**A Discussion on the School – Based **

**Mathematics Mentoring Program**

by

ERLEO T. VILLAROS, EPS

Mathematics, Research & Testing

email addresses:

ejerlourdz@gmail.com, and

etvillaros@teacher.deped.gov.ph

DIVISION OF AURORA

San Luis, Aurora

TABLE OF CONTENTS

1 THE PROBLEM AND ITS BACKGROUND

1.1 Introduction

1.2 Rationale

1.3 Statement of the Problem

2 REVIEW OF RELATED LITERATURE AND STUDIES

3 SCHOOL – BASED MENTORING PROGRAM

3.1 Quality of Mathematics Instruction, Meaning & Development

3.2 Teachers’ Knowledge and Cognitive Processes

3.3 Role of Language as Medium for Classroom Education

3.4 Implications to Mentoring

3.5 The Concept of Mentoring and its Processes for Mathematics Education

3.5.1 Intervention/Supervision Scheme

3.5.2 Mentorial Frameworks

3.5.3 Relationships and Goals

3.6 Mentoring Realities and Events in the Philippines

3.7 A Gateway to Teachers’ and Students’ Mathematics Proficiency

4 CONCLUSIONS & RECOMMENDATIONS

CHAPTER 1

THE PROBLEM AND ITS BACKGROUND

### “No person is more influential in the day-to-day life

*of students than the teacher in the classroom.”*

– **California Education Policy Seminar** (1998)

1.1 INTRODUCTION

In the context of the Philippines and worldwide educational reforms that require teachers to understand and respond to the student thinking about mathematics in new ways, ongoing teacher training is a necessity. Teacher quality is the key to improving student learning. Effective teacher training is a major component of teacher quality, along with ongoing opportunities for teacher development through effective mentoring of teachers.

Effective teachers know their content, understand how their students learn, are able to develop and teach curriculum, and also know how to determine and meet their students’ needs. Accordingly, effective teacher training includes a coherent curriculum that tightly intertwines theory and practice, fieldwork that is integrated with class work, coupled with support from carefully selected mentors, and emphasis on learning-theory and child development, with extensive training in the ability to address the diverse needs of the students (California Education Policy Seminar, 1998).

It is important to take into account the professional education and development of mathematics teachers and educators in the Philippines. It is the premise of this discussion to consider the continued development of teachers as a key to students’ opportunities to learn mathematics. What teachers of mathematics know, care about and do is a product of their experiences and socialization prior to and after entering teaching, together with the impact of their professional education, whether formal or informal, to teaching and learning. This impact is variously significant: in some systems, the effects of professional education appear to be weak or even negligible, whereas other systems are structured to support effective ongoing professional education and instructional improvement.

It is recognized that the Philippines faces challenges in preparing and maintaining a high-quality teaching force of professionals who can teach mathematics effectively, and who can help prepare young people for successful adult lives and for participation in the development and progress of the society.

1.2 RATIONALE

Upgrading and strengthening teachers’ competencies has been a focus and thrust of the Philippine education since 1961. The teacher training was conducted using the cascading model (Talisayon, et al., 1998). It is observed that the participants’ knowledge on the subject matter was inadequate, making it difficult from them to adapt the materials to the students’ level. It is also observed that the trainees who participated in the lower level training are not as good as the national level trainees due to the decrease in the quality of training as it goes down to the school level training.

Three main reasons underlie the decision to make a discussion on mathematics teachers’ education and training through mentoring. One reason rests with the central role of teachers in students’ learning of mathematics, nonetheless too often overlooked as taken for granted. Concerns about students’ learning compel attention to teachers, and to what the work of teaching demands, and what teachers know and can do. A second reason is that no effort or may be less effort to improve students’ opportunities to learn mathematics can succeed without parallel attention to their teachers’ opportunities for learning. The professional formation of teachers is a crucial element in the effort to build an effective system of mathematics education. Third, institutionalizing a mentoring program is a great approach to empower the teachers within the Department of Education (DepEd).

The timing is right for this discussion. The past decade has seen substantial increase in scholarship on mathematics teachers’ education and development. The National Educators Academy of the Philippines ( NEAP ) with its National English Proficiency Program (NEPP) has recently started mentoring English, Mathematics and Science teachers for English proficiency believing that English plays important part in improving students’ mathematics performance.

Mentoring mathematics teachers is a developing field, with important contributions to teaching practices, policy, theory and research. Theories on mathematics teachers’ learning are still emerging, with much yet to know about the knowledge, skills, personal qualities and sensibilities that teaching mathematics entails, and about how such professional resources are acquired. The outcomes of mentoring are mathematics teachers’ practice and the effectiveness of that practice in the contexts in which teachers work. Yet we have much to learn about how to track teachers’ knowledge into their practice, where knowledge is used to help students learn. We have more to understand about how mentoring can be an effective intervention in the complex process of learning to teach mathematics, which is all too often most influenced by teachers’ prior experience as learners, or by the contexts of their professional work.

