Chapter II METHODOLOGY
C. The Instruments
1. Beliefs Questionnaires of Teachers 1.1. Preparation of the questionnaire
The three sub-components of the questionnaire prepared by Bernardo et al. (2000) has been adopted and modified for the purpose of this study. These are the perception of the respondents on (1) the goals of mathematics education, (2) the characteristics of effective teaching in mathematics, and (3) the characteristics of effective learning in mathematics.
From the questionnaire of Bernardo et al. (2000), different indicators were listed in a two-column form such that the two indicators describe the same component of the goals of mathematics education, or the nature of mathematics teaching or the nature of mathematics learning. One is the column showing the indicators for the School Math Tradition and the other is for the Inquiry Math Tradition as shown in Appendix C, p. 139.
Then a questionnaire was reconstructed where the respondents will evaluate each of the statements in terms of specified criterion (e.g. agreement or importance). Each item is followed by a rating scale, which was used by the respondents to indicate their
response. The initial form of the questionnaire is found in Appendix C1, p 141. The questionnaire was shown to the adviser and to two Math faculty members of the PNU.
Some suggestions were considered and the revised questionnaire is found in Appendix E, p. 146.
1.2. The Try-out of the Questionnaire
To test the clarity of language, the questionnaire was tried out to ten (10) graduate students of Philippine Normal University (PNU) in December 2002. These graduate students are enrolled in the Master of Arts in Teaching Mathematics program. They are all elementary mathematics public school teachers and come from either Metro Manila or nearby provinces such as Bulacan and Batangas. The target respondents of this study are also elementary mathematics public school teachers in Metro Manila.
The Cronbach alpha coefficient has been computed to assess the internal consistency of the six subtests. Since each component comprised statements, which are anchored on both traditions, then each component was divided into two subtests, one for school math tradition and the other is for the inquiry math tradition. The results are summarized in Table 2.
Table 2
Reliability Statistics of the Beliefs Questionnaires
Test Mean
score
variance Inter-item correlation
minimum
Inter-item correlation
maximum
Inter-item correlation
mean
Alpha coefficient
SMT- Goal 2.73 .04 .64 .92 .78 .96
SMT- Teaching
2.91 .06 .36 .96 .70 .94
SMT- Learning
3.07 .03 .46 .92 .76 .95
IMT-Goal 3.20 .06 .54 .96 .79 .96
IMT- Teaching
3.21 .12 .35 .93 .70 .94
IMT- 3.07 .07 .59 .96 .74 .94
Learning
The last column reflects the reliability coefficients of the tests, which are all above 0.85, indicating that the questionnaire is reliable.
2. Beliefs Questionnaire focused on content knowledge structure
To determine the beliefs of the teacher-participants on the content knowledge structure of Mathematics, an open-ended questionnaire was developed based on Shulman’s (1987) statement:
As Shulman (1987) puts it,
“Knowledge of mathematics includes all the various topics, concepts, number facts, rules, procedures, and processes in mathematics.
Furthermore, it includes the inter-relationships between concepts and approaches to various kinds of problem solving. The most critical part of this knowledge base is the understanding of the organization of the whole subject area” (p15).
The items included in the questionnaire and the reason for the inclusion of such items is found in Appendix F, p. 149.
The researcher then studied the Philippine Elementary Learning Competencies (PELC) being prescribed by the Department of Education. Summary of the PELC for Grades 4, 5, 6 are shown on Appendix G, p. 151.
After studying the PELC, the researcher constructed a concept map to show the sequences of the topics covered in Grades 4, 5, 6. Such concept map is reflected on Appendix H, p. 153.
The answers of the teacher-participants were compared to the constructed concept map and rated accordingly based on the scoring rubrics below:
Table 3
Scoring Rubrics for Content Knowledge Beliefs
Scores Indicators
3 • If the participant’s answers on the pre-requisite, current and higher topics matched completely with the concept map prepared by the researcher. This suggests that the teacher-participant’s content knowledge belief leans toward IMT.
2 • If the participant’s answers on the pre-requisite, current and higher topics partially matched with the concept map prepared by the researcher. This suggests that the teacher-participant’s content knowledge belief falls midway IMT and SMT.
1 • If the participant’s answers on the pre-requisite, current and higher topics do not match completely with the concept map prepared by the researcher. This suggests that the teacher-participant’s content knowledge belief leans towards SMT.
Both the questionnaire and the concept map were shown to an expert for face validation. The answers of the teacher participants are summarized on Appendix I, p.156.
3. Questionnaire on teaching experience and seminars attended
This questionnaire aims to determine the length of teaching experiences and the different seminars attended by the teacher-participants, as of the time of this study.
To determine the extent of the respondents’ exposures to seminars, conferences, and/or workshops, the following scale was adopted:
Table 4
Scoring Rubrics for Seminars/Workshops Attended
Levels Scores
Local/ Division 1 point per 8 hours attendance National Level 5 points per 8 hours attendance International Level
10 points per 8 hours attendance
4. Checklist for the Classroom Observation (COC) to determine the practices of teachers 4.1. Preparation of the Checklist
The lesson plan followed in an ordinary public school was studied, particularly the Method or Approach of the teacher. The parts are (A) Preliminary Activities which include opening, prayer, drill, review, checking of assignment; (B) Lesson Proper which includes motivation, presentation, comparison and abstraction or fixing skills, exercises or application, generalization and (C) Evaluation. Activities of the teacher from the very start of the lesson until the evaluation were itemized. Indicators inclined to both School Math and Inquiry Math traditions were listed as shown in Appendix J, p. 164.
The following scoring rubrics was used to rate the teachers’ practices in each item indicator.
Table 5
Scoring Rubrics for Each Item in the COC
Scores Indicators
3
• If the practices lean towards inquiry math tradition (IMT). That is, IMT is more evident in the teacher’s practice.
2 • If the practices stand midway between IMT and SMT. That is, IMT and SMT are almost equally evident in the teacher’s practice.
and SMT are almost equally evident in the teacher’s practice.
1
• If the practices lean towards school math tradition (SMT). That is, SMT is more evident in the teacher’s practice.
0 • If the indicator was not observed in the teacher throughout the observation session
To determine the participant’s score in the teaching practices, the mean is computed to include only the indicators observed.
4.2. The evaluation of the checklist
Three faculty members of the PNU Math Department were asked to gauge the face validity of the checklist and following their suggestions, revisions were made
accordingly. Their suggestions and the corresponding action taken by the researcher were reflected in Appendix K, p. 171. The revised checklist is shown in Appendix L, p.175.
To evaluate the usability of the revised checklist (RC), a questionnaire was developed and was shown to an expert for face validation. A copy of the questionnaire is reflected on Appendix M, p. 181.
Four faculty members of the PNU Math Department evaluated the usability of the revised checklist. These faculty members were involved in classroom observations during the students’ on and off campus practice teaching, and during in-service trainings. The evaluators gave an average rating of 4.875 interpreted as “strongly agree” on the usability of the classroom observation as reflected in Appendix N, p. 182.
5. The Interview questions
These are the questions asked to the teacher participants to determine the following:
a) What/Who influenced them to exhibit that practice?
b) What kept them to hold on to their practices?
c) What could possibly change their practices?
d) What/Who influenced them to have such beliefs?
e) What kept them to hold on to their beliefs?
f) What could possibly change their beliefs?
The researcher constructed two sets of flowcharts that would set the direction for the series of questions to be asked during interview. The two sets of questions are focused on the teacher-participants’ (a) beliefs and (b) practices. The flowcharts are shown in Appendices O, p. 183 and P, p. 184.
The flowcharts for the interview questions were shown to an expert for face validation.