# Lesson 4principles of teaching

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### Lesson 4:

Lesson 4 Developing a Lesson in Mathematics

### Direct Teaching Versus Concept Attainment Strategy:

Direct Teaching Versus Concept Attainment Strategy This strategy allows the students discover the essential attributes of a concept. It can enhance students’ skills in (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 identity its essential attributes. b. Present examples and non-examples of the concepts. c. let studies identify of define the concept based on its essential attributes. d. Ask students to generate additional examples.

### Slide3:

Activities under Direct teaching Activities under concept attainment The teacher will define proper fraction. “A fraction a/b is proper if │a│<│b│.” Then the teacher will give examples (and non examples). Examples of proper fractions are 2/3, 2/5, 7/8. Examples of improper fractions 3/3, 5/2, 8/7. The teacher will give a task to the students The teacher will give a set of examples. 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, 7/8, 2/3, 2/5, 2/10, 12/15, 3/7, 25/43, 78/79 Then the teacher will give a set of non-examples; the following are not proper fractions: 5/5, 6/5, 7/5, 8/8, 9/8, 10/8, 14/8, 12/12, 34/23. 16/12, 29/13, 15/11, 15/5, 15/6, 80/79 The teacher will give the students the opportunity to verify their conjecture about proper fraction by asking the following:

### Slide4:

Activities under Direct teaching Activities under concept attainment Determine if the given fraction is proper or not: 4/5, 5/6, 6/6, 7/6, 7/9, 8/9, 9/9, 10/9, 11/9, 14/16, 15/16, 16/16, 17/16, 20/21, 21/21, 22/21, 34/35, 35/35, 36/35, 60/63. Which of the following are proper fractions: 4/6, 5/6, 6/6, 7/6, 7/9, 8/9, 9/9, 10/9, 11/9, 14/16, 15/16, 16/16, 17/16, 20/21, 21/21, 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) Then the teacher asks the students to complete the sentence: A proper fraction ‗‗‗‗‗ (Expected answer: A proper fraction is a fraction whose absolute value of the numerator is less the absolute value of the denominator.)

### Slide5:

The use of concept attainment strategy is successful is the students are able to: Generate their own examples. To describe the process they used to find the essential attributes of the concept.

### Direct teaching versus concept formation strategy:

Direct teaching versus concept formation strategy This strategy is used when you want to make connections between and among essential elements of the concept. It includes the following steps: Present a particular question or a problem. Ask students to generate data relevant to the questions or problem. Allow the students group data with similar attributes. Ask students to label each group of data with similar attributes. Have students explore the relationships between and among the groups. They may group the data in various ways and some groups may subsumed in other groups based on their attributes.

### Slide7:

Activities under Direct Teaching Activities under Concept Formation The Teacher will give the Definitions: The different kinds of triangle according to sides are: a.) scalene triangle has no congruent sides. b.) isosceles triangle has exactly two congruent sides. c.) equilateral triangle where all three sides are congruent. The three triangles according to interior angles are : a.) acute Triangle has three acute angles. b.) Right angles has one right angle and two acute angles. c.) Obtuse triangle has one obtuse angle. The Teacher will give task to the students to solve: Task: Show a diagram that will illustrate the relationship of the different kinds of triangles. Possible output from students: Group 1: output Possible output1: The different kinds of triangles are : a.) scalene triangle wherein no two sides are congruent. b.) isosceles triangle wherein exactly two sides are congruent. c.) equilateral triangles wherein all three sides are congruent.

### Slide8:

Activities under Direct Teaching Activities under Concept Formation The teacher will ask the students to define the following: What is a/an a.)scalene triangle? b.)isosceles triangle? c.)is equilateral? d.)acute triangle? e.)right triangle? f.)obtuse triangle? Or, the teacher may ask the following: Determine what type of triangle is given: a.)∆ABC, if m<A = 30  B.)∆DEF, if m<G = 120 C.)∆GHI, if m<1 = 150 Group 2 : Output Possible output: The different kinds of triangles are: a.) acute triangle wherein all interior angles are acute. b.) right triangle wherein one of the angles is aright angle and the two others are both acute. c.) obtuse triangle wherein one of the angles is an obtuse angle and the two others are acute.

