university of nigeria · mathematics education it is not easy to give one definition of the term...

University of Nigeria Virtual Library

Serial No

ISSN: 1115-6787

Author 1 AGWAGAH, U.N.V.

Author 2 Author 3

Title Making Mathematics Education Self - Reliant

Keywords

Description Making Mathematics Education Self - Reliant

Category Science Education

Publisher

Journal of Science and Computer Education

Publication Date December, 2001

Signature

I

I

THE JOSCED I

Vol. 1 ( 3 ) (DECEMBER) 2001

Journal of Science and Computcr Education

publication of Science and Computer Education Department Enugu State University of Science Technology, Enugu.

ISSN: 1 1 15 - 6787

JOURNAL OF SCIENCE AND WMPUTER EDUCATION 1 I

i JOURNAL OF SCIENCE AND COMPUTER EDUCATION

I

VOL. 1 NO 3 (DECEMBER) 2001 A Publication of Science and Computer Education Department

ESUT, Enugu I

Editorial Board

Prof. J . 0. Mogbo

Dr. A. E Eze

Dr. H.C.O. Aniodoh

Dr. C. U. Eze

C. A. Ezeano

Dr. E. C. lloputaife

Consulting Editors

1. Prof. N. J. Ogbazi

2. Prof. H. C. lnyiama

3. Prof. M. N. Maduabum

4. Prof. N. N. Okoye

5. Dr. M. 0. Nwadiani

I I

I

1 I

I

I

I Editor in Chief , I

I * I

I Associate Editor , 1

Associate Editor \

Associate Editor

Associate Editor I

Business Editor I

I

UNN 1

ESUT

NAU

JOURNAL OF SCIENCE AND COMPUTER EDUCATION

MAKING MATHEMATICS EDUCATION SELF-RELIANT

BY I

DR. U. N. V. AGWAGAH (MRS) MMAN, SUB-DEPARTMENT OF SCIENCE EDUCATION

UNIVER'SITY OF NIGERIA NSUKKA

INTRODUCTION There is a steadily worsening

unemployment prospects of young people leavrng school in Nigeria and elsewhere. Thrs srtuatron has been attributed to the economrc ,:isrs in many countr~es (Malone, 1980) In N~ger~a, researchers have shown that about 60%0 of the unemployed youths are mostly secondary school leavers, and th~s IS as a result of lack of the required skills (Ta~wo, 1980) Th~s report could suggest that schools are not adequately preparing therr graduates to succeed rn the world outside the classroom, as stated by Ball and Goldman (1 997) In other words, schools are not preparing their graduates to be self-reliant.

One of the five man natlonal goals of Nlgerra, as stipulated in the Nat~onal Pollcy on Education, is 'the building of a united, strong and self-rel~ant nation' (F R N , 1998, 7) The national educational goals which derive from the philosophy ~nclude:

the inculcation of the right type of values and attitudes for the survival of the individual and the N~gerian society, and the

6 ' 4

acquisition of appropriate skills, and also the development of mental, physical and social abilities and competencies as equipment for the individual to live in and contribute to the development of his society (p. 8).

In consequence, the qual~ty of instruction at all levels has to be or~ented towards i ncu~ca th~ , among other values, "the acquisition of competencies necessary for self-reliance" (p. 8). {

To achieve the inculcation of these values In the learners, and to pursue the goals of education at the various levels, '

various subjects, such as mathematics are taught in schools. The question then is, how does the acquisition of mathematical compe-tencies enable one to be self-reliant? Or to what extent does mathematics instruction at all levels of education enable the learner to acquire competencies necessary for self- reliance?

It is generally accepted that being mathematically competent mvolves more than the acquisition of knowledge and the mastery of skills. ath he ma tical'. competence requires that mathematical knowledge and sk~lls should be effectively


T

j used and applied, in order to investigate i and solve problems in a range of contexts , (Bell et al, 1993 Ball and Davies, 1997).

Mathematical knowledge and skills are acquired through mathematics education. Thus, the above question may be put slmply 1 -w does mathematics education enable one to be self-reliant? To answer th~s quest~on, the following issues are d~scussed. * Meanmg of mathemat~cs/mathematics education.

Aims of mathematics education. Meaning of self-reliance.

* The way forward.

MEANING OF MATHEMATICS1 MATHEMATICS EDUCATION

It is not easy to give one definition of the term 'mathematics', hence, people have perceived mathematics differently and at different trmes. The follow~ng are some attempts at e~plain~ing the meaning of mathematics.

Mathematics is a changing body of knowledge (Lindquist, 1989), that serves the physical and social scientists, the phdosopher, the logician, and the artists. Osibodu (1 982), defined mathematics as a model for thmking, for developing sc~entific structure, , for drawing conclus~ons and solving problems.

As a model for thinking, mathematics is a method of thinking about patterns and relationsh~ps of numbers and shapes. It is the means of sharpenmg the individual's mind, shaping his reasoning ability and developing his personality.

Mathematics IS a pivot on which other sciences revolve ( ~ a b e l ' and Sherwood, 1983: Odili, 1990). Presenting examples of the relations between mathematics and science, Descartes in Eyo (1991), explained that in Chemistry, the knowledge of mathematics IS

indispensable if we must balance I chemical equations, determine the rate of

chemical reactions, molecular weight, etc. In physip, one cannot study simple pendulum, laws i$ electricity, light, electromagnetism, etc, without the knowledge of transformation, of formula, graphs, linear simultaneous and quadratic equations, etc. in economics, accurate population of a country, determination of budget, etc cannot be achieved without mathematics. Mathematics is therefore said t~ be the queen of all sciences and no nation can hope to achieve any meaningful technological advancement without proper foundation in school mathematics.

