2b

THE TEACHING

OF MATHEMATIC

SGloria G. Salandanan, Ph. D.

Mathematics has been considered a necessary part of general education and has become a required subject in the curriculum across instructional levels.

The Teaching of Mathematics:INTRODUCTION

Mathematics contributes to more specialized education of various professionals like scientists, accountants, statisticians, engineers and other professions which rely heavily on accurate measurements and quantification in order to understand better the studies they are conducting.

NATURE OF MATHEMATICSMath 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. 

NATURE OF MATHEMATICS

Math deals with solving problems. Such problems are similar to all other problems everyone 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. 

SCOPE – GRADES 1 and 2Mathematics in these grades include the study of whole numbers, addition and subtraction, basic facts of multiplication and division, basics of geometry, fractions problems based on real life activities.SCOPE – GRADES 3 and 4Grade 3 and 4 deals with the study of whole numbers, the four fundamental operations, fractions and decimals including money, angles, plane figures, measurement and graphs.

SCOPE – GRADES 5 and 6

In Grade 5 and 6 the child is expected to have mastered the four fundamental operations of whole numbers, performs skills in decimals and fractions, conceptualize the meaning of ratio and proportion, percent, integers, simple probability, polygons, spatial figures, measurement and graphs. A simple concept in Algebra is also introduced to be articulated in the high school.

SCOPE – SECONDARY LEVELSFirst year is elementary algebra

Second year is intermediate algebra

Third year is geometry

Fourth year is still the existing integrated (algebra, geometry, statistics and a unit of trigonometry) spiral mathematics

STRATEGIES BASED ON OBJECTIVES

1. 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.

2. Problem Solving Goals- Problem solving is regarded by mathematics educators and specialists as the basic mathematical activity. Hence, considerations should be given to the teaching of problem solving skills.

STRATEGIES BASED ON OBJECTIVES

2. Understanding Goals - The distinguishing characteristics of understanding goals is that “understanding must be applied, derived or used to deduce a

consequence.”

STRATEGIES BASED ON OBJECTIVES

2. Understanding Goals Some strategies used in understanding are:a) Authority Teaching

b) Interaction and discussionsc) Discoveryd) Laboratorye) Teacher-controlled presentations

STRATEGIES INTEACHING MATHEMATICS

1. PROBLEM SOLVINGa) Make sure students understand the problemb) 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 in their own words?

STRATEGIES INTEACHING MATHEMATICS

1. PROBLEM SOLVINGc) Helps the students gather relevant thought material to assist in creating a plan

d) Provide students with an atmosphere conductive to solving problemse) Once students have obtained a 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

1. 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 knowledge.2. Cognitive Theory

– The cognitive theory encourages students’ creativity with the implementation of

technology such as computers which are used to create practice situations.

THEORETICAL BASIS OFPROBLEM-SOLVING

STRATEGY

3. Guided Discovery Learning – Tool engages students in a series of

higher order thinking skills to solve problems.

4. Meta cognition Theory- The field of meta cognition process hold that students should develop and explore

the problem, extend solutions, process and develop self-reflection. Problem solving must challenge student to think.

THEORETICAL BASIS OFPROBLEM - SOLVING

STRATEGY

5. Cooperative Learning- The purpose of cooperative learning

groups 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.

THEORETICAL BASIS OFPROBLEM - SOLVING

STRATEGY

This strategy has the following steps:1. Restate the problems2. Select 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 problem.8.Check the solution.

STEPS OF THE PROBLEM SOLVING STRATEGY

1. Obtain the answer by trial and error2. Use an aid, model or sketch3. Search for a pattern4. Elimination strategy

OTHER TECHNIQUES INPROBLEM - SOLVING

STRATEGIES INTEACHING MATHEMATICS

1. PROBLEM SOLVING2. CONCEPT ATTAINTMENT STRATEGY

- This strategy allows the students to discover the essential attributes of a concept.

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

EVALUATINGMATHEMATICS LEARNINGEvaluation procedures may be classified into following:

1. Testing Procedures

2. Non-testing Procedures

EVALUATINGMATHEMATICS LEARNING

1. Testing Proceduresa. Individual and group testsb. Informal and standardized testsc. Oral, essay, and objective testsd. Speed, power, and mastery

testse. Verbal, nonverbal and

performance tests

f. Readiness and diagnostic tests

EVALUATINGMATHEMATICS LEARNING

2. Non-testing Proceduresa. Interview such as teacher-pupil

interviewb. Questionnairesc. Anecdotal Recordsd. Socio-metric Devicese. Ranking and Rating Procedures

EVALUATINGSTUDENT PERFORMANCE

1. work on assignments outside the class

2. class participation

3. attitudes and effort

4. extra credit work