The multi-year study from which this paper derives was undertaken in order to explore the complexities of teaching and learning within the transformed Namibian educational system. This paper examines the influences of the fundamental transformation of the Namibian educational system on mathematics teachers. The findings reveal that national educational reform efforts influenced the teachers’ beliefs about mathematics, instructional practices, and perceptions of students. As described in this study, the teachers’ beliefs and perceptions of students reflected their socio-cultural and socio-political orientations.
Following a protracted armed struggle for liberation, Namibia gained its independence from the colonial apartheid government of South Africa in 1990. The illegal and repressive apartheid regime left as its legacy an educational system shaped by divisive and dehumanizing imperialist policies. Recognizing that knowledge and power are inextricably connected and interrelated in the achievement of subjugation (Foucault, 1983), the Bantu educational system was designed to entrench the privileged position of Whites. In an effort to maintain social, economic, and academic segregation, the architects of apartheid fragmented Namibia into eleven education authorities based upon ethnicity. Designed to inculcate racism, the philosophy underlying the apartheid-era educational system was premised upon the notion that Blacks were incapable of learning mathematics and science (Clegg, 1989). The Bantu educational system ensured that the colonial power would be provided with a steady supply of semi-literate, subservient farm and house laborers (Christie & Collins, 1984). Informed by a belief that indigenous Namibians were not qualified to make decisions and shape their own destiny (Angula, 1990), very few Black students were offered academic courses. Because this system was exam-driven, it further marginalized and disadvantaged indigenous Namibian students by ensuring that only a small number of privileged students would succeed.
The apartheid dispensation, which was responsible for inequitable funding, resources, and access to education, left as its legacy teachers with eight to ten years of education, student-teacher ratios of 60:1, and dropout and failure rates of 82 percent (Amukugo, 1993). As they dismantled the discriminatory and inequitable Bantu educational system, the newly independent Namibian government embarked upon the process of developing a new praxis. Modeling their transformed educational system along democratic, empowering, and reconstructive lines, the Namibian government mandated reforms based upon the goals of access, equity, quality, and democracy (MEC, 1993).
The reconstructed system rejects the authoritarian Bantu dispensation, which required that indigenous Namibian students paid ritual obeisance to their White colonial teachers and under which punitive measures, including caning and other forms of corporal punishment, were commonplace. Recognizing that education is essential to a country’s social and economic development (MEC, 1993) and a liberator and equalizer of individuals regardless of race or ethnicity (Freire, 1985), the Constitution of the Republic of Namibia guarantees all persons the right to an education.
Under apartheid, education was utilized to maintain existing power bases. However, in newly independent Namibia, education is seen and understood as a means of social and cultural reconstruction (Bowe, Ball, & Gold, 1992). Moreover, educational change has consequences for social justice, equity, and democracy (Ball, 1994). Student-centered learning, the use of English rather than Afrikaans as the medium of instruction, and consideration of students’ prior experiences and their intellectual, emotional, social, physical, aesthetic, moral and spiritual development are the cornerstones of Namibia’s transformed education system. The redesigned school curriculum is structured upon a constructivist view of knowledge, learning competencies in content areas, developing a reflective attitude, and promoting creative, analytical and critical thinking (NIED, 1998). A decade after independence, vestiges of this past subjugation remain, presenting socio-cultural and pedagogical challenges. Therefore, this multi-year study of teachers in a Namibian secondary school was undertaken in order to explore the complexities of teaching and learning mathematics within the transformed Namibian educational system. Of particular interest was how collaboration, mentoring, and engaging in critical and liberating dialogue (Freire, 1970), empowered the teachers to challenge the vestiges of past subjugation.
