CURRENT TRENDS IN MATHEMATICS EDUCATION: QUALITIES OF AN EXPERIMENTAL MATHEMATICS TEACHER
This paper articulated who an experimental mathematics teacher is. A teacher who is trained to teach mathematics and who has the skills and competence needed to carry out the task effectively. Unfortunately the department has been saturated with unqualified teachers who are specialists in other disciplines like chemistry, physics, economics, engineering etc. The paper however, describes the dimensions of an experimental mathematics teacher as teacher’s personality, knowledge of the subject and methodology which play a role in the teaching and learning of mathematics. The paper also identified and explained the modern methods of teaching mathematics. These are problem solving, cooperate/group, computer assisted instruction, and interactive method. It recommended, among others, that government and school authorities should engage the services of qualified teachers of mathematics and provide appropriate teaching and learning equipment/facilities. Also, it is important for teachers to identify with professional organizations so as to meet the challenges of the fast growing trends.
Research findings have confirmed the dearth of mathematics teachers at all level of education in the country. Obioma (2005) has drawn attention to the depreciating capacities of mathematics teachers, observing that the old generations of mathematics experts were fast disappearing and where there were any replacements at all, younger persons who had little or no guidance in the profession and research generally dominated the skyline. The lack of enough teachers to handle the subject particularly at the secondary level has led to borrowing teachers who are specialists in other disciplines like chemistry, physics, economics, engineering etc. to teach mathematics. In many cases, such borrowed teachers are not professional teachers because they are not trained teachers. Hence, they lack the skills, competence and the teaching methods required to teach mathematics effectively. Usually, such teachers avoid the teaching of some topics which they find difficult to handle. In essence, it means that short supply of qualified teachers leads to mathematics teaching been handled by incompetent hands who in turn can only produce poorly bred mathematics students. The students therefore become victim of poor teaching. This trend confirms the assertion by Fakuade (1973) that a shortage of suitably qualified teaching staff will result in poor teaching which invariably will result in a production of another generation of poor students.
Freudenthal (1991) maintained that to learn mathematics means to engage in the process of mathematising through which mathematics is re-invented. His emphasis on mathematising carries a strong evolutionary stance and is further elaborated subsequently by Wittmann (2001) who proposed that mathematics education should be viewed and studied as a ‘systemic evolutionary design science’. He also proposed that the study of teaching units called substantial learning environments should form the core of mathematics education. “The design of substantial learning environments around long-term curricular strands should be placed at the very centre of mathematics education. Research, development and teacher education should be consciously related to them in a systematic way (Wittmann, 2001).
Experimental Mathematics Teacher
From research evidence, econometric analyses have equivocally demonstrated that, some teachers are dramatically more effective than others and that these differences have lasting effects on student learning (Rivkin, Hanusahek, and Kain, 2005). The teacher is the most indispensable factor in effective administration of any educational system. Also, it has been established that no amount of resources put into the nation educational system, without adequately prepared and motivated teachers, nothing tangible can ever be achieved from the system. The role of teachers at all levels of education is emphasized in the National Policy on Education (FRN, 2004) that no educational system may rise above the quality of its teachers. This declaration in the policy document underscores the need for teachers’ effectiveness in teaching and learning. Eso (1998) conceptualized teachers’ effectiveness as the managerial skills essential for enhancing classroom control and discipline. It is the teachers’ competence, ability, resourcefulness, and ingenuity through effective utilization of appropriate language, methodology and available instructional materials that could bring out the best from the learners in term of academic achievement. But what makes a great teacher? Some people are of the opinion that teachers are born. But Ukeje (1991) is of the view that teachers may be born but a good teacher is born and made. Maduabum (2009) explained that, this is because teaching is both an art and a science”. Some aspects of the art of teaching may be innate, but the science of teaching has to be cultivated Maduabum (1986) had argued that having knowledge and transmitting knowledge are two different things. Some people have both abilities but many do not. The ‘born teacher’ exists but he is a rare bird! (Maduabum, 2009). However, ability to transmit can be acquired if one is not lucky enough to be born with it. Adepoju (1995) categorized these teachers into four categories, they are:
- Those who know mathematics but do not know how to teach it
- Those who know how to teach mathematics but do not know much mathematics
- Those who do not know mathematics and do not know how to teach it
- Those who know mathematics and know how to teach it.
