• Not only for arts and humani1es students but for science and engineering students as well
• Inclusion of Math apprecia1on course in the B.S.
Math curriculum
• We can make math more fun and relevant!!!