Mathematics is a language. Galileo in Eyo (1 991), identified the mathematics language as the language of nature. It is the language used in all cultures of the world and in all works of life (Osafehmti, 1990). As a basic language c& quantification, qualification, estimation and precision consequent upon measurement, mathematics is an art. But as a systematic body of knowledge, rules/laws and processes ' used in interpolatons, extrapolation of an investigation into phenomena and the manipulation and control of relationship, it is a scieqce (Ogomaka, 1996). However, either as n art or a science, mathematics

I P


is one of the foremost tools man uses to interact with his environment and solve his problems. It is therefore a useful and powerful subject. It is ' considered as knowledge indispensable to the educated man, hence, it is a key subject in the school curriculum. In many countries, attainment in mathematics is used as a sifting devic2 (Howson and Malone, 1980). Most employers demand a good knowledge of elementary mathematics from the graduates of our schools and colleges. To secure, admission for most courses at higher levels of education, a credit pass in mathematics is an advantage. From these considerations, one could see that learning of mathematics in schools or mathematics education represents first, a basic preparation for adult life and second, a gateway into a vast array of career choices.

Mathematics education is a discipline and a professional field whose domains of reference and actions are characterized by an extreme complexity: the complex phenomenon 'mathematics' in its historical and actual development, and its interrelation with other sciences, areas of practice, technology and culture; the complex structure of teaching and schooling~ within our society; the highly differentiated factors in the learner's individual cognitive . and social development, etc (Steiner, 1985).

It presupposes mathematic knowledge systematically ordered in any way, originating from solving problem, generalizing methods, classifying results, etc, combined with teaching methods

reflecting to some extent the educatroni goals of very different societies in histor (Keitel, Schubring and Stowaser, 1985 According to Pellery (1 985), mathematrc education is a process by which a chi1 enters mto two basic reasons of tt- mathematics world. mto concepts ar theories on one side, and mathematic xt iv i ty on the other. Such inrtiat~o~ fostered and made easrer by teacher take place within a well-kn~t syste where, as many as four mqn poles ex€ their mteractive influence. Mathematic education therefore, is a d~scipline or field of study which deals with tt problems of the teaching and learntng mathematics at all levels of educatio The drscipline of mathematcs educatic would provide both the just~ficat~on and self consrstent integrated methodology fl the teacher, both as practitioner and researcher.

AIMS OF MATHEMATICS EDUCATlOl According to Travers (1985), tt

aims of mathematics can be classific into five categories as: * those dealing with mathemati1 itself, in relation to the s~gnificance ar the characterist~cs of mathematics.

those dealmg with the utility mathematics, which relate to the use maihematics in the day-to-day busme! of life, and also the use of mathematics other academic fields of knowledg particularly science, technolog sociology, economics.


* those dealing with mathematics as an intellectual discipline. It is believed that mathematics imparts a mental training to those who study it. The qualities or faculties which are alleged to be hones by mathematics include: logic, imagination and creativity, precision, clarity, resourcefulness and judgement.

* those dealing . with moral perceptions or attributes. It is believed that the study of mathematics plays an important part in character development. According to Halls in Travers (1985), the French expressed this aspect best when they used in their statements of aims of mathematics education, such expression as, 'to teach one to distinguish the true from the false, amid the cont'radictions of mankind'.

Mathematics, as also believed, plays as important part in the appreciation of aesthetic values. For the Germans, the task of the Mathematics teacher is to 'give insight into the many beautiful relationships in numbers and figures that exist and to recognize relationships of size and form . . . in the outside world' (Travers, 1985). * These classifications of the aims of mathematics education are consistent with the general objectives of mathematics education at the school level, formulated on the basis of the National Policy on Educati'on, and as simplified by educators. For instance, for Obioma (1988), .the general objectives centre on explaining the physical world, showing the extensive applicability of the subject to other, fields, emphasizing

transfer values and appreciatron of the elegance of nature. According to Ezike (1 989), the general objectives, among others are: to generate interest in mathematics and to provide a sohd foundation for everyday living; to foster the desire and abllity to be accurate to a degree relevant to the problem in hand; to develop precise, logical and abstract thinking; to develop ability to recognize problems and to solve them with relevant mathematics background; and to stimulate and encourqge creativity. How are these objectives related to the achievement of self-reliance?

MEANING OF SELF-RELIANCE Self-reliance refers to both

aspirations and policies that followed the dismantling of colonial empires in the mid-twentieth century. It became enunciated as national policy since 1960, primarily by formerly colonized countries, especially in Africa and Asia (Ball, 1985). The roots of self-reliance lie in the demand for self-determination, and ~t symbolizes a rejection of contmued dependence on former metropoles for capital, technology and skills, thus acquiring local autonomy and cultural authenticity.

Nigeria was not left out in this policy. Hence, it established the Directorate of Mass Mobilization for Social Justice. Self-reliance and Economic Recovery (MAMSER) decree of 1987, which came into operat~on on 2nd September, 1987. It has as its objectives, "to create a new cultural and productive work, s If-discipline and self-reliance, 7

' 1

U

JOURNAL OF SCIENCE AND COMPUTER E

among others. Since the national educational system was also expected to play a major role in fac~litating and nurturing self-reliance, (by developing needed skills), and authenticity (by

' socializing learners both children and adults, to new values), educational policy was to embody the commitment of self- reliance

Accordmg to lkoku (1980), one cannot slmply def~ne the term 'self- reliance', but one can describe it, g~ving it body and content He stated that Tanzanians call ~t 'Uja~naa' which means 'development through c ne's own effort. He further explalned that the idea of local self-reliance in the sense of a community relying on its own forces is as old as human~ty ~tself because ~t was the normal form of existence For instance, the self- help efforts of villages rn the development of their communities without ass~stance from government.

