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Feature Article of Tuesday, 8 June 2004

**Columnist: **Fredua-Kwarteng, Y.

There is a national aversion to mathematics?. Math phobia has permeated all rungs of the education ladder? Mathematics learning has been a problem even when Ghana had the best educational achievements in Africa. It is a problem that parents, teachers and education authorities are continually grappling with, because mathematics forms the basis of science and technology from which industrial development can take off (Ghanaweb, General News July, 22, 2003).

The above quote is very illuminating, in that it captures the fundamental fact that a strong national mathematics culture is a prerequisite to building an industrial culture in Ghana. Indeed, after British colonization countries such as India and Pakistan have been to build a strong national mathematics culture that is influencing their industrial development. However, why is the learning of mathematics in Ghanaian schools (elementary and secondary schools, colleges, polytechnics and universities) an enormous problem that continues to bother stakeholders of the system- parents, teachers, students and administrators? What are the causes of this problem? How do we solve this problem? What resources do we need to solve this problem? If you recall from your secondary school days in Ghana you might remember that mathematics was a subject that a vast majority of your classmates, and perhaps yourself, disliked so much. As a result, your classmates, and perhaps yourself, disliked your mathematics teachers. Mathematics teachers in secondary and colleges in Ghana are usually perceived as strange people whose main objective is to teach a strange subject that has little relevance to real-life situations. To present date this basic belief has not only changed, it has unfortunately become more deeply entrenched in Ghanaian society where politicians and policy leaders are calling for an industrialized economy.

It is very common in Ghana to hear science-oriented students expressing an interest in becoming engineers, accountants, medical doctors, pharmacists, and architects but not in becoming mathematicians. The narratives of three junior secondary school (JSS) students in Ghana are instructive here. These three students achieved distinction in mathematics in the Basic Education Certificate Examination (BECE), a final public examination for three years of junior secondary education.

Boateng: I want to be a medical doctor, not mathematician. How would I make a living if I become a mathematician? What would I do in Ghana? I learn mathematics because it is one of the subjects I need to go to medical school in Ghana; it isn?t because I want to be a mathematician.

Afua: I don?t know of any Ghanaian who makes a living in Ghana as a mathematician. Do you know of anyone? I want to study pharmacology in a university. I don?t know how I would fare if I were to become a mathematician in Ghana. I love mathematics, don?t get me wrong. But mathematics alone would not get me anywhere.

Amoah: I have never heard of mathematics as a profession. My brother did wood technology in Kwame Nkrumah University of Science and Technology. My brother and I talk together very often. But he never told me that you could study mathematics as a profession at university. To me mathematics as a profession would be very ?dry? indeed. The only thing a mathematician in Ghana could do is teaching in college or university. It is not possible to get a job with the government or the private sector.

From the narratives it is clear that those students do not regard mathematics as a viable profession in Ghana. On the contrary, they see it as a prerequisite to gain entry into programs that lead to professional designations. Why? It could well be those students do not know what mathematics is really about or whether mathematics could be a profession in its own right. The reader is also likely to support the views of those students. However, there are Ghanaian mathematicians who are mostly employed as university professors and are not known to most Ghanaians. Indeed, the influence of these professors does not go beyond the walls of their universities. We do not hear their names in the national daily newspapers, nor do we hear the government appointing them to head a commission, to do a research or study a problem in our society. Certainly, we do not hear Ghanaians saying that they are mathematicians as much we hear them saying they are engineers or scientists. This is sad indeed. So if those students perceived mathematics as a periphery to their professional or career interests, we should understand that they are using their lived experiences as a frame of reference.

