ARTICLES

 

Opinions of pre-service pre-school teachers on the use of mathematics activities

 

 

Oguz Serdar Kesicioglu

Department of Early Childhood Education, Faculty of Education, University of Giresun, Giresun, Turkey. kesiciogluserdar@gmail.com

 

 

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ABSTRACT

The research reported on here was designed in a qualitative approach to present the opinions of pre-service pre-school teachers on the use of mathematics activities. The sample consisted of 10 pre-service teachers, who in their fourth year of pre-school education in the teaching department in 2017 to 2018. The pre-service teachers in the study group were selected from those with a grade point average (GPA) of above 3 and who completed the teaching practice course. In the research, the data were collected from the pre-service teachers through interviews. A semi-structured form, developed by the researcher, was used as a data collection tool in order to reveal the opinions of pre-service pre-school teachers on the application of mathematics activities. The results of the research show that the participating pre-service pre-school teachers used more than one-to-one correspondence in mathematics activities of which the most difficult concepts were classification and geometrical figures - difficult situations in which to attract the attention of children and a crowded class of 36 to 48 month old children. Most of the mathematics activities were integrated into games and art through the narration and gamification method. The participants mostly used prepared mathematics activities in practice.

Keywords: mathematics; pre-school; pre-service teacher

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Introduction

There is a clear parallel relationship between the size of countries' economies and levels of education. While an increase of education levels contributes to the economy, economic growth also contributes to the education system. Studies conducted in various countries reveal that education has contributed significantly to economic growth. When comparing the budget allowance amounts set aside for either the Ministry of National Education or universities in Turkey with those in developing countries of the Organisation for Economic Co-operation and Development (OECD), this rate falls short. While Turkey spent 4.1% of its gross domestic product (GDP) on education in 2004, OECD countries set aside on average 5.7% of their budgets for education. The educational expenditure per student at all levels of education from pre-school to high school in Turkey is below the OECD average. For example, this rate was 7% in England, 14% in Belgium, 15% in the United States, 16% in Argentina, and 25% in Canada (OECD, 2005). Due to the lack of investment in education, the need for physical infrastructure and educators at all levels of education continues. The low expenditure negatively impacts the quality of education. While Japan, Germany, Italy, and Greece spent 950 dollars, 817 dollars, 523 dollars, and 240 dollars respectively, on education, the rate in Turkey is approximately 90 dollars. When Turkey is compared with the educational indicators of member countries to the European Union, Turkey is far below the European Union (EU) average. This situation shows that, if there is not enough investment in education, it is impossible to close the gap between development and income levels between countries (Eres., 2005).

As the appropriation for education declines in most countries, the quality of education declines at a similar rate. The insufficiency of the education budget in Turkey negatively affects the pre-school education and teacher-cultivation system. This situation clearly shows itself in international exam results like Trends in International Mathematics and Science Study (TIMSS), The Progress in International Reading Literacy Study (PIRLS), and the Programme for International Student Assessment (PISA). The international exam results of developed countries like the United States of America, Finland, South Korea, and Denmark that set aside a large budget for education, are significantly higher compared to those of developing countries like Turkey, Chile, Uruguay, and Romania (OECD, 2018). The results of a study conducted by Orçan (2013:2) supports this view that problems like teachers not having sufficient information about the contents of programmes, not including adequate mathematical activities, the excessiveness of classroom materials, and a lack of insufficient instructional toys result in poorer education. Similarly, the results of an OECD (2018) report show that the status of insufficient or absent educational materials is greater in Turkey compared with the OECD.

