> 5@ 0qbjbj22 (XXi2|42IBIDIDIDIDIDIDI$gKRMhIhI}IBIBICF OA`fzD"I,I0IDNNDF22NF(6DhIhI22d22Problems and Challenges in Implementing the
New Teacher Education Curriculum (NTEC) in Math Education
by
Auxencia A. Limjap, Rosemarievic V. Diaz, Richard K. Pulmones, Celia C. Cruz,
Milagrina A. Gomez, Lilia L. Lagrimas, Archieval A. Rodriguez,
Jimmy M. Romero, & Arlyn S.Tumala
CHED Zonal Research Group in Math, Southern Metro Manila, Philippines
The New Teacher Education Curriculum (NTEC) in mathematics education, requires the establishment of a new benchmark in teaching and learning mathematics. There are implied knowledge and skills in the NTEC that practicing teachers in Teacher Education Institutions (TEIs) must possess to fully implement the new curriculum. However, there is a prevailing perception that practicing teachers might not be ready with the implementation of the NTEC in math education. There are without doubt, potential problems, concerns and impediments that math teacher educators and TEIs have to address to fully implement it. This study explores one of the factors identified as crucial in the implementation of NTEC, which is the math teacher educators academic preparation, their pedagogical content knowledge and beliefs, and their perceptions on how identified problems, concerns and impediments can be addressed. It explores the extent to which math teacher educators are ready to implement the NTEC as regards to the cognitive demand, and pedagogical content knowledge and beliefs implied in the NTEC in Math Education.
The New Teacher Education Curriculum
The Commission on Higher Education (CHED) promulgated guidelines for the undergraduate teacher education programs in a Memorandum Order (CMO) 30 Series 2004 otherwise known as the New Teacher Education Curriculum. Accordingly, this is CHEDs response to the issues and challenges besetting Philippine education especially in the areas of mathematics and the sciences. Its goal is to rationalize the undergraduate teacher education in the country to keep pace with the demands of global competitiveness. The revisions in policies and standards made the new Bachelor of Elementary Education and the Bachelor of Secondary Education programs closer to the prescribed curriculum of the UNESCO (1985 UN model).
The United Nations Education Scientific Cultural Organization Principal Regional Office of Asia and Pacific (UNESCO PROAP, 1992) enumerated the following abilities needed to ensure development of competencies in any teacher education program:
Apply scientific and mathematical knowledge and skills to the dynamic real-life problems of the learner;
Facilitate learning that is relevant to the learners own background and entry characteristics, by simplifying the teaching of science and mathematics, while at the same time moving on from this point to the wider considerations of the community and the world at large;
Nurture motivation for learner performance on a continuing basis; and
Make societal/macro concerns relevant and meaningful to individual learners.
The NTEC recognizes the need to equip future teachers with a wide range of theoretical and methodological skills that will allow them more options and greater flexibility in designing and implementing learning environments that will maximize their students learning.
Truly, much is expected of a BSEd graduate in the way he/she should deliver the lecture up to the way he/she should manage the learning environment. This expectation requires that the BSEd graduate acquire competencies that will enable him/her to plan and implement activities that will engage the students in the learning activities that would result to meaningful learning. Similarly, much is also expected from the teachers implementing the NTEC. Without access to the pedagogical skills demanded by the NTEC, many teachers find themselves unprepared to face the challenges of this new curriculum.
Another major expectation from BSEd graduates of this NTEC is that they can facilitate learning of diverse types of learners, in diverse types of learning environments, using a wide range of teaching knowledge and skills. However, the way they are taught will influence the way they will teach. That is, if they are expected to be facilitators of learning, then they must be given enough opportunities to be exposed in such learning environment. This consists of a shift in paradigm from the math tradition that dominated teaching and learning in the past to a more inquiry based tradition prescribed by the NTEC. Furthermore, this requires that an investigation be made about the pedagogical content knowledge and beliefs of implementers of the new curriculum.
Pedagogical Content Knowledge and Beliefs for Effective Teaching
This study explores the linking of the pedagogical content knowledge and beliefs of mathematics teachers in learning and instruction. It is asserted that this can affect the teachers practice as they implement a new curriculum.