It is unfortunate that students at all levels of the Ghanaian educational ladder still have problems learning mathematics. And this problem persists. The sad fact is that our present and past governments have not seriously looked at the underlying causes that make it very difficult for Ghanaians to learn mathematics. As usual if the government were accused of negligence in this matter, government?s spoke persons would arise quickly to their feet to blame the problem on lack of resources and logistics. Other government spokespersons may also say that the government is more concerned with the improvement of the whole education system rather than mathematics education. Nonetheless, we do not think that the solution of the problem needs a massive amount of financial resources. In fact, improving mathematical achievements of Ghanaian students requires a transformation of attitudes of teachers, students, school administrators, parents, and society. It also entails both structural and contentual transformation of teaching practices at all stages of the educational ladder. How teachers are prepared in teacher colleges to teach mathematics in our schools may be the entry point to start such a transformation. We believe that if the reform of Ghanaian education system includes changing the general teaching culture, mathematics education would also improve to a significant extent.

From our accumulated experiences and careful observations of mathematics education in Ghana and outside, we trace the problem of mathematics learning to four major causes?historic, culture of mathematics teaching, language of instruction, and culture of mathematics learning. This paper will analyze these major causes with a view to suggesting how we can promote effective mathematics education in Ghanaian education system, and thus establish a strong mathematical culture for future industrial development. We would like to stress that these causes that we have identified are not by any means exhaustive. For example, the reader may identify the lack of mathematics textbooks and materials as one of the problems that hampers mathematics learning in Ghanaian schools. Others may trace the problem of mathematics learning to lack of ?qualified mathematics teachers? in both elementary and secondary school. Nevertheless, we decided to focus on those causes we have identified as the most significant of all the causes of mathematics learning problems in Ghana.

Though British colonialism sowed the seed of mathematics aversion in Ghana, over the years Ghanaian policy-makers have not developed or implemented any policies to change that pandemic blight destroying Ghana?s education system. However, other countries formerly colonized by the British such as India and Pakistan have successfully forged an effective national mathematics culture, where the learning of mathematics is regarded as any other subjects in the school curricula and parents play an increasing role in promoting mathematics as an important subject to learn. In such countries mathematics learning is based on effort, not on the belief of genetic inheritance or innate ability. That is, parents do not tell their children that since they were not good at mathematics during their school days, it is not surprising if their children are also not good at it. Instead parents and community members promote positive beliefs and attitudes toward mathematics by presenting it as a learnable school subject. As well, in those countries students allocate time to learn mathematics consciously as much as they do in regard to other subjects in the school curricula.

Consequently, if mathematics learning has been a problem then mathematics teaching has not been effective in our education system. Certainly, we cannot exclusively attribute all mathematics-learning problems in Ghanaian educational institutions to the culture of mathematics teaching. Indeed, the availability of mathematics resources, students? socio-economic background, students? perceived usefulness of mathematics, and parental and community beliefs are equally significant factors that impact mathematics learning. Nevertheless, the way mathematics is taught is the most significant factor in any task of identifying or analyzing the etiology of mathematics learning problems in Ghanaian education system. Put another way, mathematics teachers? competencies and attitudes are an important factor in tracing mathematics phobia in Ghanaian schools. Weak mathematics teachers beget weak mathematics teachers. So goes the cycle. Indeed, weak mathematics teachers usually perpetuate the difficulties that students have with mathematics learning, which turn off many students, turning them into math-phobic learners and adults. In turn, this scares them away from pursuing mathematics studies and mathematics education at the post-secondary level, leading to a shortage of qualified mathematics teachers; leading to teachers teaching mathematics who are unqualified to do so; leading to adults who pass their math phobic beliefs to their children, relatives, and friends. This vicious cycle continues for another reason: In Ghana it is generally believed that teaching is a commonsensical activity and that a formal education in teaching methodology is not necessary to become an effective teacher. Accordingly, it is very common to hear a senior secondary school (SSS) graduate who did not make it to the university uttering the following statement: ? I will take up mathematics teaching, since I am good at mathematics, and try again to rewrite my examination to go to university.? On the contrary, we know from our professional practice and research that mathematics teachers require commitment and three set of knowledge and skills in order to be effective: knowledge of mathematics, knowledge and skills to teach mathematics, and knowledge of the students? interests, culture, and worldview. Mathematics pedagogies must be theoretically based and practically validated. A good mathematics teacher education will help prospective teachers to achieve pedagogical knowledge in order to improve their practices. This is because mathematics teachers are more likely to teach in the way they were taught during their school days, which has been shown to be ineffective to meet the needs of diverse mathematics learners in Ghana?s schools.

