1) The document discusses the teaching of mathematics across different grade levels, covering topics such as the nature of mathematics, scope at primary and secondary levels, strategies based on objectives like problem solving and concept attainment, theoretical basis for problem solving strategies, techniques for problem solving, and evaluating student performance. 2) Key strategies discussed include problem solving, concept attainment, and understanding goals through approaches like authority teaching, interaction, discovery and teacher-controlled presentations. 3) Evaluation of mathematics learning incorporates both testing procedures like individual/group tests and non-testing procedures such as interviews, questionnaires and anecdotal records.

1. THE
TEACHING
OF
MATHEMATICS
Gloria G. Salandanan, Ph. D.

2. Mathematics has been considered
a necessary part of general education
and has become a required subject in
the curriculum across instructional
levels.
The Teaching of Mathematics:
INTRODUCTION

3. Mathematics contributes to more
specialized education of various
professionals like scientists,
accountants, statisticians, engineers
and other professions which rely
heavily on accurate measurements
and quantification in order to
understand better the studies they
are conducting.

4. NATURE OF MATHEMATICS
Math is definite, logical, and objective. The
rules for determining the truth or falsity of
a statement are accepted by all. If there
are disagreements, it can readily be tested.
It is in contrast with the subjective
characteristics of other subjects like
literature, social studies and the arts.

5. NATURE OF MATHEMATICS
Math deals with solving problems.
Such problems are similar to all other
problems everyone is confronted with.
It consists of:
a) defining the problem,
b) entertaining a tentative guess
as the solution,
c) testing the guess, and
d) arriving at a solution.

6. SCOPE – GRADES 1 and 2
Mathematics in these grades include the study of
whole numbers, addition and subtraction, basic
facts of multiplication and division, basics of
geometry, fractions problems based on real life
activities.
SCOPE – GRADES 3 and 4
Grade 3 and 4 deals with the study of whole
numbers, the four fundamental operations,
fractions and decimals including money, angles,
plane figures, measurement and graphs.

7. SCOPE – GRADES 5 and 6
In Grade 5 and 6 the child is expected to
have mastered the four fundamental operations of
whole numbers, performs skills in decimals and
fractions, conceptualize the meaning of ratio and
proportion, percent, integers, simple probability,
polygons, spatial figures, measurement and
graphs. A simple concept in Algebra is also
introduced to be articulated in the high school.

8. SCOPE – SECONDARY LEVELS
First year is elementary algebra
Second year is intermediate algebra
Third year is geometry
Fourth year is still the existing integrated
(algebra, geometry, statistics and a unit
of trigonometry) spiral mathematics

9. STRATEGIES BASED ON
OBJECTIVES
1. Knowledge and Skill Goals
- Knowledge and basic skills compose a large
part of learning in mathematics. Students may
be required to memorize facts or to become
proficient in using algorithms.
2. Problem Solving Goals
- Problem solving is regarded by mathematics
educators and specialists as the basic
mathematical activity. Hence, considerations
should be given to the teaching of problem
solving skills.

10. STRATEGIES BASED ON
OBJECTIVES
2. Understanding Goals
- The distinguishing characteristics of
understanding goals is that
“understanding must be applied,
derived or used to deduce a
consequence.”

11. STRATEGIES BASED ON
OBJECTIVES
2. Understanding Goals
Some strategies used in understanding are:
a) Authority Teaching
b) Interaction and discussions
c) Discovery
d) Laboratory
e) Teacher-controlled presentations

12. STRATEGIES IN
TEACHING MATHEMATICS
1. PROBLEM SOLVING
a) Make sure students understand the problem
b) Ask the following questions:
Do the students understand the meaning
of the terms in the problem?
Do they take into consideration all the
relevant information?
Can they indicate what the problem is
asking for?
Can they state the problem in their own
words?

13. STRATEGIES IN
TEACHING MATHEMATICS
1. PROBLEM SOLVING
c) Helps the students gather relevant thought
material to assist in creating a plan
d) Provide students with an atmosphere
conductive to solving problems
e) Once students have obtained a solution,
encourage them to reflect on the problem and
how they arrived at the solution.
f) Encourage them to present alternate ways of
solving the problem

14. 1. Constructivism
– This is based on Bruner’s theoretical
framework that learning is an active
process in which learners construct new
ideas or concepts based upon their
knowledge.
2. Cognitive Theory
– The cognitive theory encourages students’
creativity with the implementation of
technology such as computers which are
used to create practice situations.
THEORETICAL BASIS OF
PROBLEM-SOLVING STRATEGY

15. 3. Guided Discovery Learning
– Tool engages students in a series of higher
order thinking skills to solve problems.
4. Meta cognition Theory
- The field of meta cognition process hold
that students should develop and explore the
problem, extend solutions, process and
develop self-reflection. Problem solving must
challenge student to think.
THEORETICAL BASIS OF
PROBLEM - SOLVING STRATEGY

16. 5. Cooperative Learning
- The purpose of cooperative learning groups
is to make each member a stronger
individual in his/her own right. Individual
accountability is the key to ensuring that all
group members are strengthened by
learning cooperatively.
THEORETICAL BASIS OF
PROBLEM - SOLVING STRATEGY

17. This strategy has the following steps:
1. Restate the problems
2. Select appropriate notation.
3. Prepare a drawing, figure or graph.
4. Identify the wanted, given and needed
information.
5. Determine the operations to be used.
6. Estimate the answer.
7. Solve the problem.
8.Check the solution.
STEPS OF THE PROBLEM
SOLVING STRATEGY

18. 1. Obtain the answer by trial and error
2. Use an aid, model or sketch
3. Search for a pattern
4. Elimination strategy
OTHER TECHNIQUES IN
PROBLEM - SOLVING

19. STRATEGIES IN
TEACHING MATHEMATICS
1. PROBLEM SOLVING
2. CONCEPT ATTAINTMENT STRATEGY
- This strategy allows the students to discover the
essential attributes of a concept.
- STEPS:
a. Select a concept and identify its essential
attributes.
b. Present examples and non-examples of the
concepts.
c. Let students identify or define the concept
based on its essential attributes.
d. Ask students to generate additional examples.

20. EVALUATING
MATHEMATICS LEARNING
Evaluation procedures may be
classified into following:
1. Testing Procedures
2. Non-testing Procedures

21. EVALUATING
MATHEMATICS LEARNING
1. Testing Procedures
a. Individual and group tests
b. Informal and standardized tests
c. Oral, essay, and objective tests
d. Speed, power, and mastery tests
e. Verbal, nonverbal and performance
tests
f. Readiness and diagnostic tests

22. EVALUATING
MATHEMATICS LEARNING
2. Non-testing Procedures
a. Interview such as teacher-pupil
interview
b. Questionnaires
c. Anecdotal Records
d. Socio-metric Devices
e. Ranking and Rating Procedures

23. EVALUATING
STUDENT PERFORMANCE
1. work on assignments outside
the class
2. class participation
3. attitudes and effort
4. extra credit work