IMPROVING TEACHING MATHEMATICS OF PRIMARY SCHOOLIN EGYPT
Ebada, Nasser Elsayed Abdel-hamed
NCERD
This article summarized the JICA project for improving teaching mathematics inprimary school in Egypt from the begging of April 2003 to the end of M arch 2006.
This long-term study depends on centered students-study approaches focus onproblem solving as a teaching method to develop students’ achievement and attitude.
The main process of this project centralized on improve performance of teacher andits activities in mathematical class, in specific of using problem solving as teaching
method to be skilled in its process. By our observation of students and analysis ofachievement test during this project the mathematical class was improved, forexample: students' oral and writing communication, representation, solving daily life
problems, discussing mathematical thinking and assessment.
Theoretical framework
By the beginning of the twentieth century, several important developments had takenplace in the world of the mathematics. New branches of the subject had beendeveloped, and more refined and powerful problem-solving techniques had graduallyreplaced established standard methods of working. Many traditional areas ofmathematics had been re-conceptualized in an attempt to put the subject on a firm
logical foundation
Now Mathematics instructional programs should focus on solving problems as part ofunderstanding mathematics so that all students: build new mathematical knowledge
through their work with problem, develop a disposition to formulate, represent,
abstract, and generalize in situations within and outside mathematics, apply a wide
variety of strategies to solve problems and adapt the strategies New Situations,monitor and reflect on their mathematical thinking in solving problems.
Problem solving is an integral part of mathematics learning. Students should
regularly work on tasks where the solution path is not readily apparent and where
solving the problem requires more than just merely applying a familiar procedure.
Solving problem is not only a goal of learning mathematics but also a major means of
doing so. Students should have frequent opportunities to formulate, grapple with, andsolve complex problems that require a significant amount of effort and should then be
encouraged to reflect on their thinking (NCTM, 2000,49). As students think about
new problems, they not only learn how to solve similar ones, they can also develop
new skills and ideas.

Mathematics Education in Egypt
In Egypt, mathematics is a core subject. Through visiting school and observation ,teacher in action, the style of mathematics education was described as explanationstyle: in mathematics class teacher depends on presenting one or more example ofconcepts , and write the rules, generalizations, characters related to this concepts,
then he gives students time to solve more practices individually to evaluate them,finally he make conclusion in blackboard. Maybe he uses some concrete materials to
explain when teacher teach skills. You can say teacher works and talks more thanstudents.
In general teacher thinks solving more practices is important to understand, but in thiscase the students use some rules, operations and procedures to get right solutions.
Also about solve daily life problem, teacher depends on textbook to select problems,
but most of these problems aren’t logical with daily life problems. Teacher needs toknow how to posing problem or making word problem. One point related to solving
problems is process not right answer. Process is very important. It gives students
chance to express to their ideas. It includes mathematical thinking process. Alsoteacher should know how to make expectations of students answer, and how to use
the wrong answer.
Why the JICA Project
JICA project is very important for students, teachers and schools. For example ithelps the NCERD staff (fifteen Researchers) to give proper instruction to teachers on
the new teaching methods in Egypt, that is, the child-centered and problem solving
methods including lesson plan. Then the teachers at the selected schools mastered the
new teaching methods and practiced them in class, and the methods were proved tobe effective. In general it helped teacher to change his teaching method from only
explanation to child-centered study, so students’ academic performance effected on
their understanding, attitude and interest in mathematics.
Principles of project (protocol)
1- depending on cooperation between JICA, Hokkaido Univ. of education staff and
NCERD staff, Hokkaido Univ. of education staff present experiences of mathematics
education through long time experts and short time experts, they present theirexperiences about teaching methods, teacher training courses, and evaluation. Also
visiting NCERD staff Japan to take training course in action in Hokkaido Univ. of
Education and visiting primary schools.
2- depending on child-centered study including problem solving as teaching method.
3- Review the guidebooks of teaching mathematics

