New mathematics for Ethiopian elementary schools

New mathematics for Ethiopian elementary schoolsAuthor(s): WILBUR H. DUTTONSource: The Arithmetic Teacher, Vol. 15, No. 2 (FEBRUARY 1968), pp. 115-125Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41187347 .

Accessed: 19/06/2014 11:15

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 62.122.76.48 on Thu, 19 Jun 2014 11:15:44 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=nctm

http://www.jstor.org/stable/41187347?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


New mathematics for Ethiopian elementary schools WILBUR H. DUTTON

University of California, Los Angeles, California

Mr. Dutton worked under a Fulbright-Hays Scholarship and was professor of education at Haile Selassie I University in Addis Ababa, Ethiopia, He taught courses to directors and supervisors from fourteen provinces scattered throughout Ethiopia. He returned to the University of Calif onia last fall.

JYLodern education in Ethiopia is very young, a phenomenon of this century. In less than sixty years a primary school system embracing 1,600 schools, 380,000 pupils, and over 9,000 teachers has been established.

Important as this achievement is, only a small proportion of school-age children are able to attend school. For example, about 323,000 pupils are enrolled in Grades 1-4 in all types of schools - government, private, mission, and church schools. Esti- mates show that there are at least 2,558,- 500 children in this age group. Thus about 12.6 percent of the pupils in this age group are going to school.1

Ethiopia, as well as most of Africa, is continuing its planning for the development of education. The recommendations of the ECA-UNESCO-sponsored Confer- ence of African States held in Addis Ababa in May 1961 provided guidelines for short- and long-term plans directed toward the "preparation of personnel to move on to universal primary education of high quality by 1980, while forging ahead socially and economically." 2

One of the most important aspects of this planning is the development of a mod-

1 Statistical data secured from School Census for Ethiopia, 1965-66 (1958 Ethiopian Calendar).

2 EGA-UNESCO Conference report. Ata Million Neq- niq acted as chairman of the conference.

February 1968

ern curriculum for elementary school pupils. To date very little progress has been made in general curriculum improvement. Curriculum changes which have been made, with the exception of the introduction of Amharic as a medium of instruction for elementary school pupils, have not been accompanied by serious study or research work. The consideration of one basic area of the elementary school curriculum, mathematics, is timely and important to the total program. It is timely because of current developments in mathematics and the introduction of new programs into African states, particularly Uganda. It is important because of the need for modern mathematics in a developing nation and because of the model which can be developed for curriculum improvement in other content fields.

Purpose of this study

The writer accepted a Fulbright-Hays Scholarship, during the academic year 1966/67, to teach a methods course in elementary school mathematics for directors and supervisors enrolled in a one- year diploma program at Haile Selassie I University in Addis Ababa. Other duties included preparing a course of study for teaching arithmetic and conducting a study of elementary school mathematics in Ethi- opia.

115



In this article data are presented on three of Ethiopia's major problems in curriculum improvement: (1) foundations for curriculum improvement, including cultural factors and success of their present program; (2) content for the mathematics curriculum; and (3) instructional practices in the teaching of mathematics. Each of these problems will be discussed.

Foundations for curriculum development

The writer made a study of the following: the reports of pupil achievement in arithmetic; preschool experiences of young children; seventh-grade pupils' understanding of basic arithmetical concepts; teachers' understanding of basic concepts; and goals for the teaching of arithmetic in Ethiopia.

Pupil Achievement in Arithmetic Evidence collected from the School Cen-

sus for Ethiopia showed that children are having much difficulty with arithmetic. Re- sults of the Ethiopian School Leaving Cer- tificate Examination for 1961 showed that 52 percent of the elementary school pupils failed the Math A examination and 73 percent of the older students failed the Math B section.3

Achievement is also influenced by the quality of instruction, the attendance of children, and the length of time children remain in school. Children in rural areas have to travel several kilometers to school. There is much absence because of bad weather conditions during winter months and children's staying out of school to do farm labor. Serious problems of wastage and student dropout exist. In Grades 2-8 in government and community schools 46 percent drop out during the first year, 60 percent during the second year, 70 percent by the end of three years, and 85 percent by the end of six years.4

3 Ministry of Education and Fine Arts, School Census for Ethiopia, 1961-62 (Addis Ababa: Bureau of Educa- tion Research, 1962), p. 29.