1.3 STATEMENT OF THE PROBLEM

With the underlying discussion objectives, it is needed to present these principal questions:

- What are the factors that are needed to attain quality education? What are its implications to mentoring? Will these serve as objects of mentoring?
- What are the mentoring functions, interventions/observation styles and Mentorial frameworks that the mentors may employ?
- What are the different mentors behaviors in establishing good mentor – mentee relationship?
- What is mentoring in the context of Philippine mathematics education and its processes?
- What is the present practice of mentoring in the Philippine education? What are the concerns or problems raised by the mentors for and during the implementation of this program?
- What contribution can the present mentoring program do for the school – based Mathematics mentoring program?
- How must the Mathematics mentors and teachers behave in order to attain their Mathematics teaching proficiency & professionalism, and Mathematics proficiency respectively?

CHAPTER 2

REVIEW OF RELATED LITERATURE & STUDIES

Mathematics educators have articulated a vision for teaching mathematics that includes engaging students in problem solving, mathematical argumentation, and reflective communication (NCTM, 1991, 2000). Calls for instructional reform in mathematics have been accompanied by demands, in many countries, for radical changes in teaching practices. Many teachers have learned to teach in ways consistent with calls for reform (Cobb, Wood & Yackel, 1990; Cobb & McClain, 2001; Fennema, et al, 1997; Jaworski, wood & Dawson, 1999; Schifter & Fosnot, 1993; Sullivan & Mousley, 2001). Without attention to how teachers learn, however, our understanding of instructional reform is seriously incomplete (Franke, Carpenter, Levi & Fennema, 2001; Hammer & Schifter, 2001; Richardson & Placier, 2001; Schön, 1983; Sherin, 2002).

“Classroom mathematics is experienced by students as ‘blind activity’ and ‘dead labour’, and ‘real-world problems’ are not considered by students as a word gambit without any relation to reality or meaning” (Goodchild, 2001). Insisting on the perspective that mathematics is a tool for gaining power, status and worth, he explains why mathematical activities are perceived by students as having factual and symbolic power, but no meaning. By unfolding the complexity of mathematics classroom practice and revealing the various, partly conflicting “models of behavior” and rationales and their effect on daily practice, he demonstrates that the identified predominant rationales and social constraints in arena and setting for teachers and learners include learner-centeredness, participation of learners and active and productive learning mathematics by conceptual understanding and communication, problems of classroom practice with which teachers are overburdened and need support.

One hypothesis is the conviction that conceptions and goals in mathematics learning, as patterns of behavior and thinking, are embedded in their social, cultural and class discourses and can be appropriately analyzed as “texts”. These texts manifest themselves not only in the specificity of the words they use (and their meanings), but also how and in which context they use the words, in which kind of practice they are created and in the specific stories they tell. The characteristics of these collective patterns are that they are effective in daily life, learned from others and shared with others (Goodchild, 2001). Therefore, they should be best unfolded in a collective discourse among students in which they become explicit, first unconsciously, but by continuous reflection more consciously.

With this situation, it is assumed that teachers need to know how pupils/students learn mathematics in order to design effective instructional programs. Thus, teacher education programs should provide opportunities for growth in content knowledge, pedagogical content knowledge and pedagogical reasoning. The NCTM *Curriculum and Evaluation Standards for Teaching Mathematics *(NCTM, 1989) and *Professional Standards for Teaching Mathematics* (NCTM, 1990) give some guidance as to the content and pedagogy teachers must understand in order to teach appropriate mathematics well. Both sets of standards provide the direction, but not the mechanism, for reform in school mathematics.

The socialization research, together with Ball’s (1990) analysis of knowledge, beliefs and dispositions held by prospective teachers when they enter teacher education, suggest that teacher education programs must sometimes help participants to “unlearn” as well as to learn. That is, mathematics teacher education must help teachers discard some of the knowledge, beliefs, and dispositions regarding mathematics and pedagogy they bring to the pre-service and in-service programs.

The research on teacher development indicates that participants in teachers education programs may be at different developmental stages and have very different needs for assistance. For example, teachers with poorly developed egos may be reluctant to see cooperative learning as a viable way of teaching mathematics, while preferring to learn more teacher-centered styles of classroom instruction. The developmental perspective argues that for teacher education programs to be most effective – that is, to help students achieve higher levels of development – they should assess participants’ level of development and then provide experiences either at the teachers’ level or one stage higher in the developmental hierarchy.

In the proceedings of the NARST 2004 Annual Meeting, it has reported that there is a statistical evidence that participation in the mentoring program has a noticeably positive effect on enhancing teachers’ implementation of standards – based professional practices (NARST 2004 Annual Meeting).

Turnover and shortages among science and mathematics teachers has been a big educational problem in the United States. Studies to solve this problem (Ingersoll, 2001; 2003) suggest more support from the school administration to teachers, such as induction and mentoring program, which is indispensable in improving teacher retention. Teacher educators in the US have developed mentoring programs at both preservice and induction levels to support novices’ learning to teach (Odell, Hulin, & Sweeny, 1999). With the assistance of experienced teachers, novices have an opportunity to learn to teach and to form a base for their continued professional development (Feiman – Nemser & Buchmann, 1987). An implicit assumption underlying such a strategy is that experienced teachers can be an active variable in novices’ learning to teach, and in the end, support the reform of teaching (Wang, 2001).