Pre-school students in Turkey are children between the ages of 36 to 68 months, and schooling is not mandatory for these children. In Turkey, 38% of children aged 3 to 5, 50% of children aged 4 to 5, and 66% of children aged 5 attend pre-schools. Turkey lags significantly behind OECD and EU countries in terms of rates of schooling (ages 3, 4, and 5). In OECD and EU countries about 95% of children attend pre-schools at age 5, 90% at age 4 and 70% at age 3. In Turkey these numbers are 71%, 30% and 10% respectively. It is thus clear that the pre-school rate in Turkey needs to increase for ages 3 and 4 (Kazu & Yilmaz, 2018; Mill! Egitim Bakanligi [MEB], 2019). These insufficiencies negatively influence mathematics education in particular. International exams generally reveal the quality of the education of countries in addition to success in mathematics. The fundamental aspect that sets developed countries apart from developing countries is the possession of knowledge and the capacity to use it. The most important people who apply knowledge are teachers (Koç Aytekin, 2015). For this reason, it was important to determine the problems that candidate teachers experience regarding mathematics instruction before they starting in the profession. In this study we sought to reveal the concepts that teaching candidates used, the struggles they faced, which materials they used and how, methods and techniques used, and the age groups with whom they struggled in order to provide a significant contribution to the national and international literature. The causes of failure in other developing or developed countries that are unsuccessful on international exams originates from similar situations. For this reason, the results of this research should give researchers and educators the opportunity to compare the current situation in their own countries. These international comparisons are quite important in terms of viewing the rearing preferences of different teachers. It is thought that comparative analyses conducted with consideration of countries' own social, cultural, and economic conditions will contribute to the educational processes of the countries (Altintas & Yesjltepe, 2016).

Literature Review

Mathematics in early childhood

The pre-school period is the period in which children learn and practise basic concepts and scientific process skills. The experiences of children in this period create an appropriate environment for the acquisition of concepts that are considered to be building blocks of knowledge. And the education programme developed for preschool children also aims to make children, who continue pre-school, grow up healthy by means of the rich teaching experiences; to make them reach the highest level in motor, social and emotional, language and cognitive development areas, to make them gain self-care skills and to prepare them for elementary school (Kamay & Kasker, 2006; MEB, 2013). Children develop these skills at pre-school education institutions. Educational activities used in pre-school education institutions are stated as Turkish, art, drama, music, movement, games, science, mathematics, preparation for reading and writing and field trips. Mathematics is one of the mandatory and necessary activities taught in preschool as well as in all levels. The increase in research that supports the opinion that mathematics is innate and a set of skills created during the first years of life emphasises the importance of mathematics in pre-school education (Tarim, S 2015). Regarding mathematical skills, the early academic skills in pre-school are skills such as size concepts (big-small), recognition, naming, matching, comparison, grouping, sorting, numbers, addition, subtraction and division, modelling, geometry, spatial logic, measuring, and charting (Charlesworth & Lind, 2007; Güven, 1999). Teachers are critical in enabling children to acquire these skills that will enable the effective practising of mathematics efficiency. The teacher' s beliefs/opinions/perceptions of mathematics will have an effect on the children (Kamay & Kasker, 2006).

The role of teachers in early childhood mathematics teaching

As in all levels of education, the importance of teachers in any subject and how they convey mathematics affects the children's attitudes towards mathematics (Baki & Bektas Baki, 2016; Karakus, Akman & Ergene, 2018). That is why it is important to know how mathematics concepts are taught to children in pre-school. The teacher should make mathematics interesting for children and present it to children as a fun activity (Arnas Aktas, 2005). The teacher can do structured/semi-structured/unstructured activities suitable for the physical condition of the class, the type of activity and the individual differences of the children, and the activities can be practised individually or in small or bigger groups. However, to keep children' s attention, children should be provided with different strategies, materials and options (MEB, 2013; Tarim, K & Bulut, 2006). According to literature, it is stated that teachers' self-sufficiency affects the teaching of mathematics in the preschool period (Lee & Ginsburg, 2007; Ng & Rao, 2008; Wang, Elicker, McMullen & Mao, 2008). People who do not consider themselves proficient in mathematics do not want to use mathematics (Ashcraft & Krause, 2007; Ashcraft & Ridly, 2005; Finlayson, 2014). However, teachers' pre-service attitudes will affect the quality of education. For this reason, teachers, especially pre-school teachers, should be aware of the fact that children' s mathematical perceptions develop in a process. Similarly, teachers' perceptions of mathematics and learning to teach mathematics also change throughout their teaching lives (Warfield, Wood & Lehman, 2005).

