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Appendix A
Participating Schools
Division School Number of Teachers Code
San Jose Elementary School 3 A
F. Benitez Elementary School 4 B
Guadalupe Nuevo Elementary School 3 C
Cembo Elementary School 5 G
Makati
Makati Elementary School 5 H
Kaunlaran Elementary School 6 D
Libis Talisay Elementary School 8 E
Caloocan
Kasarinlan Elementary School 6 F
Appendix B
Grade Level and topics Discussed
school Teacher Grade Level
Dates Topics
H1 4 Jan 20,
21, 22, 23
1) transforming word problems into number sentences
2) Problem Solving: Similar Fractions 3) Finding a fractional part of a number
H2 5 Jan 20,
21, 22, 23
1) Comprehension of 3-4 sided polygons 2) Comprehension of 5 or more sided polygons 3) Congruent and similar polygons
4) Different kinds of angles A
H3 6 Jan 20,
22, 23
1) Finding the percentage when the rate and the base are given
2) Finding the base when percentage and rate are given 3) Find the rate when the percentage and the base are
given
H4 6 Feb 4, 5, 6 1) Types of angles 2) Congruent angles 3) Congruent polygons
H5 5 Feb 4, 5, 6 1) finding the circumference of a circle
2) analyzing word problems involving circumference measure
3) transform the word problem into a number sentence, solve the problem using the correct operation H6 4 Feb 3, 4, 5 1) Identifying line, line segment and ray.
2) Identifying parallel lines, intersecting lines, perpendicular lines, vertical/horizontal lines 3) Identify the different kinds of plane figures B
H7 6 Feb 4, 5, 6 1) Congruent angles
2) Commission
3) Congruent polygons 4) Congruent angles
H8 6 Feb 10,
11, 12
1) area of a parallelogram 2) area of trapezoids 3) area of circles
H9 4 Feb 10, 12 1) Polygons
2) parts of circle C
H10 5 Feb 11,
12, 13
1) Visualizing and identifying the different kinds of polygons
2) Finding the perimeter of polygons 3) Area of parallelogram
H11 5 March 10, 11
1) Converting percent to fraction
2) Determine the percentage of a given number H12 6 March 10,
11
1) multiplication of fraction 2) division of fractions H13 5 March 10,
11
1) bar graphs 2) line graphs H14 4 March 10,
11
1) kinds of polygons 2) perimeter of polygons G
H15 6 March 10, 11
1) Reads and interpret line and bar graphs 2) Reads and interpret circle graphs H16 4 March 19,
20
1) different kinds of polygons 2) perimeter of polygons H17 4 March 19,
20
1) visualizing integers in their order on the number line
2) operation involving integers H18 5 March 19,
20
1) area of circles
2) solve word problems involving the areas of circles H19 5 March 19,
20
1) space figures
2) volume of rectangular prism H
H20 4 March 19, 20
1) kinds of shapes
2) different kinds of plane figures
school Teacher Grade
Level Dates Topics
L1 4 Feb 17,
18, 19
1) Perimeter of polygons 2) Perimeter of rectangle 3) Perimeter of a square
L2 Feb 17,
18, 19, 20
1) Area of Parallelogram 2) Area of trapezoid 3) Area of triangle
L3 5 Feb 17,
18, 19, 20
1) area of a rectangle
2) area of a rectangle and a square 3) area of a parallelogram
4) area of a triangle
L4 4 Feb 17,
19
1) Finding the area of a triangle.
2) Finding the area of a parallelogram.
