# THE TEACHING OF MATHEMATICS

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### THE TEACHING OF MATHEMATICS:

THE TEACHING OF MATHEMATICS

### Slide2:

MATHEMATICS has been considered a necessary part of general education and has become a required in the curriculum across instructional level. Contributes to more specialized education of various professionals like scientists, accounts, statistics, engineers and others professions.

### Nature of Mathematics:

Nature of Mathematics Math is : Definite Logical Objective Math deals with solving problem. 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 d) arriving at a solution

### Math Competencies in the Basic Curriculum-Elementary:

Math Competencies in the Basic Curriculum-Elementary Grade 1 and 2 includes the study of whole numbers, addition, and subtraction, basic facts of multiplication and division, basics of geometry, fractions, metric and local measurements, the use of money and their application to practical problems based on real life activities. Grade 3 and 4 deals with the study of whole numbers, the four fundamental operations, fractions and decimals including money, angles, plane figures, measurements and graph.

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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. Simple concepts in Algebra is also introduced to be articulated in high school.

### Math Competencies in the Basic Education Curriculum- Secondary:

Math Competencies in the Basic Education Curriculum- Secondary First Year is Elementary Algebra - it deals with life situations and problems involving measurement, real number system, algebraic expressions, first degree equations and inequalities in one variable, linear equations in two variables, special products and factoring Second Year is I ntermediate Algebra - it deals with systems of linear equations and inequalities, quadratics equations, rational algebraic expressions, variation, integral exponents, radical expressions, and searching for patterns in sequences ( arithmetic, geometric, etc.) Third Year is Geometry - it deals with the practical application to life of the geometry of shape and size, geometric relations, triangle congruence, properties of quadrilaterals, similarity, circles, and plane coordinate geometry. Fourth Year is still the existing integrated (algebra, geometry, statistics and a unit of trigonometry) spiral mathematics

### GOALS and OBJECTIVES of TEACHING MATHEMATICS:

GOALS and OBJECTIVES of TEACHING MATHEMATICS Mathematics has its : > broad aims > goals > specific objectives

### Aims of Mathematics as a Discipline:

Aims of Mathematics as a Discipline A mathematician is a disciplined person. Generals aims of mathematics as a discipline : 1. To teach students the concepts basic to quantitative thinking 2. To d evelop students’ ability to think logically 3. to inculcate such mental habits and attitudes as seeking to understand relations, intellectual curiosity, persistence, a love for precisions, accuracy, thoroughness, clarity, and orderly and logical organization. 4. To train students in formal thinking

### Other aims are labeled aesthetic, intellectual, and ethical, respectively.:

Other aims are labeled aesthetic, intellectual, and ethical, respectively . They are as follows: 1. T o develop appreciation of beauty in the geometrical forms in nature, art and industry. 2. To develop appreciation of logical structure, precision of statement and thought, and logical reasoning. 3. To develop appreciation of the power of mathematics, the part it has played in the development of civilization and, in particular, that of science.

### Mathematics students should::

Mathematics students should: h ave an understanding of the deductive nature of mathematics. u nderstand the basic properties of operations on numbers and be able to determine whether a given system possesses any of these operations. b e able to perceive patterns. be aware that mathematics is used not only in the natural sciences but also in the behavioral and social sciences and art. recognize that some professions require knowledge of sophisticated and complex mathematical techniques. know the ways in which computers are used in science, technology, business, and government. be aware of the extent to which mathematical skills are used by individuals in their daily lives.

### Goals and Objectives in Teaching Mathematics for Philippine Elementary Schools:

Goals and Objectives in Teaching Mathematics for Philippine Elementary Schools GOAL: Demonstrate understanding and skills in computing with considerable speed and accuracy, estimating, communicating, thinking analytically and critically, and in solving problems in daily using appropriate technology At the end of Grade VI , the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on decimals, fractions, ratio and proportion, percent, integers, simple probability, geometry, measurements, and graphs; integers; exact and estimated computation of the four fundamental operations involving decimals, money, fractions and measurements ; and apply the concept learned in solving problems. At the end of Grade V , the child is expected to have mastered the concepts and operations of whole numbers; demonstrate understanding of concepts and perform skills on fractions, decimals including money, ratio, percent, geometry, measurement and graph; exact and estimated computation of the four fundamental operations on rational numbers including money and measurement apply the concepts learned in solving problems.