Self-reliance therefore means reliance upon oneself, one's own powers etr "mpson and Weiner, '1989). It means havmg confidence, trust in oneself; relying on oneself for development rather than on someone else In terms of mathematics education, self-reliance could imply the development in or through mathematics study by one's own effort.

MATHEMATICS EDUCATION FOR SELF-RELIANCE

This can be addressed from different perspectives. It could relate to the ability of an individual to use the study of mathematrcs at a lower level of

education, say primary school level, lr study mathematics at a higher level, sa, secondary school level. It can also relata to the issue of using the mathematic knowledge and skills learned in school fo

. self-employment. Another dimension ma, relate, to educational provisions tha would make the recipients of educatia self-reliant. Based on these dimensions certain questions to ask may be:

* Do students have confidence is and are they competent to stua mathematics? Or does the study c mathematics at the sch. actually , enable one to study it at th secondary school? * What type of curriculum should a offered to make students self-reliant? * What teachmg approaches c

techniques should be used for the stua of mathematics to make students se? reliant? * What instructional materials an facilities should be available and utilize in teaching mathematics to ma students self-reliant? * What assessment procedura should be adopted to make the study; mathematics self-reliant? * How would mathematics teachs be trained to enable them to acquire sG that will help them to teach for %

reliance? * In what ways can the study; mathematics aid the individual to be & employed? r"

To answer the first question, I ha.' to present the report of a research tha


conducted wlth secondary school children.

Purpose of the Study Specifically, the study was

designed to: . Determine students' opinion on

the confidence and competence they have to study mathematics on their own.

Ascertain whether there are differences in the opinions of male and female students concerning their confidence and competence in the study of mathematics.

Ascertain whether there are differences in the opinions of urban and rural school students concerning their confidence and competence in the study of mathemaltics

Identify the reasons for students' lack of confidence in mathematics.

Research Questions 1 What are students views

concerning th5ir confidence and competence in studying mathematics?

2. Why do students lack confidence to study mathematics?

Hypotheses Hol : There 1s , ,d significant difference in

the proportion of male and female students concerning their

confidence and competence in the study of mathematics, p < .05

Ho2: There is no sign~ficant difference in the proportion of urban and rural students concerning their confidence .ind competence in the study of mathematics, p.< .05

Method Design: The study was a descriptive survey aimed at finding out whether students have confidence, and are competent to study mathematics. Sample: Stratified random sampling technique was used to select 520 senior secondary school students from Nsukka education zone of Enugu State. The units of strat~iication were gender (male = 280, and female = 240), and school location (urban = 290, rural = 230). The use of senior secondary school students was based on the fact that the junlor secondary school students might not be able to respond to the questionnaire.

Instrument: The instrument was a questionnaire containing eleven items. The first two ~tems sought information on the gender and school location of the respondents, while the rest sought information on their confidence and competence in mathematics, and reasons for the lack of confidence in the study of mathemat~cs. Data Analysis: Simple frequency counts, and percentages were used to answer the research questions, while X* statistic was used to test the null hypotheses , at the .05 level of significance.

t


Results Table 1: Summary of subjects' responses on their confidence

Items Do you have confidence studying mathematics on your own7 - - - - - - - - -- -- -- Do you study mathemat~cs only when someb* -- -- IS there to gurde you? Do you enjoy studymg mathematics, even when you cannot solve given problems? D O yo; make extra efforts to study and to solve mathemat~cs problems even when you are trying and fa1ling7 --- Do you pers~st rn solvrng mathematrcs problems even when you do not have satisfact~on - andleasure doing that7 Are you competent in solvmg mathematrcs problems? -- Do you find it easy to relate the mathematics concepts you have learnt in school to every day problems? Does your study of mathematics at the primary school help you in studying the subject at the secondary - schools?

Yes

k

and competence in

Table 1 shows that 40% of all the respondents indicated that they have confidence1" studying mathematics on their own, while 60% indicated otherwise; 62% indicated that they study mathematics only when guided by someone, while 38% indrcated otherwise, 28% said that they enjoy studying mathematics, while 72% do not; and 49% said that they make extra efforts to study and to solve mathematics problems, while 51 O h do not.

Moreover, 34% of the ~espondents indrcated that they persist in solving rnathemat~cs problems, while 66% do not, 40% of the subjects are competent in solving mathemat~cs problems, whle 60% are not competent, i

17% find it easy to relate the mathematics concepts learnt in school to everyday problems, whle 83Y0 do not frnd that easy, and 33% Indicated that their study of mathematics at the1 prlrnary school helps them in their study of the subject at the secondary school, whrle 67% fell otherwise.


Tables 2: x2 table of the difference in the proport~on of male and female students on thl confidence and competence in mathematics, p < .05.

I - I - Male Female r--l- . . - - - - - - -

Yes No Yes No F O/O F % F O h X' Decision

-- -- -- 89 37 151 63 0.75 NS - --

180 64 222 93 18 7 70.9 S -- 122 158 56 2 1 9 - 219 91 31.4 S

72 79 28 56 23 184 77 48.1 S 135 48 145 52 44 18 196 82 20.4 - 167 60 1 1 1 3 40 42 1 8 198 82 m ~ 4

x2critical = 3.84 at 05 level of significance, Id f .

Table 2 shows that all the items had X' values exceeding the critical x2 value of 3.84, 2

the 05 level of significance, and ld f , except item 1, which had x2 value of 0.75.

Table 3: X' table of the difference in the proportion of urban and rural school students or their confidence and competence in mathematics.

