28) Fixing Skills (type of activities prepared)
Executing mathematical operations, computations with speed and accuracy are given emphasis.
Explaining and justifying actions on mathematical objects are given emphasis.
29) what the teacher values at the end of the activity
The teacher
emphasizes that the work should be clean and pays more attention to the output than the process.
The teacher accepts messy work and pays more attention on the process than the output.
30) (Fixing Skills) What the teacher does to help the students perfect the math skill
The teacher gives many exercises so the students can perfect the important skills.
To perfect the math skills, the teacher gives tasks to students that will allow them to
discover the meaning of mathematical concepts by discovery and exploration.
31) the nature of the learning
environment
The students are to work silently on their seats and individually.
The students may work anywhere and may work in groups.
32) Are the students allowed to discuss during class?
The students are not allowed to talk to their classmates while activity is going on.
The students are allowed to talk to their classmates to discuss the activity.
33) Are the students encourage to memorize formula or to generate solutions?
The teacher encourages the students to memorize the appropriate solution equations for different types of
problems. (Rote learning)
The teacher encourages the students to generate their own solutions to problems.
34) Does the teacher entertain alternative solutions
The teacher does not entertain other solutions.
The teacher entertains other solutions.
35) Are the students’ out put simply checked or explained?
The output is simply checked. The students explain their outputs.
36) Are the students’ output displayed for discussion?
The students’ outputs are not displayed on the board or wall.
The students’ output are displayed on the board or wall.
37) arrangement of seats
The seats are arranged in a formal way.
The seats are arranged conducive for interaction.
38) Does the teacher entertain students’
questions
The teacher does not entertain students’ questions students nor he allows them to ask questions from each other.
The teacher encourages the students to ask questions or to ask from each other. The teacher encourages the students to pose their own problems.
39) source of questions for discussion
The teacher is the only one asking questions.
The students are given the opportunity to pose their own problems for everyone to solve.
40) emphasis in the Generalization part
Definitions of concepts, principles and algorithms are given emphasis.
Connectedness, relationships, processes are given emphasis.
41) type of activity for Evaluation
The teacher wants the students to follow procedural
instructions to obtain the correct answer.
The students are to apply problem solutions that they learned to novel problems.
42) Over-all The teacher follows the lesson plan as closely as possible at all times.
The teacher presents the lesson in a highly structured
The teacher allows discussion to continue longer as planned when students show particular interest.
manner.
43) allotment of classroom time
The teacher does more talking than the students.
The teacher does less talking than the students.
44) allotment of class time
The students spend more time listening to teacher talk than engaged in their own work.
The students spend more time engaged in their own work than listening to teacher talk.
45) purpose of the problem solving activity
The teacher uses the problem as an end of the learning activity.
The teacher uses the problem as a means for developing concepts.
46) Students’
activity during board work
While some students are working on the board, the other students are watching them.
While some students are working on the board, the other students are encouraged to work on the same problems (or they are to work on a different task prepared by the teacher.)
47) Treatment of teacher when the student’s answer is correct during board work
If the works are correct, they are simply checked without justification.
If the output is correct, the teacher encourages the students to explain their works, even in Filipino. And the teacher encourages the students to ask questions for deeper discussion.
48) Treatment of teacher when the student’s answer is wrong during board work
If the work is wrong, the teacher simply declared it as wrong and calls on another student to work on it (or shows himself the correct answer.)
If the work is wrong, the teacher facilitates the
discussion for the students to realize what was wrong in the solution. Then he allows the student to correct his mistakes.
49) Are the students allowed to go back to the board to correct his mistakes
If the student commits a mistake, he allows his student to go back to board to correct his mistakes but in a very threatening mood (or the teacher is angry.)
If the student commits a mistake, he allows his student to go back to the board to correct his mistakes in a very encouraging mood.
50) Are the students allowed to discuss with his classmates during board work
A student working on the board is not allowed to talk to his other classmates.
A student working on the board is allowed to interact with his other classmates.