4- the new teaching methods are interdicted in existing teachers training courses, thenrecognized by the people in education field.
Methodology, Design and Procedures
Eight experimental schools were selected in this project, four of them as a pilot
school, and four of them as control schools. In this project there are two targets wedeal with them (teachers is first target and direct operation, students are the second
target and indirect operation,).It is long Term - Study, the same students from Fourth
grade to Sixth grade, also it depends on pre _ post Test and Questioner
TargetA pilot School

Teacher
Students

7
About35 each class

Control school
7

Variables
Teaching Strategy
Achievement &Attitude

Table1:Targets of projectThis project depends on the good technique to support the teachers using childcentered- study. There are a lot of activities that were done, For example: Visiting
school, In-service training courses, Open class
Visiting school: In the pilot school, teachers required background about the projectmathematics education, guide book (GB), child centered-study and problem andproblem solving as teaching methods. The members of this project (JICA member
and NCERD)have visited each school weekly. They used to observe the teacher inmathematics class to see how the teacher teach, how the teacher encourage students
to depend on the previous experience to deduce new concepts, also how the students
develop the ideas, working in group or individually. In general, they have observed
how the teacher prepared the teaching plan and follow it to achieve the aims oflesson.
After the end of class (one hour), the member has made a meeting with mathematics
teachers to discuss good point in class and how to improve their performance inteaching mathematics. This open discussion as part of strategy was very important forteachers. They learn what the differences among ways depending on explanation andother ways depending on child centered- study. The member of project have observed
improving performance of mathematics teacher in pilot school gradually most ofthem use problem solving as teaching method well. They depend on concreted
mathematics instead of symbolic mathematics.
In-service training courses: The members of project have thought of providing
mathematical teachers in another experimental school background about this projectand good practice lesson. The technique of this training course have tacked care ofpresenting framework of teaching mathematics including how to deal with the unit intest book depending on guide book (what to teach, why to teach how to teach), also
process of problem solving as teaching method, then presenting good practice using
micro teaching, finally open discussion to develop precipitant' ideas all this paint wasin the first day, in the second day teachers have presented good practices depending
on strategy. Through discussion, the idea of teachers have improved and theirbelieves have been changed. In the third day teachers observe open class in pilot
school and discuss it to require more experiences and skills.
CONTANT OF TRAINING COURSES
Using Guide Book:
In this point, teachers are presented what the philosophy of the GB and how they canuse it. It is very essential the teachers recognize dealing with units and subject inEgyptian Mathematics Textbooks through presenting an example like this:
Unit 2 Proportion and its application
A. Aims of the Unit, 1. Aims of the Instruction, The students should be able to:(1-1) calculate the second, third, or forth proportion in a proportion involving four
numbers. (1-2) use the property of product of extremes = product of means. (1-3)
express missing term in a proportion by a symbol, and then calculate its value using
more than one property in the proportion.
2. Lessons(2-1) The meaning of proportion(2-3) Application on proportion(2-5) Percentage(2-7) General exercises
3. Flow Chart of Related Units

Grade 5
Unit1 Decimals
1. Adding decimals
2. Subtracting decimals
3. Multiplying decimals
4. Multiplying by 10,100,1000
5. Dividing by 10,100,1000(2-2) Properties of proportion(2-4) Proportional division(2-6) Applications using percentages(2-8) Activities
Grade 6
Unit 1:Ratio and its application
1. The meaning of ratio
2. Applications on ratio
3. Ratio of three numbers
4. General exercises
5. Activities
Grade 6
Unit 2 Proportion and its application
1. The Meaning of Proportion
2. Properties of Proportion
3. Applications on Proportion
4. Proportional Division
5. Percentage
6. Applications on Percentage
7. General exercises
8. Activities