Ego development & teacher education / staff development

Loevinger (1976, 1980) conceived of ego development as holistic, encompassing moral and personality development, cognitive complexity, and interpersonal style. The beginning stages of model, the presocial (I-1) and impulsive (I-2) are rarely found in adults. Later stages, more common in adults, are conformist (I-3), characterized by a conventional, stereotypical view of the world; self-aware (I-3/4), characterized by increased awareness of inner feelings and multiplicity of thinking; conscientious (I-4), characterized by differentiated thinking about self and others; individualistic (I-4/5), characterized by increased awareness of inner conflict and toleration of paradox; autonomous (I-5), characterized by cherishing individual differences and toleration of ambiguity; and integrated (I-6), characterized by integration of inner conflict (Cummings & Murray, 1989). These ego stages are thought to occur in an invariant, irreversible sequence. Loevinger proposes that it is through interaction with the environment that one grows or moves to higher levels of ego development.

Oja’s (1980, 1989; Oja & Ham, 1984) program of research on staff development, suggests ways to assist teachers grow developmentally. In his staff development project called Action Research on Change in School (ARCS), he used three phases.

Phase I. Building supportive interpersonal relationships within small groups to create an environment necessary for developmental growth.

Phase II. Learning new skills appropriate for more complex role-taking. For example: skills in interpersonal effectiveness, indirect teaching, individualizing instruction, and supervision. Familiarizing teachers with the theory of developmental stages of growth.

Phase III. Applying the newly acquired skills and theory to the teachers’ own classroom setting with consistent on-going supervision in small groups and advising in individual conferences (Oja, 1980)

In the study, Oja concluded that age, life period and teaching experience can help explain key issues in teachers’ life and career and can often explain why a teacher will choose to become involved in staff development activities. However, teachers’ performance, thoughts, problem solving, and group behavior while participating in a particular staff development activity appear to be related to their cognitive-developmental stages (Oja, 1989). Oja argued that teachers’ performances are not simply idiosyncratic and grounded in the individual. Rather, cognitive cognitive-development stage characteristics help explain how certain teachers think and perform in staff development. Based on this analysis, Oja argued that staff development programs attending to the developmental characteristics of participating teachers will be more successful in achieving their goals than programs that ignore teachers’ development. Thus, according to Oja, staff development programs should be designed to involve teachers at different developmental levels and also to create safe environments that allow for teachers to development further. The importance of helping teachers to reach higher levels of development is supported by classroom-based research that provides evidence that states, in general “… persons judged at higher stages of development function more complexly, posses a wider repertoire of behavioral skills, perceive problems more broadly, and can respond more accurately and emphatically to the needs of others” (Sprinthall & Thies-Sprinthall, 1983).

CHAPTER 3

SCHOOL – BASED MENTORING PROGRAM

Teaching, as we all know but often fail to remember, is a complex, bewildering and sometimes painful task. It involves developing a practical knowledge base, changes in cognition, developing interpersonal skills and also incorporates an affective aspect. This chapter initially discusses some factors which are needed to quality teaching and its implications to mentoring, and later examines the ways in which teachers, acting as mentors, can most effectively help mentee in the process of teaching. These factors will then be the objects of the school – based Mathematics mentoring program.

3.1 Quality of mathematics instruction, meaning and development

There are different perspectives of recent research on teaching and learning in mathematics. To name some, they are *constructivist approach, cognitively guided instruction, sociological or epistemological view and mathematics content view*. Though they are varied, but comparing them reveals important differences among the models. All these perspectives accept the premise that students are not passive absorbers of information, but rather have an active part in the acquisition of knowledge and strategies. All of these perspectives view the teacher as an informed and reflective decision maker.

Putnam, Lampert and Peterson (1990) discuss on different views of what it means to know and understand mathematics in terms of *representation, knowledge structures, connections among types of knowledge, active construction of knowledge and situated cognition*. These different views of the acquisition or construction of knowledge lead to different views of teaching. Cobb, et al. (1991) believe that teachers can work from lessons that have been developed with cognitive strategies in mind and can modify those lessons as necessary. Lampert believes that teachers need to focus on selecting and posing appropriate problems, and Leinhardt (1989) focuses attention less on specific content but more on structure of lessons. Borko and Livingston (1989) explain that teachers improvise as they teach, using a rich repertoire of instructional moves.

Although there are multiple perspectives from which research on teaching can be approached (see, for example Grouws, Cooney, & Jones, 1988), and multiple interpretations of the teaching act, one thing that needs to be addressed in all research on mathematics teaching is the notion of quality of instruction.

Quality of instruction can be considered analytically or holistically. Grouws (1988) points out that many teaching actions – such as asking questions, giving examples, and drawing a diagram – have a quality dimension associated with them. He notes that “it is relatively easy to identify actions that would fall at the extreme ends of a quality continuum: making diagrams that cannot be read, asking ambiguous questions, using examples that do not fit the conditions of a definition, and so on”. Consideration of instruction quality should not be limited, however, to evaluating specific teaching behaviors. It should include examining “the way classroom events fit together to form a meaningful learning situation.”

In the early studies on development the value of increasing development time was clearly shown, but no consideration was given to the quality of development. Development as it has been more recently defined, however, actually encompasses more than teacher lecture. A more current definition of development, Good, Grouws and Ebmeier (1983), is “the process whereby a teacher facilitates the meaningful acquisition of an idea by a learner.” This process includes whatever the teacher may do to facilitate learning, whether it be structuring small-group work, providing guided-discovery activities leading a class discussion, organizing individual investigations, or presenting a lecture.