The teaching of mathematics in Ghanaian schools, colleges, and universities follows a consistent pattern that we label as the national culture of mathematics teaching. We identified this culture through our own participation in it (both of us taught mathematics in Ghana), our observations of mathematics instruction in Ghanaian schools, and also our interactions with mathematics teachers in Ghana. We should say that not every individual mathematics teacher practices this culture. Of course there are variations in the manner in which some mathematics teachers teach the subject or the sources of their philosophical reference that inform their teaching practices, instructional programming, instructional delivery strategies, assessment modalities, and choice of mathematics text. Nonetheless, the characteristics of mathematics teaching in Ghanaian education system, regardless of its location, can be used as a basis of theorizing the culture of mathematics teaching in Ghana. This culture underlies teachers? own beliefs about how students learn, their assumptions of the nature of mathematics, their pedagogy, their instructional strategies repertoire, and their perception of school mathematics. The national culture of mathematics teaching in Ghana, which is summarized below, mimics to a considerable extent, the general culture of teaching in Ghana? educational organizations:

1. Mathematics teachers normally appear before their classes, give a definition of a mathematical concept, work a few examples from the mathematics text on the chalkboard and at the end of the instruction assign students some exercises to do. In other words, mathematics teachers act before a passive audience that is supposed to absorb the knowledge transmitted.

2. Usually when students do not understand a teacher?s method of presenting a mathematical concept, the teacher would not change the method of presentation. Instead, the teacher would blame the students for being lazy or unintelligent. Thus, the students are required to learn the teachers? method whether they like it or not.

3. Mathematics teachers are mostly interested in answers or solutions to mathematical questions or problems rather than the processes or methods used to obtain the answers or solutions. Teachers simply give answers or solutions to their students without first having the students worked for those solutions.

4. Mathematical concepts are taught as objective, discrete facts without linking them together. For example, elementary school teachers do not demonstrate to their students that there is an affinity between decimal, ratio, rate, fractions, percentage, and proportion.

5. Students are hardly encouraged to ask questions, make comments or suggestions about what is being taught. Students? primary responsibility is simply to listen passively to the teacher, take notes when necessary, and store the knowledge in the dustbins of their brains, so to speak. The teacher brands students who dare to ask questions or disagree to a particular solution of mathematical question ?challengers? or a threat to his/her authority in the classroom. Such students would suffer harassment from the teacher and possibly isolation from their peers who might label them ?too known?. This atmosphere of fear and hostility is not conductive to effective mathematics learning. And it may be one of the greatest sources of epistemological anxiety in mathematics learning and a major cause of mathematics underachievement in Ghanaian schools.

6. Mathematics teaching is decontextualized. Teachers hardly connect mathematical concepts that they are teaching to the lives of their students or cultural practices in our society. Mathematics is taught as if it has no social or economic referents or relevance in our society. For instance, a teacher is teaching her students how to calculate simple interest but fails to talk about traditional arguments for and against charging interest and the fact that interest is normally quoted in a non-percentage term. 7. Mathematics teachers simply give formulas or algorithms to their students to use in doing mathematics. Normally, the underlying logic or philosophy of the formulas or algorithms is not explained to the students. In fact, students are required to regurgitate the formulas or algorithms and recall them during tests, quizzes, class assignments, home assignments, and examinations. Mathematics learning becomes a matter of memorization.

8. Examinations or tests are the only instrument for assessing students? understanding of mathematical concepts. Scarcely do mathematics teachers include class or homework assignments as a part of the weighing of the final marks.

9. Mathematics is taught without using any other materials except chalk and chalkboard. If mathematics is the study of patterns and quantitative relationships--- arithmetic and number theory study the pattern of numbers and counting; geometry studies the patterns of shape; calculus allows us to handle patterns of motion; logic studies the patterns of reasoning; probability deals with patterns of chance--- one would have expected that teachers use other materials to enhance the teaching of mathematics. Admittedly, at the primary 1,2 and 3 level teachers encourage students to use stick counters, marbles and their fingers or toes to do the four basic operations of mathematics.