I I Yes I NO I Yes I NO I I Urban

Table 3 shows that all the items had x2 values exceeding the critical X' value of 3.84, at the 05 level of s~gn~ficance and 1df.

Rural I I

!

', JOURNAL OF SCIENCE AND COMPUTER EDUCATION

Table 4: Summary of students' responses on reasons for lack of confidence to study mathematics (n = 310).

r - r - Reasons F 1 O/O 1 -- ---- - - - .- - ( 1 I Poor . . -. background - - in the primary SC~%JIS A -- 3 0 7 t 9 9 1

mathematics teachers

6. 7.

In table 4, items 1, 2, 3, 4, 8, and 10 had percentage responses exceeding 5O0/0, while

298 22 3 21 1 47

Lack of interest in mathematics examples/illustrations in textbooks not succeeding_

items 5, 6, 7, 9 had percentage responses less than 50%. -

96 72 68 15

Insufficient teaching of mathematics in school Lack of instructional materials

Decision Results of this study have revealed

that majority of the students (60%) lack the confidence to study mathematrcs; rnany do not enjoy studying mathematics (72%), and are not competent is solvlng mathematics problems (60%) Also, a large number of students are not able to [elate the mathematics concepts learned in school to everyday problems (83%), and the students feel that their study of niathemat~cs at the primary school IS not helping them to study mathematic at the secondary school (67%). These find~ngs could be related to the apparent poor performance of ' secondary school students In both internal and external examinations, as reported in literature (Agwagah, 1993).

However, results of the study shows that there were signrficant d~fferences in the opinions of male and female students (table 2), and that of

1 89 7 1 177

urban and rural school students (table 3), concerning their confidence am competence in mathematics. The malt students showed more confldence ano were more competent in solving mathematics problems, than therr femak counterparts. Simrlarly, the urban schoa students were more confident and more competent in the solution of mathematrcs problems than their rural schoa counterparts. These fmdings conforn neatly with previous findings (Obodo 1 990).

The probable reasons for student! lack of conf~dence in the study o mathematics include: poor background II the primary school (99%), mathematics I! difficult to understand (96%), porli teaching methods (72%), lack of qualifier mathematics teachers (68%), students lack of interest in mathematics (61 %) and fear or not succeeding Ir

mathematics (57%). These findings art

' I

9 16

3 5

6 1 23 57

t

JOURNAL OF SCIENCE AND COMPUTEF' .'"ICATION

consistent with those of Ojo (1986) and Adegboye (1991). Results of this study suggest that the present school system is not actually achieving the objectives of the National Policy on Education which states that mathematics in the primary school must prepare ' the child for successful training in the secondary school (F.R.N.,.> 1998). It is also not achieving the objective for which primary school was transformed into basic education, designed to equip young people to become competent and responsible participants in adult society (Ball, 1985). Mathematics curriculum for self-reliance.

The most pressing issue as far as the present situation in mathematics education is concerned, is that of deciding what should constitute mathematics programmes to be taught in schools at all levels of education, and how it should be taught so as to make the recipients of such education self-reliant. There is need to call for curriculum and instruction that engage and challenge students and prepare them for continued study and growth in mathematical skills and understanding.

As pointed out by Hendrickson (1983), what we know of how children learn has not been applied to the current mathematics curricula, with only a few exceptions. For instance, the theory of constructivism -has not been adequately applied in the development of the mathematics curriculum. According to constructivism, knowledge is constructed through the individual's material or mental actions (Marton and Neuman, 1990). In

constructivism, knowledge is a property of the individual. Hence, thinking , and learning opportunities should permeate the whole mathematics curriculum.

The current mathematics curricula consist of materials drawn largely from a culture the child only faintly comprehends. The curricula are not useful outside the classroom. Children are not able to use the mathematics skills learned in schools in village life. Thus, the interplay of the environment, of the abstract, and of the social is disregarded in mathematics education. This points up the issue of the inclusion . o f ehtnonmathematics in mathematics curricula as presented by D'Ambrosio (1 986).

Ethnomathematics holds that mathematics ideas are pan human and are developed within cultures (Ascher and Ascher, 1994). They stressed that mathematics ideas refer to those that involve number, logic, spatial configuration and the combination and organisation of these into systems or structures. Thus, mathematics ideas appear in various contexts, which are neither clearcut nor mutual exclusive from culture to culture, and within any culture. How and where these ideas fit in must be understood if they are to be properly appreciated.

Ethnomathematics relates the mathematics taught in school to the background culture and experiences of the learners. For instance, a child whose background cultural activities include farming should be able to related the mathematics concepts taught in the

?


classroom to his daily experiences and interactions with farming activities. This implies that there should be a horizontal transfer of the knowledge of mathematics concepts taught in the classroom to their farming practices. Similarly, there should be some ideas or knowledge based on his experiences of farming transferred to his mathematics classroom which will aid his understanding of mathematics concepts. Similarly, a child whose cultural activities include fishing should be able to learn mathematics concepts through the fishing activity. For instance, what mathematical concepts are involved in the fishing instrument (fishing line or fishing rod or fishing tackle or .net), the construction of the instrument, the position the fishing instrument will be cast in order to make a bigger catch, etc. illustrating further the concept of ethnomathematics, DIAmbrosio (1 986)' used the contexts of boat construction in an Amazon Indian community and house- bullding among Yawanwa Indians in the Brazilian Amazon. ~ccord ing to him,

Boat construction in an Amazon lndian community is done totally without formal schooling. The presence of children during the process of building assumes the transmission of the practice from one generation to another. In house-building among Yawanwa Indi?ns in the Brazili8n Amazon, from the early stages of preparing the wood, the presence of children is spontaneous. There is no doubt of the strong presence of mathematics in both examples.