4 Ibid. (1961), p. 21.

116

Preschool Experiences of Children Two preschool factors are extremely im-

portant: (1) the basic population pattern of Ethiopia, which determines where people live and the kinds of experiences children have with arithmetic, and (2) the inequality of educational opportunity.

Population pattern. - Ethiopia's population of over 22 million lives in an area of 1,221,900 square kilometers - an average population density of 18 persons per square kilometer.5 Of the 22 million people, 21,065,000 live in rural areas. Thus over 93 percent of the total population live in rural areas, and less than 7 percent live in urban centers.

Inequality of educational opportunity. - Children in rural areas have experiences counting sheep or cows, bartering or buy- ing at a local market, measuring grain with several types of baskets (dar ota, saffi, karawa, kuna, segunda), measuring poles for their houses (tukuls), and playing a variety of games including "gebeta" (played with small rocks placed in a series of holes) Little if any teaching of arithmetic is provided by parents, the illiteracy rate being about 93 percent. With approximately 7 percent literacy in rural areas, estimates are that fewer than 1 percent of the women are literate. They tell time by the use of the sun - hours after sunrise and hours after sunset. There is a sequency of events important to daily life such as getting up, eating, attending church, and participating in a variety of festivals. There are no schools for the preschool group.

In the urban areas (Addis Ababa particularly), children have many opportun- ities to use money in purchasing things at the mercato or at local stores. There are private kindergartens for children of upper- class families. Parents and siblings coach preschool children in reading and arithmetic. Some attend church schools for

5 Statistical Abstract (Ethiopian Government, 1965), Table A, p. 23.

The Arithmetic Teacher



one or two years. National surveys suggest that perhaps 50 percent of the men and over 1 0 percent of the women in urban areas are literate.

Differences in preschool experiences of children found in rural and urban areas influenced test results of first-grade children. The writer constructed a test to measure pupil understanding of the following: rote counting, identification and reproduction, crude comparisons, exact comparison, number facts, reading and writing numerals, identifying geometric shapes, identifying common Ethiopian coins, and telling time. However, in using the test the writer was unable to find six- or seven-year-old children in the urban schools. The average age of first-grade children in Addis Ababa was 9.8. (In one sampling reported in the School Census for Ethiopia, of 1,095 first- grade children in Addis Ababa the median age was 9.8. There were 519 pupils between the ages of 10-15.)

A random sampling of fifty children from twelve first-grade classes in Addis Ababa showed that they could perform at about 95 percent correct on all items in this test with the exception of telling time, identifying geometric shapes, and understanding borrowing, regrouping, and place value. These children (ages eight and nine) could identify a clock but could not tell time. They could do simple sub- traction and addition examples but could not tell what was regrouped or carried. They did not understand place value in any of the examples used.

Children in rural areas were quite different in their performance on this preschool test. The writer was able to secure a sampling of twenty-five six-year-old children from three rural schools. (The range of ages of children enrolled was from six to sixteen.) These children were re- tarded in reading and writing numerals, understanding place value, recognizing geometric shapes, telling time, and knowl- edge of the value of Ethiopian coins. Their instruction, like that of the urban sampling, had been based upon an abundance of

February 1968

oral work, memorization, drill, and routine use of examples taken from textbooks.

Seventh-Grade Pupils' Understand- ing of Basic Arithmetical Concepts

The writer tested a sampling of seventh- grade pupils to discover pupils' understanding of basic arithmetical concepts learned after completing six years of elementary school. Due to wastage and dropout factors mentioned earlier, these children represented a selected group.

There were seventy children in this random sampling. They came from seventeen sections (820 pupils) of seventh-grade pupils enrolled in the two largest government schools in Addis Ababa. An equal number of boys and girls was selected. Chil- dren enrolled in these schools came from many parts of the city and represented the total population. They had received instruction in a variety of elementary schools scattered throughout the city. Their teachers were typical of those employed in most elementary schools throughout Ethiopia.