With these categories of teachers in the school system there is the need for professional competence among teachers, so that teachers can be confident in doing their job while helping students learn mathematics.
Ezenweni (2002) define an experimental mathematics teacher as a teacher trained to teach mathematics as a science to secondary school students. That is, the teachers use different teaching method to reduce the persistent problem of mathematics abstractness and in a null shell, an experimental mathematics teacher is a lover of mathematics.
An example will be helpful to illustrate a pedagogy -caused student difficulty. Tanner (2000) states that teachers generally use “fruit and salad approach” to introduce the addition of two algebraic expressions, such as, 2a+3b in algebra teaching. This kind of expression is often explained to students by teachers through the use of some materials, such as 2 apples and 3 bananas. However, Pimm (1987), as cited in Tirosh, puts forward reservations regarding this approach, warns against its potential role in causing learning difficulties for students and notes that it leads to confusion between a being apples and a being the number of apples. The algebraic expression is not an analog of 5 apples, nor is 5 apples a possible interpretation of 5a, the letters themselves are standing for numbers. In fact, some studies have shown the disadvantages of using this approach in introducing algebraic expressions. Booth (1988), for example, shows that some students thought that the expression 2a + 5b is equal to 7ab on the grounds that 2 apples plus 5 bananas is 7 apples-and bananas. Tirosh, (1998) also point out that this approach may lead students to think algebraic expressions, such as 2a and 3b, cannot be multiplied, that is one cannot multiply apples and bananas.
All these suggest that sometimes the way materials are used and the way the teaching is conducted can be the causes of, or at least play a role in the emergence of student learning difficulties for mathematical concepts.
Fennema and Franke (1992) argue that if a teacher has a conceptual understanding of mathematics, this influences classroom instruction in a positive way, therefore, it is important to have mathematics knowledge for teachers. Teachers’ interrelated knowledge is very important as well as procedural rules. They also emphasize the importance of knowledge of mathematical representations, because mathematics is seen as a composition of a large set of highly related abstractions. They also stated that ‘if teachers do not know how to translate those abstractions into a form that enables learners to relate the mathematics to what they already know, they will not learn with understanding’.
Traditional indicators of teacher quality, such as educational level and certification, do not predict student outcomes (Rivkin, Hanushek, and Kain 2005), certain aspects of teacher education are relevant. For example, mathematics teachers who have completed PhD course work in mathematics and an advanced certificate course in Education are more effective than peer teachers without such advanced training in education. An experimental mathematics teacher should be able to use modern methods of teaching and learning in order to bring out a desirable outcome (Ezenweani, 2002). He outlined the characteristics of experimental teachers to include the following:
- They are emotionally balanced
- They are active and never lazy
- They are cognitively balanced
- They are mentally healthy and ready to find solutions to problems
- They are friendly to all people and see things from other people’s point of view to learn on their part
- They are very enthusiastic in academic work
- They are cultured in dealing with issues affecting human relations
- To avoid the bad characteristics generally identified in them, they are supposed to be neat in appearance all the time, become more careful the way they dress and careful in the choice of vocabulary and expression. They should avoid being harsh to students and speak clearly not only to the students but in public
- They are supposed to be creative in their experimental pursuit which should make for some originality in their activities and findings.
Here are three dimensions of an experimental mathematics teacher they are:
- Teachers personality
- Knowledge of the subject matter
The teacher’s personality is one of the characteristics to look for in the teaching and learning of mathematics. Anybody can become a teacher, but it takes special person to be a great experimental teacher. He/she must rise above the crowd and make empathy, enthusiasm, creativity, dedication, and discipline in the process of teaching.
Knowledge of the subject
The knowledge of an experimental mathematics teacher are defined as the skills effectively and efficiently acquired when teaching mathematics. That is, the ability to organize and teach in interesting and flexible ways. Knowledge of the subject matter content is vital for the experimental teacher. It determines the line of activity the teacher should follow to achieve the desired objective and being acquainted with the content to be taught.
