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.
Notes de l'éditeur
Emphasize that one of the factors is psychology of learning mathematics
making it difficult for children to grasp the meaning of new concept in the classroom. and so everyday experience interferes with classroom learning. everyday experience of learners.
because although insightful performance is a more ambitious aim, it actually has a better chance of success. It yields faster and permanent results. The same mathematics should be taught to all students because no one can know in advance which students will eventually use mathematics professionally.
Piaget described two processes used by the individual in its attempt to adapt: assimilation and accommodation. Both of these processes are used throughout life as the person increasingly adapts to the environment in a more complex manner.
Sensorimotor stage (Infancy). Knowledge of the world is limited (but developing) because its based on physical interactions / experiences. Pre-operational stage (Toddler and Early Childhood). intelligence is demonstrated through the use of symbols, language use matures, and memory and imagination are developed, but thinking is done in a non-logical, non-reversible manner.Concrete operational stage (Elementary and early adolescence). intelligence is demonstrated through logical and systematic manipulation of symbols related to concrete objects. Formal operational stage (Adolescence and adulthood). In this stage, intelligence is demonstrated through the logical use of symbols related to abstract concepts.
