Strategies In Teaching

Mathematics

1. PROBLEM SOLVING STRATEGY

Creative Problem Solver?

Why teach problem solving?

• The elementary math curriculum must prepare children to become effective problem solvers.

About Teaching Mathematics, Marilyn Burns

1. PROBLEM SOLVINGThe teacher’s task in relation to these are:

• 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 is asking

for?Can they state the problem in their

own words?

1. PROBLEM SOLVINGThe teacher’s task in relation to these are:

• c. Help the students gather relevant thought material to assist in creating a plan.

• d. Provide students with an atmosphere conducive to solving problems.

• e. Once the students have obtained a solution, encourage them to reflect on the problem and how they arrived at solution.

• f. Encourage them to present alternate ways of solving the problem.

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. . . . if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems.

- Mathematical Discovery George Polya

THEORETICAL BASIS OF PROBLEM-SOLVING STRATEGY• CONSTRUCTIVISM

THEORETICAL BASIS OF PROBLEM-SOLVING STRATEGY• COGNITIVE THEORY

THEORETICAL BASIS OF PROBLEM-SOLVING STRATEGY• GUIDED DISCOVERY LEARNING

THEORETICAL BASIS OF PROBLEM-SOLVING STRATEGY• METACOGNITION THEORY

THEORETICAL BASIS OF PROBLEM-SOLVING STRATEGY• COOPERATIVE LEARNING

STEPS OF THE PROBLEM SOLVING STRATEGY1. Restate the problem2. Select an 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 problem8. Check the solution.

Simple Questions withHuge Impact• “Why?”• “How do you know?”• “What other problems can you

remember that are similar to this one?”

• “Are there other ways you could solve this problem? Other strategies?”

• “Do you agree with this approach to the problem? Why or why not?”

Problem types Routine• Traditional word problems

• Skills/memorization

• Formulas

Problem TypesNon-routine• Logical reasoning

• Riddles

• Puzzles

Connect the dots by drawing 4 straight lines. Do not pick up your pencil!

OTHER TECHNIQUES IN PROBLEM-SOVING

1. Obtain the answer by trial and error.

2. Use an aid, model or sketch.

3. Search for a pattern There are 1000 lockers in a high school with 1000 students. The first student opens all 1000 lockers; next, the second student closes lockers 2, 4, 6, 8, 10, and so on up to locker 1000; the third student changes the state (opens lockers that are closed, closes lockers that are open) of lockers 3, 6, 9, 12, 15, and so on; the fourth student changes the state of lockers 4, 8, 12, 16, and so on. This continues until every student has had a turn. How many lockers will be open at the end?

4. Elimination strategy

2. CONCEPT ATTAINMENT STRATEGYEnhances students’ skills in:• Separating important from

unimportant information• Searching for patterns and making

generalizations• Defining and explaining concepts.

STEPS:

1. Select a concept and identify its essential attributes.

2. Present examples and non-examples of the concepts.

3. Let students identify or define the concept based on its essential attributes.

4. Ask students to generate additional examples.

DEFINING PROPER FRACTIONSThe following are proper fractions:

The following are not proper fractions:

Which of the following are proper fractions?

Expected answer:

A PROPER FRACTION IS _______________.Expected answer:

a proper fraction is a fraction whose numerator is less than the denominator.

EFFECTIVE USE OF THE CONCEPT ATTAINMENT STRATEGY:• Students are able to identify

the essential attributes of the concept.

• Students are able to generate their own examples.

• Students are able to describe the process they used to find the essential attributes of the concept.

CONCEPT FORMATION STRATEGYThis strategy is used when you want the students to make connections between and among essential elements of the concepts.

STEPS• Present a particular question or

problem• Ask students to generate data

relevant to the question or problem.

• Allow the students group data with similar attributes.

• Have students explore the relationships between and among the groups.

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