STRATEGIESIN

TEACHING

LESSON 3

MATHE

MATICS

Three objectives or goals of the learning process

1. Knowledge and skill

goals

2. Understanding goals

3. Problem solving goals.

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Knowledge and skill goals

require automatic

responses which could

be achieved through

repetition or practice.

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Understanding goals

understanding must

be applied, derived

or used to deduce a

consequence.

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Strategies used in understanding

a. Authority teaching

b. Interaction and discussion

c. Discovery

d. Laboratory

e. Teacher-controlled presentations

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Techniques used in Authority teaching

Telling which is defined

stating an understanding

without justification

by analogy

by demonstration

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Interaction and discussions

Interaction is created by

asking questions in order to

provide means for active

instead of passive

participation.

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DiscoveryLESSON 3

techniques where learners

are not given everything by

the teacher but they have

to work out the rule and

meaning by themselves.

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Elements of a discovery experience

Motivation

primitive process

an environment for discovery

opportunity to make conjectures

a provision for applying the

generalization.

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Laboratory

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done through experimental

activities dealing with concrete

situations such as drawing,

weighing, averaging and

estimating

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Advantages

a. maximizes student participation

b. provides appropriate level of

difficulty,

c. offers novel approaches

d. improves attitudes towards

mathematics

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Teacher-controlled presentation

The teacher uses educational technology

such as films and filmstrips, programmed

materials, and audio materials.

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Problem solving goals

. Problem solving is

regarded by mathematics

educators and specialist as

the basic mathematical

activity

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Mathematical activities based on problem solving

Generalization

Abstraction

concept building

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STRATEGIES IN TEACHING MATHEMATICS

1. Problem solving

2. Concept attainment

strategy

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Problem solving

Teacher’s task:

a. Make sure students understand the problem. The

students will lose interest in a subject they do not

understand. The question presented may not even

present a problem.

b. Ask the following questions:

1. 1 Do the students understand the meaning of the

terms in the problem?

2. 2 Do they take into consideration all the relevant

information?

3. 3 Can they indicate what the problem is asking for?

4. 4 Can they state the problem in their own words?

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c. Help the students gather relevant thought

materials to assist in creating a plan. Assist

the students in gathering information by

helping them analyze the given conditions.

d. Provide students with an atmosphere

conducive to solving problems.

e. Once the students have obtain the

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.

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Theoretical basis of problem solving strategies

a. Constructivism

b. Cognitive theory

c. Guided discovery learning

d. Metacognition theory

e. Cooperative learning

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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 current/past knowledge.

Cognitive theory

the cognitive theory

encourages students’ creativity

with the implementation of

technology such as computers

which are used to create

practice situations.

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Guided discovery learning

tools 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 the students to think.

Cooperative learning

the purpose of cooperative learning

groups is to take each member a

stronger individual in his/her own right.

Cooperative skills

a. forming groups

b. working as a group

c. problem solving as a group

d. managing differences

STEPS OF THE PROBLEMS SOLVING STRATEGY

a. Restate the problems

b. Select appropriate notation. It can help

them recognize a solution.

c. Prepare a drawing, figure or graph. These

can help understand and visualized the

problem.

d. Identify the wanted, given and needed

information.

e. Determine the operations to be used.

f. Estimate the answer.

g. Solve the problems.

h. Check the solution. Find a way to

verify the solutions in order to

experience the process of actually

solving problems.

OTHER TECHNIQUES IN PROBLEM SOLVING

1. Obtain the answer by trial and error.

2. Use an aid, model or sketch.

3. Search for a pattern

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.

4. Elimination strategy

Concept Attainment Strategy

Allows the students to discover

the essential attributes of a

concept.

Enhance students skills in:

a. Separating important from

unimportant information.

b. Searching for patterns and making

generalization.

c. Defining and explaining concepts.

Concept Attainment Strategy

Steps

a. select a concept and identify is essential attributes.

b. present example and non-examples of the concepts.

c. let students identify or define the concept based on its essential attributes.

d. ask the students to generate additional examples.

SAMPLE ACTIVITY: Defining proper fraction

The following are proper fractions;

1/5,2/5,3/5,4/5,1/8,2/8,3/8,4/8,5/8,6/8,2/3,2/4,2/10,12/15,3/7,25/43,78/79

The following are not proper fractions:

5/5,6/5,7/5,8/8,9/8,9/9,10/9,11/9,14/16,15/16,16/16,17/16,20/21,22/21,34/35,35/35,36/35

(expected answers: 4/6,5/6,7/9,8/9,14/16,15/16,20/21,34/35)

A proper fraction is ____________.

(expected answer: a proper fraction is a fraction whose numerator is less than the denominator)

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Effective use of the concept attainment strategy:

successful when:

a. Students are able to identify the essential

attributes of the concepts.

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.

CONCEPTS FORMATION STRATEGY

This strategy is used when you want

the students to make connections

between and among essential

elements of the concept.

Steps

a. Present a particular question or problems.

b. Ask students to generate data relevant to the questions or problem.

c. Allow the students 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 may be subsumed in other groups based on their attributes.