The test was composed of 41 multiple- choice items designed to measure pupils' understanding of basic arithmetical and mathematical concepts. Little if any emphasis was placed upon computation. The test items were selected from a longer test, prepared by the writer, with an established reliability of .89. The validity of the instrument was established by studying the sixth-grade general examination prepared by the Ministry of Education to see if test items were typical of topics covered in Ethiopian schools. The test was then criti- cized by two Ethiopian professors who teach mathematics and who are familiar with instructional practices in Ethiopia.

The test was written in English and Amharic. Two preliminary trials of the test were made (sixth- and seventh-grade classes at Haile Selassie I University Lab- oratory School).

Four directors enrolled in a diploma course at the University were trained by the writer to administer the examinations. All pupils tested could speak and write

117



Amharic and were tested in this language. None of the group chose to use the En- glish form of the test.

Due to space limitations, only the main conclusions will be reported. They are as follows:

1. Neither pupils nor teachers had recognized the importance of the meaningful learning of basic concepts in arithmetic and mathematics.

2. The most crucial finding was that pupils did not understand the basic structure of our number system. There were 95 percent of the pupils who did not know the base of our number system, meanings of zero, or value of partial products in multiplication.

3. The relationships between operations with whole numbers, fractions, and decimal fractions were not recognized or under- stood by pupils.

4. The importance of measurement, as an aspect of modern living and in relation to industrial development, had not been stressed in Ethiopian schools.

5. The effects of six years of instruction based upon enforced memorization of rules and procedures were quite evident in pupil responses and in their lack of flexibility in working with problems.

Teachers' Understanding of Basic Arithmetical Concepts

The same test used for seventh-grade pupils was administered to 139 directors, supervisors, and degree candidates at HSIU during the fall semester of 1966/67. This sampling included 100 directors who came from the fourteen provinces of Ethiopia and had been selected on the basis of the number of elementary schools in each province. Most students were twelth-grade graduates and would receive the one-year diploma in June 1967. There were no women elementary school teachers enrolled at the university. Very few women, less than 2 percent, teach in elementary schools.

There were twenty-one test items which

118

indicated students' failure to understand basic arithmetical concepts. Shown by percent incorrect, the range was from a low of 29 percent (knowing the value of a factor in multiplication) to a high of 86 percent (knowing place value and base ten). While all twenty-one items were important, four large areas of weakness predominated: ( 1 ) place value and base of decimal num- eration; (2) fundamental processes with whole numbers; (3) common fractions and decimal fractions; (4) measurement, especially telling time with a watch and using European and airline standards.

The findings were not surprising. Ethi- opian teachers had not been taught to understand the basic concepts and principles involved in arithmetic. As pupils they learned their arithmetic lessons through memorization and drill processes. .They were products of Ethiopian schools. Their performance was almost identical with that of the seventh-grade pupils. Years of teaching and perhaps one brief exposure to the teaching of arithmetic enabled them to make slightly better scores than the seventh graders.

Based upon one year's work with these students, the writer has found that without exception the system of education used in Ethiopia has produced a generation of pupils who do not know how to solve problems or how to do creative thinking. Memorization, use of drill, harsh discipline, and respect for authority have conditioned them so that they need to be told what to do, what to memorize, and what to think!

Goals for Mathematics Program The goals for elementary education for

Ethiopia have been set forth in a recent publication of the Ministry of Education and Fine Arts.6 While the Handbook includes such goals as understanding and applying arithmetical concepts and solving problems of everyday life, teachers are not using these goals to guide their instructional

0 Handbook for Elementary Schools (Addis Ababa: Department of Elementary Education, 1964).




practices. Courses of study and textbooks, when available, do not embrace these goals. Topics included in modern mathematical programs have not been considered. Clearly defined goals for modern mathematics for Ethiopia must be prepared. These goals must take into consideration the needs of children and the society in which they live. Emphasis needs to be placed upon the learning of basic mathematical concepts, understandings, skills, and attitudes in a sequential pattern appropriate for children and efficient for the instructional program.7

Mathematical content for Ethiopian elementary schools

Two aspects of mathematical content will be discussed: (1) the content pres- ently used in textbooks and (2) the content which is needed by this developing nation. Both of these factors must be considered in relation to the needs of Ethiopia - basically a rural population (93 percent) using many different languages. (Estimates vary on the number of languages. There are between fifty and eighty, depending on the variations of dialects used. )

Mathematical Content Used in Ethiopia

One basic textbook and a supplementary textbook determine the mathematical content for Ethiopia's elementary schools. The "Highway Series," published in England, has been rewritten in Amharic for use in elementary schools. The series stresses computation without understanding; drill; and memorization. The sequencing of topics is very inadequate - moving from relatively simple examples to very difficult examples without careful attention to pupil preparation or understanding.