10. Mathematics teachers have a hidden assumption that only the most brilliant students are capable of learning mathematics. So that students who experience difficulties understanding mathematical concepts are left behind to fend for themselves, while the so-called brilliant few are motivated by provision of extra assistance.

11. Mathematics teachers assume that teaching is the same as learning. So if students are incapable of solving a specific mathematical problem on an examination or test, the teacher is likely to say that the students are unintelligent because he or she taught them that concept before. 12. English language is primarily the exclusive means of instruction, even if the teacher speaks the same indigenous language as the students or majority of the students. The students might not have attained any proficiency in English language in order to process mathematical ideas efficiently. The teacher may also have difficulties expressing mathematical ideas precisely in English.

13. Students in elementary schools are usually drilled mentally on the multiplication table, addition and subtraction facts under the label ?mental?. Some students are made to recite the times table in a parrot-like fashion in the belief that once mastered it would facilitate the learning of other mathematical concepts.

14. Most mathematics teachers do not allow their students to use hand-held calculators during tests, examinations, or quizzes, in the belief that they give students an unfair advantage. Yet some of these teachers use calculators when checking students? assignments.

In a pivotal work titled Education and Culture, Jerome Bruner states that the ways teachers construct their students? learning patterns influences how they approach their instruction. This in turn influences and shapes how students learn mathematics, how they hate or love learning mathematics. Bruner puts forward four theories, which he calls folk pedagogy that teachers formulate about how their students learn. First, teachers regard their students as imitative learner. In this case, teachers give their students examples, steps, and emphasize skills in learning mathematical concepts. Second, teachers view their students as didactic learners. Applying this theory to mathematics learning, students are thus provided with facts, principles, and rules of mathematics without explaining the logic undergirding those rules, principles or algorithms. The failure to explain why the rules exist invariably results in rote learning and inability to adapt those rules to a different set of circumstances. As well, teachers expect students to regurgitate those rules, algorithms, and principles and reproduce them during examinations.

This ?banking education? (mathematics education), to use Paulo Freire?s term, is a stifling experience for students who are creative, critical, and reflective thinkers. It is also a frightening experience for students who are not good at memorizing a myriad of rules, principles, and algorithms. Third, teachers see students as thinkers, and base their instructions on helping students to make sense of their society. Applying this theory to mathematics teaching, teachers help their students to learn mathematics with meaning, understanding, and relevance. This is achieved through oral presentation, investigation, discussion, group project, individual project and teacher-student dialogue. Lastly, teachers regard students as knowledgeable and help them to see the difference between personal knowledge or experience and cultural knowledge. Teachers with this construction of their students do not regard them as? tabula rasa? or empty-minds to be filled with facts or information. In fact, the knowledge that students bring from their culture is validated and legitimized. To be more specific, teachers espousing this pedagogy use the cultural knowledge students bring to school as an entry point in teaching them mathematics.

The first two theories of Bruner can be used to describe the national mathematics teaching culture in Ghana as we have itemized them above. It is a culture that must be transformed in order to build a strong national mathematics culture in Ghana. The last two theories should help to establish the foundation for that change. The two pedagogic theories are more effective in teaching mathematics than the first two, because they are based on helping students to gain understanding and meaning of mathematics. Further, they do not strip students of their cultural knowledge and resources. Instead, they use them as a base for instruction. For example, the Ghanaian traditional methods of measurement provide the basis of learning other methods of measurement. Furthermore, they relate mathematics to students? lives and referents in Ghanaian society. In simple terms, it is a pedagogy that recognizes the importance of including students? cultural references in all aspects of teaching and learning.

Y. Fredua-Kwarteng is school administrator and mathematics educator in Canada?s newest territory of Nunavut.

Views expressed by the author(s) do not necessarily reflect those of GhanaHomePage.