The learning of mathematics depends on the way it is presented to the learner, the way the learner actively interacts with the learning experiences presented to him and the environment within which the learning takes place. With the current increase in scientific knowledge, much demand is placed and emphasis is laid on the teacher, the learner and the environment in the whole process of teaching and learning of mathematics. Today’s mathematics teachers are experiencing major changes not only in the mathematics content they teach, but also in the way they teach.
Modern Method of Teaching Mathematics
Problem solving method: This approach is characterized by the teacher in helping students to construct a deep understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring and testing. Polya’s (1965) describe problem solving processes into four stages:
- understand and explore the problem
- find a strategy
- use the strategy to solve the problem
- Look back and reflect to the solution.
Alio and Harbor-Peter (2000) recommended that polya’s problem solving strategy should be used by secondary school mathematics teacher to teach mathematics. The learning of mathematics in this case proceeds from the concrete to the abstract. Approaching mathematics through problem solving can create a context which stimulates real life and therefore justifies the mathematics rather than treating it at the end.
Cooperate / Group method: Cooperate learning method of teaching is an instructional strategy that simultaneously addresses academic and social skill learning by students. It is one way of providing students with a well-defined framework from which to learn from each other. Cooperate method of teaching is a team approach where the success of the group depends upon everyone pulling his or her weight. Group members share the various roles and the interdependent in achieving the group learning goal. Cooperate learning can take place in a variety of circumstance. For instance brainstorming and tutorial group, when employed as instructional strategy provides opportunity to develop cooperative learning skills and attitudes
Computer Assisted Instruction: this approach uses computer as a substitute for the teacher, that is, the students interacts with the computer directly, usually as a terminal. Although the teacher is involved in planning the system and supervising it’s operation, a well-planned system frees the teacher from routine teaching tasks, so that he may spend more time in working closely with individual students (Odili, 2006). NCTM (2000) asserted that educational technology (computer) can help teach content. It can offer students a bridge from concrete to abstract thinking, enabling them to observe and create multiple representations of mathematical ideas. For instance, students can use geometric instruction software to investigate the relationship between circumference and diameter of a circle (Agwagah, 2013).
Interacting method: Interactive method of teaching includes giving students something to do and getting what they have done, so that you can decide what would be best to do next. If a teacher asks questions in class, gives assignment, and check homework then you are already teaching interactively. Interactive instruction relies on discussion and sharing among participants which allows for a range of groupings and interactive method. Interactive method requires the refinement of observation, listening, interpersonal and intervention skill and abilities by both teachers and students
Teachers Development Programs
Effective instruction in school is defined through teacher education program, which is the key towards understanding the knowledge and skills of teaching and learning (Ololube, 2005a, 2005b). The education of pre-service and in-service science teachers is meant to help individual teacher grow and develop as a person, provide him or her with the skills and professional abilities to motivate children to learn, assist them in acquiring the right types of understandings, concepts, values and attitudes to manage classroom instruction and be productive members of the society in which they are born, grow and live (Lawal, 2003).
If mathematics teaching is to be effective, the pre-service training of teachers must be very sound, while they also need to be exposed to in-service training at regular intervals. Where teacher preparation is inadequate it will lead to teaching failure in the classroom; this is an area that needs to be improved upon. Teacher development is considered particularly effective, when teachers are in charge of the agenda and determine the focus and nature of the programming offered (Ball, 1996). This concur with, the FRN (2004) National Policy on education stipulates that teacher education shall continue to take cognizance of changes in methodology and in curriculum. Furthermore, that teacher shall be regularly exposed to innovations in their profession (p 34). Fennema, Carpenter, Levi and Franke (1998) learned that engaging teachers in current reforms requires more than showing them how to implement effective practices. Hence the government agencies are committed to development and training of teachers which is aimed at increasing the ability of the individual and groups to contribute to organizational effectiveness.