In the studies conducted by Talisayon et al (UP-ISMED, 1998) and Ibe & Ogena (1998), it was found out that facilitating the students processing skills rarely happens in the Philippine science and mathematics classrooms, if not at all. Ibe et al (1998, p. 10) found out that high school experiments in science classes are like cookbooks where students go through the steps in procedures without thoughts of whys, but rather with concern about getting the laboratory reports done and using predetermined results. Talisayon et al (1998) on the other hand claims that instead of creating opportunities for the students to discover science concepts, principles, generalizations and theories, they were simply passed on to students to memorize. In addition to that, during the problem solving activity, instead of allowing the students to explore on how they will solve the problems given, the teacher simply demonstrates the steps to be followed by the students. Teachers feel more confident telling the students the facts and principles than facilitating the meaning of these learning. While various in-service trainings have been conducted on new ways of teaching mathematics and the sciences, most teachers prefer to conduct their classes using the old and familiar strategies. But this is what pedagogical content knowledge is all about. It consists of finding ways to make the mathematics content understandable to students at different levels.
For many teachers, moving away from the old tradition to try new strategies anchored on constructivism, or on inquiry approach as defined by Bernardo, Prudente & Limjap (2003) would require a change in their perceptions and beliefs on the nature of mathematics, and about what it means to learn and teach mathematics (Brown, Cooney, & Jones, 1990).
The term beliefs as mentioned by Villena (2004) has been used in research in different contexts. According to Pajares (1992, as cited in Villena, 2004) such terms as beliefs, values, attitudes, judgements, opinions, ideologies, perceptions, conceptions, conceptual systems, preconceptions, dispositions, implicit theories, personal theories, and perspectives have frequently been used almost interchangeably. Sometimes, it is quite difficult to identify the distinguishing features of beliefs, and how they are to be separated from knowledge.
Nespor (1987, as cited in Villena, 2004) said that beliefs tend to be organized in terms of larger belief systems, which are loosely bounded networks with highly variable and uncertain linkages to events, situations, and knowledge systems. The larger belief systems may contain inconsistencies and may be quite idiosyncratic. He further suggested however, that they have great value in dealing with complex, ill-defined situations. These beliefs help interpret and simplify classroom life, to identify relevant goals, and to orient teachers to particular problem situations. Because of the complex and multi dimensional nature of classroom life, knowledge alone would be inadequate in making sense of classroom situations and prioritizing problems to be tackled and actions to be undertaken. Thus, teachers beliefs affect the directions they take and goals they set in classroom instruction.
Studies here and abroad underscore the fact that students achievement is best attributed to teacher quality. They claim that the positive effects of teacher quality appear to accumulate over the years. That is, students who were enrolled in a succession of classes taught by effective teachers demonstrated greater learning gains than did students who had the least effective teachers one after another.
What then brings about effective teaching? Many studies reveal that teaching competency and effectiveness depends largely on the teachers system of beliefs, which usually tends to become his/her philosophy. Ernest (1989) supports this when he said that teaching reforms couldnt take place unless teachers' deeply held beliefs about mathematics and its teaching and learning change. He added that the practice of teaching mathematics depends on a number of key elements such as the teacher's mental contents or schemas, particularly the system of beliefs concerning mathematics and its teaching and learning, the social context of the teaching situation, particularly the constraints and opportunities it provides; and the teacher's level of thought processes and reflection. He further added that the key belief components of the mathematics teacher are the teacher's view or conception of the nature of mathematics, model or view of the nature of mathematics teaching, and the model or view of the process of learning mathematics.
Borko and Putnam (1996) and Richardson (1994), all agreed that the order in which beliefs and practices are addressed in staff development programs may not be that important. What is critical is that both practices and beliefs become the object of reflection and scrutiny. Lastly, they noted that meaningful change in practice requires change in the beliefs as well.
Significance of the Study, Statement of the Problem and Research Goals
Results of the study will definitely be significant to the CHED. A systematic identification of the various issues, concerns, problems and, impediments of TEIs, math department heads as well as math teacher educators, would guide the CHED on how best to extend assistance to fully implement the NTEC in math education. Over and above what CHED can provide, the TEIs themselves can structure and design their curriculum and in-service training of their math teacher educators to address the new competencies implied in the NTEC in math education.
One result of this study is a profile of teachers in terms of their pedagogical content knowledge and beliefs as culled from the administration of the Teaching Beliefs and Practices Questionnaire (TBPQ). Math teacher educators can be tagged as transmissive or inquiry teachers depending on their scores in the TBPQ (Bernardo et al, 2003). Belief systems are important considerations on ones choice of teaching strategies to affect desired learning outcomes. By inquiring into teachers beliefs, we can have a deeper appreciation, understanding of how these beliefs can be linked to actual practices of teachers, and ultimately how such practice can address the implied competencies in the NTEC in math education.
