The document summarizes key aspects of teaching mathematics, including: 1) The goals of mathematics are critical thinking and problem solving. 2) Mathematics should be taught using a spiral progression approach, revisiting basics at each grade level with increasing depth and breadth. 3) Effective mathematics teaching employs methods like problem-solving, concept attainment, concept formation, and direct instruction.

1. Written Report
in
Principles of Teaching 2
(The Teaching of Mathematics)
Submitted by:
Bea Joy P. Pepinas BSED 2-6
Shawntel Anne Petilla BSED 2-6
MTh 1:00-2:30
Submitted to:
Mrs. Ripalda
Professor

2. The Teaching of Mathematics
A number of students are scared of Math. Many struggle with their Math subject for one reason or
another. Your mission as a Math teacher is to reduce, if not eliminate, the negative attitudes towards Math.
How should it be taught so that it becomes a palatable menu and that students begin to like it and in effect
fall in love with it.
The Nature of Mathematics
 Mathematics is the science of patterns and relationship
o Mathematics reveals hidden patterns that help us understand the world around us.
 Mathematic is a way of thinking
o It relies on logic and creativity and it is pursued for a variety of practical purposes and for
its intrinsic interest.
 Math is an art
o Because of its numerous patterns that can be found in numbers and in geometric figures.
 Mathematics is a language
o It has a language of its own. It is such a useful language and tool that is considered one of
the “basics” in our formal educational system.
 Mathematics is a discipline
o Archaeology, biology, chemistry, economics, history, psychology, sociology are some of
the common disciplines and Mathematics is a broad and deep discipline that is continuing
to grow in breadth and depth.
The Goals of Mathematics
 Critical thinking
 Problem solving
We can achieve these goals through the pupils’ exposure to numbers, equations, mathematical
problems, formulas and many others. And through critical thinking, or if pupils had developed their critical
thinking, it wold be an ease for them upon solving problems.
When can we say that a pupil’s thinking is already a critical thinking? The table below would let
you determine as to what number your pupil’s critical thinking belongs to. The numbers indicate the level
of the pupil’s critical thinking. If the pupil can do certain skills that is written in a certain number in the
Rubric, that number shows the level or his score in thinking critically.
Holistic Critical Thinking Scoring Rubric
4
Consistently does all or almost all of the following:
o Accurately interprets evidence, statements, graphics, questions, etc.
o Identifies the salient arguments (reasons and claims) pro and con
o Thoughtfully analyses and evaluates major alternative points of view
o Draws warranted, judicious, non-fallacious conclusions
o Justifies key results and procedures, explains assumptions and reasons
o Fair-mindedly follows where evidence and reasons lead
3
Does most or many of the following:

3. o Accurately interprets evidence, statements, graphics, questions, etc.
o Identifies the salient arguments (reasons and claims) pro and con
o Offers analyses and evaluation of obvious alternative points of view
o Draws warranted, non-fallacious conclusions
o Justifies some results or procedures, explains reasons
o Fair-mindedly follows where evidence and reasons lead
2
Does most or many of the following:
o Misinterprets evidence, statements, graphics, questions, etc.
o Fails to identify strong, relevant counter- arguments
o Ignores or superficially evaluates obvious alternative points of view
o Draws unwarranted or fallacious conclusions
o Justifies few results or procedures, seldom explains reasons
o Regardless of the evidence or reasons, maintains or defends views based on self-interest or
preconceptions
1
Consistently does all or almost all of the following:
o Offers biased interpretations of evidence, statements, graphics, questions, information, or the
points of view of others
o Fails to identify or hastily dismisses strong, relevant, counter-arguments
o Ignores or superficially evaluates obvious alternative points of view
o Argues using fallacious or relevant reasons and unwarranted claims
o Does not justify results or procedures nor explain reasons
o Regardless of the evidence or reasons, maintains or defends views based on self-interest or
preconceptions
o Exhibits close-mindedness or hostility to reason
Learning Area Standard
These two big goal of teaching Math are expressed in the learning area/program standards: 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,
making connections, representations, and decisions in real life.
Key Stage Standards
K-3 4-6 7-10
At the end of Grade 3,the learner
demonstrates understanding and
appreciation of key concepts and
skills involving:
whole numbers and number
sense up to 10,000 and the
four fundamental operations
including money, ordinal
numbers up to 100th
, basic
concepts of fractions
time, length, mass, capacity,
area of square and rectangle
At the end of Grade 3,the learner
demonstrates understanding and
appreciation of key concepts and
skills involving:
Whole numbers, number
theory, fractions, decimals,
ratio and proportion, percent,
and integers
Time, speed, perimeter,
circumference and area of
solid/space figures,
At the end of Grade 3,the learner
demonstrates understanding and
appreciation of key concepts and
skills involving:
Numbers and number sense,
sets and real numbers
Conversion of units
Linear equations and
inequalities in one and two
variables, linear functions,
systems of linear equations
and many others

4. 2-dimensional and 3-
dimensional objects, lines,
symmetry, and tessellation
Continuous and repeating
patterns and number
sentences
Data collection and
representation in tables,
pictographs and bar graphs
and outcomes
temperature, and meter
reading
Parallel and perpendicular
lines, angles, triangles,
quadrilaterals, polygons,
circles and solid figures
Continuous and repeating
patterns, number sentences,
sequences and simple
equations
Bar graphs, line graphs, and
pie graphs, simple
experiment, and
experimental probability
Polygons, axiomatic
structure of geometry,
triangle congruence,
inequality and similarity and
basic trigonometry
Measures of central
tendency, variability and
position; combinatory and
probability
To capsulize these self-explanatory key stage standard, it means that in learning Math, there are stages that
should be followed wherein there are prerequisite skills needed before going to the next stage.
Example:
It is hard for a Grade 5 pupil to be learning number theories if he is not equipped with the necessary skills
in Grade 3.
That is why it is called stages because you have to be equipped with the knowledge of the first stage before
going on to the second or third stage.
If the foundation is not good, the upcoming stages will surely be affected.
Content Areas in the Curriculum
 Numbers and Number Sense
 Measurement
 Geometry
 Patterns and Algebra
 Probability and Statistics
Educational Theories
 Experiential learning
 Situated learning
 Reflective learning
 Cooperative learning
 Discovery learning
 Inquiry-based learning

5. The Spiral Progression Approach
The teaching of Math makes use of the Spiral Progression Approach. This means that the basics of Math
are revisited in every grade level but are taught in increasing depth and breadth as one goes up in grade
level of the K to 12.
Principles of Teaching Math
 Balance Principle
 Three-tiered Principle
For effective Math teaching employ experiential and situated learning, constructivism, cooperative
learning and discovery and inquiry-based learning.
Teaching Methods
1. Problem-solving
Steps:
a. Understand the problem
b. Planning and communicating solution
c. Reflecting and generalizing
d. Extension
2. Concept Attainment Strategy
Steps:
a. Select a concept and identify its essential attributes
b. Present examples and non-examples of the concept
c. Let the students identify or define the concept based on its essential attributes
d. Ask students to generate additional instructions, examples.
Grades 7-10
Grades 4-6
Grades 1-3
K-
Algebra, Geometry,
Statistics and
Probability

6. 3. Concept Formation Strategy
Steps:
a. Present a particular problem
b. Ask student to generate data
c. Allow students to group data with similar attributes
d. Ask students to label each group of data
e. Have students explore the relationships between and among the groups
4. Direct Instruction