L5 Feb 17,
18, 19, 20
1) Area of rectangle 2) Area of trapezoid 3) Area of triangle 4) Area of circle D
L6 5 Feb 17,
18, 19, 20
1) Area of a parallelogram 2) Area of triangle 3) Area of a trapezoid
L7 5 Feb 24,
26, 27
1) solve word problems involving area of plane figures 2) comprehension of volume (telling the unit to be used to
measure the volume of given solids)
3) converting one cubic unit of measure to a larger or smaller unit
L8 6 Feb 26,
27
1) analyze one step word problems involving division of decimals including money
2) transform one-step word problems into a number sentence involving division of decimals including money
L9 6 Feb 26,
27
1) volume of a cone 2) volume of a sphere 3) volume of a cone
L10 4 Feb 24,
26
1) perimeter of a polygon
2) analyzing word problem involving perimeter
L11 6 Feb 26,
27
1) volume of a rectangular prism 2) volume of a cube
L12 6 Feb 26,
27
1) volume of a rectangular prism 2) volume of a cube
L13 5 Feb 26,
27
1) area of circle
2) solve word problems involving the area of plane figures E
L14 4 Feb 24,
26, 27
1) Solving word problem involving perimeter 2) Measuring the area of a triangle
3) Measuring the area of a parallelogram
L15 4 March 3, 4, 5, 6
1) converting units from smaller to greater, and vice versa 2) perimeter of a polygon
L16 6 March
3, 4, 5
1) surface area of cubes and rectangle prism 2) surface area of cylinders
3) surface area of pyramids 4) surface area of a sphere
L17 5 March
3, 4, 5, 6
1) telling the unit of measure used for measuring the volume of cubes
2) converting one cubic unit of measure to a Longer or Smaller unit
3) derive the formula for finding the cube of a volume.
L18 4 March
3, 5, 6
1) Polygons
2) Perimeter of polygons
L19 4 March
5, 6
1) Polygons
2) Perimeter of polygons F
L20 5 March
3, 4,5, 6
1) telling the unit of measure used for measuring the volume of cubes
2) converting one cubic unit of measure to a Longer or Smaller unit
3) derive the formula for finding the cube of a volume.
Appendix C
Initial List of Indicators for the Beliefs Questionnaires
A. Goals of Math Education
At the end of a mathematics class, students should be able to …
SCHOOL MATH TRADITION INQUIRY MATH TRADITION
1) master mathematical facts, principles, and algorithms
1) generate his/her own solutions to problems
2) perform computations with speed and accuracy
2) apply problem solutions they learned to novel problems
3) develop the ability to follow procedural instructions to obtain correct answers
3) think of alternative solutions to one mathematics problem
4) execute mathematical operations 4) develop an ability to explain and justify actions on mathematical objects
5) solve mathematical tasks as quickly as possible
5) develop awareness of the importance of mathematics in everyday life.
6) remember the appropriate solution equations for different types of problems
6) think, solve problems, and reason mathematically
7) define important mathematical concepts and principles.
7) evaluate which among alternative solutions is better.
B. Effective mathematics teachers
SCHOOL MATH TRADITION INQUIRY MATH TRADITION
1) present the content in a highly structured manner
1) provide an opportunity for students to discover concepts and procedures for themselves
2) give students detailed step by step directions on what they are to do before an activity begins
2) allow discussions to continue longer than planned when students show particular interest
3) make sure that students know exactly what they should be doing at any given time
3) serve as facilitator of students’ inquiry and learning
4) immediately correct false statements made by students
4) use and give a wide variety of mathematics problems to illustrate a concept/operation
5) give students many exercises so they can perfect the important skills
5) let students discover the meaning of mathematical concepts by discovery and exploration
6) show the quickest way of solving a mathematics problem
6) take student preferences into account when planning lessons
7) demonstrate the appropriate solutions to mathematics problems
7) let students understand math operations by exploring varied tasks and problems.
Effective mathematics classes involve..
SCHOOL MATH TRADITION INQUIRY MATH TRADITION
1) giving lectures or explanation in teaching students
1) argumentation, proving, problem solving, and collaboration
2) implementing of specific computational operations in mathematics problem solving
2) discussions and negotiations among students and between students and teacher 3) requiring students to constantly and
repeatedly practice the important mathematical skills
3) spending more time letting students work in small groups
4) demonstrating correct use and approach of mathematical problem
4) letting students discover their own solutions to math problems.
Appendix C1
INITIAL TEACHING BELIEFS QUESTIONNAIRE
This questionnaire seeks to determine your beliefs about Mathematics and the teaching of Mathematics. There is no right or wrong answer for this questionnaire.
Instead, your most honest responses to each item are needed. There are three sections in this questionnaire.
Section A: GOALS OF MATHEMATICS EDUCATION
The items below state the possible goals of Mathematics Education. Read each item carefully and decide whether you agree or disagree with each item. Encircle the number corresponding to your response using the following scale: 1 – (SD) Strongly Disagree; 2 – (D) Disagree; 3 – (NDA) Neither Disagree nor Agree; 4- (A) Agree; 5 (SA) Strongly Agree.