EXPLORING OF MATHEMATICS TEACHER’S OPNIONS REGARDING THE INTRODUCTION OF COMPULSORY MATHEMATICS CURRICULUM AT SENIOR SECONDARY PHASE IN OSHANA REGION

A RESEARCH PROPOSAL IN MATHEMATICS EDUCATION

SUBMITTED BY:

MARIA T. NAKALE

STUDENT NUMBER:

2013065959

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF BACHELOR OF EDUCATION IN MATHEMATICS AND PHYSICAL SCIENCE

SUPERVISOR: Anonymous for marking purposes

THE DEPARTMENT MATHEMATICS AND SCIENCE

FACULTY OF EDUCATION

FEBRUARY 2018

Table of Contents

CHAPTER 1: Introduction4

1.1 Background4-5

1.2 Statement of the problem5

1.3 Research Questions5

1.4 Significance of the study6

1.5 Limitation of the Study6

1.6 Delimitation of the Study6

1.7 Definition of terms …………………………………………………………………. 6-7

CHAPTER 2: Literature Review8

Overview8

Curriculum Implementation8

2.2.1 Factors that influence curriculum implementation ………………………. 9

2.2.1.1 Implementing Agents …………………………………………………9

2.2.1.2Teacher …………………………………………………………………

2.2.1.3The learners ……………………………………………………………

2.2.1.4 Resources material and facilities ……………………………………….

2.3.1.5 The school environment …………………………………………………

Summary10

Chapter 311

3. Methodology11

3.1. Research Design11

3.2. Population11

3.3. Sampling Procedures11

3.3.1 Schools11

3.3.2 Mathematics teachers12

3.4. Research Instruments12

3.4.1 Questionnaire12

3.4.2 Interview13

3.5. Data collection procedure13

3.6. Data analysis14

3.7. Research Ethics14

References15

Appendix 117

Appendix 219

CHAPTER 1: INTRODUCTION

Background

Elaine (2013) describe mathematics as a science that deal with the logical of shape, quantity and arrangement. He also state that Mathematics is a powerful means in a technology-oriented and information-rich society to help students acquire the ability to communicate, explore, conjecture, reason logically and solve problems using a variety of methods. At the senior secondary phase, mathematics curriculum is aimed to develop learners’ ability to think critically and to solve problem in daily life using mathematics, with regard of meting 21 century challenges, therefore “The Kenyan government has underscored the importance of Mathematics literacy in educational institutions. Having recognized the role of Mathematics in national development, the Kenyan government has made Mathematics compulsory in primary and secondary schools under the 8:4:4 system of education. As such, students? performance in Mathematics and Sciences is of great concern to education stakeholders” (Kenya National Examination Council, 2001, as cited in Alice, 2015).

In Namibia Mathematics had been a compulsory subject as form grade 1 up to 10 before 2012 therefore MOE had also introduce compulsory mathematics at Senior Secondary phase (grade 11 and 12) for the best interest of learners and the nation at large. The New Era’s article titled “Mathematics a promotional subject and essential” (Paulus, 2013 p.4) attest to this. According to Angula (2015) in his study had state that in Grade 11 and 12, subjects had been grouped in four different fields of study, namely: the Natural Science and Mathematics (Mathematics, Biology and Physical Science), the Commerce (Accounting, Economics and Business Studies), Technical (Design and Technology, Physical Science and Mathematics) and the Social Sciences (History, Development Studies and Geography) but only two of these flied of study in Namibia that had mathematic as a compulsory subjects namely: the Natural Science and Mathematics field and the Technical field had Mathematics. Learners from the other fields (Commerce and Social Sciences ) had a choice to either take Mathematics or any other subject of their choice as an additional subject to their field of study (Ministry of Education, 2010).

The Ministry of Education (MoE) (2010) noted that mathematics is the key to success in this world where the economy requires workers who are prepared to absorb new ideas, to perceive patterns and to solve unconventional problems. It’s against this background that the researcher decided to conduct the study to find out what are the opinions teachers had regarding the introduction of mathematics as a compulsory subject at senior secondary phase.