Number of questions asked:
Restricted questions
Extended questions Other questions Day 1
Day 2 Day 3 Day 4
Instructional devices used:
________ poster/illustrations/pictures _______ manipulative devices
________ video tapes _______ blackboard
________ newspaper/magazine _______ OHP
________ powerpoint
Appendix K
Results of Evaluation of the COC, Suggestions and Actions taken by the researcher
Item # of the Initial Checklist (IC)
Suggestion Reasons/Remarks 1) Opening of classes
Removed
Opening of classes or the type of greeting could be influenced by the culture of the school. Singing songs or prayer or by simply greeting the teacher is more of a culture of the school than the practice of the teacher.
2) Drill method Removed Although a certain teacher can conduct the drills using the process “from whole to part”, most teachers conduct the drills on a behaviorist approach. This is so because this is the practice being imposed by most schools.
3) Mental problem Retained
4) Checking of assignment Retained 5) Review of previous lessons Retained
6) Motivation Removed This is embedded already in item # 45 of IC.
7) Does the teacher to stimulate students’ thinking
Removed This is included in items # 8, 9 of IC.
8) Start of Presentation Retained 9) Teaching the concept Retained 10) Approached used by the
teacher for the students to learn the concept
Retained 11) Does the teacher use
manipulative/ concrete models/
materials?
Removed A teacher may use the manipulative models and yet demonstrate himself the concept in the class. In that sense, having the concrete model does not guarantee that teacher’s practice is anchored on IMT.
The use of concrete materials/
manipulative models is imbedded in # 10.
12) Type of examples used Revised Please refer to item # 7of the revised checklist (RC).
13) Nature of teacher talk Retained
14) Type of questions posed by the teacher
Revised Since the classes observed are in the elementary level (Grades 4, 5, 6), it is but natural that the teachers ask more
restricted questions than extended.
Hence, for the purpose of this study, a teacher who asked at least three extended questions in a single session is classified under IMT in this component.
Please refer to item # 32 of the RC.
15) Treatment of teacher if the student’s answer is incomplete
Revised Please refer to # 9 of the RC.
16) Treatment of teacher if the student’s answer is wrong
Retained 17) Treatment of teacher if the
student’s answer is correct
Retained 18) Does the teacher allow
students to express their own ideas?
Revised Imbedded with # 9 and #34 of IC.
19) How does the teacher handle the student’s questions in class
Revised Please refer to # 11 of the RC.
20) Classroom atmosphere Revised Please refer to # 12 of the RC.
21) Does the teacher encourage the students to reflect on their own ideas
Revised
22) Application of the concept Revised Please refer to # 13 of the RC.
23) Emphasis in the generalization part
Retained
24) Discussion Revised Please refer to # 14 of the RC.
25) Discussion Revised Include this to # 24 of the initial checklist (IC). Please refer to #4 of the RC.
26) Nature of student’s voice Removed In the usual public elementary schools, pupils are generally obedient and polite.
Hence, using his normal voice does not guarantee that the teacher practices IMT.
27) Nature of teacher’s voice Removed In the usual public elementary schools, pupils are generally obedient and polite, and yet noisy. Raising the voice on the part of the teacher does not mean that he is practicing SMT.
28) Fixing Skills
(type of activities prepared)
Retained 29) What the teacher values at
the end of the activity
Revised Please refer to # 19 of RC.
30) (Fixing Skills) What the teacher does to help the students perfect the math skill
Revised Please refer to # 20 of RC.
31) The nature of the learning environment
Revised Please refer to #21 of RC.
32) Are the students allowed to discuss during class?
Removed Merged with # 31 of IC. Please refer to # 21 of RC.
33) Are the students encourage to memorize formula or to generate solutions?
Revised Merged with #21 of IC. Please refer to # 14 of RC.
34) Does the teacher entertain alternative solutions
Retained 35) Are the students’ out put
simply checked or explained?
Retained 36) Are the students’ output
displayed for discussion?
Retained
37) Arrangement of seats Removed The classes observed are classes in public schools where spaces are limited, and hence seats are inevitably arranged in the usual form of rows/columns.