Ethiopia uses the metric system for all measurement and business transactions.

7 National Council of Teachers of Mathematics, Eval- uation in Mathematics, Twenty-sixth Yearbook (Wash- ington, D.C.: The Council, 1961).

February 1968

The monetary system is based on the Ethiopian dollar of 100 centimes, broken down into 25-, 10-, 5-, and 1-cent coins. Yet this textbook devotes many pages to English measurement and monetary system.

Word problems are poorly done and not meaningful to Ethiopian children. For example, one problem for first grade de- scribes a "lorry" (British for truck) carry- ing 18 kilo (39.6 lbs.) and asks children to add or subtract from this amount. Even a child from the remotest area would know that a lorry would carry more than 40 pounds - these trucks haul large 100-kilo- gram sacks weighing about 220 pounds each. Practically all word problems are drill exercises rather than practical problems requiring thinking or problem solving. Textbooks are organized so that exact examples are provided in order that pupils can routinely work pages of drill material.

There are great shortages of arithmetic textbooks in all elementary schools. Often there is only one textbook for each primary-grade teacher. Because of these shortages there is much oral work, writing of exercises on the chalkboard, and memorization. The content is further restricted by these procedures to the examples that will probably be included in the School Leaving Examination.

Need for New Mathematics The mathematics needed in Ethiopia's

elementary schools must be part of the total education program described by Dr. Aklilu Habte, Chairman of Research Com- mittee, HSIU:

We need to think in terms of the majority of the people, the people that live in the country- side, the people that will perhaps continue to live there for several decades to come, so far in harmony with or dominated by nature. Edu- cation must now add a different dimension, the dimension of controlling nature. . . . Expansion of primary education should be geared in objectives, content, and other supporting services for rural development. . . . Primary education will thus be conceived not primarily as a "gate- way to urban life" nor as a preparation for

119



second-level education. Primary education for years to come will be the only formal education thousands of children will be exposed to.8

His proposal is that primary community education be expanded to four years and a plan adopted for controlled expansion of upper-primary, second-level and third- level education.

Another aspect of Ethiopia's rural population which is worth noting in determining the type of mathematical content needed is the age structure. Ethiopia's population is very young, approximately 45 percent being under fifteen years of age and 42 percent between fifteen and forty-four years.9

The objectives established for mathematics education in Ethiopian elementary schools should determine the content provided in textbooks. This content needs to be enriched and extended by instructional practices. The writer will enumerate the objectives which could be used and will expand upon one of these.

Elementary school pupils making progress toward learning arithmetic and mathematics appropriate for their needs and the needs of Ethiopia should: (1) know the importance of mathematics to Ethiopia's development; (2) understand basic processes, facts, skills, concepts; (3) understand the structure of our number system; (4) be able to compute with understanding, accuracy, and efficiency; (5) use mathematics in problem solving as an aid to creative thinking; and (6) develop language necessary for reading and using mathematics.

While all six objectives are needed, the first has great importance for Ethiopia, now! Mathematics required for Ethiopia's development will include: stressing the use of Ethiopian currency to replace bartering in local markets; using metric mea-

8 Aklilu Habte, Educational Reform in Ethiopia: The Challenge of the Century (mimeographed interdis- ciplinary seminar; Addis Ababa: Department of Educa- tion, 1967), p. 15.

»Reported from the National Sample Surveys' Cen- tral Statistical Office in Addis Ababa.

120

sûrement and adequate instruments for measurement in agriculture and industry; using the metric system in weight and measure in local markets; and discovering the need for accuracy in telling time and recording data for modern transportation and communication.

Mathematical topics to include in the program could be: whole numbers, number systems, operations with whole numbers, rational numbers, number sentences, measurement, simple algebra, geometry, and simple graphs. Number sentences, it seems to this writer, will be much more practical than set concepts as a means of developing language, aiding thinking, and providing for the discovery of mathematical principles. Concepts of set can be intro- duced in the junior-secondary program. Both teachers and pupils would have extreme difficulties with the language of sets.