### Possible output 3:

Possible output 3 Triangle According to interior angles According to sides scalene isosceles equilateral acute right obtuse

### Example 2 ( on concept formation):

Example 2 ( on concept formation) The teacher will give the following definitions: A quadrilateral is a 4 sided-polygon. A general quadrilateral is a quadrilateral with no parallel sides. A trapezoid is a quadrilateral with exactly one pair of opposite sides, which are parallel. A parallelogram is a quadrilateral with two pairs of opposite sides, which are parallel. A rectangle is a quadrilateral with t wo pairs of opposite sides, which are parallel; and whose interior angles are all right angles. A rhombus is a quadrilateral with pairs of opposite sides, which are parallel; and whose sides are all congruent . A square is a quadrilateral with two pairs of opposite sides, which are parallel and whose interior angles are all right angles and whose sides are congruent. A general parallelogram is a quadrilateral with to pairs of opposite sides which are parallel such that the angles are not right angles and the sides are not all congruent.

### The teacher will ask the students to construct a diagram showing the relationship of the terms with one other.:

The teacher will ask the students to construct a diagram showing the relationship of the terms with one other. Quadrilateral General quadrilateral trapezoid parallelogram General parallelogram rectangle rhombus square

### Effective use of the concept formation strategy::

Effective use of the concept formation strategy: It is useful when: Students are able to group the data in one way or in different ways. Students arte able to label the different groups Students are able to identify relationships and hierarchies between and among groups.

### EVALUATING MATHEMATICS LEARNING:

EVALUATING MATHEMATICS LEARNING LESSON 5

### Evaluation procedures:

Evaluation procedures 1. Testing procedures Individual and group tests Informal and standardized tests Oral, essay, and objective tests Speed, power and mastery tests Verbal, non-verbal and performance tests Readiness and diagnostics tests 2. Nontesting procedures Interview such as teacher-pupil interview Anecdotal records Sociometric devices Ranking and rating procedures

### Types of test for evaluation purposes:

Types of test for evaluation purposes Achievement test includes simple quizzes on the work during a single period to full scale examinations. Diagnostics test attempts to locate areas of misunderstanding or areas where teaching has not taken place t o enable suitable remedial instruction to be given. Inventory test are often referred to as pre-test and are used to determine the improvement of the students. They are given before and after the course of instruction. Individual test require careful questioning and observation of the reaction of an individual and needs an expert to administer. Speed test are tests wherein a student is required to complete as many test or problems in a predetermined time. Power test require a student to do as many problems or task out of a set of increasing difficulty. Sociometric test which test sociability of students require them to select or identify their classmates whom they like very much.

### Evaluating Student performance:

Evaluating Student performance Students achievements could be based on: A.) work on assignments outside class B.) class participation C.) attitudes and effort D.) extra credit work

### Evaluating Student performance:

Evaluating Student performance Students need practice in solving problems and completing exercises related to the subject matter, sometimes teachers assign more problems and exercises than students do in class. Another factor considered in evaluating students performance is the contributions they make to the academic activities in the classroom. A teacher may consider the attitude and effort of student in evaluation performance. Sometimes students gets interested in doing extra credit work, knowing that it may influence the teacher’s assessment of their performance.

### Students Performance as Indicator of Teacher performance:

Students Performance as Indicator of Teacher p erformance 1.) In addition to considering test scores in assessing students’ progress, they can also be used in evaluating teachers’ performance. If the test scores show that the students are making satisfactory academic progress, it can inferred that the teachers’ performance is likewise satisfactory. However, If the result is unsatisfactory then the teachers teaching methodologies might contribute to the situation. Some factors are: validity of the tests The selection of subject matter The determination off teaching strategies.

### Slide19:

2.) The classroom environment can also be an indicator of teacher performance. 3.) In addition to examining students’ academic progress and social behavior, it is appropriate to analyze the teaching strategies employed. 4.) Another way is to videotape or audiotape a lesson to analyze the teachers behavior.