SD D NDA A SA
1. the teacher giving lectures or explanation in teaching students.
1 2 3 4 5
2. argumentation, proving, problem solving, and
collaboration among students and between students and teachers.
1 2 3 4 5
3. the teacher implementing specific computational operations in mathematics problem solving.
1 2 3 4 5
4. discussions and negotiations among students and between students and teacher on how to solve a given problem.
1 2 3 4 5
5. the students engaged in constant and repeated practice to master the important mathematical skills.
1 2 3 4 5
6. the teacher demonstrating correct use and approach of mathematics problem.
1 2 3 4 5
giving the students difficult word problems to solve so that the students pay more attention to the teacher (as the teacher shows the solutions).
1 2 3 4 5
spending more time letting the students to work in groups to derive the formula.
1 2 3 4 5
7. spending more time letting students work in small groups to decide what is right and what is wrong.
1 2 3 4 5
8. students engaged in wide variety of tasks to discover their own solutions to math problems.
1 2 3 4 5
Appendix D
Revised list of Indicators for Beliefs Questionnaire
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 (i.e. can recite
multiplication table)
1) generate (produce) his/her own solutions to problems
2) perform computations with speed and accuracy
2) apply problem solutions they learned to new problems
3) develop the ability to follow procedural instructions to obtain correct answers
3) think of alternative solutions (different from the one discussed in class) to one mathematics problem, even if it will consume longer time
4) execute mathematical operations 4) develop an ability to explain and justify actions on mathematical objects
5) solve mathematical tasks as quickly as possible by using the solutions presented by the teacher
5) create a pattern that would show the inter relatedness of concepts, principles and processes.
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 or follows the lesson plan as closely as possible
2) 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) give students tasks that will allow them to discover the meaning of mathematical
concepts by discovery and exploration 6) show the quickest way of solving a
mathematics problem
6) consider the student preferences when planning lessons
7) demonstrate the appropriate solutions to mathematics problems
7) let students understand math operations by exploring varied tasks and problems.
C. Effective mathematics classes involve.
SCHOOL MATH TRADITION INQUIRY MATH TRADITION
1) the teacher giving lectures or explanation in teaching students
1) argumentation, proving, problem solving, and collaboration among students and between students and teachers 2) the teacher implementing of specific
computational operations in mathematics problem solving
2) discussions and negotiations among students and between students and teacher on how to solve a given problem
3) the students engaged in constant and repeated practice to master the important mathematical skills
3) spending more time letting students work in small groups to decide what is right and what is wrong
4) the teacher demonstrating correct use and approach of mathematical problem
4) students engaged in wide variety of tasks to discover their own solutions to math problems.
5) the teacher giving the correct formula on how to solve a problem to save time and to cover more drills to master the use of formula
5) spending more time letting the students to work in groups to derive the formula 6) giving the students difficult word
problems to solve so that the students pay more attention to the teacher (as the teacher shows the solutions)
6) giving the students activities that build upon their experience to enhance math learning.
Appendix E
REVISED 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.
At the end of a mathematics class, students should be able to …
SD D NDA A SA
1. master mathematical facts, principles, and algorithms (i.e. can recite multiplication table).
1 2 3 4 5
2. generate (produce) his/her own solutions to problems. 1 2 3 4 5 3. apply problem solutions they learned to new problems. 1 2 3 4 5 4. perform computations with speed and accuracy. 1 2 3 4 5 5. develop the ability to follow procedural instructions to
obtain the correct answer.
1 2 3 4 5
6. think of alternative solutions (different from the one discussed in class) to one mathematics
problem, even if it will consume longer time.
1 2 3 4 5
7. execute mathematical operations. 1 2 3 4 5
8. solve mathematical tasks as quickly as possible by using the solutions presented by the
teacher during discussion.
1 2 3 4 5
9. develop an ability to explain and justify actions on mathematical objects.
1 2 3 4 5
10. create a pattern that would show the inter relatedness of concepts, principles and processes.
1 2 3 4 5
11. remember the appropriate solution equations for different types of problems.
1 2 3 4 5
12. define important mathematical concepts and principles.
1 2 3 4 5
13. think, solve problem and reason mathematically 1 2 3 4 5 14. evaluate which among alternative solutions is better. 1 2 3 4 5
Section B: EFFECTIVE TEACHING
The items below state the beliefs about characteristics of effective teaching in Mathematics. Read each item carefully and decide whether you agree or disagree with each item. Encircle the number corresponding to your response using the same scale you used earlier.
Effective mathematics teachers …
SD D NDA A SA1. provide an opportunity for the students to discover concepts and procedures for themselves.
1 2 3 4 5
2. follow the lesson plan as closely as possible at all time.
1 2 3 4 5
3. give students detailed step by step directions on what they are to do before an activity begins.
1 2 3 4 5
4. allow discussions to continue longer as planned when students show particular interest.
1 2 3 4 5
5. serve as facilitator of students’ inquiry and learning. 1 2 3 4 5 6. make sure that students know exactly what they
should be doing at any given time.
1 2 3 4 5
7. immediately correct false statements made by students.
1 2 3 4 5
8. use and give a wide variety of mathematics problems to illustrate a concept/operation.
1 2 3 4 5
9. give students tasks that will allow them to discover the meaning of mathematical concepts by discovery and exploration.
1 2 3 4 5
10. give students many exercises so they can perfect the important skills.
1 2 3 4 5
11. show the quickest way of solving a mathematics problem.
1 2 3 4 5
12. demonstrate the appropriate solutions to mathematics problems.
1 2 3 4 5
13. consider the student preferences when planning lessons.
1 2 3 4 5
14. let students understand math operations by exploring varied tasks and problems.
1 2 3 4 5
Section C: EFFECTIVE TEACHING
The items below state the beliefs about effective learning activities in Mathematics class. Read each item carefully and decide whether you agree or disagree with each item. Encircle the number corresponding to your response using the same scale you used earlier.