Imbedded in the revision of item #31. Please see #21 of the revised checklist.
38) Does the teacher entertain students’ questions
Retained 39) Source of questions for
discussion
Retained 40) Emphasis in the Generalization
part
Revised Please refer to # 27 of RC.
41) Type of activity for Evaluation Retained
42) Over-all Retained
43) Allotment of classroom time:
Who does more talking? The teacher or the students?
Removed Imbedded in # 44. The whole class session is not spent on talking and listening alone. A part of it is spent on group work and activity where the students are not talking to the whole class but discussing only in small groups.
44) Allotment of class time Retained 45) Purpose of the problem
solving activity
Retained 46) Students’ activity during board
work
Retained
47) Treatment of teacher when the student’s answer is correct during
Retained
student’s answer is correct during board work
48) Treatment of teacher when the student’s answer is wrong during board work
Retained
49) Are the students allowed to go back to the board to correct his mistakes
Removed Imbedded with # 49 of IC.
50) Are the students allowed to discuss with his classmates during board work
Removed Imbedded with # 49 of IC.
Appendix L
Classroom Observation Checklist
The checklist for classroom observations was developed to determine the math tradition by which the teachers’ practices lean towards to. The two contrasting traditions by Bernardo (2000a) was presented below:
Dimension School Math Tradition Inquiry Math Tradition Nature of
mathematics
Formalized mathematics as collection of facts and procedures
Mathematics as a mode of inquiry &
problem solving Mathematical
Learning activities
Replicating and mastering specified mathematical procedures and operations
Exploration, conjecturing, argumentation, proving, problem posing, problem solving &
collaboration Classroom
interactions/
discourse
Teacher-controlled, initiation-reply- evaluation pattern
Discussion & negotiations among students & between students &
teacher Role of teachers Authority and transmitter of
mathematical knowledge
Facilitator of students’ inquiry and learning
Role of textbook Authority of mathematical knowledge
Resource and stimulus for students’
inquiry and problem solving Indicators of
students Learning
Ability to follow procedural
instructions to obtain correct answers
Ability to explain and justify actions on mathematical objects
1. Objectives of the checklist:
v To describe the activities of the math teachers in the classroom based on the two contrasting traditions presented by Bernardo (2000a).
v To categorize the practices of the math teachers based on the two contrasting traditions.
2. How to use the checklist:
v Put a tick mark on the corresponding indicator, every time the teacher exhibits the said indicator.
v At the end of the observation, rate the teacher on each item as follows:
o 3 – if the practice leans towards inquiry math tradition o 2 – if the practice falls midway the SMT and IMT o 1 - if the practice leans towards school math tradition
o 0 – if the indicator was not observed in the teacher throughout the session
v To determine the inclination of the practice, compute the mean considering only the number of indicators observed. Interpret the computed mean as follows:
o Above 2.15 – Teacher’s practice leans towards Inquiry Math tradition o 1.85 – 2.15 - Teacher’s practice falls midway the SMT and IMT o Below 1.85 – Teacher’s practice leans towards School Math Tradition
Checklist for Classroom Observation
Teacher: ________________________ Dates Observed: ______________________
School: _________________________ Topics Covered: ______________________
Grade Level: _____________________
SCHOOL MATH TRADITION INQUIRY MATH
TRADITION
Preliminary Activities
1) Mental Problem
Students simply answer the problem.
(If wrong, another student will be called.
If correct, then no explanation is given.)
Students are to explain the solution for the problem.
(The teacher does a follow up through art of
questioning.) 2) Checking of
Assignment
The teacher or the student simply writes the correct answers on the board and the students check the assignment.
Students explain the solutions to their
assignments. (The teacher encourages students to do brainstorming.)
3) Review of previous lesson
The review is focused on the facts, principles, algorithms Students are to define concepts. (Answering the questions What)
The review is focused on the relationships and connectedness of concepts and processes. Students are to give real life
examples of the concepts.
(Answering the questions Why and How?)