Ombuwa Secondary School is a diverse coeducational secondary school located in a provincial region of Namibia. Because the area for the school contains communities of migratory laborers, the teachers and students represent several ethnic groups: Damara, Ovambo, Kavango, Tswana, and Herero. In addition, a small number of teachers and students identify themselves as “Coloured” or “Cape Coloured”, vestigial terms from the apartheid era used to describe people of both black and white origin. Within the apartheid context, this classification was favored over “Black” but subordinate to the classification, “White.” Because of the ongoing, nationwide teacher shortage, in addition to the indigenous Namibian teachers, Ombuwa is also staffed by expatriate teachers from other African countries. The Ombuwa teaching staff is occasionally supplemented by short-term volunteer classroom teachers from the United States and Europe.
At Ombuwa, the mathematics teachers and their students are heterogeneous in socioeconomic status, ethnicity, gender, educational attainment, and mathematical achievement. Both teachers and students at Ombuwa are linguistically diverse. In addition to their mother tongue (Damara, Oshiwambo, Kwangali, Tswana, or Herero), the students and teachers also speak Afrikaans and English as their second and third languages. Teachers and students who identify themselves as “Coloured” speak two languages: Afrikaans as their first language and English as their second. Although none of the teachers or students at Ombuwa speaks English as their mother tongue, most are proficient in English, which is the medium of instruction in all classrooms. English is also the language used for all school communications. It is spoken at all staff meetings, assemblies, and other official school gatherings. Despite the official status of English at Ombuwa, staff room verbal exchanges occasionally take place in Afrikaans.
The mathematics teachers at Ombuwa represent a broad range of educational and teaching experience. The novice teachers, with two years or less of teaching experience, have completed the Basic Education Teachers’ Diploma (BETD). Introduced in 1993, the three-year post grade twelve BETD was designed to support the effective teaching of the post-independence basic school curriculum. Several of the veteran teachers, who began their careers prior to independence, have secondary school educations supplemented by post-independence inservice training courses designed to enhance the education of under-qualified inservice teachers. A small number of the veteran teachers began their teaching careers as classroom apprentices after completing only eight years of schooling themselves.
At Ombuwa, the students who are enrolled in mathematics classes in which first-year algebra content is included in the syllabus are typically fifteen to nineteen years old. Like their teachers, the students who attend Ombuwa are culturally diverse and represent a cross-section of educational backgrounds. Although the surrounding community attracts migratory laborers from throughout the country, and many students live with guardians rather than their parents, the student population is remarkably stable.
Guided by naturalistic inquiry, the researcher employed a qualitative methodology to understand phenomena in context-specific settings (Lincoln & Guba, 1985) and to “make sense of phenomena in terms of the meanings people bring to them” (Denzin & Lincoln, 1994, p. 2). This approach assumes that meaning is constructed by both participants and observers (Lincoln & Guba, 1985), and includes the storying element of a narrative study (Mishler, 1986). This methodology enabled the researcher to probe beneath the mundane, surface appearance of social existence to display a multiplicity of alternative meanings (Thomas, 1993).
Seven (six females and one male) teachers who taught mathematics at Ombuwa Secondary School during the two-year period in which this study took place were the focus of this study. At the time of this study, the teachers had between one and eleven years of teaching experience and taught grades seven through twelve. Demographic data gathered during this study revealed that, mirroring the typical Namibian teacher population, the teachers were from diverse educational and linguistic backgrounds. Three of the teachers (two females and one male) were Ovambo, the dominant ethnic group in Namibia. These teachers had between one and five years of teaching experience and spoke Oshiwambo as their first language. One female teacher was Damara, an ethnic and linguistic group that had been forcibly resettled to northwestern Namibia by the apartheid regime. She had five years of teaching experience and had completed several inservice training courses. Three female teachers were “Coloured” and spoke Afrikaans as their first language. Because their classification as “Coloured” according them more privileges during the apartheid era, these three teachers had the highest level of educational attainment and teaching experience (nine to eleven years).