It is important to note that the emphasis in recent definitions of development is on *meaningful acquisition of ideas*. Pirie (1988) points out that “if we, mathematics educationalists, are to devise effective teaching strategies, make sense of students’ actions, provide experiences which enable students to construct their own mathematical concepts, we must first have a viable model of understanding on which to build.”

The importance of meaning and understanding has also been recognized in the work of Good, Grouws, and Ebmeier (1983) who identified five components of development as part of their study of successful mathematics teachers: attending to prerequisites, attending to relationships, attending to representation, attending to perceptions and generality of concepts. They emphasize that “development is a very complex phenomenon and the particular elements that constitute successful development may vary from one teaching context to the next,” and suggest that “it is also important to realize that effective development may not be composed of the same combination of behaviors, even in similar classroom environments.”

The components of development that they identified were not mutually exclusive and did not necessarily span all the dimensions of development that could be identified. They may, however, provide a useful starting point for a study of the quality of mathematics instruction that takes account of the student and also provides a focus on the teacher’s role in the process.

3.2 Teacher’s knowledge and cognitive processes

Cognitive psychological research on teacher knowledge begins with the assumption that human knowledge is organized and structured. Schema theory (Anderson, 1984) provides one model for the representation and organization of knowledge: Schema is an abstract knowledge structure that summarizes information about many particular cases and the relationships among them. People store knowledge about objects and events in their experiences in schemata representing those experiences.

Shulman’s theoretical model of domains of teachers’ professional knowledge is particularly relevant to research on learning to teach (Shulman & Grossman, 1988; Wilson, Shulman & Richert, 1987). Shulman et al. hypothesized that teachers draw from seven domains of knowledge as they plan and implement instruction: knowledge of subject matter, pedagogical content knowledge, knowledge of other content, knowledge of the curriculum, knowledge of the learners, knowledge of educational aims, and general pedagogical knowledge. Their research program focused primarily on the first two domains. It provided the educational research community with elaborated definitions of subject matter knowledge and pedagogical content knowledge and findings about their relationship to classroom practice. Subject matter knowledge consists of an understanding of the key facts, concepts, principles and explanatory frameworks in a discipline, known as *substantive knowledge*, as well as the rules of evidence and proof within the discipline, known as *syntactic knowledge* (Shulman & Grossman, 1988). In mathematics, for example, substantive knowledge includes mathematical facts, concepts and computational algorithms; syntactic knowledge encompasses an understanding of the methods of mathematical proof and other forms of arguments used by mathematicians.

Pedagogical content knowledge, or knowledge of a subject matter for teaching, consists of an understanding of how to represent specific subject matter topics and issues in ways appropriate to the diverse abilities and interests of the learners. It includes “the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations – in a word, the ways of representing the subject that make it comprehensible to others …. [It] also includes an understanding of what makes the learning of specific topics easy or difficult: the conceptions and preconceptions that students of different ages and backgrounds bring with them to learning.” (Shulman, 1986)

Ball (1990) developed a conceptual framework for exploring teachers’ subject matter knowledge specifically in the area of mathematics. She claimed that understanding for teaching entails both knowledge *of* mathematics and knowledge *about* mathematics. Knowledge *of *mathematics is closely related to Shulman’s dimension of substantive knowledge, and it includes both prepositional and procedural knowledge. To teach mathematics effectively, Ball argued individuals mast have knowledge of mathematics characterized by an explicit conceptual understanding of the principles and meaning underlying mathematical procedures and by connectedness – rather than compartmentalization – of mathematical topics, rules and definitions.

Knowledge *about* mathematics is related to Shulman’s dimension of syntactic knowledge, and it includes an understanding of the nature of knowledge in the discipline – where it comes from, how it changes, how truth is established, and what it means to know and do mathematics.

** Cognitive Processes.** Researches of teachers’ thinking traditionally have drawn a distinction between planning, which occurs in the empty classroom, and the thought processes in which teachers engage during classroom interaction. Wilson and colleagues describe six common components of teaching: comprehension, transformation, instruction, evaluation, reflection and new comprehension (Wilson, Shulman, & Richert, 1987). Comprehension is the process of critically understanding a set of ideas to be taught. During transformation, the teacher moves from a personal comprehension of the ideas to be taught to an understanding of how to facilitate students’ comprehension of these ideas. Instruction, the process of facilitating students comprehension, consists of a variety of teaching acts, such as organizing and managing the classroom, presenting clear explanations, and providing for student practice. Evaluation, or checking for students understanding, encompasses more formal testing and evaluation procedures. Reflection entails evaluating one’s own teaching; it is the set of processes that enables a professional to learn from experience. As a result of engaging to these processes, the teacher develops new comprehension of the subject matter.

Central to this model of pedagogical thinking and action is the concept of pedagogical reasoning, the process of transforming the subject matter “into forms that are pedagogically powerful and yet adaptive to the variations in the ability and background presented by the students” (Shulman, 1987). Pedagogical reasoning includes the identification and selection of strategies for representing key ideas in the lesson, and the adaptation of these strategies to the characteristics of the learners. Like pedagogical content knowledge, it is unique to the profession of teaching.