The grade placement of mathematical content is an extremely difficult problem. Schools in Europe and the United States have not solved this problem, and they have little to offer Africa. In Ethiopia, schools must contend with cultural factors such as these: scattered population, making it difficult to establish schools and in- fluencing the age when children can travel to school; age ranges of five or six years for each grade; and attendance problems due to rugged physical terrain, weather conditions, or seasonal labor requirements. Thus the sequential arrangement of content (from simple to complex) must be worked out. Instructional practices appropriate for this type of organization must also be planned for.

Improving instructional practices Extensive treatment of this topic can

not be given in this article. Only the identification of major problems and a few suggestions for improvement will be made. Five important factors will be considered: (1) instructional materials; (2) basic principles for instruction; (3) in-service education; (4) teacher education; and (5) evaluation.




Instructional Materials

There is an extreme shortage of textbooks, paper, and instructional supplies in all Ethiopian schools. These shortages are caused by insufficient funds to finance schools, undeveloped use of government printing presses, and inadequate distribu- tion systems. Textbooks now being used have inappropriate content, inadequate sequencing of mathematical concepts, and no provision for individual differences.

Textbooks are distributed to school directors and principals and a strict accounting made. If books are lost or stolen, these officials must pay for them. Because of this system, many textbooks remain in locked rooms in elementary school build- ings. Class size is greatest in primary grades - often ninety or more in Grade 1 and seventy or more in Grades 2 and 3. Due to failure, wastage, and dropouts, class size may decrease to fifty or sixty in Grades 5 and 6. Overcrowding, due to size of classrooms and inadequate seating, is common.

Children enrolled in Grades 1 through 6 in government, private, mission, and church schools account for about 1 1 .4 percent of children in the age group eight through thirteen. This means that for every child who now gets an educational opportunity, there are nine others who are denied this privilege! These data provide some indication of the magnitude of the task of securing and distributing educational materials for future expansion, when at present shortages are extreme.

The solution of the problem of providing good instructional materials will require a multiple approach. The government printing press is capable of mass produc- tion of books and workbooks, but the equipment is not being used. Low-cost materials must be provided so that directors will not be faced with present accounting procedures and so that children can pay for lost materials. Increasingly, the local communities must pay for educational materials used in their schools. Government

February 1968

support will always be minimal. Teachers' courses of study and textbooks must contain detailed plans, sequential organization of content, follow-up lessons, assignments, provision for use of aids, and evaluation instruments. Then when textbooks are not available for children, the teacher will have one good source to guide instruction. Due to paper shortages and the difficulties involved in having children carry books or assignment sheets when they travel several kilometers to school (often in heavy rain), consideration should be given to the preparation of workbooks with tear- out pages that could be used at school.

Basic Learning Theories Learning theories now used to guide

teaching in Ethiopian schools are anti- quated and do not reflect modern research findings. Learning is viewed as a conditioning process based upon memorization and drill. These views are perpetuated by teachers who come from traditionally oriented backgrounds which emphasize subject matter and the School Leaving Examination. The influence of European education, particularly that of England and India with its own interpretation of British education, is great. Harsh punishment re- tards learning and inhibits thinking.

Modern learning theory applied to mathematics stresses the importance of the learner's background and previous educational experiences; his goals for learning and motivation; the building of relationships and continuity of learning; his ma- turity and intellectual capacity to learn; and the importance of understanding the number system and its operation. During the next decade emphasis must be placed upon modern learning theories and particularly upon helping children to think, to understand, and to discover basic mathematical concepts.

In-Service Education In-service education enables continuous

progress to be made in curriculum improvement. It is relatively easy to change

121



a curriculum or to obtain new courses of study or textbooks. However, the spirit of a school and the teaching methods used are determined by the preparation teachers have, the extent to which they are involved in changing the curriculum, and the desire of teachers to improve their teaching procedures.

Three important steps need to be taken in Ethiopia to improve the instruction of the regular staff: (1) Prepare courses of study and textbooks carefully so that new content and instructional procedures are meaningful to the teacher and to pupils. (2) Establish the fact that in-service education is a required part of the teaching profession. (3) Plan a variety of in-service workshops based upon the use of new curriculum materials and schedule them throughout the year.

