The document discusses the foundations of mathematics teaching and learning in the Philippines. It describes mathematics as a study of patterns and relationships, a way of thinking, an art, a language, and a tool. It outlines the goals of mathematics in the Philippine education system, including facilitating life skills, making sense of the world, communication, and national progress. It also discusses principles of mathematics instruction, the 2011 Mathematics Education Framework, the K-12 curriculum developed under the Enhanced Basic Education Act of 2013, and goals and standards for intermediate grades.

1. Foundations of
Mathematics
Teaching and
Learning
RyanB.Bernido
Instructor
Credit: Illustration by Paddy Mills

2. Nature of
Mathematics
Mathematics is a study of patterns
and relationships.
https://www.slideshare.net/knowellton/module-63-mathematics

3. Nature of
Mathematics
Mathematics is a way of thinking.
https://www.slideshare.net/knowellton/module-63-mathematics
What can you put between 4 and 5, to get the answer greater
than 4 and less than 5?
https://www.lasipes.com/2019/

4. Nature of
Mathematics
Mathematics is an art.

5. Nature of Mathematics
Mathematics is a language.
https://www.slideshare.net/knowellton/module-63-mathematics

6. Nature of Mathematics
Mathematics is a tool.

7. Nature of Mathematics
• Mathematicsisastudyofpatternsand
relationships.
• Mathematicsisawayofthinking.
• Mathematicsisanart.
• Mathematicsisalanguage.
• Mathematicsisatool.
https://www.slideshare.net/knowellton/module-63-mathematics

8. Nature of
Mathematics
(NOM)
Mathematics Teacher: Learning and Teaching PK-12 114, 5; 10.5951/MTLT.2020.0226

9. Roles of
Mathematics in the
Philippine Education
1. Facilitating participation
in productive life skills

10. Roles of
Mathematics in the
Philippine
Education
2. A way of making
sense of the world

11. Roles of
Mathematics
in the
Philippine
Education
3. Means of
communication

12. Roles of
Mathematics
in the
Philippine
Education
4. A gateway for
national
progress

13. Principles in
Mathematics Instruction
• Principle 1. Being mathematically competent means
more than having the ability to compute and perform
algorithms and mathematical procedures.
• Principle 2. The physical and social dimensions of a
mathematical environment contribute to one’s
success in learning mathematics.
• Principle 3. Mathematics is best learned when
students are actively engaged.
• Principle 4. A deep understanding of mathematics
requires a variety of tools for learning.
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

14. Principles in
Mathematics
Instruction
• Principle 5. Assessment in mathematics
must be valued for the sake of knowing
what and how students learn or fail to
learn mathematics.
• Principle 6. Students’ attitudes and beliefs
about mathematics affect their learning.
• Principle 7. Mathematics learning needs
the support of both parents and other
community groups.
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

15. Mathematics
Education
Framework
2011
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

16. Mathematics Education Framework 2011
Mathematical
Content
The Philippine mathematics education program at the elementary
and secondary levels aims to teach the most fundamental and useful
contents of mathematics and organizes these into the following
strands: Numbers and Number Sense; Measurement; Geometry;
Patterns, Functions and Algebra and Data,Analysis andProbability.
This organization of the contents was influenced by the 1995, 1999
and2003TIMSSstudies.
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

17. Mathematics Education Framework 2011
Cognitive Demands
Higherexpectationsarenecessary,butnotsufficientto
accomplishthegoalsofPhilippineschoolmathematics
educationforallstudents.Tisframeworkstartsfrom
thepremisethatequalopportunitiesmustbegivento
allstudentsregardless oflearningstylesandlevelsof
abilityinordertomeetthedemandsinlearningquality
mathematicsandassimilatethevaluesintrinsictothe
discipline.Thecognitivedemandsundertheproposed
frameworkareclassifiedunderthesixgeneral
categories:Visualization,Knowing,Computing,Solving,
ApplyingandProving.
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

18. Mathematics Education Framework 2011
Cognitive Values
Criticalandanalyticalthinkingcannotbefullydevelopedwithout
promoting desirable cognitive values. The cognitive values that
mustbetaughtamongothersare:
a. Objectivity
b. Flexibilityandcreativity
c. Utility
d. Cultural-rootedness
e. Introspection
f. ProductiveDisposition
https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.pdf

19. Philippine’s K-12 Curriculum
Republic Act
(RA) No. 10533
known as
Enhanced Basic
Education Act
2013
https://www.deped.gov.ph/wp-content/uploads/2019/08/DO_s2019_021.pdf

20. Philippine
Mathematics
Curriculum
- conceived with the twin goals
of developing students’ critical
thinking and problem solving
The contents are clustered into
five strands:
1) Numbers and Number
Sense;
2) Measurement;
3) Geometry;
4) Patterns & Algebra; and
5) Statistics and Probability
(DepEd, August 2016)

21. Numbers and
Number Sense
include concepts, operations and
applications of numbers; whole
numbers, number theory, fractions,
decimals, ratio and proportion,
percentandintegers
https://www.ejmste.com/download/looking-through-philippines-k-to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-7747.pdf
Philippine Mathematics Curriculum