Rhoder and French (1 999), calle for 'School-based' programmes in whic curriculum developers try to figure 04 what knowledge and skills are needed I( a particular job and then attempt to teadi these thmgs in school. This makes ta, clear and specific connections betweenb school and work, and between the mathematics knowledge and skill; learned in school and the applications made in the workplace. Students must see the study of mathematics as C something worth doing and leatning mus\ be seen as relevant. Hamilton and Hamilton (1 997), also specifled 'work- based' learning. According to them, work. based learning is a means of rncreas~n~! students' engagement in learning and ol 1

preparing young people for employment! It could occur from kindergarten throughi the university. Examples of work-based; learning include field tr~ps to workplaces The mathematics curriculum should\ identify the field trips and the! mathematics knowledge and skills l~nkedl with them, and these are to bet emphasized. This helps to link theory w~thi practice. I Mathematics curr~culum shouldl also include the use of everyday1 problems in which children become active1 participants in the creation of knowledge, rather than passive recipients of rules and' procedures. Thus, activities provided in

k the curriculum should suggest to childreni the relevance of the curriculum in the~ri lives after taking their place in socretyt (Mitchell and Miller, 1995: Ball, 1985). 1


relevance in terms of the potential for helping students, live out their future lives in neighbourhoods and communities yet to be developed. The curriculum should aim at developing students' awareness of the importance of mathematics to their future work, increasing their confidence and competence in doing mathematics and "ecouraging persistence in taking mathematics courses (Damerow et all 1 986).

Mathematics curriculum should be designed to related mathematics to other areas, such as Science, Technology, Economics, Humanities, ethical issues including personal ethics, etc. the integrated nature of mathematics with other areas, must be clearly reflected in the curriculum. Damerow et al suggested that students should be able to achieve mathematics 'literacy' through the use of mathematics in other subjects. Also, Steiner (1986) , viewed interdisciplinary work in mathematics education as important.

According to Garden (1985), the key concepts of mathematics from a curriculum point of view are those which are a wide and powerful application in the development of mathematical knowledge and understanding. But, it has been reported that many curricula programmes are found to consist of little more than complications of facts and 'hands-on experiences' that rarely provide occasions for students to use scientific and mathematics knowledge in a meaningful way (Anderson and Lee, 1997). When such is the case, students do have opportunities to learn with

understanding. Th~s provides one reason for the persistent pattern of students' under-achievement in mathematics and science.

A suitable mathema$ics curriculum assumes greater importance as societies in the world become more technological and sophisticated. In 1980, the National Council of Teachers of mathematics of the United States of America, recommended, among others, that problem s~ lv ing should become the major focus of school mathematics and that full advantage be taken of the power of calculators and computers at all grade levels (Travers, 1985). Have these been incorporated in the mathematics curriculum of the various levels of education in Nigeria? To what extent are calculators and computers provided in schools?

A manipulative - based mathematics curriculum, involving a mathematics laboratory which includes calculators and computers has also been suggested. This helps to facilitate the progression from concrete to abstract understanding of mathematics (Fraser et all 1986). However, a deep concern is that a large majority of our educational society and evaluation agencies still ignore the omnipotent existence of calculators. The use of calculators or similar electronic devices is not allowed in external examinations in Nigeria such as

' school Certificate examinations and Joint Admission and Matriculation Board (JAMB) examinations (JAMB, 2001). Teaching ApproacheslTechniques in Mathematics Education for Self-reliance.


In Nigeria schools, as elsewhere, students are still fed an instructional diet of meaningless contextless exercises and worksheets. Though those practices, as supported by researcher and by theory, virtually ensure failures, (Schmoker, 1997), they continue unbated. Even in our so-called good schools, we still fail to avail ourselves of the best we know about effective teaching.

A constructivist, active learning model, in which students are actively engaged in learning and in guiding their own instruction, has been favoured by brain-based educators, in this model, teaches teach for meaning and L,, . . . ,!andi;.ig. They create learning environments that are low in threat and high in challenge, providing children the opportunity to be actively engaged in immersed in complex experiences. According to Bruer (1999), if more teachers adopt the constructivist approach, teaching for understanding and if more teachers have the resources to do so, our schools would be better, learning environments. 0'Br;ien (1 999), also supported the activity-based approaches, derived from the constructivist philosophy and involving the real basics of classifying, it as someone else's construction (Hendrickson, 1983). Suggesting ways of teaching mathematics in . primary school, Hendrickson highlighted the need for mathematics-related activities and exploration of all materials available. According to him, with this approach, children become quite self-reliant and confident of their ability to think their way

through the mathematics challenges. They are willing to take risks and are not always dependent on the teacher.

The activity-based approaches relates to the concrete apparatus-based learning. However, although concrete apparatus-based learning experiences are' being provided for children, especially in our primary schools, teachers generally fail to draw their pupils' attention to the . mathematical implications of these practical activities. This introduces a missing link in children's minds between the activities they do Bnd the symbol- showing algorithms they are asked to use to arrive at the correct answer. Supporting the activity-based learning, Bay, Reys and Reys (1999), highlighted that in the learning of mathematics, students should be encouraged to explore, to guess, and even to make and correct errors so that they gain confidence in their ability to solve complex problems. Confidence is a requirement for self-reliance.