3.3 Role of language as medium for classroom education

Classrooms generate some typical structures of language use, patterns that reflect the nature of teaching and learning as a social, communicative process that takes place in the distinctive institutional settings of school. Some features of classroom language, described below have been found in classrooms across the world; and to some extent at least this reflects the fact that language has similar function in schools across the world over. There are also some local, regional and national characteristics in the ways that language is used in the classroom, and different expectations are made of students in different cultures and even by different teachers within one country’s education system, which may also be reflected in the language. Moreover, according to their out – of – school experience, students may find the language of classroom life more or less intelligible or compatible with their out – of – school life. Teachers have responsibility for guiding students’ use of language as a social mode of thinking, and to express their understanding in the appropriate language genres or discourses.

** Function.** Schools are special kinds of places, social institutions with particular purposes, conventions and traditions. There are some interesting differences in how teachers’ and learners’ interests interact in classrooms in different communities. But the schools the world over also have much in common in how they function and this functional similarity is reflected in the ways language is used in the classrooms.

One of the most obvious functions of spoken language in a classroom is for teachers to tell students what they are to do, how they are to do it, when to start and when to stop. Teachers may also assess students’ learning through talk. Dialogue between students and teachers provides students gain knowledge and helps teachers understand the students for relevant guidance and evaluation.

** Questions. **Questions help students improve their thinking skills. These must be based on Benjamin Bloom’s Taxonomy of educational objectives. Questioning, if used properly, is an effective technique that helps to produce a positive, interactive classroom. Good questions cause students to pay attention, to process information, to organize their ideas, and to compose an answer, a neat summary of thinking and problem solving (Cruickshank, Bainer, & Metcalf, 1995). Teachers need to know how to ask questions, how to obtain good answers and how to follow up responses. These are the three issues critical to teachers’ effort to frame up thoughtful questions.

** Code – switching. **In circumstances where the classroom language is not the students’ first language, a teacher who is bilingual may ‘code-switch’ to the first language if problems of comprehension arise. However, when code-switching amounts to translation by the teacher of the curriculum content being taught, its use as an explanatory teaching strategy is somewhat controversial (Moon, Mayes & Hutchinson, 2002). Thus, teachers have to use code – switching in more complex ways than simply translating content directly into another language.

3.4 Implications to mentoring

Teachers are the forefront of the battle against mediocrity in schools. Upgrading and improving teachers’ competency and proficiency in teaching the content are of mathematics is a great endeavor to make them succeed in their effort at improving their classrooms and their schools.

Quality instruction is very hard to achieve if teachers are just left to improve them by themselves. It is with the help of the competent mathematics teachers who will serve as mentors of their colleagues in improving competencies in math. It is needed to put teachers first, and school first.

Mentoring is a social process in which communication is very important. If math teacher’s ego is developed, his communication skills will also develop, at the same time, his competencies in teaching will also improve.

In the book of Kerry and Mayes (1995), it is said that the school – based training of teachers through mentoring has real potential. The move to school – based training implies that teachers need to change their traditional orientation to their role. The notion of the school as a “learning community” in which learning occurs at various levels is widely accepted. In such a community, teachers interact with each other, challenge and support each other in order to sustain challenge. Many mentors often refer to their happy and friendly school and what is required is the transformation of this climate to sustain professional development for all (Kerry & Mayes, 1995).

The burden to improve the quality of education in the country should rest not only in the DepEd officials. Administrations at all levels and teachers should work collaboratively. Making a difference is difficult but if you have this spirit: John Wesley said “set yourself on fire and the whole world will come and watch, and maybe they will read by the light you give. The capacity you have is enormous. Your capacity to live, grow, to share, to sacrifice. That is the fire within you.”

3.5 The concept of mentoring and its processes for mathematics education

The term “mentor” has its roots in Homer’s epic poem, *The Odyssey.* In this myth, Odyssey, a great royal warrior, entrusted Telemachus to his friend, advisor and tutor named Mentor. Mentor served as advisor and guardian to the entire royal household. In modern English, tutor’s name has become an eponym for a wise, trustworthy counselor or teacher.

The account of Mentor in *The Odyssey* gives us several conclusions about functions and activity, which bears his name. First, mentoring is an *intentional process*. Mentor intentionally carried out his responsibilities for Telemachus. Second, mentoring is a nurturing process, which fosters the growth and development of the protégé toward full maturity. It was Mentor’s responsibility top draw forth the full potential in Telemachus. Third, mentoring is an *insightful process* in which the wisdom of the mentor is acquired and applied by the protégé. Clawson (1980) asserts that it was Mentor’s task to help Telemachus grow in wisdom without rebellion. Fourth, mentoring is a *supportive, protective process.* Telemachus was to consider the advice of Mentor, and Mentor was to “keep all safe” (Kerry & Mayes, 1995).

Other concepts of mentoring are centered on career development in the field of business. In this field, Phillips – Jones (1982) defines mentors as influential people who significantly help protégés reach their life goals: “They have the power – through who or what they know – to promote … welfare, training or career.”

Zey (1984) defines mentor as a person who oversees the career and development of another person usually a junior, through teaching, counseling, providing psychological support, protecting and at times promoting and sponsoring. The mentor may perform any or all of the above functions during the mentor relationship.