B. Brief Explanation of the Contents
1. What to Teach
Proportion is a concept applicable for quite various uses. For example:(1-1) The weight of a nail can be calculated by weighing 100 nails and dividing thevalue by 100. The number of nails is proportional to the total weight of the nails.
(1-2) The distance that a car drove at 60 km/h can be calculated if the driving time isgiven. The driving time at a fixed speed is proportional to the distance covered.
(1-3) A spring balance is an application of the proportion of the weight of a subject tothe extension of the spring. The samples above indicate the following features of
proportion.
Proportion is a quantitative correlation.
Sample 1) is a correlation of the number of nails and the total weight of the nails.
Sample 2) is a correlation of the driving time and the distance covered.
Sample 3) is a correlation of the weight of a subject and the extension of the spring.
The proportional ratio is fixed.
In the case of sample 1), the quotient of the “total weight of nails” divided by the“number of nails” is always the numerical value of the “weight of a nail.” In the caseof sample 2), the quotient of the “distance covered” divided by the “driving time” isalways the “driving speed.” In the case of sample 3), the quotient of the “weight of a
subject” divided by the “extension of the spring” is always the “spring constant.”
One of the proportional changes twofold/threefold, the other also doubles/triples.
There are two approaches necessary to learn for the application of proportion as
follows: Approach to verify if the two values concerned are proportional, AnotherApproach to solve a problem based on the proportional correlation between thevalues concerned. Both approaches are based on the features of proportion. To verify
if the two values concerned are proportional, it is necessary to measure the values inmore than one case as reference data. For example: The following table deals with thedata on the length of a burning candle. The elapsed time from lighting and the lengthof the candle that has been burned at the point of time are measured.
Time (minute)

5

10

15

Burned length (mm) 3

6

9The correlation between the elapsed time and the burned length is regarded to be
proportional, as the ratio is fixed. Therefore, it is possible to predict how much thecandle will be burned down in one hour after it is lit. It can be calculated from by
how much shorter the candle was three minutes after the lighting.

The burned length of the candle is 3mm after five minutes from the lighting. Basedon the constant of the proportionality, the burned length after three minutes fromlighting can be calculated at 1.8mm, by the expression 3×3÷5. (Refer the following
table.)
Time (minute)3

5

Wore length (mm) ?

3

2. Why to Teach
The contents of this unit are essential from the following viewpoints:
Most of the previous studies on number and calculation can be utilized forunderstanding proportion. The concept of proportion, similar to that of ratio, isessential not only in our daily life but also for scientific studies.
3. How to Teach(3-1) Methods for Achieving the Aims
As shown by the examples with nails and candles, proportion is a correlation of
concurrently changing volumes, e.g. the number of nails and the total weight of thenails, or the burning time of a candle and the decrease in length. It is necessary toknow if a correlation is proportional, or what a proportional relation indicates. Pupils
need to work on these examinations before learning how to process proportion withcalculation.
In our daily life, there are some situations by which pupils can make sense of theimportance of proportion: for example, the sense of ingredient proportion isnecessary for cooking. The teacher should try to give such situations for pupils toeasily understand proportion.
(3-2) Planning Classes: In this case, the timetable is distributed. Teacher understands
number of lessons, hours, and determines aims of each lesson.
C. Examples of Instruction Scenarios
The GB present example to explain how the teacher shows the problem, give students
chance to read it and discuss, then make expected answer, also how the students
think, work: grouping, individual, whole class. Finally, students should makecommunication to present their ideas to solve the problem.( see index1: teachingplan for a good practice)
One important point included in content course is Teaching Process in ProblemSolving-Study. It includes this process: Teacher shows the problem of this lesson to
students, Students ask the teacher some questions about the problem and discuss witheach other. They take notes, then Teacher shows the theme of this lesson to students,
and Students think of how to solve the problem individually or in groups, after thatteacher helps the class to learn during a student’s presentation, Teacher puts toseveral students’ thoughts, now students can understand how to solve the problem;
finally teacher evaluates students’ understanding of the aim and contents of lesson.
Result & Discussion
Through working with the teachers & students there are improvement in performanceteachers & students and attitudes as following:
Teachers in pilot schools use problem solving as a teaching method, depending on
process of teaching. They give students chance to deduce new concept and build theirmathematical knowledge (conceptual knowledge, procedural knowledge, problem
solving).They encourage students to use previous experiences to expect answers.
Teacher works as facilitator for students to think and work themselves.
On the other hand, teacher could deal with textbook including organize information,
select the suitable problems and modify them for lessons, transform the problem todaily life problem, and connect between mathematical concepts and skills, also,
determine the process that is necessary as simulation for students.
Students in pilot school communicate to discuss problem, and express their thought
in oral and communication. They can explain the process and operation of solving
and give different way to solve problem. Also they learn new concepts and skills
when they work. This strategy gives students chance to discover the value ofmathematics, they make connections among mathematics through daily life problem
and applications. The students now make word problems to show how they haveunderstood clear and give examples from life expressing mathematical expression.
Now, this strategy makes students have good thought, high achievement and positive
attitude.
Challenges & difficulties
In general changes; mathematical teacher believes about nature of mathematics as a
subject and mathematics education is very essential: mathematics is not symbolic
language or group of operation the students have performed them. Mathematics is alanguage that all people speak, and is ways of thinking that students should learn.
Also mathematics education isn’t only explaining and presenting concepts, it is fieldhelping teacher to recognize (what, why, how) to teach. The second point should bereformed is mathematical textbook. It includes more example and practice to present
concepts and skills, but there is no process that students must do it to deduce andunderstand these concepts and skills.
About the problem solving as a teaching methods, the teachers need more experience
about how to present problem and give students time to read, analysis, remember
previous experiences related before thinking to expect and solve. Also they must
finish teaching plan on time.