Experimental mathematics teachers are key determinants of mathematics learning outcomes. The learning of mathematics depends on the way it is presented to the learners, the way the learners actively interact with the learning experiences presented to them. With the current increase in scientific knowledge, emphasis is laid on the teacher in the whole process of teaching and learning of mathematics. The Teachers personality, knowledge of the subject, and methodology play a significant role in the mind-set of students towards the learning of mathematics. All these factors could also be applicable to mathematics learning since mathematics is regarded as the language of science. It is on this premise that the mind-set of the teacher’s disposition to the subject, students, and classroom environment could make or mar the mind-set of the students towards the learning of mathematics. Hence the mathematics teacher should be psychologically prepared to teach the subject efficiently.
It is important for mathematics teachers to identify with professional organizations so as to meet the challenges of the fast growing trends. Such as, Mathematical Association of Nigeria (MAN), Science Teacher Association of Nigeria (STAN), Curriculum Organization of Nigeria (CON), and African Mathematical Union (AMU) etc. Government and school authorities should engage the services of qualified teachers of mathematics and provide appropriate teaching and learning equipment/facilities. The state government should as a matter of urgency send mathematics teachers for training and seminars for effective teaching of mathematics, particularly in our primary and secondary schools. Teachers should try as much as possible to relate their lesson to real life situation in order to reduce abstract nature of the subject.
Agwagah, U. N. V. . The teaching of number bases in junior secondary school
mathematics. The use of the base board. ABACUS. The Journal of the Mathematical
Association of Nigeria [Mathematics Education Series]. 26, 1-7.
Alio, B.C. & Harbor – Peters, V.F. (2000). The effects of Polya’s problem solving technique on
Secondary school students’ achievement in mathematics. The Journal of the Mathematical
Association of Nigeria, 25 (i), 27-39.
Ball, D. L. (1996). Teacher learning and mathematics reforms: What do we think we know and
what do we need to learn? Phi Delta Kappan, 77, 500-508
Booth, L. Algebra: Children’s Strategies and Errors. Windsor (UK): NFER-Nelson, 1984.
Fennema, E. & Franke, M. (1992). Teachers’ knowledge and its impact in: D.A. Grouws (Ed)
Handbook of Research on Mathematics Teaching and Learning. New York Macmillan
Franke, M.L., Carpenter, T. P., Levi, L.W., & Fennema, E. (1998). Teachers as learner:
Developing understanding through children’s thinking. Paper presented at the annual
meeting of the AERA, San Diego, Ca
Freudenthal, H. (1991). Revisiting mathematics education : China lectures. Dordrecht ; Boston:
Kluwer Academic Publishers.
Federal Republic of Nigeria (2004). National Policy on Education. (Revised Edition). Lagos:
Federal Ministry of Education.
Eso, O.T. (1998). Assessment procedure and student locus of control as determinants of
achievement in Integrated Science. An Unpublished Ph.D Thesis, University of Ibadan,
Ezenweani, U.L (2002). Experimental Mathematics Teaching. Enugu: Fulladu publishing
NCTM (2000). Principles and standards for school mathematics. Reston Va: The National
Council of Teachers of Mathematics inc.
Maduabum, M.A. (1986). A critical appraisal of university teaching in Nigeria. Journal of
curriculum and instruction 1 (1), 114-112.
Maduabum, M.A. (2009). Science Teacher Effectiveness and National Goal Attainment in
Nigeria: In search and solution.11th Inaugural Lecture Abia State university 1-37.
Obioma, G.O. (2005). Popularizing Mathematical Sciences for Technological Development in S.O. Ale and L.D. Adetula (ed) Reflective and Intellective Position Papers on Mathematics Education Issues Garki Abuja: Marvellous Mike Ventures Ltd. 102-117.
Wittmann, E. C. (2001). Developing mathematics education in a systemic process. Educational
Studies in Mathematics, 48(1), 1-20.
Rivkin, S.G., Hanushek, E.A., and Kain, J.F. (2005): Teachers, Schools and Academic achievement. Econometric, 73,417-458.
Ukeje, B.O. (1991): The Education of Teachers for a new social order. The Nigeria teacher, 1 (1), 4-12.