The importance of mathematics education in pre-service period

While pre-service teachers are equipped with the necessary theoretical knowledge, pre-service teachers are forced to learn how to transfer the information through their own experiences. When the undergraduate programmes are examined in detail, it is seen that the course contents and the practise forms that are expected to enhance knowledge of the field are not sufficient. In order for the undergraduate programmes to equip prospective teachers effectively in terms of teaching knowledge, there is a need for research on how to improve pre-service teachers' knowledge and make recommendations based on their results (Bektas, 2016). From literature it seems that it is widely believed that pre-service teachers do not possess the required skills (National Research Council, 2001; World Bank, 2011). However, in a report by Anne Çocuk Egitimi Vakfi ([AÇEV], 2002), the qualifications of teachers in terms of the objectives of pre-school mathematics programmes and the courses and contents of these faculties are criticised. In this report, the mathematics course in the pre-school education department in the faculty is criticised and the proposed solution is to provide pre-school teachers with more practical lessons.

Research shows that it is important to determine pre-service teachers' attitudes towards mathematics (Brown, 2003; Krows, 1999). Studies show that teachers find it difficult to support mathematical skills and have limited knowledge about early mathematics education. In this case, it is seen that teachers do not present pre-school children with proper mathematical skills as a result (Griffin, 2004; Smith, 2001; Starkey, Klein & Wakeley, 2004). In his study named "Analysis of Educational Activities of Preschool Teachers" Kesicioglu (2018) states that pre-service pre-school teachers use art activities, Turkish activities, and game activities - mathematics activities are among the least used activities. Oskay, Erdem, Akkoyunlu, Soran and Yilmaz (2010) found that pre-service education is theoretical and disconnected from practice. Aydin (2009) states that although they thought that it was necessary to plan mathematics education for pre-school teachers, they could not find good examples and models for planning mathematics teaching, and that sufficient infrastructure was not provided in pre-service. While the literature review revealed the existence of many studies about pre-service teachers, we could only find a limited number of studies about the quality of pre-school teacher education (Yildirim, K 2016). Based on all of this information, we aimed to present the opinions of pre-service pre-school teachers about the use of mathematics activities. For this purpose, answers for the following questions were sought:

1) What are the concepts most used by pre-service preschool teachers in mathematics activities?

2) What are the concepts that pre-service pre-school have the most difficulty with in using mathematics activities?

3) What are the situations in which pre-service preschool teachers have the most difficulty in applying mathematics activities?

4) What are the pre-service pre-school teachers' use of materials in mathematics activities?

5) What are pre-service pre-school teachers' integration of mathematics activities with other activities?

6) What are the methods/techniques used by pre-service pre-school teachers in applying mathematics activities?

7) Do the pre-service pre-school teachers write their own mathematical activities?

8) How much difficulty do pre-service pre-school teachers have in using age-appropriate mathematics activities?

 

Methodology

Model of the Research

In this research a qualitative design was used to present the opinions of pre-service pre-school teachers on the use of mathematics activities. Qualitative research is defined as research that follows a qualitative process to reveal perceptions and events in a natural environment as realistic as possible using qualitative data collection methods such as observations, interviews and document analysis (Creswell, 2013:183).

Study Group

The sample for this research consisted of 10 pre-service teachers in the fourth year of their education in the pre-school teaching department in 2017 to 2018 education year. The pre-service teachers in the study group were selected from the students whose GPA was above 3 and had completed the teaching practice course. Purposeful sampling was thus used to create the study group (Patton, 1987). Purposeful sampling methods have literally emerged in the process of qualitative research. Purposeful sampling allows in-depth study of situations thought to present rich data (Yildirim, A & Simçek, 2006). The sample selected according to these criteria was considered to represent the research universe with all its qualities (Tavsancil & Aslan, 2001).