Teachers should therefore avoid the traditional teaching approach which is still the norm in our Nigerian schools. According to Battista (1 999), in traditional mathematics instruction, everyday is the same. The teacher shows students several examples of how to solve a certain type of problem, mathematics 4

lessons begin with the teacher telling the students a fact or giving them the steps in an algorithm. The teacher then works a textbook example and assigns students to work exercises from the textbook to help them remember the fact. In such traditional approaches, the teacher

i

JOURNAL OF SCIENCE AND COMPUTER EDUCATION t

1

emphasizes product forgetting the process. But emphasis on the teaching of mathematics should be on process rather than product (Hendrichson, 1983). Also, such 'lessons are devoid of experiences whereby students discover, invent or apply mathematics, to problems they find meaningful (Fuson, l992), which are necessary requirements for self-reliance.

Borko and Elliott (1999), advised that teachers should increase their pedagogical attention to problem solving, mathematical communication and connections to real-world situations. According to them, teachers should use very dynamic 'hands-on' style of teaching, which includes modeling problem solving approaches, demonstrating with manipulatives, and providing feedback on students' work.

Ball and Davies (1997), called for the use of 'Investigative approach' in the teaching of mathematics. According to them, investigation approach involves the practical investigations and problem solving investigations. The practical investigation should involve children in the design, construction and testing of a piece of equipment or apparatus. The teacher's role in developing investigative work is that of 'facilitator'. 'motivator' and 'instigator'. However, teachers may lack the teaching skills necessary for the successful adoption an investigation approach. Instructional materials and facilities for teaching mathematics for self-reliance.

We can hardly teach the principle of self-reliance with imported technology, hence the suggestion that we introduce

and make proper use of local materials within our own communities in the teaching of mathematics This raises the issue of indigeneous technology, which serves as the initial aids for learning and understanding the use and importance of mathematics.

Also, we l~ve today in the age of the electronic computer, and information technology, which has served to shape much of our thinking about how education can and should proceed. Hence, we are concerned with examining in some details, how technology relates to the teaching of mathematics, and we ask, how specifically can the power of technology improve mathematics education for self-reliance?

Mawer and Davidson (1999), asserted that technology adds the power of efficiency. It provides expanded access to information and a wider select~on of data, and computer workstations can engage one or more children in the classroom while the teacher works with others. According to Pollack (1986), the most readily apparent effect of technology on the teaching of mathemat~cs is that it helps to overcome the innumerable pedagogic difficulties experienced by the teacher, motivate students, and helps the teacher to do a better job. The microcomputer can be used to provide practice for the student with a new technique, to tutor the student at a place where the background is weak, to show new applications of the current subject- matter, to diagnose a persistent pattern of error, to try out special cases in a situation I in which the mathematics


pattern is not clear, or to manage a series of individualized tests. Other effects of technology' on the teaching of mathematics include; it makes certain topics possible to teach, for example 'data analysis; it makes subjects like combinatorics and graphs and logic; the overall priorities in school mathematics have changed because of the technology. For example, certain topics such as, estimation, and others mentioned above are more irr.,?ortant today than they used to be. Issues that one may raise are, have our mathematics teachers acquired the skills and competencies that will enable them teach mathematics with computer? In other words, do teachers have the confidence and are they competent to use cpmputer in teaching mathematics?

Assessment for self-reliance: Since ways are sought to provide

students with the needed mathematical competencies for daily living in an increasingly technological society, it will be imperative to take into account cultural factors not only in the teaching and learning of mathematics but in assessment activities as well.

Also, as suggested by Travers, Robitaille and Garden (1986), in any attempt to interpret achievement results of children .in mathematics, 'appropriateness' ratings and 'opportunity-to-learn' measures which provide important contextual information should be employed. The appropriateness ratings should indicate the degree of appropriateness of each

item to the curriculum, while the opportunity-to-learn measure provide data from teachers indicating whether their students had been taught the mathematics required to respond correctly to a given item Such ratings and measures are necessary because the inability for teachers to teach some mathematics content may account, in large part, for the relatively poor performance by students in the subject. The major purpose of assessment IS as an essential part of the teaching process that provides feedback so that future teaching can be effectively planned, Therefore, whatever is taught should be assessed. In assessment the process of . finding an answer should be focused on as well as the answer itself.

Moreover, assessment procedures should not neglect relevant student activities such as verbal description of simple but mathematically rich and interesting situations, construction of examples and counter examples, and ability to choose suitable methods for solving problems that are stated in an open formulation. Such assessment procedures provide students practice in problem solving strategies. Training of Mathematics Teachers for Acqulsltion of Skills on Teaching of Self- reliance:

To meet the challenge of computing and other information technology in mathematlcs education, the crucial change agent will be classroom teachers. Hence, mathemat~cs teachers should be trained to acquire the skllls necessary for the use of computers in

I


teaching mathematics. These skills include: rebooting a computer, using a mouse, formatting a computer diskette, saving an open file, using a database application, getting on the internet and using a browser, communicating with e- mail, logging on to a remote computer via telecommunications network, and drawing or editing pictures using a computer, etc. (Usman, 2001).

The training and education of teachers should provide them some guidance about how to help children identify the mathematical implications of the practical activities they carry out in class. lnservice teachers should also be exposed to various indigeneous technologies and how they can be used in the teaching of mathematics. An effective professional development of mathematics teachers is one that exposes the teacher to clinical methods which can help him probe the students' mind in order to determine at first the ground upon which to build and then to see how the learner negotiates his construction of , the new concept (Horscvics and Bergemrl, 1980). Ways in which the study of Mathematics can aid self-reliancelself-employment;

Self-reliancelself-employment can, and have been achieved through the following ways:

1. Production . of Mathematics Equipments, and Materials: The study of mathematics leads to

acquisition of manipulative skills, creative and constructive thinking. Through the acquisition of such skills, the intellect of

one can be developed in the product~on of the materials used in the teaching and learning of the subject. Varlous science and mathematics equipment centers have been established which produce essential materials and hence the setting up of mathematics laboratories for stock of materials used in teaching, to enhance the learning of mathematics in schools Examples of such efforts are: ~ i ~ ~ n a games and Dikeohamatics.