Statement of the problem

Mathematics is one of the key subjects examined at all levels of education in Namibia. The subject is very important for all careers of business, science and technology, The Ministry of Education made mathematics a compulsory subject in grade 11 and 12 for the development of science, technology and commerce as from 2012 (MOE 2010). According to ( Nico, 2012) has stated that some teachers questioned the ministry’s decision saying that they only expect more disaster in school results while TUN support the ministry’s decision, provided that two type of mathematics are introduced in the curriculum, namely applied and pure mathematics. Regarding this implementation it brought some confusion among teachers at senior secondary level and this made the researcher to recognise that mathematics teachers have different views regarding this implementation of curriculum. The researcher also realise that there are lot of challenges faced by mathematics teachers when teaching this compulsory subject. During TP at Oshiwa secondary school (pseudonym) the researcher observed that not all teachers are happy with the implementation and this raised the researcher’s nosiness to explore the teacher’s opinions about the implementation of compulsory mathematics curriculum at Senior Secondary phase.

Research questions

The study will addressed the following questions:

What are the grade 11 and 12 mathematics teachers opinions regarding the introduction of compulsory mathematics curriculum in Oshana region?

What are the challenges experience by mathematics teachers in the teaching of compulsory mathematics curriculum?

Significance of the study

The aim of the study is to explore the opinions of mathematics teachers regarding the introduction of compulsory mathematics curriculum at Senior Secondary phase. This study can be useful to the NIED, as it might be used as a guide to govern if the introduction of CM at grade 11 and 12 is a challenge to mathematics teachers and make use of this study if there are some changes to be made.

Limitation of the study

One of the limitations the researcher might face is that not all the teachers that will be included in the study to be interviewed in English but it might be most of the teachers do prefer to be interviewed in Oshiwambo, as they will feel that they could express themselves much way better in Oshiwambo, However the fact remains that English is the official language in schools, the researcher will interview them in English. Another limitation is that not all participants will return the questionnaires while some will not be interested in answering the questionnaires and they will tear them up. This will result in some information to be lost.

1.6 Delimitation of the study

The study will be limited to the grade 11 and 12 mathematics teachers in the 2 selected schools in Oshana region. It will also be limited to the grade 11 and 12 mathematics teacher’s opinions regarding the introduction of the compulsory mathematics curriculum in the Oshana region. The grade 11 and 12 mathematics teachers will be the ones that are mostly affected by the change of the curriculum and hence it will be of the importance to hear from their opinions regarding the introduction of compulsory mathematics to seek for ways to amend.

1.7 Definition of term

Amend: to make minor change to (text, piece of legislation) in order to make it fairer or more accurate.

Curriculum: in this study, ‘curriculum’ is defined as the official policy for teaching, learning, and assessment and gives direction to planning, organising and implementing teaching and learning in schools.

Opinion: In this research, opinion is understood to mean the feelings, thoughts and views or ideas that the teachers perceive and acknowledge in the introduction of compulsory mathematics.

Govern: to officially control and direct the public business of the country, city, and group of people.

Mathematics: in this study, mathematics refers to the study of numbers quantities or shapes.

Implementation: in this study, implementation takes place when the teacher and the curriculum materials interact with the learner.

CHAPTER 2: Literature Review

2.1 Overview This chapter will reviews the literature under the headings: curriculum implementation; views and attitudes towards Mathematics Education; challenges in the teaching and learning of Mathematics. Due to the limited literatures in Namibia about the problem of interest, literature was drawn from studies done in other countries.

Curriculum implementation

” Schubert (1986 p.42 as cited in Tubaundule, 2014) define curriculum implementation as traditionally, the delivery process or a system of engineering that takes design specifications through various channels to the teacher and classroom. Furthermore, Tubaundule (2014) state in this study that “Aspects of the implemented curriculum that might reflect school quality include not only the content of the implemented curriculum (the curriculum topics usually addressed in the classroom), but also the pedagogy (or instructional practices), the materials and equipment (such as technology), and the conditions under which the curriculum is implemented (such as the number of students in the class). Regard this each of these aspects must be related to student learning.

Curriculum implementation entails putting into practice the officially prescribed courses of study, syllabuses and subjects. The process involves helping the learner acquire knowledge or experience. It is important to note that curriculum implementation cannot take place without the learner. The learner is therefore the central figure in the curriculum implementation process. Implementation takes place as the learner acquires the planned or intended experiences, knowledge, skills, ideas and attitudes that are aimed at enabling the same learner to function effectively in a society (University of Zimbabwe, 1995 p. 8 as cited in Chikumbu and Makamure, 2000 p.50) module 13.