In order to enhance the validity of the findings the researcher utilized multiple data sources (Lincoln & Guba, 1985). Qualitative data consisted of observations and field notes of the mathematics classes and three semi-structured, open-ended interviews (Spradley, 1979; Novak & Gowin, 1984) conducted with each participating teacher. Because staff room discussions emerged as significant episodes for the majority of exchanges between teachers, observations and field notes of staff room conversations and activities were made on a periodic basis. Secondary data sources in the form of the teachers’ lesson plans and samples of student work were utilized to triangulate these data (Glesne & Peshkin, 1992). Quantifiable data on the teachers’ knowledge were elicited utilizing pre- and post-study questionnaires. A pre- and post-study rubric provided quantifiable data on the teachers’ instructional practices. A wealth of contextually related material supplemented these data. These included donor agency reports, statistical data, academic papers, and non-government organization reports.
Qualitative data collection and analysis took place simultaneously over a two-year period. The analysis of data was grounded in a symbolic interactionist framework (Blumer, 1979), and it was further guided by the constant comparative method (Glaser & Strauss, 1967). Quantitative data were analyzed by computing statistical means and standard deviations. Major themes were developed utilizing thematic analytic strategies (Spradley, 1979). Of the most salient broad categories discovered and coded in the data, the themes that emerged were focused on teachers’ beliefs about mathematics learning and instructional practices. Further data collection, revisiting field notes and transcripts, and analysis resulted in the emergence of two additional themes: perceptions of students and student learning patterns.
Teachers’ beliefs about mathematics, as well as the social context of the situation, influence mathematics teaching (Ernest, 1991). For the teachers at Ombuwa, their beliefs about mathematics teaching and learning reflected their apartheid-era experiences and were shaped by socio-cultural and socio-political factors. Initial interviews and observations revealed that, for the most part, the teachers at Ombuwa viewed mathematics as a tool consisting of a body of procedures to be transmitted to students. The words of Paulus, a teacher with three years of teaching experience, typify this, “Mathematics is a very useful thing. Really, I would say that you must know how to do it. It is a basic skill that all of us need. It is important that we teach our students this skill.”
Believing the teacher is in a privileged position and that learning mathematics is a process of internalization, the teachers at Ombuwa employed drill-and-practice and teacher-centered instruction. This is in direct contradiction to the student-centered pedagogical reforms mandated by the government of Namibia. Rosalia, a teacher with five years of teaching experience, made a comment that suggests that there is a discontinuity between her beliefs about teaching mathematics under the new regime and what actually transpired in the mathematics classroom during the apartheid era:
To tell you the truth [pause] I never actually thought that teaching would be so complicated. I simply thought that I would teach the way I was taught. The students come to school, I teach them maths. I never realized that the students would be so involved.
The data from this study provide some evidence that collaboration and mentoring between researcher and teachers within a mutually supportive environment encouraged the teachers to begin to reconsider their beliefs about teaching mathematics. As the teachers embarked upon the process of rethinking several of their beliefs about teaching mathematics, including the notion of teaching through transmission, they slowly came to embrace student-centered and conceptually focused teaching. Several of the teachers made statements indicating that they came to recognize that teaching mathematics requires not only knowledge of the procedures, but also an understanding of the meaning underlying those procedures. For example, Rosalia’s comment at the conclusion of the study reveals that she has been through a process of re-examining her own beliefs:
My beliefs about teaching have changed, I think, now, I understand that teaching is more [pause] more questions [pause] more ways to solve problems [pause] more questioning and answering, back and forth, between us, teachers and students.
Research supports the view that teachers of mathematics’ instructional practices are shaped by their beliefs about mathematics (Cooney, 1985; Thompson, 1984). Teachers perceive of teaching in terms of revisiting teaching as they experienced it (Borasi, 1990). Instructional practices embody teachers’ beliefs, which are a reflection of their own experiences and background (Cabello & Burstein, 1995). This was evident in the early weeks of the study when classes observed were reminiscent of the colonial period. The teachers were the primary source of authority, instruction was directive, and obedience and conformity were expected from students. Mathematics instruction emphasized formal notations and procedural operations. It appears that these instructional practices reflected teachers’ own experiences as students of mathematics, which encouraged them to view teaching mathematics in terms of a repertoire of computational activities. Within the directive, teacher-centered lessons, emphasis upon procedures appears to have encouraged the students to focus on the process rather than the concepts. Observations of these lessons revealed that the students were led through a series of decomposed mathematical tasks, and in incremental steps.