References
Ministry of Education (2004): Mathematics Textbook for Sixth Grades, Book Section,
Egypt.
National Council of Teachers of Mathematics (2000): Principles and Standards for School
Mathematics. Reston .Va: National Council of Teachers of Mathematics.

Index (1)Teaching Plan

Lesson: Applications on percentage (6th grade 1st Term Unit2)
Aims of this lesson: By the end of this lesson students will be able to1- solve daily life problems related to proportion
2- think how to solve in many ways, those are, by using figures, formulas and themeanings of percentages, etc.
3- know the meaning of the formula by using figure.
Development of this lesson
Teacher’s Activity

Students’ Activity

Remark

T: We have studied themeaning of percentage andconverting of percentage tofraction and vice versa.
(Teacher asks students to readthe problem.)Students read the problem
They think about…
EX.
*the meaning of the sentence.
*the meaning of %.
*the meaning of 6% etc.
* mathematical exertions

Teacherasks
students tothinkthemselves

OPENING

Problem (1)In a primary school there are 600 pupils. One day 6% of
the total were absent. Find the number of the pupils who
were absent on that day.

Teacher presents thisStudents think how to solve
problemby each group.
and gives handouts to each
（Expected answers）
student.
* Absent; 600×6%=36
Teacher makes students*
solve
Absent Total
the problem and explain their
Value
.……
600
ideas.
Per %6
6
Absent =600 × 6= 36
100

Absent present Total
Value ……
……
600
Per
6
94
100
600 × 6
Absent =
= 36
100
*
100%
94%

(Students

solve thisproblem ingroup.)
Teacherwalks amongdesks tosupport eachgroup. It isconvenient
to use thefigure forunderstanding
the meaning.

6%

600pupils

Development

Value of 1%=600÷100=6
Absent =6×6=36 6%= •
•
6
6%=
100
6
Absent = 600×=36
100
Students present their ideas.

Closing

Teacher asks students discuss
which solution is useful.
Teacher gives students a similar
exercise .
Problem(2)Your father bought a T.V set with a discount of 15% if
its listed price was L.E1280, find the money your father
paid after the discount
Teacher rounds off today’s classwith review.
Teacher gives homework.

Today we learnt how to solve thelife problem in many ways.

Students solve it
individually.