In the context of the Philippine mathematics education for school-based mentoring, a MENTOR is a GABAY, a wise and trusted person who accompanies the mentee in his or her professional journey. A mentor is a resource, a positive role model for new or younger teachers. In other words, a mentor is a facilitator of on-going teacher learning. This being the case, the mentor should be the first learner. Mentors do not serve as evaluators or judges. Instead, they offer an insider’s guidance who diagnose, assist, and then, asses in view of on-going mentee formation.

Mentoring therefore can be defined as a nurturing process in which a more skilled or more experienced person, serving as a role model, teaches, sponsors, encourages, counsels, supervises, and befriends a less skilled or less experienced person for the purpose of promoting the latter’s professional and/or personal development. Mentoring functions are carried out within the context of ongoing, caring relationship between the mentor and protégé or mentee (Anderson, 1987).

Nurturing implies a developmental process in which a nurturer is able to recognize the ability, experience and psychological maturity of the person being nurtured and can provide appropriate growth – producing activities. The concept of nurturing also implies several notions embedded in the ‘gardening’ metaphor. The nurturer helps provide an environment for growth, considers the total personality of the person being nurtured in deciding how best to be helpful, and operates with a belief that the person being nurtured has the capacity to develop into fuller maturity.

Closely related to nurturing process is the act of serving as a role model. Mentors provide the mentees with a sense of what they are becoming. Mentees can see a part of their adult selves in other adults. By their examples, mentors stimulate growth and development in the mentees.

Mentoring is focused on professional and/or personal development through its four functions: teaching, sponsoring, encouraging, counseling, supervising, and befriending. It is an ongoing process, which is found within the kind of relationship that exists between the mentor and mentee.

With this concept of mentoring, there is a need to identify dispositions that mentors should have as they carry out mentoring functions and activities. Dispositions are broader constructs than skills and denote recurring patterns of behavior. Mentoring dispositions may arise from the concept of mentoring and also from the values held by those who develop mentor programs. First, mentors should have the dispositions of opening themselves to their mentees. Second, mentors should have the disposition to lead their mentees incrementally over time. Third, mentors should have the disposition to express care and concern about the personal and professional welfare of their mentees.

3.5.1 Intervention/supervision scheme

Since mentors are expected to observe and supervise mentees, mentors may use any of the four intervention styles.

** Intervention style card – Directive. **In the directive form of intervention … the mentor comments on the mentee’s teaching, making concrete proposal for change. The mentor establishes the purpose of the intervention, determines the points to be raised with the mentee based on the observation, and makes a brief statement on each point to which the mentee may or may not respond. Discussion often ensues from the intervention, but the roles are very clear: the mentor ‘directs’ and the mentee ‘does’ (Freeman, 1990).

In directive supervision, the role of supervisor is to direct and inform the teacher about model teaching behaviors, and evaluate the teacher’s mastery of defined behaviors (Gebhard, 1990).

** Intervention style card – Non-directive. **The purpose of this intervention … is to provide the mentee with a forum to clarify perceptions of what she or he is doing in teaching and for the mentor to fully understand, although not necessarily to accept or agree with, those perceptions. Further, it allows the mentee to identify a course of action based on his or her own perceptions and what the mentor offers, and to decide whether or how to act (Freeman, 1990).

The essence of non-directive supervision is captured in the following observation by a mentee – in – preparation: “My mentor usually attempts to have me come up with my own solutions to teaching problems, but he is not cold. He is giving a person, and I can tell that he cares. Anyway, my mentor listens patiently to what I say, and he consistently give me her understanding of what I have just said” (Gebhard, 1990).

** Intervention style card – Alternatives. **In this style, the mentor chooses a point from the teaching and raises it with the mentee. The mentor then proposes a limited number of alternative ways to handle that point in the lesson. The mentee rejects or selects from among the alternatives. Discussion follows about the mentee’s criteria for the choices he or she has made. The purpose of this intervention is to develop the mentee’s awareness of the choices involved in deciding what and how to teach, and more importantly, to develop the ability to establish and articulate the criteria the inform those decisions (Freeman, 1990).

The supervisor’s role is to suggest a variety of alternatives to that what the teacher has done in the classroom. Having a limited number of choices can reduce teacher’s anxiety over deciding what to do next, and yet still then the responsibility of decision-making… The purpose of offering alternatives is to widen the scope of what a teacher will consider doing (Gebhard, 1990).

** Intervention style card – Collaborative. **Within a collaborative model, the supervisor’s role is to work with teachers but not direct them. The supervisor/mentor actively participates with the teachers in any decisions that are made and attempts to establish a sharing relationship… The teacher/mentee and supervisor work together in addressing a problem in the teacher’s classroom teaching. They pose hypothesis, experiment, and implement strategies that appear to offer a reasonable solution to the problem under consideration (Gebhard, 1990).

3.5.2 Mentorial frameworks

Mentorial frameworks are designed to guide mentors for helping mentees in making decisions in the future. These are frameworks for post-lesson and pre-lesson discussions.

** Framework for a post – lesson discussion. **If at the end of any phase, the mentee has reached his/her own decision for future action as a result of going through stages of describing, interpreting and evaluating, then the discussion has reached its natural conclusion. In other words, if the mentor behavior and style of one phase is enough to help the mentee interpret, evaluate and make decisions for the future – for their teaching or for their own professional learning – then the mentor moves on the next phase with its corresponding slight change of behavior and style. Here is a chart that suggests the mentoring style.