Although the majority of teachers at Ombuwa were not formally trained as mathematics teachers, they were expected to teach a variety of secondary mathematics courses. In addition to the Ombuwa teachers’ inadequate academic preparation, the data suggest that their prior school experiences had a strong influence on their instructional practices. Under the racist Bantu system, in place when these teachers were students, they witnessed the explicit differentiation of education based upon color. The Bantu educational system inculcated in them a belief that they were inferior to their White colonial masters.
As students in the Bantu educational system, the Ombuwa teachers were subjugated and prepared only for passive rote-learning and teacher-centered instruction. Affirming a belief in the privileged position of the teachers, students were not provided with opportunities to redefine problems, initiate topics, or offer alternative explanations. However, through the process of mentoring and collaboration, the teachers began to implement inquiry-based teaching strategies, pose open-ended questions, and reorganize instruction to actively engage students in explaining and justifying their thinking. At the conclusion of the study, April (a teacher with three years of teaching experience) affirmed that the collaboration and mentoring had enhanced her instructional practices:
Honestly, I was not; I was not, prepared to teach in this way. But this process we shared, it helped me, in some respect, to put together a lesson that would involve the students. One time, I felt as if it was going in too many directions [pause] but I took a breath and listened. And, I understood [pause] for the very first time, the way the students were thinking. From that time, for the very first time, I believed that I could teach in this way.
Staff room observations revealed that the teachers were often engaged in critical dialogue and reflection on their instructional practices. A frequent topic of staff room discussions between teachers and researcher was the educational policy of post-independence Namibia. The document, Toward Education for All (MEC, 1993), the seminal policy statement of the independent Namibian government, provided a starting point for many of these discussions. In particular, the discussions centered on two critical elements contained within this document. The first, student-centered teaching, requires that “teaching methods allow for the active involvement and participation of learners in the learning process” (MEC, 1993, p. 60). The second element defines learning itself: “Learning is a lifelong activity - a process not an event. It is not something that happens once and then is over. It is something that we do, not something that we receive. (MEC, 1993, p. 11).”
As the study progressed, the changes to the teachers’ beliefs about mathematics teaching and learning were reflected in their instructional practices. These included a panoply of strategies that provided students with opportunities to initiate discussion, debate issues, and offer their own strategies and explanations. Moreover, rather than examining educational outcomes in behavioristic terms, the teachers began to move toward evaluating student learning in terms of comments that illustrated understanding. This included requiring students to elaborate upon their responses, demonstrate an ability to explain their reasoning processes, apply skills and problem solving strategies, and transfer their knowledge to novel situations. For example, during a follow-up interview, clearly pleased with her lesson, Taimi, the teacher who orchestrated a student-centered lesson shared her thoughts:
I have read about teaching in this way; I attended a workshop. But I have never watched it done - how to actually do this kind of teaching. I didn’t know where they [students] were taking me [shakes head]. You know actually, after, I felt good about it really, seeing what they [the students] could do.
Despite these positive responses to change, it was evident that some teachers were struggling to find appropriate ways to implement the reforms under prevailing conditions, including overcrowded classrooms and a shortage of books and instructional materials. At the conclusion of the study, Patience, a veteran teacher, voiced her response to change:
This is a difficult process [pause] change, so much change. We were not prepared - for teaching [pause] in another way [pause] our expectations were tremendous but [pause] there are many obstacles. Still, we are making progress.