Viewed from this perspective, curriculum implementation also refers to the stage when the curriculum itself, as an educational programme, is put into effect. Putting the curriculum into operation requires an implementing agent. Stenhouse (1979 p.4 as cited in Chikumbu and Makamure, 2000 p.50) module 13, identifies the teachers the agent in the curriculum implementation process. She argues that implementation is the manner in which the teacher selects and mixes the various aspects of knowledge contained in a curriculum document or syllabus. Implementation takes place when the teacher-constructed syllabus, the teacher’s personality, the teaching materials and the teaching environment interact with the learner (University of Zimbabwe, 1995 p. 9 as cited in Chikumbu and Makamure, 2000 p.51) module 13.Hence, in this study, curriculum implementation refers to how the planned or officially designed course of study is translated by the teacher into syllabuses, schemes of work and lessons to be delivered to students.

Factors that influence curriculum implementation

Will outlined some of the factors that influence the implementation of a curriculum and discussed how each factor influences the implementation process, which include teacher, the learner, resources material and facilities, the school environment.

2.2.1.1 Implementing Agents

Curriculum imlementers view their role in curriculum implementation as an autonomous one. They select and decide what to teach from the prescribed syllabus or curriculum. Since the implementation takes place through the interaction of the learner and the planned learning opportunities, the role and influence of the curriculum implementers in the process is indisputable (University of Zimbabwe, 1995 as cited in Chikumbu and Makamure, 2000).

If the curriculum is what teachers and students create together, as Wolfson (1997 as cited in Angula, 2015) states in Curriculum Implementation, the implementing agents must play a more vital role in designing the curriculum. Angula (2015, p.19) also state in his study that the implementers must be involved in curriculum planning and development so that they can implement and modify the curriculum for the benefit of their learners.

2.2.1.2 Teacher

As Whitaker (1979) asserts in the University of Zimbabwe (1995 p.26) module, the teachers view their role in curriculum implementation as an autonomous one. They select and decide what to teach from the prescribed syllabus or curriculum. Since implementation takes place through the interaction of the learner and the planned learning opportunities, the role and influence of the teacher in the process is indisputable (University of Zimbabwe, 1995 p.28).You could be thinking, “I understand that teachers are pivotal in the curriculum implementation process, but what is their role in the curriculum planning process?” If the teacher is to be able to translate curriculum intentions into reality, it is imperative that the teacher understand the curriculum document or syllabus well in order to implement it effectively (University of Zimbabwe, 1995 p. 8). If the curriculum is what teachers and students create together, as Wolfson (1997) states in Curriculum Implementations (University of Zimbabwe, 1995 p.28), the teacher must play a more significant role in designing the curriculum. Teachers must be involved in curriculum planning and development so that they can implement and modify the curriculum for the benefit of their learners.

The learners

Learners are also a critical element in curriculum implementation. While teachers are the arbiters of the classroom practice, the learners hold the key to what is actually transmitted and adopted from the official curriculum. The official curriculum can be quite different from the Curriculum that is actually implemented. The learner facto influences teachers in their selection of learning experiences, hence the need to consider the diverse characteristics of learners in curriculum implementation (University of Zimbabwe, 1995 p. 31). For example, home background and learner ability can determine what is actually achieved in the classroom.

Resources material and facilities

From your experience, many are aware that no meaningful teaching and learning take place without adequate resource materials. This applies to curriculum implementation as well. For the officially designed curriculum to be fully implemented as per plan, the government or Ministry of Education should supply schools with adequate resource materials such as Textbooks, teaching aids and stationery in order to enable teachers and learners to play their role satisfactorily in the curriculum implementation process. In Curriculum Implementation (University of Zimbabwe, 1995 p. 2), it is suggested that the central government must also provide physical facilities such as classrooms, laboratories, workshops, Libraries and sports fields in order to create an environment in which implementation can take place. The availability and quality of resource material and the availability of appropriate Facilities have a great influence on curriculum implementation of compulsory mathematics.