In this study readiness is conceptually defined as the ability of the TEIs to fully implement the NTEC in math education. This ability could be in terms of how instruction could be effected to address the NTEC in math education as well as the capability of the school in terms of its resources. The math teacher educators academic preparation, their pedagogical content knowledge and beliefs, and their perceptions on how identified problems, concerns and impediments can be addressed are also possible factors that can affect the implementation of the NTEC in math education. Thus, it is in these contexts how the research problems are posed and how the research goals of the study are written.
This study aims to answer the following questions:
How ready are the TEIs in implementing the NTEC in Math Education in terms of curriculum and instruction?
To what extent are Math Teacher Educators ready to implement the NTEC as regards to the cognitive demand, and pedagogical content knowledge and beliefs implied in the NTEC in Math Education?
What potential problems, concerns, and impediments are encountered by math teacher educators in implementing the NTEC in math education?
What courses of action may be recommended to address the problems, concerns and, impediments in the implementation of the NTEC?
Methodology
The study is descriptive in nature with the end view of identifying the problems and concerns of TEIs in implementing the NTEC in math education. Thus, both the qualitative and quantitative approaches were employed in data collection. The NTEC was analyzed to identify the competencies expected of Math Teacher Educators. The Teaching Beliefs and Practices Questionnaire (Bernardo et al, 2003) measured teachers pedagogical content knowledge and beliefs. Focus Group Interviews were conducted to extract vital information on the problems, and concerns of TEIs in implementing the NTEC in Math Education. Information about the extent of implementation of the NTEC to include problems and concerns of mathematics education teachers were elicited using the Implementation Readiness Questionnaire (IRQ).
The participants of the study were ten selected TEIs both university and nonuniversity institutions with a math education program in the National Capital Region. The Teaching Beliefs and Practices Questionnaire (TBPQ) were administered to the Math Teacher Educators of these TEIs. Eighty math teacher educators were asked to answer the TBPQ and IRQ. Likewise, ten different Math Department Heads and Math Teacher Educators from these TEIs were the participants of the focus group discussions.
Instruments include the Teaching Beliefs and Practices Questionnaire (TBPQ)
designed to measure five (5) sub areas conceptualized as components of teachers beliefs and practices in Math Education. These areas are (a) Goals of Mathematics Education; (b) Goals of Science Education; (c) Effective Teaching; (d) Effective Learning Activities; and (e) Your Own Teaching Practices. Thus, the instrument has five sections to represent these five constructs. Each item is measured on the extent of the participants degree of agreement (from SD-strongly disagree to SAstrongly agree)
The Implementation Readiness Questionnaire (IRQ) is an instrument designed to obtain information on the extent of the implementation of the NTEC. Questions were also framed to determine the different mathematics subjects already taught by the participants, their degree of confidence in teaching these subjects, reasons that contributed to this confidence and tools they used in teaching these subjects.
Focus group discussion was employed as the main source of qualitative data for the study. These include mathematics coordinators, school heads and mathematics teacher educators from the 10 participating institutions.
Results of the Study
Results show that 70% of the participants have undergraduate degrees majoring in Mathematics while 30% are not; 13.8% have PhD/EdD in Math, while 28.8% have either MA or MS degree in Math. It also shows that 78% are experienced college teachers; 64.6% handle major courses and 20% have 1-10 years of teaching at the graduate level. The mathematics teacher educators have sufficient academic preparation to handle the NTEC.
The TBPQ reveals that 90% either agree or strongly agree with School Math Tradition (SMT) on goals, nature of learning and teaching mathematics. SMT can be described as one that involves classroom routines and discourses that are usually rigidly controlled by the teacher. Mathematics is viewed as a collection of facts and procedures and doing mathematics involves simply repeating procedures specified in the text and in the class. Moreover, the teacher and the textbook are perceived to be the authorities of mathematical knowledge and the activities in the classroom mainly involve the transmission of knowledge from these authorities to the students.
The goals of math education under SMT is for the students to master mathematical facts and principles, execute mathematical operations, perform computations with speed and accuracy, and define mathematical concepts and principles. Effective math classes under the SMT are those in which the teachers give lectures or explanation, implement specific computational operations in solving math problems, and require students to constantly and repeatedly practice important mathematical skills. Effective mathematics teachers under SMT are those who give the students detailed step by step directions on what to do, give students many exercises so they can perfect the important skills, show the quickest way of solving mathematics problem, demonstrate the appropriate solutions to mathematics problems.
