Figure 1
The Research Paradigm
In the diagram, the one-directional arrows suggest that the teacher’s length of experience in teaching mathematics and his/her exposures in math seminars/ workshops/
trainings each could influence his/her beliefs and teaching practices.
The two-directional arrow between the beliefs and practices suggests that the teacher’s beliefs influence and are reflected in his/her teaching practices in the same manner that the teaching practices influence and are reflected in his/her beliefs. Thus, the diagram shows that the teacher’s beliefs on the goals of math education, nature of math teaching and nature of math learning are mirrored in his teaching practices, and vice versa.
Length of math teaching experience
Beliefs on
• Goals of math education
• Nature of math teaching
• Nature of math
Teaching Practices
Degree of exposures in math seminars/
workshops/ training
Statement of the Problem
This study is an exploratory investigation of the beliefs and practices of the elementary teachers in the high and low performing schools in Metro Manila. The beliefs cover the goals of mathematics education, the nature of mathematics teaching and the nature of mathematics learning.
Specifically, this study provides answers to the following questions:
1) Do the elementary math teachers’ beliefs lean towards the SMT or IMT?
2) Are there differences between the beliefs of elementary math teachers from low performing schools with those of elementary teachers’ from high performing schools?
3) Do the elementary math teachers’ practices lean towards the SMT or IMT?
4) Are there differences in the practices of elementary math teachers from low performing schools and those from high performing schools?
5) Are the beliefs of the elementary math teachers related to their practices?
6) Are the elementary math teachers’ beliefs and practices related to the length of their experience in teaching mathematics?
7) Are the elementary math teachers’ beliefs and practices related to the degree of their exposures to seminars or workshops?
Scope and Delimitation of the Study
This study is descriptive in nature. Its primary goal is to investigate the teaching beliefs and teaching practices of the elementary teachers in the high and low performing
schools in Metro Manila. Beliefs and practices are focused on the nature of mathematics, goals of math education, nature of mathematics learning and math teaching.
Elementary teachers are chosen as the respondents because of the following reasons:
1) The basic concepts in mathematics are introduced in the elementary level. The interaction between a teacher’s beliefs system and his/her practices is assumed to be evident at this stage.
2) Elementary teachers are not required to take mathematics specialization course, hence their academic preparation in mathematics (in general) is just part of the General Education of the Bachelor in Elementary Education (BEED) curriculum. Commission on Higher Education’s (CHED) minimum requirements for BEED is 6 units of mathematics (usually, Algebra and Trigonometry).
3) Master’s courses in mathematics are not geared to teaching elementary mathematics. Hence, it is interesting to know how these teachers understand
mathematics, and where they draw their ideas from while teaching the different concepts in mathematics.
4) Most of the studies in the Philippines are focused on high school mathematics teachers, since they have specialization courses. Only few studies are into studying the status of elementary mathematics teachers.
The sources of data are the twenty (20) teacher-participants from five (5) high performing schools, the twenty (20) teacher-participants from three (3) low performing schools, and the forty (40) math classes they handled at the time of the study. Thus, generalizations and conclusions made on the basis of the findings should not be indiscriminately applied to all mathematics teachers/classes.
The teacher-participants’ beliefs were determined by analyzing their answers in the beliefs questionnaire. Their teaching practices were determined by analyzing their classroom interactions, specifically those of the components listed in the classroom observation checklist developed by the researcher for this purpose.
The accuracy of the research data might have been affected by three factors: a) the fact that the researcher was the sole rater in analyzing the classroom interactions, i.e.
there was no other rater, b) the clarity and exactness of the teacher-participants’ responses to the interviews since some of the participants refused to have the interviews recorded and c) the presence of the researcher and the video camera in the classroom could have affected the flow of interaction between teacher and students, and among students.
Significance of the Study
To be a more effective mathematics teacher, one must possess more than just knowledge of specific mathematical content and pedagogical skills. In fact, one must have the knowledge that involves a whole philosophy about mathematics teaching and learning. At present, much of this knowledge is not taught explicitly in schools or in teacher preparation programs; hence, much of it were learned through classroom experiences.