Supervision in Ethiopian elementary schools has been patterned after practices used by Great Britain - an inspection and authoritative procedure. During the last three years, the University has worked co- operatively with the Ministry of Education to improve the educational preparation of school directors and supervisors from the fourteen provinces. Each year about 120 of these men are given a one-year diploma course. After two years of service about 20 percent of them will return to complete their baccalaureate degree. The education of these men is highly essential so that they can conduct workshops in their communities.

Because school administrators have not been educated to help their staff and because most of Ethiopia's schools are in remote rural areas, mobile units and a special staff will have to be used. Since teachers are paid on a twelve-month con- tract, this will enable in-service education to be increased during summer months. Provision for regular university credit must be achieved so that upgrading of teachers will take place. The development of democratic ways of working together will take time, guidance, and much patience. Years of conditioning and the use of autocratic

122

methods have hindered creative thinking and constructive problem solving.

Teacher Education A realistic approach must be taken when

considering teacher preparation for Ethi- opian elementary schools. The recommen- dation of the Board of Education Study Committee is that 10 percent of the primary school staff should receive secondary schooling and three years of general and professional preparation; 45 percent should receive primary schooling followed by four years of professional training; and 45 percent should receive primary schooling followed by two years of professional education.10 Until this plan can be financed and carried out, teachers will have to be re- cruited from the eighth-grade graduating classes.

The selecting and educating of teachers for rural community schools along the lines suggested (four years of primary education and selected education thereafter) constitutes a difficult, crucial problem. At present elementary school teachers and directors want to work in the urban areas. Teachers and directors probably should be educated in a rural setting and expected to remain there.

To supply teachers for this program, eighth-grade graduates will have to be used - including women. Social customs now prohibit women from leaving their local communities to work. Illiteracy rates for women are high. But teacher shortages in primary grades will not be satisfactorily met until this important resource is used.11 Dr. Habte suggests that one or two years of professional preparation be provided for these eighth-grade graduates. This plan will take time and money. For the next decade or more, in-service education for these teachers will have to suffice. If pri-

10 Ethiopian Board of Education Study Committee, Development of Education in Ethiopia (Addis Ababa: Ministry of Education, 1961), p. 2.

11 A study of manpower resources must differentiate by sex as well as by region. See Eli Ginzberg and H. H. Smith, A Manpower Strategy for Ethiopia (Ad- dis Ababa, July 1966).




mary education were made available to all children in Ethiopia, 2,700 to 3,800 new teachers would be needed each year, without considering teacher mortality or wastage.12 Even with monthly salaries of Eth. $125.00 ($50.00 in U.S. currency), the cost would create serious financial problems.

At present Ethiopia does not have enough teacher-education schools. There are now three small schools, called "teacher training institutes," at Harrar, Asmara, and Addis Ababa, that enroll tenth-grade graduates for a two-year course. The total graduating group is about a thousand students. A plan for increasing the number of teacher training institutes and improving the quality of professional preparation needs to be made. Dr. Habte suggests that there should be one teacher training insti- tute in each province to prepare teachers for the rural community schools.

Along with an expanded program of teacher preparation, there must be continued upgrading .of directors, supervisors, and headmasters. Very little will be ac- complished in improving instructional practices or in the securing and retaining of teachers until the administrative staff can help and encourage the new teachers.

Evaluation Evaluation as an educational concept

and as an important aspect of curriculum improvement is just emerging in Ethiopia. The contributions which evaluation can make need to be stressed in four areas: ( 1 ) evaluation as an integral part of teaching and learning, involving pupils in the setting of purposes; (2) evaluation of the total personality of children; (3) evaluation which includes computational skills and understanding of basic mathematical concepts in School Leaving Examinations; and (4) evaluation as an important aspect of all planning (instruction and curriculum) to discover valid progress and to redirect educational work.

12 Habte, op. cit., p. 19.

February 1968

The implementation of these four aspects of evaluation should be started immedi- ately. Valid objectives for the total mathematics program must be established. When new teachers' guidebooks are prepared, evaluation procedures must be included and carefully detailed. As textbooks are written for Ethiopia, evaluation must be made essential to each lesson and to pupils' appropriate use of these books. Evaluation must be seen as an important part of the democratic process of working with teachers and administrators-*-providing the opportunity for constructive thinking and constructive criticism.

