This document discusses several learning theories that can be applied to teaching secondary mathematics, including Piaget's stages of cognitive development and theories of assimilation and accommodation. It outlines Piaget's four stages of development and recommends teaching strategies appropriate for students in the formal operations stage of adolescence, such as exploring hypothetical concepts, justifying solutions, and relating concepts to students' lives. The document also briefly mentions Polya's view of education as developing intelligence and problem-solving skills.

1. SOME BASIC LEARNING THEORIES FOR
TEACHING SECONDARY MATHEMATICS
ITLM Topic 7-8

2. LEARNING OBJECTIVES
 Be aware of and understand some basic
psychological learning theories advocated by Piaget
and Bruner that can be applied to the teaching and
learning of secondary mathematics
 Be aware of the difference between Piaget stages of
developmental theories and his learning theories
applied to the teaching and learning of secondary
math
 Use the learning theories to show examples how
mathematics are taught
 Make students more independent to read texts on
learning theories

3. PROBLEM SOLVING PROCESS
 Recent problem solving researches agree
that children actively construct theories at all
times, including conceptions about the
manipulation of quantity and how the
physical world works.
 This leads to notions that children’s
difficulties in school are due to the absence
of relevant everyday experiences or to their
faulty conceptualization in non-school
setting.

4. ROUND ROBIN
 Give a list of possible factors that students
have problem in learning and solving
mathematical problems.
 Explain all possible factors that students
have problem in learning and solving
mathematical problems.

5. THREE COMMON LEARNING DIFFICULTIES
 Everyday life provides too little relevant
experience,
 Everyday life provides erroneous experience,
or children actively construct erroneous
concepts of it,
 Too little and too weak a connection between
what is being taught and the intuitive.

6. STRENGTHENING MATH LEARNING IN SCHOOL
 According to Polya, a major aim of education is
the development of intelligence to teach young
people to think.
 In primary school, children should be taught to
do their arithmetic insightfully rather than
mechanically
 In secondary school, mathematics should offer
something to those who will, and those who will
not, use mathematics in their later studies or
careers.

7. PIAGET'S THEORY OF COGNITIVE DEVELOPMENT
 Process of Cognitive Development: the
process of coming to know.
 Stages of Cognitive Development: the stages
we move through as we gradually acquire
this ability

8. PROCESS OF COGNITIVE DEVELOPMENT
 Assimilation is the process of using or
transforming the environment so that it can
be placed in preexisting cognitive structures.
 Accommodation is the process of changing
cognitive structures in order to accept
something from the environment.

9. STAGES OF COGNITIVE DEVELOPMENT
 Sensorimotor stage (Infancy).
 Pre-operational stage (Toddler and Early
Childhood).
 Concrete operational stage (Elementary and
early adolescence).
 Formal operational stage (Adolescence and
adulthood).

10. TEACHING STUDENTS BEGINNING TO USE
FORMAL OPERATIONS (ADOLESCENCE)
Continue to use many of the teaching
strategies and materials appropriate for
students at the concrete operational stage:
 Use visual aids such as charts and
illustrations, as well a simple but somewhat
more sophisticated graphs and diagrams.
 Use well-organized materials that offer step
by step explanations.

11. TEACHING STUDENTS BEGINNING TO USE
FORMAL OPERATIONS (ADOLESCENCE)
Give students an opportunity to explore many
hypothetical questions:
 Provide students opportunities to discuss
social issues.
 Provide consideration of hypothetical "other
worlds."

12. TEACHING STUDENTS BEGINNING TO USE
FORMAL OPERATIONS (ADOLESCENCE)
Encourage students to explain how they solve
problems:
 Ask students to work in pairs with one student acting
as the problem solver, thinking aloud while tackling a
problem, with the other student acting as the listener,
checking to see that all steps are mentioned and that
everything seems logical.
 Make sure that at least some of the tests you give
ask for more than rote memory or one final answer;
essay questions, for example, might ask students to
justify two different positions on an issue.

13. TEACHING STUDENTS BEGINNING TO USE
FORMAL OPERATIONS (ADOLESCENCE)
Whenever possible, teach broad concepts, not
just facts, using materials and ideas relevant to
the students:
 While discussing a topic such as the Civil
War, consider what other issues have divided
the country since then.
 Use lyrics from popular music to teach poetic
devices, to reflect on social problems, and so
on.

14. ASSIGNMENT
 Browse internet and find other learning
theories such as Bruner, Ausubel, Vygotsky,
or others (in pairs).
 Make a summary and an example of
secondary mathematics that could be taught
by the learning theory you chose.