Although many of the teachers’ instructional practices were informed by an archaic colonial mentality, the data suggest that changes to the teachers’ beliefs were reflected in instructional practices that focused on an inquiry-based approach to the mathematics being taught. Observations revealed instances in which students were encouraged to explain and construct different solutions to problems. Thobias, a student, commented on this transformation, “Maths used to be quiet, following the teacher, doing sums. Here, we are speaking, questioning and they are listening to our ideas.”
The biases that teachers are socialized in within their society are unconsciously reproduced in their own classrooms (Ernest, 1991). Moreover, because teachers act upon their expectations of learners, negative teacher perceptions or low expectations for their students influence classroom practices and may adversely affect student performance (Brophy, 1985). In many cases, the expectations that teachers have for their students vary along ethnicity and socioeconomic status (Spindler & Spindler, 1982). Traits of the school environment signify social stratification and empower and validate the behaviors of particular groups. As students negotiate their way through this environment, they become acutely aware of their social limitations. Eventually these students come to accept these limitations, to accept less of themselves and, ultimately, to aspire to less (Bourdieu & Passeron, 1977).
The racist apartheid system left as its legacy an overemphasis on the importance of ethnic classifications. This legacy was reflected in the Ombuwa teachers’ perceptions of ethnically and linguistically diverse students. It appears that the teachers’ perceptions and treatment of diverse students have been strongly influenced by the apartheid-era segregationist ideology, one that relied upon government institutions, including schools, for its transmission. These perceptions found an echo in the teachers’ instructional practices. For example, during the early months of the study, teachers who perceived themselves as being members of the dominant culture were more likely to engage in teacher-centered, procedurally focused instruction. This was particularly evident in classrooms comprised of “Coloured” teachers and Black students. It appears that these teachers’ drill and practice, skill-based lessons were designed to uphold their privileged positions and to maintain order in the classroom. Their teaching philosophies appear to be informed by the apartheid-era notion that, “People who believe in equality are not desirable teachers for the Natives” (Amukugo, 1995, p. 57). Veteran teacher Beatrix’s articulation of her perceptions of her non-dominant culture students reflects her negative expectations, both academically and behaviorally, for diverse students:
They are our school leavers; education does not mean the same thing to them. There are certain elements. They are more likely to take chances with teachers. It requires that we are being vigilant.
These impressions appear to have originated in the apartheid system, under which educational access and resources were inequitably distributed. There is a stark dichotomy between the teachers’ perceptions of diverse students and the Ministry of Education and Culture’s vision of equity and equality in classroom dialogue and participation (MEC, 1993, p. 19). Veteran teacher Loini’s comments on past educational experiences provide some insight into the complexity of the socio-cultural and socio-political processes that shaped the teachers’ perceptions of students.
The old system, under the oppressors, everything was designed to divide us [pause] and I suppose in some ways it worked. As for the schools, nothing was doled out in an equal manner. Here we have many students, from all regions. Now we are told to consider the individual learner [pause] but, our beliefs run deep, it is not so easy to change them. This process of talking, together, about these things, helps us.
Initial observations revealed that the students at Ombuwa were passive learners obediently following a sequence of steps lay out by their teachers. For the most part, the students were engaged in rote memorization and followed a step-by-step, formula-oriented approach to instruction. Because their prior learning experiences offered them virtually no opportunity to participate in active, experiential, student-centered learning, the students were often reluctant to respond to open-ended instruction. During the early weeks of the study, the students revealed a preference for closed problems. Bernardus, a student shared his thoughts on learning mathematics with his teacher and the researcher, “Personally, for me, it is difficult, thinking in this way. I like to see it [formula] and then take it and put in the numbers. Just [pause] to solve the problem. That’s all.”
However, as the study progressed, and the teachers began to cultivate a student-centered approach to teaching, the classes were distinguished by several important characteristics. Within these classes students were motivated to freely express their thoughts without fear of sanctions or reprisals, encouraged to listen to and respect their peers, and empowered to offer alternative explanations and redefine mathematical problems. Several of the teachers initiated a collaborative approach to learning in which students shared and explained their thinking, discussed strategies, and assisted one another in the co-construction of meaning:
When requesting respect for one another and in asserting their freedom of speech, the students often cited the Constitution of the Republic of Namibia. One student explained, “Before, we couldn’t speak but now our government has given us the right to speak, to question. We don’t have to stay silent.” Many of the students recognized that the transformed Namibian educational system empowered them. This sense of empowerment encouraged the students to engage in new learning patterns and to participate in mathematical discussions.