** Framework for a pre – lesson discussion. **The focus of post – lesson discussion is on the mentee’s professional learning but in this framework, talking through a mentee – prepared lesson plan, the focus is on the students’ intended learning.

The aim is that the mentee articulates planned procedures and their rationale that seem likely to achieve the lesson objectives, and has taken into account and considered how to handle difficulties or problems that might arise. Here is the suggested mentoring style.

3.5.3 Relationships and goals

The diagram below describes the various kinds of appropriate behavior in conflict situations that the mentor may do during mentoring.

In Teddy – bear quadrant, relationship is more important than the goal. This behavior is appropriate at the beginning of the mentor – mentee relationship; establishing relationship is more important than anything else.

Behavior as Turtle quadrant is probably not appropriate in mentor-mentee situations because relationship is always important. Example of this in real life: you are walking home and you decided to take an alternate route but there is an addict on the road. So, you changed your mind to take the alternate route and return to the original road – you withdraw – as your goal is not that important to you and you want no relationship at all with the addict.

The Shark – like behavior is unlikely to be appropriate in mentoring situations, unless the goal you are pursuing is urgent and essential and the relationship is strong enough to, temporarily, put at risk.

The fourth quadrant, the Owl – like behavior, is most likely to be needed in mentoring. Both the relationship and the achievement of the goal are of high importance. If there is a conflict in these situations, it is appropriate to “confront”, which basically means talk about it openly and negotiate a solution in which both parties are satisfied and the relationship remains intact or is strengthened.

The essence of mentoring and its basic components is summarized in *Figure*1 below.

3.6 Mentoring Realities and Events in the Philippines

The National English Proficiency Program (NEPP) was established in 2003 to solve the problem on the decline in the English language proficiency at both teachers and students levels. It is established to upgrade and improve teachers’ competency and proficiency in the use of English, in teaching the content area of Science, Math and English in order to attain an increase in student fluency in English (DepEd thru NEPP).

The DepEd feels that if the teachers will raise their proficiency level of English and commit to use only pure English as the medium of instruction in the classroom, the students’ level will follow. Eventually, students’ performances in Math and Science will also follow.

Last 2004, the Phase I of English Proficiency Program was conducted. Five thousand six hundred twelve (53, 612) teachers were given the Self – Assessment Test (SAT). Those who scored high (the upper 10% of teachers tested) were selected to undergo the Phase II: The Mentor Training Program: Facilitating Mentor Learning. Those who were trained are now mentor teachers of their colleagues in English, Math and Science. The mentoring program thru the NEPP is solely a Philippine program designed by the consultants to the DepEd from Ateneo Center for English Language Teaching (ACELT). Occasionally, the DepEd seeks input and observation of the program from the consultants from other countries and organizations, but still the responsibility and inception lies within the agency.

After the Phase II program, the mentors are now working to achieve the goals of NEPP through the following methods: (1) making focused formal classroom observation visits; (2) providing written feedback to the mentee following formal visits; (3) using evaluative instruments to chart the mentee’s and students’ performance and progress; (4) providing concrete strategies and suggestions to help improve the mentee’s teaching skills and students’ response in English; (5) providing English language support within the specific content area, both in vocabulary and grammar; (6) offering help and support through informal meetings with the mentee; (7) being an available resource for other teachers in the specific content area who are not designated mentees; (8) inviting mentees to observe a mentor-taught class during their free periods; (9) involving the principal, department heads or any other supervisory staff in the program by giving monthly reports regarding all mentoring activities and requesting their help when needed; and (10) holding division – wide meetings monthly with other mentors in specific content areas to discuss and network together in order to provide peer support and solution resources for any identified future needs.

How are the mentees identified? Since the goal of NEPP is to improve the English teaching competencies, the mentees are identified based on their English proficiency level along with observed classroom teaching or pedagogical skills. The SAT scores are also used as indicator. The school principals, supervisors, and department heads also help in determining the mentees with their observation results. The novice or new teachers are included in mentoring, but years of teaching experience, ages, degrees, or other qualifications are not relevant selection criteria.

To increase the English proficiency and competency of each mentee, the NEPP identified the training components of English mentoring. The theories, techniques and skills are focused on: (1) How we learn – theories, processes and taxonomies by Kolb, McGrath and Bloom; (2) increasing English use and competency by eliminating code – switching; (3) strategies for increasing student output in English; (4) presentation skills for optimum input: (5) pronunciation, stating objectives, appropriate vocabulary use, discourse markers, linking concepts and logical order, task setting, clarity of instructions and reading fluency objectives; (6) discussion skills for optimum learner involvement: (7) asking appropriate questions, group work strategies for monitoring and processing output, and use of critical thinking skills; and (8) mentoring framework: reflective practices, contexts and roles of mentor versus mentee, active listening techniques, giving appropriate feedback, conflict resolution skills, and action planning for both mentor and mentee.

As part of the program, the NEPP has also conducted orientation training for the principals and other administrators right after the intensive mentor training to acquaint them with the program. In some schools divisions, there have been numerous meetings with the administrators and other mentors for its implementation and structuring of the program in the divisions.