2. ConsultancylCo~ching Services: An individual who studies

mathematics can engage himself in consultancy services and tutorials or private lessons and still fend for himself Such private lessons can sometimes metamophose into a pre-primary, primary or secondary school. Some have gone up even to university level. However, some people go into this aspect of business not because they have the mterest and the zeal to engage in it, but because they have no choice, since the white - collar job is becoming difficult to come by. There is always a great difference between those who go into the business with zealous motive and those who engage in it by chance.

3. Production of Textual Materials: Eminent scholars write texts and

workbooks used in teachmg students. Many of them are also specialised in development of standardized tests

4. Decision making and Success in Private Enterprises:


With the knowledge of basic mathematics operations, many people have engaged themselves in private businesses to earn profits and hence their hvmg This gets them the rid of employing clerks and keeping record of their accounts. They could be well informed personally on hcw to carry out their busmess and plan well for their future.

5. Proficiency and Competency in the Study of Science and Technology: Mathematical ability determines

whether an individual can cope with the study of the sciences and technological courses. This has enabled students to read courses like prmting technology and electronics for self-employment. Without good knowledge of mathematics they cannot fit themselves into those fields of study or rather succeed, should they dabble into the courses accidentally or through foul means.

6. Designing and Interior Decoration Services: The study of mathematics leads to

the acquisition of the knowledge of various patterns and shapes which can be used for designing and interior decoration services.

THE WAY FORWARD 1. The mathematics curriculum at every level of the educational system should be reviewed to incorporate contents, teaching approaches, teaching aidslhints and evaluation procedures that would make for self-reliance.

2. Small groups of teachers can begin regular discussions of what they want students to able to accomplish and what they themselves have found to be most effective in helping students reach those goals. This would increase the~r effectiveness exponentially.

3. Government and professional associations should organize workshops for teachers on regular basis, for the acquisition of skills on teaching mathematics for self-rdliance acquisition of skills on teaching mathematics with computer, and for awareness on currenl and innovative teaching approaches and instructional materials for self-reliance. 4. Government should take the professional development of teachers more seriously. 5. Mathematics, educators administrators, textbook writers must all be alert to their responsibilities in gearing the mathematics education of childrer; towards self-reliance.

6 . There is a great need to creatt mathematics awareness among Nigeriar so as to help the inculcation of E mathematics culture, in Nigeria.

REFERENCES Adegboye, A. 0. (1991). Toward

an Assessment of the Standard c Mathematics Education in Nigeria: Kwai, State as a Case Study. ABACUS 21. (1 71-91.


Agwagah, U.N.V. (1 993). Instruction in Mathematics Reading as a Factor in Studerls' Achievement and Interest in Word Problem-solving. ~n~ubl ished F h D Thesis, U.N.N.

Anderson, C. W. & Lee, 0. (1997). Will Students Take Advantage of Opportunities for Meaningful Science Learning? KAPPAN. 78 (9), 720-724.

Ascher, M. & Ascher, R. (1994). Ethnomathematics. In Grattan-Guinness, I. (ed)., Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. 2

Ball, S. (1 985). Self-reliance: Policies. In Husen, T. & Postlethwaite, T. N. (eds). ' The International Encyclopedia of Education

Ball, G. C. & Davies, L. (1997). Using and Applying Mathematics at KS3 of the National Curriculum. Education Today. 48 (4)) 11 -1 9.

Ball, G. C. & Goldman, S. (1997). Improving Education's Productivity. RAPPAN. 79 (3), 228-232.

Battista, M. T. (1999). The Mathemslkal Mic-education of America's Youth. Ignoring Research and Scientific Study in Education. KAPPAN. 80 (6), 425-433.

Bay, J. M.; B. J.; & Reys, R. E. (1999). The Top 10 Elements that must be in place to , Implement Staridards- based Mathematics Curricula. KAPPAN. 80 (7), 503-506.

Bell, A. W.; Costello, J. & Kuchemann, D. E. (1993). Research on Learning and Teaching, Windsor: NFER-Neslon.

Borko, H. & Elhott, R. (1999). Hands-on Pedagogy Versus Hands-off Accountability: Tensions Between Competing Commitments for Exemplary M4th Teachers in Kentucky. KAPPAN. 80(5), 394-400.

Burer, J. T. (1999). In Search of Brain-based Education KAPPAN. 80 (9), 649-657.

D' Ambrosio, U. (1986). Soc~o- Cultural bases for Mathematics Educator. In Marjorie Carss (ed.). Proceedings of the Fifth-International Congress on Mathematical ~ducatior?. Boston: Birkhauser.

Damerow, P.; Bienveido Nsbres; Mervyn Dunkley; & Bevan Werry (1986). Theme Group 1: Mathematics for all. In Marjor~e Carss (ed). Proceedings of the Fifth lnternational Congress 012

Mathematical Education. Boston: Birkhauser.

Eyo, A. E. (1991). Mathematics and National Development. Paper presented at the 29Ih Annual Conference of the Mathematical Association of Nigrsrla LMAN), held at University of Benin, ?" -6'h Septcmber.

Ezike, R. 0 (1989). Teaching Mathematics for Transfer to Science, Subjects In the Secondary Schools. ABACUS. 19 ( I ) , 64-70.

Federql Repubhc of Nigeria (FRN) (1998). National Policy on Education. Lagos: NERDS Press.

