# Foundations of Mathematics Teaching and Learning (Philippine Context)

This article presents the preliminary lessons in the course, Teaching Mathematics in the Intermediate Grades. It discusses the foundations of mathematics teaching and learning including the nature of mathematics, the five-point view of nature of mathematics, the principles of mathematics teaching and learning, and other relevant topics taken from various sources and were put together to grasp an understanding of the foundations of mathematics instruction; particularly in the context of the Philippine Mathematics Education.

## Nature of Mathematics

•Mathematics is a study of patterns and relationships.

•Mathematics is a way of thinking.

•Mathematics is an art.

•Mathematics is a language.

•Mathematics is a tool.

## Roles of Mathematics in the Philippine Education

1. Facilitating participation in productive life skills

2. A way of making sense of the world

3. Means of communication

4. A gateway for national progress

## 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.

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.

## Mathematics Education Framework 2011

This Mathematics Education Framework is developed and proposed by the Science Education Institute, Department of Science and Technology (SEI-DOST) and the Philippine Council of Mathematics Teacher Education (MATHTED), Inc. prior the enactment of Republic Act 10533 (Enhance Basic Education Act 2013) which established the Philippine K-12 Curriculum.

As per Mathematics Education Framework 2011, mathematics empowerment can be made possible through the following important pillars: mathematical content, cognitive demands, and cognitive values. These three should be developed among Filipino learners,

**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 and Probability. This organization of the contents was influenced by the 1995, 1999 and 2003 TIMSS studies.*

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**Cognitive Demands **

*Higher expectations are necessary, but not sufficient to accomplish the goals of Philippine school mathematics education for all students. Tis framework starts from the premise that equal opportunities must be given to all students regardless of learning styles and levels of ability in order to meet the demands in learning quality mathematics and assimilate the values intrinsic to the discipline. The cognitive demands under the proposed framework are classified under the six general categories: Visualization, Knowing, Computing, Solving, Applying and Proving.*

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**Cognitive Values **

*Critical and analytical thinking cannot be fully developed without promoting desirable cognitive values. The cognitive values that must be taught among others are:*

*a. Objectivity *

*b. Flexibility and creativity *

*c. Utility *

*d. Cultural-rootedness *

*e. Introspection *

*f. Productive Disposition *

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## Philippine’s K-12 Curriculum, Mathematics Curriculum

The Philippine's K-12 Curriculum was established through the enactment of the Republic Act 10533 also known as the Enhanced Basic Education Act 2013. The K-12 curriculum states that pedagogical strategies must include constructivist, inquiry-based, reflective, collaborative, differentiated, and integrative. Along Mathematics curriculum, the goal is develop learner's critical thinking and problem solving skills. The contents of the mathematics curriculum are grouped into 5 strands. These are:

a. Numbers and Number Sense

b. Measurement

c. Geometry

d. Patterns and Algebra

e. Statistics and Probability

Number and Number Sense

This strand include the following topics: concepts, operations and applications of numbers; whole numbers, number theory, fractions, decimals, ratio and proportion, percent and integers.

Measurement

This strand provides learners opportunity to master competencies along measures and applications of length, mass, weight, capacity, time, money, temperature, angles, perimeter, area, surface area, and volume.

Geometry

This focuses on the two-dimensional and three-dimensional figures (parallel and perpendicular lines, angles, triangles, quadrilaterals, polygons, circles, and solid figures like cube and prism).

Patterns and Algebra

this strand studies patterns, relationships, and changes among shapes and quantities (continuous and repeating patterns, number sentences, sequences and simple equations)

Statistics and Probability

it focuses on skills in data collection, organization( bar graphs, line graphs and pie graphs) and interpretation including making predictions about outcomes (simple experiment and experimental probability).