However, many questions or concerns have been raised by the mentors about the mentoring program. These are: How many mentees will be mentored per school year? How can the mentor help the other teacher mentees when he does not even have time to prepare for his own classes, his principal cannot deload him due to heavy schedule, and some of his mentees’ schedules do not fit with his free periods? What can the mentor do if he is only one in the school and he feels uncomfortable to make suggestions to English and Science mentees because he teaches math? What can the mentor do to lessen the tension of observing and giving feedbacks to the mentee who has a lot more teaching experience and is older than him? And what can the mentor/mentee do if he speaks 100% English and does not code – switch at all, but his students do not understand him?

With these concerns of the mentors, it is doubtful if the program has been still moving until now.

3.7 A Gateway to Teachers’ and Students’ Mathematics Proficiency

Since the DepEd thru NEPP has started its mentoring program, it is quite very timely to start the mentoring for Mathematics teachers. English proficiency is not enough to improve mathematics proficiency of both teachers and students, though language plays important part in teaching. Language is nothing if the teachers in Mathematics do not know the content; thus, they do not know how to structure the lesson in Mathematics that must be meaningful to the learners.

The present mentoring program that happens in the Philippines does not suffice the training that the Mathematics teachers need. In an interview with the Mathematics mentees, they said the mentoring that happens in their respective schools only focuses on language proficiency of both teachers and students. Thus, contentwise, they lack. But if we simultaneously include the objects of mentoring program we discuss in this paper, we will definitely have better or best Mathematics teachers, eventually, the best students. Our school – based mentoring program shall focus not only on the language proficiency of both teachers and students but also on other objects of mentoring. Remember that the objects of Mathematics education (NCTM, 1997) do not only focus on how the students communicate mathematically, but also underline how students must value Mathematics, learn to become Mathematics problem solvers and eventually help students solve problems of everyday life, participate intelligently in civic affairs and prepare them for their future lives. Thus, teachers need to be prepared for this challenge.

Upgrading mathematics teachers contextualized to their culture and needs will improve their teaching proficiency. With the help of English mentoring program, Mathematics mentoring program will meet its goals to the optimum level. Yes, (if mentors will commit themselves to work on it and the mentees will absorb what the mentors give to them), to the highest level since Mathematics mentoring is focused on its objects (*see the factors that are needed in quality teaching*).

The time has come now to harvest the fruits of scholarships. The DepEd must now enjoy the profit it has invested in the mathematics education. These scholars of the DepEd in the content areas must now work as mentors of their fellow teachers. They must now outpour the learning and knowledge they gained. If there is a lack of mentors, the department heads, principals, and supervisors who are mathematicians, mathematics educators or experts may serve as mentors.

It is the aim of Mathematics mentoring to realize the mentors’ and Mathematics teachers’ Icebergs that contain the qualities they need to attain what is dreamt of: the highest level of mathematics performance of both teachers and students. As students, teachers, and mentors are bounded by the school, education system, society and culture, they communicate with each other mathematically and, at the same time, they also learn with each other. The Mathematics Proficiency, and teaching proficiency and Professionalism are shown in the following figures (*see Figures *2 & 3).

The tip of the iceberg of the Mathematics mentor is the mentoring behavior. Mentoring behavior is affected by the mentor’s beliefs, attitudes, values and feelings intertwined by the culture, conceptualized and contextualized through the teacher’s knowledge. The same process as in the Mathematics teacher’s iceberg; Mathematics teacher’s iceberg is only seen with his professional behavior. Below the tips of the icebergs are the processes that the mentors and teachers must undergo and the attributes that they must possess. It is through Mathematics mentoring that these attributes will be processed.

Teaching Proficiency and Professionalism

(Adapted from: Malderez, et al., 1999)

Mathematics Proficiency

(Adapted from: Malderez, et al., 1999)

CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS

Teachers greatly influence students inside the classroom. Students’ learning and development depends on how the teachers perform in school. Therefore, teacher needs further professional development that will help him and his students perform better.

To attain the Mathematics teaching quality and proficiency, teachers must possess the knowledge *of* and *about* their students and the content as manifested in their teaching behavior with their language, activities, values, attitudes and others.

To offer help of any kind is better than offering none. Sharing knowledge in any ways is part of mentoring since its focus is to help students. It is the aim of the school – based Mathematics mentoring program to attain this quality and proficiency of Mathematics teachers in order to realize the best performances of both teachers and students. Teachers, acting as mentors, help improve the professional and personal lives of the mentees through the mentoring processes discussed. As observed in the Philippine education, mentoring program is merely focused on English proficiency. In support to the NEPP, school – based Mathematics mentoring program is introduced.

It is realized that there will be many challenges in implementing the mentoring program properly. In relation to the issues that have been raised earlier, we would like to suggest further the following activities:

- School system should develop structured induction programs that include mentoring.
- The school / schools division office should provide professional development for all mathematics teachers.
- There must be a research on the relationship between English proficiency and the mathematics performance of the students.
- Further research on how English language affects Mathematics performances of both Mathematics teachers and students.
- Each mentor is hoped to work with at least 5 mentees during the course of the school year. Some mentees may need (or want) a full year of help while others are not.
- A number of visits depend entirely upon the mentor’s teaching load, schedule and mentee’s progress. The principal, mentor and menteees must arrange the visit properly.
- There must be a mentors’ regular meeting or session in the division to help other mentors in other schools especially in sharing the content area. Regular meeting between the mentor and mentee must also be observed.
- The mentees must also observe how the mentors perform inside the classroom.

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