The school environment

This is one other factor that influences curriculum implementation concerns the particular circumstances of each school (University of Zimbabwe, 1995). Schools located in rich socio-economic environments and those that have adequate human and material resources can implement the curriculum to an extent that would be difficult or impossible for schools in poor economic environments

challenges experienced by teacher in teaching and learning mathematics

Challenges in mathematics teaching and learning are observed at secondary school level as well as at higher education level. Tom (2011) state that if teachers encounter challenges during the implementation of curriculum change, the successful implementation may not occur. Fullan (2001as cited in Tom,2011), warned that if teachers perceive challenges in enacting the curriculum, then low-take up, dilution and corruption of the reform is likely to follow. Curriculum as a set of education plans should be prepared and adapted based on the learning situation and future demand.

However chapman (2012) state that “Mathematics teachers’ beliefs and attitudes toward a new curriculum are likely to be directly related to their beliefs and attitudes toward their learning and teaching of it. For example, if the teachers’ beliefs are not in harmony with those framing the curriculum, this can affect the level of their participation and success in activities to help them to understand and implement the curriculum as intended. In general, teachers’ beliefs and attitudes can play either a facilitating or an inhibiting role in their learning of the new curriculum” (p.263). Based on a study to investigate mathematics teachers’ beliefs and attitudes in implementing a new project-based high school (grades 10–12) mathematics curriculum (Chapman and Wood 2004 as cited in Chapman, 2012), I briefly highlight the nature of these beliefs. This curriculum emphasizes ”the application and relevance of mathematics in daily life.” It is intended for students who are not likely to attend university or pursue an academic area at university that requires mathematics. The textbooks produced for it consist predominantly of projects. Therefore more teachers believe that teaching and learning through project was the good way to teach mathematic and should result in more interesting way of learning for learners.

In addressing the role of technology in the teaching and learning of mathematics, the NCTM (2008) states: ”Technology is an essential tool for learning mathematics in the Twenty-first century, and all schools must ensure that all their students have access to Technology” (”Implementing a new curriculum”). However, having access is only one of the necessary ingredients to support integration of technology in the mathematics classroom. “Implementation of such recommendations is dependent on the teacher and the knowledge they hold or ought to hold to use technology to enhance mathematical understanding for themselves and their students. Given that teachers educated in traditional mathematics classrooms have not learned mathematics with these technologies, they are likely to have limited knowledge of both the technologies for use in mathematics and how to use them. So the challenge for teacher education is to identify what knowledge is needed and how to prepare prospective and practicing mathematics teachers to use technology in a way that leads to the development of technological pedagogical content knowledge (TPCK) for teaching mathematics” (Chapman, 2012, p.267).

View and attitude toward mathematic education

A person attitude toward mathematics is often described as positive or negative. (Zacharos, Kaliopoulos, Dokimaki & Kassoumi, 2007) state teacher’s attitude and beliefs toward mathematics and instruction are often their students’ attitudes, interest and success in mathematics. Many children due to their misunderstanding, non-understanding and failure during previous lessons they develop fear towards Mathematics therefore effort must be exerted to resolve this fear before proceeding to the next section as students learn new Mathematical concepts and procedures by building on what they already know.

(Yohannes, 2007) state that Negative attitude towards Mathematics is also common among most Parents. Parents believe that Mathematics is hard to understand and they try to avoid it for their children as far as possible. Simple example which shows us the negative attitude of Ethiopian parents is their reluctance to send their children to college or university faculties which offer Mathematics as a course. They encourage their children to enrol in the social science faculty where they think there are “no” Mathematics courses. He further noted that “the existing traditional way of teaching in our schools is teacher cantered; the teacher is expected to do every activity while the students are mere listeners. It doesn’t’t give the students a chance to learn by doing and hence learn from their mistakes. The outlook of students, that the role of students is to receive Mathematical knowledge and to be able to demonstrate it; the role of the teacher is to transmit this knowledge and to ascertain that the students have acquired it, is a common phenomenon in our schools”.

Therefore the researcher barbed out earlier that there is a mass of factors to account for success in implementation, but being positive about the implementation of a curriculum is also a factor that can contribute to that success. Therefore, the researcher assumes that Mathematics teachers might successfully implement the curriculum provided that they are positive, among other factors, about the introduction of the compulsory Mathematics curriculum at senior secondary schools in Oshana region.

Ponte et al. (1994) documented that the Education system in Portugal is in the midst of a period of intensive reform. In particular, they discuss the teachers’ and learners’ views and attitudes toward Mathematics, Mathematics teaching and curriculum innovation. They found that teachers struggled with a contradiction: whilst they approved the new orientations, which were seen as adequate and innovative, they complained about the design and implementation of the programme (as cited in Angula, 2015).