All participants of the study either agree or strongly agree with the Inquiry Math Tradition (IMT). Among the goals of math education under IMT is for the students to generate his/her own solutions to problems, apply problem solutions learned to novel problems, think of alternative solutions to ones mathematical problems, reason mathematically, and develop awareness of the importance of mathematics in everyday life.
The IRQ reveals that only 42.2% of those who think they can teach the major courses claim that they have high level pedagogical content knowledge of these courses. There is also a big percentage (40%) of those who claim that their pedagogical content knowledge is somehow high. Since the teacher participants are less convinced about their ability to facilitate students learning in mathematics, then this is an indicator of their lack of readiness to implement NTEC. Their confidence to teach the NTEC mathematics courses does not match their content knowledge of mathematics. There seems to be a need to develop the pedagogical content knowledge of mathematics teacher educators for them to become effective implementers of the NTEC.
The TBPQ further reveals that 78.8% of the participants anchor their teaching practices on SMT while 83.3% anchor their teaching practices on IMT. Coefficients of correlations were computed involving the variables considered in the study. Only the following pairs yielded some significant correlations. The SMT practice and SMT beliefs are significantly correlated at .01 level of significance. Similarly, the IMT practice and IMT beliefs are significantly correlated. Interestingly, the IMT practice and the SMT practice are significantly correlated also. It seems that the mathematics teacher educators practice both the SMT and IMT. They are eclectic in terms of teaching practices.
The TBPQ reveals that teachers engage their students in solving mathematical problems most of the time. However they also engage their students oftentimes in activities with such cognitive demands as visualizing, knowing, computing, applying and proving. Mathematics teacher educators seem to have the competencies needed to implement the NTEC. However, the IRQ reveals the participant teachers low confidence in addressing the cognitive demands of the mathematics courses included in the NTEC.
Surprisingly, only 13.3%-22 % indicated their confidence in teaching such basic mathematics courses as History of Mathematics, Action Research in Math, Seminar in Technology in Math, Instrumentation in Math and Math Modeling and Investigation, while 51% are confident to teach contemporary mathematics. Among the subjects that belong to the abstract mathematics strand, only 24% are confident to teach Modern Geometry. The range of percentages of teachers who can teach the mathematics courses that require a high cognitive level of rigor is 24% to 44%. However, teachers have higher levels of confidence (53%) in teaching Linear Algebra which is considered rigorous, than in teaching Probability and Statistics (24%) which is not classified in that category. It leads the researchers to wonder at what level teacher educators bring such abstract courses as Linear Algebra. This is the reason why the researchers realized the need to collect syllabi for document analysis.
Conclusion
There is a clear need expressed by the participants for their training for proper implementation of the NTEC. They recognize the need to address the problems and challenges posed by the NTEC. Firstly, while their educational background provide them with competencies to teach the mathematics content, they expressed low level of confidence in teaching the basic mathematics courses found in the NTEC like contemporary mathematics, mathematical modeling and investigation, probability and statistics, history of mathematics, action research in mathematics, and the higher level mathematics like modern geometry. Secondly, their confidence in teaching the mathematics courses is rarely drawn from their pedagogical content knowledge which consists of the knowledge of the learners level of cognitive development, deep understanding of the learning process and wide range of teaching process skills. This may explain why their beliefs on mathematics teaching and learning is still eclectic, as shown by the significant correlation of both the IMT & SMT. Thirdly, there seems to be a need to train teacher educators to prepare syllabi because very few among them have participated in the design of the syllabi on NTEC mathematics courses. In fact, one surprising revelation of some teacher educators is that they are not even aware that there is a new teacher education curriculum. This usually happens in schools were education students who major in mathematics take their major courses in other colleges; or are made to take their courses together with engineering students and science students. Some professors who teach the major courses are not aware of changes in policies on teacher education. Fourthly, while there are TEIs that recognize the need to train education students to become facilitators of learning, it seems that there are not enough role models around based on the responses on the IRQ. Consequently, some education students do not get the exposure that they need on teaching mathematics in an inquiry based learning environment, which is the core of the NTEC. Lastly, there seems to be a need for more institutional support in terms of learning materials, facilities, technologies, and training of the teacher educators themselves. In other words a clarification of the vision of the NTEC is necessary in order to help teacher educators appreciate and understand the goals of the program for it will explain why NTEC is anchored on the IMT.
References
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