The document outlines the nature and strategies for teaching mathematics, emphasizing its logical, objective nature compared to subjective subjects. It categorizes teaching goals into knowledge and skill goals, understanding goals, and problem-solving goals, while detailing various teaching methods such as authority teaching, interaction, discovery, and cooperative learning. Additionally, it highlights problem-solving as a fundamental activity in mathematics, providing strategies for effective problem solving, concept attainment, and concept formation.

1. THE
TEACHING
OF
MATHEMATICS

2. 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.
Math deals with solving problems. Such problems are
similar to all other problems anyone 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.
Nature of Mathematics

3. . …
The strategy for teaching Mathematics depends on
the objectives or goals of the learning process. In
general these goals are classified into three: a)
knowledge and skill goals, b) understanding
goals and c) problem solving goals.
Strategies in
Teaching
Mathematics

4. 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.
Ex. of facts:
2 X 10= 20 Area of rectangle = B x H
Ex. of skills:
Multiplying two-digit whole numbers
Changing a number to scientific notation
Knowledge and skill goals require automatic responses which could be
achieved through repetition and practice.
Strategy Based on Objectives

5. Understanding Goals
The distinguishing characteristics of
understanding goal is that “understanding must be
applied, derived or used to deduce a consequence”.
Some strategies used in understanding are:
a. authority teaching
b. interaction and discussion
c. discovery
d. laboratory
e. teacher-controlled presentations

6. a.) Authority teaching
The teacher as an authority simply states the
concept to be learned. The techniques used are by
telling which is defined, stating an understanding
without justification, by analogy, and by
demonstration.
b.) Interaction and discussion
Interaction is created by asking questions in order
to provide means for active instead of passive
participation.

7. c) Discovery
The elements of a discovery
experience are motivation, a primitive
process, an environment for discovery, an
opportunity to make conjectures and a
provision for applying the generalization.

8. d) Laboratory
The advantages are:
a) maximizes student participation,
b) provides appropriate level of difficulty
c) offers novel approaches
d) improves attitudes towards mathematics
This is done through experimental activities
dealing with concrete situations such as drawing,
weighing, averaging and estimating. Recording,
analyzing and checking data enable students to
develop new concepts and understanding
effectively.

9. e) Teacher-controlled presentations
The teacher uses educational
technology such as films and filmstrips,
programmed materials, and audio materials.
Other activities are listening to resource
persons and conducting field trips. Suitable
places for educational trips are government
agencies such as the weather bureau, post
office and community supermarkets,
factories and transportation centers like the
bus depot and airport.

10. Problem-solving Goals
Problem solving is regarded by mathematics
educators and specialists as the basic
mathematical activity. Other mathematical
activities such as generalization, abstraction,
and concept building are based on problem
solving. Others believe that the more
important roleof problem solving in the
school curriculum is to motivate all students
not only those who have a special interest in
mathematics and a special aptitude for it.

11. 1. Problem Solving
2. Concept Attainment Strategy
3. Concept Formation Strategy
Strategies in Teaching
Mathematics

12. 1. Problem solving
Theoretical Basis for Problem-solving Strategy
 Constructivism – This is based on Brunner’s theoretical
framework that learning is an active process in which
learners construct new ideas or concepts based upon
current/past knowledge.
 Cognitive theory – The cognitive theory encourages
students’ creativity with the implementation of
technology such as computer which are used to create
practice situations.

13.  Guided Discovery Learning
Tool engages students in a series of higher
order thinking skills to solve problems.
 Metacognition Theory
The field of metacognition process holds
that students should develop and explore
the problem, extend solutions, process and
develop self-reflection. Problem solving
must challenge students to think.

14.  Cooperative learning
The purpose of cooperative learning group 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.
Teachers need to assess how much work each member is
contributing to the group’s work, provide feedback to
groups and individual students, help groups avoid
redundant efforts by members, and make sure that every
member is responsible for the final outcome.
The favorable outcomes in the use of cooperative
learning is that students are taught cooperative skills such
as: a) forming groups, b) working as a group, c) problem
solving as a group and d) managing differences

15. Steps of the Problem Solving Strategy
1. Restate the problem
2. Select appropriate notation. It can help them
recognize a solution.
3. Prepare a drawing, figure or graph. These can help
understand and visualize the problem.
4. Identify the wanted, given and needed information.
5. Determine the operation to be used.
6. Estimate the answer.
Knowing what the student should get as the answer
to the problem will lead the students to the correct
operations to use and the proper solutions.

16. 7. Solve the problem.
The student is now ready to work on the
problem.
8. Check the solution. Find a way to verify
the solutions in order to experience the
process of actually solving the problem.

17. Other Techniques in Problem Solving
1. Obtain the answer by trial and error.
It requires the student to make a series of
calculations. In each calculation, an estimate of some
unknown quantity is used to compute the value of a
known quantity.
2. Use an aid, model or sketch.
A problem could be understood by drawing a sketch,
folding a piece of paper, cutting a piece of string, or
making use of some simple aid. Using an aid could
make the situation real to them.

18. 3. Search for a pattern
This strategy requires the students to
examine sequences of numbers or geometric
objects in search of some rule that will allow
them to extend the sequences indefinitely.
Example: Find the 10th
term in a sequence
that begins, 1, 2, 3, 5, 8, 13, . . . . .
This approach is an aspect of inductive
thinking-figuring a rule
from examples.

19. 4. Elimination Strategy
This strategy requires the student to
use logic to reduce the potential list
of answers to a minimum. Through
logic, they throw away some potential
estimates as unreasonable and focus
on the reasonable estimates

20. Concept attainment strategy
This strategy allows the students to
discover the essential attributes of a
concept. It can enhance the students’
skills in (a) separating important from
unimportant information; (b) searching
for patterns and making
generalizations; and (c) defining and
explaining concepts.

21. Steps
a. Select a concept and identify its
essential attributes
b. Present examples and non-examples of
the concept
c. Let students identify or define the
concept based on its essential attributes
d. Ask students to generate additional
examples

22. (Sample Activity on Fractions)

23. Effective use of the concept attainment Strategy
The use of the concept attainment strategy is
successful when:
a. students are able to identify the essential
attributes of the concept
b. students are able to generate their own examples
c. students are able to describe the process they
used to find the essential attributes of the
concept

24. Concept Formation Strategy
This strategy is used when you
want the students to make connections
between and among essential elements
of the concept:

25. Steps
a. Present a particular question or problem.
b. Ask students to generate data relevant to the
question or problem.
c. Allow students to group data with similar
attributes.
d. Ask students to label each group of data with
similar attributes.
e. Have students explore the relationships between
and among the groups. They may group the data in
various ways and some groups maybe subsumed
in other groups based on their attributes.