Research in Mathematics education ( McLeod, 1994 as cited in Zacharos et al,2007) state that while student have a positive outlook toward mathematics at the beginning of their school life, this often change and becomes negative toward the end of high school. They also argued that another group of student viewed mathematics as an essential tool used in order to gain access to other scientific fields. Finally they were some students who mentioned the general role that mathematics plays in the formulation of scientific thought, as happened in case of the following student

“Mathematics should be in all stages of education because it exercise the mind and help from a rational way of thinking.

SummaryChapter 3: Methodology

This chapter describes the methods that will be used to collect and analyse the data from the participants. This will include the research design, population, sample and sampling techniques, the research instruments, ethical considerations, data collection procedure, and data analysis.

3.1. Research DesignThis study will follow a qualitative research methodology in the form of the qualitative case study, whereby a case study will follow an interpretative design where the researcher will be gathering information about mathematics teachers’ opinion toward the introduction of compulsory mathematics curriculum at Senior Secondary phase that was introduced in 2012 by MoE.

Population

Johnson and Christensen (2012, p. 218) define a population as “the large group to which a researcher wants to generalise the sample results”, the total group that one is interested in learning more about (as cited in Angula, 2015). The study will be carried out in Oshana region, since there is 9 secondary schools in the region, and each secondary school has 3, 4 or 5 Mathematics teachers teaching at senior secondary school phase (Ministry of Education, 2014) and the target population will be all the Grade 11 and 12 mathematics teachers in the Secondary Schools in Oshana region. The researcher will choose the Grade 11 and 12 Mathematics teachers since they are responsible for teaching Mathematics at this phase as well as directly affected by the change to teach compulsory Mathematics.

Sample and Sampling Procedures

A random sampling will be used to select the 2 out of 9 secondary schools and the 6 Grade 11 and 12 mathematics teachers in Oshana region. Carol and Iben, (2016) define random sampling as “every member of the population to be studies has an equal chance of being included in the sample” (p.60).

3.3.1 Schools

The name of all the secondary schools in Oshana Region will be written on a piece of paper, which will be folded and be placed in the box. The researcher will ask a fellow student teacher to select 2 papers from the box. The 2 selected schools are the one to be part of the sample.

3.3.2 Mathematics teachers

Only 3 Grade 11 and 12 mathematics teachers from each chosen school will be asked to participate in the study, in case the school have more than 3 mathematics teachers, the random sampling will be used to select only 3 teachers from that school by writing all the mathematics teachers name on the piece of paper, which will be folded and placed in the box. The researcher will select unwanted number of paper and left only 3 papers and those 3 paper are the mathematics teachers to be participants. Thus the total of 6 Grade 11 and 12 mathematics teachers will participate in the study.

3.4. Research Instruments

The following instrument will be used in the study during data collection process.

3.4.1. Questionnaires

Questionnaire will be one of the instrument to be used in the study to enable the participants to freely express their own opinions. This study will contain open-ended and close-ended questions to gather data about the opinion and challenges experiences by mathematics teachers regarding the introduction of compulsory mathematics curriculum.

The questionnares will be divided into 3 sections were section A, will be about the biographical information of the participants,while section B will contain close-ended questions dealing with the opinions of the mathematics teachers regarding the introduction of compulsory mathematics curriculum and the challenges in the introduction of compulsory mathematics curriculum and section C will contain open-ended questions, were respondents will be allowed to express their opinions as how the challenges faced in teaching compulsory mathematics will be amend.

3.4.2. Interviews

The interview will be also used in the study to collect data in order to provide possible answer to question 1, since the first question require the participants to freely express their opinions regarding the introduction of compulsory mathematics curriculum and to that extend each is prepared to teach it.

A recording tape and interview sheet will be used to collect data. The interview will be recorded, With the purpose of data analysis for the researcher to go back to the recording during data analysis. Only 2 mathematics teachers at each school will be interviewed.The interview will take place after school in a classroom and it will take approximately 25 minutes.

3.5. Data collection procedures

The researcher will administer the questionnaire to the selected 6 senior secondary school mathematics teachers in the sample. The participants will be expected to complete the questionnares within that day. The interview will than follow the next day with 4 purposively selected mathematics teachers and it will happen after school . the researcher will interview each participant individually whereby the interview will be conducted in a conducive classroom and it will last for approximately 25 minutes.