Fraser, R.: Hartivig Meissner; Tony Ralston: David Roseveare & Jury Mohyla (1986). Theme Group 3: The Role of Technology. In Marjorie Carss (ed.). Proceedings of the Fifth International

I


Congress on Mathematical Education. Boston' Birkhaumer.

us on, K. C: (1992). Elementary Mathematics (6'" ed.), New York: Mac. Solving in high school Chemistry. Journal of Research in Science Teaching. 20 (2)) 163-1 77.

Postlethwaite, T. N. (eds.) International Encyclopedia of Education. Oxford: Pergamon Press.

Haberman, M. (1 997). Unemployment Training: The Ideology of Nonwork Learned in Urban Schools. KAPPAN. 78 (7), 499-503.

Hamlton, S. F.; & Hamilton, M. A. (1 997). When is Learning Work-based? KAPPAN. 78 (9), 677-681.

Henrickson, A. D. (1983). A Psychologically Sound Primary School Mathematics Curriculum. Arithmetic Teacher. 30(5), 42 - 47.

t-lerscovics, N. & Bergeron, J. C. (1980). The Training of Teachers in the Use of Models of Understanding and Learning Models. in Karplus, R & Hall, L (ed.). Proceedings of the Fourth International Conference for the Psychology of Mathematics Education. California: Berkeley.

I.iowson, G. & Malone, J. (1986). Theme" Group 5: Curriculum Development. In Marjorie Carss (ed.). Proceedings of the Fifth lnternational

' Congress on Mathematics Education. Boston: Birkhauser.

Ikoku, E. U. (1980). Self - Reliance Africa's Survival. Enugu: Fourth Dimension Pub. Coy Ltd.

Joint Admissions and Matriculation Board (JAMB) (2001 ): Guidelines for the

Supervisors and lnvigilators of the University Matriculation Examination. Abuja.

Keitel, C.; Schubring, G & Stowasser, R. (1 985). Mathemat~cs Educatiori, History of. In Torsten Husen & T. Neville Postlethwaite (eds). The International Encyclopedia of Education. Oxford: Pergamon Press.

Lindquist, M. M. (1989). It's Time to Change. In Paul R. Tafton & Albert P. Shulte (eds.). New Directions for Elementary School Mathematics Reston: National Council ofi Teachers of Mathematics.

Marton, F. & Newman, 0. (1990). Constructivism, Phenomenology and the Origm of Arithmetic Skills. In Leslie P. Steffe & Terry Woods (eds). Transfo~ rning Children's Mathematics Education. Hillsdale: Lawrence Erlbaum Ass. Pub.

Mawer, M. M. & Davison, G. (1 999). Technology, Children and the Power of the Heart. KAPPAN. 80 (6), 458-460

Mclcod, D. 0. (1994). Research on Effect in Mathematics Education. In D. A. Grows (ed). Handbook on Research on Mathematics Teaching and Learning-. New York: Macmlllan.

M~tchell, C. E. & Miller, L. D. (1 995). Tech. Prep. Academ~cs: Using Real Life Connections to Develop Scientif~c and Mathematics Literacy. School Science and Mathematics . 95 (8), 41 7-422.

Obioma, G. 0 . (1988). Some Foundations of Mathematics Education. Monograoh Series. Faculty of Education, U.N.N.

I


Obodo, G. 0. (1990). The Differential Effects of Three Teaching Models on Performance of Junior Secondary School Students in some Algebraic Concepts. Unpublished Ph. D. Thesis, U.N.N. '

OIBrien, T.C.O. (1 999). Parrot Math. KAPPAN. 80 (6), 434-438.

Odili, G. A. (1990). Teaching Mathematics in the Secondary School. Anambra: Anachuna Educational Books.

Ogomaka, P.M.C, (1 996). Instructional Materials for Effective Mathematics Education at the Secondary School level. In Press.

Ojo, J. 0. (1986). Improving Matl ,"matics Teaching in our Schools. ABACUS. 20 ( I ) , 47-56.

Osibodu, B. M. (1982), Teaching Matherimtics for Science and Technology in Nigeria. Mathematics in Science and Technology. Proceedings of MAN Conference in August, 1981.

Pellery, M. (1 985). Mathematics (eds). The lnternational Encyclopedia of Education. Oxford: Pergamon Press.

Ollak, Id. 0. (1 986). The Effects of Technology on the Mathematics Curriculum. In Marjorie Carss (ed.). Proceedings of the Fifth lnternational Congress on Mathematical Education. Boston: Birkhauser.

Rhoder, C. & French, J. N. (1999). School-to-work: Making Specific Connections. KAPPAN. 80(7), 534-542.

Simpson, J. A. & Weiner, E. S. C. (1 989). The Oxford English Dictionary (2nd ed) vol. XIV. Oxford: Clarendor-I Press.

Steiner, Hans-Georg (1 986). Topic Areas: Theory of Mathematics Education (TME). In Marjorie Carss (ed). Proceedings of the Fifth lnternational Congress on Mathematical Education. Boston: Birkhauser. t

Taiwo, C. 0. (1 980). The Nigerian Education System, Past, Present, and Future. Thomas Nelson (Nig.) Ltd.

Travers, K. (1 985). Mathematics: Secondary School Programs. In Torsten Husen & T. Neville Postlthwaite (eds.). The' lnternational Encycloped~a of Education. Oxford: Pergamon Press.

Travers, K. J.; Robitaille, D. F. 1 & Garden, R. (1986). Topic Area: Evaluation, Examinations and Assessment. In Marjorie Carss (ed). Proceedings of the Fifth lnternational Congress on Mathematical Education. Boston: Birkhauser. University of Nigeria, Nsukka.

university of nigeria · mathematics education it is not easy to give one definition of the term...

Documents