By offering insights into the complexities of mathematics teaching and learning in one Namibian secondary school, this study has several implications for inservice and preservice teacher education. Because education takes place within the contexts of school, social and political cultures, teacher preparation, and inservice education courses must take into account teachers’ beliefs as well as the socio-cultural and socio-political elements that shaped them. The present study also revealed that mentoring and collaboration within a mutually supportive environment facilitated critical reflection, encouraged a re-examination of beliefs, and empowered the participants to challenge the vestiges of subjugation. This suggests that inservice and preservice education courses provide teachers with collaborative experiences, mentors, and opportunities to engage in critical dialogue. The present study generated a large body of data pertaining to the process of teaching and learning mathematics within a recently transformed educational system. These data may be presented to inservice and preservice teachers as a basis to reflect upon, challenge, and reconsider their own beliefs and their relationship to school, social, and political cultures.
The data from this study also point to several possible implications for the relationship between teaching and learning. The collaboration and mentoring that transpired between teachers and researcher appear to have encouraged the teachers to engage in reflective practice, reconsider their notions of teaching mathematics, and attempt student-centered approaches to teaching. What is, perhaps, more significant is the observation that staff room discussions amongst teachers often focused on Toward Education for All (MEC, 1993) and its implications for teaching mathematics. It appears that this process encouraged the teachers to rethink their beliefs about mathematics teaching and learning. As the study progressed and there were changes to the teachers’ beliefs, they began to move away from procedurally focused instruction and made efforts to engage in teaching in the spirit of national reform efforts. Requiring the students to reflect on and discuss the mathematics being taught appears to have enhanced the students’ learning patterns and prepared them for conceptually focused instruction.
It appears that a constellation of circumstances within the teachers’ backgrounds, including social, political, and school cultures, shaped their beliefs and perceptions. This may suggest that mathematics teaching and learning is situated within larger socio-cultural and socio-political spheres (as with many other subjects) and resounds beyond the classroom. Collaboration, mentoring, and engaging in critical and liberating dialogue (Freire, 1970), empowered the teachers at Ombuwa to challenge the vestiges of past subjugation. Providing the teachers and students at Ombuwa with opportunities to critically reflect upon, and rethink their conceptions of teaching and learning facilitated their ability to teach in the spirit of Toward Education for All (MEC, 1993). Powerful reflections on socio-cultural and socio-political issues were entwined within the teachers’ remarks about teaching and learning. The words of the teachers and students reflect the complexities of teaching and learning mathematics. This complexity can be discerned in a statement made by Elijah, a veteran teacher whose words resound with passion:
As for myself, I never imagined that teaching could happen in this way. Before [independence], to imagine this occurring and our students learning like this. It was just [pause] impossible. But now, we are learning, slowly, to teach in a new way. And, we ourselves are learning, side-by-side with our students, to succeed. All of their classifications [pause] that they [white colonials] had placed on us - none of them, none of them recognized who we are what we are capable of, our potential, our humanity.
The present study revealed that teachers’ beliefs and perceptions reflect socio-cultural and socio-political elements and are powerful determinants of the ways in which educational reforms are interpreted and implemented in the mathematics classroom. Collaboration, mentoring, and engaging in meaningful discussions empowered the participants in this study to challenge the vestiges of past subjugation. Therefore, it is imperative that directives for educational reform be supplemented with opportunities for teachers and students to engage in critical dialogue within a mutually supportive environment. By examining teaching and learning in one Namibian secondary school, this study offers some insight into the complexities of teaching and learning mathematics.
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