Results of this study would reveal the status of elementary mathematics teachers’
beliefs and practices in the high and low performing schools of Metro Manila. Data gathered from this study could serve as guide on how to prepare INSET programs to further profit elementary mathematics teachers through active reflection of their own practices. The INSET should include some ways of helping these teachers become aware
of the implied rules and beliefs that operate in their classrooms, and help them examine their consequences on the learning experiences of their students.
For the classroom teachers, the results of this study would encourage teachers to examine their current beliefs and practices. For some, this may help them realize their shortcomings in their current practices and might encourage them to consider
alternatives. As such, desirable changes might be obtained.
For curriculum planners of teacher education programs, results of this study may help them on how to strengthen teacher education programs, particularly in mathematics education. At present, elementary mathematics teachers do not have courses in the history and philosophy of mathematics. Thus, we may ask then, “in what course will our
prospective mathematics teachers be given opportunities to be aware of their beliefs on the nature of mathematics, on how mathematics is being learned and how it should be taught?”
Assumptions
The following statements were assumed to be true in the study:
1. The mathematics elementary teacher-participants’ responses to the beliefs questionnaires and interviews are true reflections of their thinking and opinions.
2. The teacher-participants’ conduct of classes during the observation periods are true reflections of their practices, even during the time the researcher was not around to make observations.
Definition of Terms
For the purpose of this study, the following terms were used and defined as follows:
Beliefs. These are the ideas/principles that the participants cling on to and value.
These are the things that influence them on how they think about classroom matters and how they respond to particular situations in a math class. In this study, the beliefs of the participants are reflected through their answers in the beliefs questionnaires.
Belief Falls Midway Between SMT and IMT. This refers to the case where the SMT and IMT belief mean scores are not significantly different.
Belief Leans Toward IMT. This refers to the case where the IMT belief mean- score is significantly greater than the SMT belief mean score.
Belief Leans Toward SMT. This refers to the case where the SMT belief mean- score is significantly greater than the IMT belief mean score.
Belief is Midway Between SMT and IMT. This refers to the case where the SMT and IMT belief mean scores are not significantly different.
High Performing Schools (HPS). These are the elementary schools in Metro manila, which achieved highly in the National Elementary Achievement Test (NEAT) - Math component. In this study, the HPS are the public elementary schools in Makati Division whose cumulative school performances during SY 1999-2002 in the Division Achievement Test were above average.
Inquiry Math Tradition (IMT). This is a tradition in mathematics education that emphasizes more active learning on the part of the students by way of exploration,
conjecturing, argumentation, proving, problem posing, problem solving and
collaboration. In this tradition, the students are assumed to learn mathematics if they can resolve problematic situations that challenge their current conceptual understanding (Bernardo, 2002a).
IMT-Goal. In the study, this refers to the goals of math education under the IMT.
IMT-Learning. In the study, this refers to the nature of mathematics learning under the IMT.
IMT-Teaching. In the study, this refers to the nature of mathematics teaching under the IMT.
Low Performing Schools (LPS). These are the elementary schools in Metro Manila, which achieved lowly in the National Elementary Achievement Test (NEAT) - Math component. In this study, the LPS are the public elementary schools in Caloocan Division whose cumulative school performances during SY 1999-2002 in the Division Achievement Test were below average.
Practices. These are the actual performance or customary actions of the participants as they perform their duties as mathematics teachers. In this study, the practices of the teachers are determined using a classroom observation checklist developed by the researcher.
Practice Falls Midway Between SMT and IMT. This refers to the case where SMT and IMT are almost equally evident in the teacher’s teaching practice.
Practice Lean Towards IMT. This refers to the case where IMT is more evident in the teacher’s teaching practice.
Practice Lean Towards SMT. This refers to the case where SMT is more evident in the teacher’s teaching practice.
School Math Tradition (SMT). This is a tradition in mathematics education that involves classroom routines and discourses that are usually rigidly controlled by the teacher. This tradition also emphasizes the formalized presentations of mathematics as a collection of facts and procedures. Students are presumed to have learned mathematics if they can follow the procedures being taught to them to obtain the correct answer
(Bernardo, 2002a).
SMT-Goal. In the study, this refers to the goals of math education under the SMT.
SMT-Learning. In the study, this refers to the nature of mathematics learning under the SMT.
SMT-Teaching. In the study, this refers to the nature of mathematics teaching under the SMT.
Chapter II