Conclusions

In this article the writer has dealt with the development of a new mathematics program for Ethiopian elementary schools. Three major problems have been discussed: (1) foundation for curriculum work, (2) new content needed, and (3) instructional practices. Based upon his research and study in Ethiopia, the following statements seem justified:

1. The evidence of failure in arithmetic shown by results of pupil achievement on Elementary School Leaving Examinations shows the inadequacy of instruction.

2. The rich cultural heritage of Ethiopia and the meaningful experiences children have with mathematics before coming to school are not utilized by teachers or curriculum workers.

3. Pupils do not understand those basic arithmetical concepts needed for effective learning or for successful work in advanced mathematics.

4. Teachers, likewise, do not understand basic arithmetic concepts and are not prepared to make instruction meaningful to children.

5. Instructional practices are based upon conditioning, memorization, drill, and harsh discipline. The school environment hinders rather than helps pupil achievement and development. The effect of this

123



type of instruction is most crucial in the areas of problem solving, creative thinking, and self-directed learning.

6. The two most crucial improvements needed in mathematics instruction are: (1) teaching so that children understand each basic mathematics concept and (2) improving instruction so that children are not afraid of being punished and will begin to think and use their minds to discover mathematical principles.13

7. Consideration must be given to those aspects of the new mathematics which are most crucial for Ethiopia. This means preparing textbooks suitable for children in rural areas. Some topics must be stressed and others delayed until children are selected for Junior-Secondary education. Consideration must be given to language development and concept development.

8. A teacher's guidebook must be prepared to do the following: show the organization of content for elementary grades; introduce appropriate methods; suggest a variety of seatwork and assignment lessons; and show how to appraise pupils' achievement in order to start their new learning at an appropriate level. This guidebook should be complete enough that the teacher could provide learning experiences from it in the event that children did not have textbooks.

9. Selection and preparation of teachers must center around in-service education for the vast number of teachers needed in primary classes. The preservice educational program must start with the present program (tenth and eleventh grades provided by teacher training institutes) and be grad- ually expanded to include new centers in the provinces. As funds are available through local and national sources, teacher training institutes can begin to provide one

13 Space is not available to present detailed recommendations on all aspects of instruction. See Wilbur H. Dutton, A Guide for the Development of an Elemen- tary School Mathematics Program for Ethiopia (Addis Ababa: Haile Selassie I University, June 1967), pp. 1-102.

124

or two years beyond the twelfth-grade program. The University should concentrate upon the preparation of directors and supervisors and secondary school teachers.

10. The use of conventional methods of curriculum improvement, including the use of English as the medium of instruction and the use of new materials prepared by mathematical experts, will not help Ethi- opia. Textbooks must be prepared in Am- haric and instruction (for Grades 1 through 6) must be in Amharic. The tremendous challenge facing Ethiopian education is to keep pace with the increase in population and to penetrate the unpenetrated rural population with mathematics education which will be realistic for Ethiopian needs and which will enable children to think reflectively.

Selected bibliography

Churchill, Eileen M. Counting and Measuring. Toronto: University of Toronto Press, 1961.

Dottrens, Robert. The Primary School Curricu- lum. Paris: UNESCO, 1962. Pp. 115-278.

Dutton, Wilbur H. Evaluating Pupils* Under- standing of Arithmetic. Englewood Cliffs, N.J.: Prentice-Hall, 1964.

. A Guide for the Development of an Elementary School Mathematics Program for Ethiopia. Addis Ababa: Haile Selassie I Uni- versity, 1967.

Entebbe Mathematics. Basic Concepts of Mathe- matics. Watertown, Mass.: African Educa- tional Program, Educational Services Incor- porated, 1964.

. Teachers* Handbook, Primary I-III. Wa- tertown, Mass.: African Educational Program, Educational Services Incorporated, 1963.

Ethiopian Board of Education Study Com- mittee. Proposed Plan for the Development of Education in Ethiopia. Addis Ababa: Ministry of Education and Fine Arts, 1961.

. Elementary School Curriculum, Years I- VI. Addis Ababa: Ministry of Education and Fine Arts, 1964.