22. Measurement
focuses on measures
and applications of
length, mass, weight,
capacity, time, money,
temperature, angles,
perimeter, area,
surface area, and
volume.
https://www.ejmste.com/download/looking-through-philippines-k-to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-7747.pdf
Philippine Mathematics Curriculum

23. Geometry
focuses on the two-
and three-
dimensional figures
(parallel and
perpendicular lines,
angles, triangles,
quadrilaterals,
polygons, circles, and
solid figures like cube
and prism)
https://www.ejmste.com/download/looking-through-philippines-k-to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-7747.pdf
Philippine Mathematics Curriculum

24. Patterns and Algebra
studies patterns,
relationships, and changes
among shapes and
quantities (continuous and
repeating patterns,
number sentences,
sequences and simple
equations)
https://www.ejmste.com/download/looking-through-philippines-k-to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-7747.pdf
Philippine Mathematics Curriculum

25. Statistics and
Probability
focuses on skills in data
collection, organization,
and interpretation
including making
predictions about
outcomes (bar graphs,
line graphs and pie
graphs, simple
experiment and
experimental probability)
https://www.ejmste.com/download/looking-through-philippines-k-to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-7747.pdf
Philippine Mathematics Curriculum

26. GOALS AND OBJECTIVES OF
MATHEMATICS IN THE K-12 BEC FOR
THE INTERMEDIATE GRADES

27. GoalsandObjectivesoftheKeyStage2oftheK-12BasicEducation
Program
LEARNINGAREASTANDARD
The learner demonstrates understanding and appreciation of key concepts and principles of
mathematics as applied - using appropriate technology - in problem solving, critical thinking,
communicating,reasoning,makingconnections,representations,anddecisionsinreallife.
http://depedbohol.org/v2/wp-content/uploads/2016/03/Math-CG_with-tagged-math-equipment.pdf

28. GoalsandObjectivesoftheKeyStage2oftheK-12BasicEducation
Program
• KEYSTAGESTANDARDS
At the end of Grade 6, the learner demonstrates understanding and appreciation of key concepts and skills
involving numbers and number sense (whole numbers, number theory,fractions, decimals, ratio and proportion,
percent,andintegers);measurement(time,speed,perimeter,circumferenceandareaofplanefigures,volume and
surface area of solid/space figures, temperature and meter reading); geometry (parallel and perpendicular lines,
angles, triangles, quadrilaterals, polygons, circles, and solid figures); patterns and algebra (continuous and
repeating patterns, number sentences, sequences, and simple equations); statistics and probability (bar graphs,
line graphs and pie graphs, simple experiment, and experimental probability) as applied -using appropriate
technology - in critical thinking, problem solving, reasoning, communicating, making connections,
representations,anddecisionsinreallife.

29. GradeLevelStandards
GRADE4
Thelearnerdemonstratesunderstandingandappreciationofkeyconceptsandskillsinvolvingnumbersandnumber
sense (whole numbers up to 100 000, multiplication and division of whole numbers, order of operations, factors and
multiples, addition and subtraction of fractions, and basic concepts of decimals including money); geometry (lines,
angles, triangles, and quadrilaterals); patterns and algebra (continuous and repeating patterns and number
sentences); measurement (time, perimeter, area, and volume); and statistics and probability (tables, bar graphs, and
simple experiments) as applied - using appropriate technology - in critical thinking, problem solving, reasoning,
communicating,makingconnections,representations,anddecisionsinreallife.

30. GradeLevelStandards
GRADE5
The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense
(whole numbers up to 10 000 000, order of operations, factors and multiples, fractions and decimals including money, ratio
andproportion,percent); geometry (polygons,circles, solidfigures); patterns and algebra (sequence andnumber sentences);
measurement (time, circumference, area, volume, and temperature); and statistics and probability (tables, line graphs and
experimental probability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning,
communicating,makingconnections,representations,anddecisionsinreallife.

31. GradeLevelStandards
GRADE6
The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense
(divisibility, order of operations, fractions and decimals including money, ratio and proportion, percent, integers); geometry
(plane and solid figures); patterns and algebra (sequence, expression, and equation); measurement (rate, speed, area, surface
area, volume, and meter reading); and statistics and probability (tables, pie graphs, and experimental and theoretical
probability) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating,
makingconnections,representations,anddecisionsinreallife.

32. References
• https://www.slideshare.net/knowellton/module-63-mathematics
• https://www.ejmste.com/download/looking-through-philippines-k-
to-12-curriculum-in-mathematics-and-science-vis-a-vis-timss-2015-
7747.pdf
• https://www.deped.gov.ph/wp-
content/uploads/2019/08/DO_s2019_021.pdf
• https://www.sei.dost.gov.ph/images/downloads/publ/sei_mathbasic.
pdf
• http://depedbohol.org/v2/wp-content/uploads/2016/03/Math-
CG_with-tagged-math-equipment.pdf