3.6. Data analysisData analysis refers to the process of inspecting, transforming, and modelling data with the goal of discovering useful information, suggesting, conclusions and supporting decision making (Polit& Beck). Information that obtained during the interviews will be transcribed, by writing down all the record words and then coded the information. During this process the researcher paid attention to the written data and start choosing what was relevant, created themes with these information and disregarded the rest of the information. These themes were presented and discussed.Information that obtained during questionnaires the researcher will read through the participants’ questionnaires and seek patterns and emerging themes and put them in categories.

3.7. Research ethics

Creswell (2014) recommends that it is very important to honour the site in which the research takes place. He further explains that respect should be shown by getting the permission before entering the site, by disturbing the site as little as possible during the study and viewing yourself as a guest at the place of study. Regard this ethical clearance will first sough with the University of Namibia (UNAM), whereby the researcher will seek permission from the university Maths and Science department at HP campus. The HOD will issue the researcher with the letter that seek permission from the school principal for the study to be conducted out at that particular school. The researcher will also set permission letters that will be given to participants to give their consent to participation in the study.The researcher will maintained high standard of profession by respecting the autonomy of all the people participating in the research, and gave them a clear explanation of what will be expected from them, thereby ensuring them that whatever information they will give will be confidential. Participants’ names will not be used in the study. Nobody will be forced to take part and participants will be allowed to withdraw any time they want to. The researcher will make sure that no harm will be done to the participants, (physical, mental or social).

Reference list

Alice, A. (2015) Factors influencing students’ performance in mathematics in Kenya certificate of secondary education in public secondary schools in Butere sub county, Kenya. (Award of Degree of Master of Education in Curriculum Studies University of Nairobi).Retrieved from http://erepository.uonbi.ac.ke/bitstream/handle/11295/92823/

Angula, R. (2015). Mathematics teachers’ views and challenges on the implementation of the compulsory Mathematics Curriculum in Otjozondjupa Region. (Master of Education thesis, University of Namibia, n.p: n.p.). Retrieved from https://respository.unam.edu.na/…/Chapman, O. (2015), Mathematics teacher education: Teacher challenges in the teaching and learning. 15(4), 263-270.

Chikumbu, T., & Makamure, R. (2000). Curriculum theory, design and assessment. Zimbabwe: The Commonwealth of Learning. Retrieved from: http://www.msu.ac.zw/elearning/material/temp/Creswell, J.W. (2014). Educational Research:Planning, conducting and evaluating quantitative and qualitative research (4th Ed.). London: Pearson.

Elaine J. H. (15 August 2013). What is Mathematics? Retrieved from: https://www.livescience.com/Ministry of Education. (2010). The National Curriculum for Basic Education. Okahandja: NIED.

Ministry of education. (2016). senior secondary Phase: Mathematics Syllabus Grade 11-12. Oshana: NIED.

National Council of Teachers of Mathematics (2008, March). The role of technology in the teaching and learning of mathematics. Retrieved from http://www.nctm.org/about/content.aspx?id=14233.

Nico, S. (2013 January 12). TUN calls for foundation changes in education, The Namibian, 56(5), 1.

Paulus, P. (2012 January 17). Promotional subject and Essential, New era, 159(2), 4.

Smith, A. (2004). Making mathematics count. An inquiry into post-14 mathematics education. England: The Stationery Office.

Tom, J. (2011), an investigation on grade 5 mathematics teachers’ perception towards the new revised grade 5 mathematics curriculum. (Degree of education in mathematics and integrated natural science, University of Namibia).

Tubaundule, G., M., evaluative research of the implemented secondary school curriculum in Namibia, (philosophia doctor in the faculty of education school of education studies at the university of the free state Bloemfontein), Retrieved from http://www.msu.ac.zw/eLearning/.

University of Zimbabwe. (1995). Curriculum implementation, change and innovation. Harare: Centre for Distance Education.

Yohannes, B. G., (2007) Barriers to teaching and learning mathematics in grade 4, Norway, Retrieved from http://www.duo.uio.no/bitstream/handle.

Zacharos, K. ,Kaliopoulos, D. , Dokimaki, M. ; Kassoumi, H. , ( 2007), View of prospective early childhood education teachers, towards mathematics and its education, 30(3), 310.