. Handbook for Elementary Schools. Ad- dis Ababa: Department of Elementary and Adult Education, 1964. Mimeographed.

. School Census for Ethiopia. Addis Ababa: Bureau of Educational Research and Statistics, 1961-62.

Greater Cleveland Research Council. Key Topics in Mathematics. Chicago: Science Re- search Associates, 1961.




Haile Yesus Abeje. Putting into Effect an Ele- mentary School Programme Geared to Ethio- pia's Needs and Objectives, Addis Ababa: Haile Selassie I University, 1963. Mimeo- graphed.

Ministry of Education and Fine Arts Long- Term Planning Committee. A Ten-Year Plan for the Controlled Expansion of Ethiopian Education. Addis Ababa: Ministry of Educa- tion and Fine Arts, 1955.

Martin, William T. "Upgrading Mathematics and Science Teaching in Central Africa," Mod- ern Education, March- April 1967, pp. 26-29.

UNESCO. Curriculum Revision and Research. Paris: Workshops of UNESCO, 1958.

U.S. Office of Education. Research Problems in Mathematics Education. Washington, D.C.: Government Printing Office O-E12008, No. 3, 1960.

Letters to the editor Dear Editor:

The article by John W. Wilson, "The Role of Structure In Verbal Problem Solving" in the Oc- tober 1967 issue of The Arithmetic Teacher, raises an extremely important question concerning experimental research in educational set- tings. In this study, fourth-grade children from one school were randomly assigned to three treatment groups, pretested, and then tested at vary- ing intervals of time. The performance of the children in one of the treatment groups was found to be significantly better on tests subse- quent to the pretest.

Obviously, educational research cannot be con- ducted independently of the past experiences of the learners. It is entirely conceivable that these experiences may interact with the treatments. If this is so, then no causality can be attributed to the treatment effect (s). It would be very interest- ing to see Dr. Wilson's study replicated where the background experiences of the children are controlled, i.e., a replication in which the children who are used as subjects are sampled from two mathematics programs representing the differing philosophies of problem solving he cited - Leslie P. Steffe, University of Georgia, Athens, Ga.

Dear Editor:

Sputnik served a much needed purpose in American mathematics education. It made the Congress aware of the need for financial assis- tance in upgrading and implementing the curriculum in mathematics. The new International Re- port can serve an equally useful purpose, and I hope it will. While I have many misgivings concerning the conclusions and statistical analysis of the report, I feel that in spite of all of its weak- nesses and the fact that topics tested were not taught at the grades tested, it points out things we should consider in our American educational system.

Japan showed up very well in this study. I visited Tokyo in 1964 and had the good fortune to visit one high school and to observe one mathematics lesson, which I had no difficulty in

February 1968

following, because the diagrams denote a universal language. I saw fifty children being lec- tured to at a rapid pace, with each student furiously taking notes. In Japan it is the responsibility of the student to learn. Looking further into this situation, I learned how difficult it is for a Japanese youngster to get into an academic high school. The student must pass a demanding examination, and here the parents get into the picture. Realizing how important is a high school education, Japanese parents are anxious that their children pass these examinations. Japanese children must learn on the elementary level, and the home exerts an influence in this direction.

In Japan, as I observed it, children and their parents consider it a privilege, not a right, to go to high school. And in a secondary school, it is the student's responsibility to succeed. - George Grossman, Board of Education of the City of New York, Brooklyn, New York.

Dear Editor:

In reviewing the article "One" by Arthur E. Jordan [The Arithmetic Teacher, October 1967], I noticed two errors. The first, in statement 11, seems to be an error in printing. It should read, "One is the quotient of a number divided by itself when the number ̂ 0." The error in statement 18, however, is not as obvious. It should read, "Any nonzero number raised to the zero power is one."

Further comment can be made concerning statement 17. "One raised to any power is one (sometimes, plus or minus one)." Here, the phrase "sometimes plus or minus one" leads one to believe that Dr. Jordan is not making use of the "principal root." If he permits

1% = vT= -1, then why not permit

'yA = vT= i, where i = -1 ? As I teach two mathematics courses for ele-

mentary teachers, I was particularly interested in [Continued on p. 132]

125



Documents

New mathematics for Ethiopian elementary schools