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At the end of Grade IV , t he child is expected to demonstrate understanding of concepts and performs skills of whole numbers up to millions and billions including money, decimals, fractions, geometry, graphs and scales; exact and estimated computation on the four fundamental operations; apply the concepts learned to solve problems. At the end of Grade III , the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one thousand, fractions, measurement, and graphs; performs the four fundamental operations of whole numbers and measurement; and apply the concepts learned in solving problems. At the end of Grade II , the child is expected to demonstrate understanding of concepts and skills on whole numbers up to one thousand including basics of geometry; perform addition and subtraction of 3 to 4 digit numbers, understand basic facts of multiplication and division; and apply the concepts learned to solve problems. At the end Grade I , the child is expected to demonstrate understanding of basic concepts and skills on whole numbers up to one hundred including money and measurements; performs addition and subtraction of 1 to 3 digit numbers; and apply the concepts learned to solve problems.

### Goals and Objectives in Teaching Mathematics for Philippine Secondary School:

Goals and Objectives in Teaching Mathematics for Philippine Secondary School The student will be able to compute and measure accurately, come up with reasonable estimate, gather, analyze and interpret data, visualize abstract mathematical ideas, present alternative solutions to problems using technology, among others, and apply them in real-life situations. At the end of Third Year , the student is expected to demonstrate understanding and skills in geometric relations, proving and applying theorems on congruence and similarity of triangles, quadrilaterals, circles and basic concepts on the plane coordinate geometry.

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At the end of Second Year , the student is expected to demonstrate understanding of concepts and skills related to systems of linear equations and inequalities, quadratic equations, rational algebraic expressions, variation, integral exponents, radical expressions and searching for patterns in sequences: arithmetic, geometric and others and apply them in solving problems. At the end of First Year , the student is expected to demonstrate understanding and skills in measurement and use of measuring devices, performing operations on real numbers and algebraic expressions, solving first degree equations and inequalities in one variable, linear equations in two variables and specials products and factoring and apply them in solving problems.

### STRATEGIES IN TEACHING MATHEMATICS:

STRATEGIES IN TEACHING MATHEMATICS The strategy for teaching mathematics depends on the objectives or goals of the learning process. Goals are classified into three: a. Knowledge and skill goals b. Understanding goals c. Problem in solving goals

### Strategy Based on Objectives:

Strategy Based on Objectives Knowledge and Skill Goals - knowledge and basic skills compose a large part of learning in mathematics. - require automatic responses which could be achieved through repetition or practice. Understanding Goals - “understanding must be applied, derived or used to deduce a consequence” -some strategies used in understanding are: a) Authority teaching b) Interaction discussions c) Discovery d) Laboratory e) Teacher-controlled presentations

### Strategies in Teaching Mathematics:

Strategies in Teaching Mathematics Problem solving The teacher’s task in relation to these are: a) Make sure students understand the problem. b) Ask the following questions: 1. Do the students understand to meaning of the terms in the problems? 2. Do they take into consideration all the relevant information? 3. Can they indicate what the problem is asking for? 4. Can they state the problem in their own words? 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 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 problems

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Theoretical Basis of Problem-solving Strategy Constructivism - learning is an active process in which learners construct new ideas or concepts based upon their current/past knowledge. Cognitive Theory - encourage students’ creativity with the implementation of technology such as computers which are used to create practice situations. Guided Discovery Learning - tool engages students in a series of higher-order thinking skills to solve problems. Metacognition Theory - holds that students should develop and explore the problem, extend solutions, process and develop self-reflection Cooperative Learning - to make each member a stronger individual in his/her own right. - the favorable outcomes in the use of cooperative learning is that students are taught cooperative skills, such as: a) forming groups b) working as a group c) problem solving as a group d) managing differences

### Steps of the Solving Strategy:

Steps of the Solving Strategy Restate the problems Select appropriate notation. Prepare a drawing, figure or graph. Identify the wanted, given and needed information. Determine the operations to be used. Estimate the answer Solve the problem Check the solution

### Other Techniques in Problem Solving:

Other Techniques in Problem Solving Obtain the answer by trial and error. Use an aid, model or sketch. Search for a pattern Elimination strategy

### 2. Concept attainment strategy:

2. Concept attainment strategy a llows the students to discover the essential attributes of a concept. It can enhance students’ skill (a) separating important from unimportant information; (b) searching for patterns and making generalizations; and, (c) defining and explaining concepts. 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.

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The use of concept attainment strategy is successful when : 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 concepts. Concept Formation Strategy This strategy is used when you want the students to make connections between and among essential elements of the concepts: STEPS: a. present a particular question or problem. b. ask students to generate date relevant to the questions or problems. 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 group. 