Limitations of the Research

The research is limited to the statements given in semi-structured interviews by 10 pre-service teachers who were fourth-year students in the preschool education department during the 2017 to 2018 academic year, spring semester.

Data Collection

The data for the research were collected from the 10 pre-service teachers in June of the 2017 to 2018 education year. In the research, the data were collected from the pre-service teachers through the interview technique. Prior to each interview, pre-service teachers were given preliminary information about the subject and an appointment was made to conduct the interview. With the participants' consent, interviews were recorded with a voice recorder. Each interview lasted for 50 to 60 minutes. I transcribed the audio recordings as MS Word documents on computer and printed the documents, which were approved by the relevant participants.

Data collection tools

A semi-structured questionnaire, which consisted of eight questions developed by the researcher, was used as a data collection tool in order to gauge opinions of pre-service pre-school teachers about the application of mathematics activities.

During the compilation of the questionnaire, a question pool was created and the questions that served the purpose of the research were selected. The identified questions were expressed for the data sources and the questions were arranged according to the ranking principles set out in the literature (Patton, 1987; Yildirim, A & Simsek, 2006). The following criteria were taken into consideration while preparing the questionnaire: the questions should be open ended, the questions should not guide the participants' answers and the questions should be easily understood by the participants. The prepared questionnaire was presented to three experienced expert academic members (one professor, two associate professors), in this field to look at the scope and face validity thereof. The questionnaire was piloted with five pre-service teachers, and two questions, which they did not understand and were incoherent, were corrected.

Analysis of the Data

Content analysis was used to analyse the obtained data. The process content analysis process involves placing similar data together as concepts and themes, and interpreting and presenting these in a way that the reader can understand. Content analysis was used in four stages in the processing of the qualitative research data obtained from documents: (1) coding of the data, (2) finding the themes, (3) regulating the codes and the themes, and (4) identifying and interpreting the findings (Yildirim, A & Simçek, 2006). The data obtained in this study were analysed by coding separately for each pre-service teacher. The purpose of the research was taken into consideration during the coding of the data and the codes were created to suit the purpose of the research. Codes were created with the open coding method. The codes obtained were tabulated first and then interpreted. During the research, we individually examined the interviewees' statements in terms of the themes specified, and performed inter-rater reliability analysis. In this process, the formula, Inter-rater Reliability = [Consensus / (Consensus + Dissidence)] x 100 (Miles & Huberman, 1994) was used, and the percentage of inter-rater reliability was calculated as 84%. According to Kabapinar (2003), if consistency between two raters is 80% and above, the research is said to be reliable. In this context, since the percentage of consistency obtained from the study was above 90%, the resulting data were considered to be reliable. In a study in which descriptive analysis is used, it is essential for validity to include direct quotes from the interviewees and to base the results on these quotes (Yildirim, A & Sims.ek, 2006). In order to ensure the transferability of the obtained results, the data were described in detail and partly supported with direct quotes. In the direct quotes, the actual names of the participants were kept confidential, and the direct quotes were expressed as those of pre-service teacher 1, 2 (PT1, PT2) etc. We included quotes that we considered important and similar comments by different respondents were combined.

 

Results

From Table 1 it is clear that the pre-service teachers used one-to-one correspondence (f = 7), classification (f= 4) and geometrical figures (f= 3) the most in mathematics activities. It is also clear that numbers/numeration, operation, pattern, sorting and creating graphics were only used once and time and measuring concepts were used almost never. The pre-service pre-school teachers' opinions on the results in Table 1 were examined in detail (see Table 2).

From Table 3 it is clear that pre-service preschool teachers struggled most with classification, geometrical figures, sorting, charting, time, and measuring. The pre-service pre-school teachers' opinions on the results in Table 3 were examined in detail (see Table 4).

From Table 5 it is clear that the pre-service pre-school teachers struggled most with capturing the children's attention f = 5), having a crowded class f = 4) and the unsuitability of the physical area (f = 3). The pre-service pre-school teachers' opinions on the results in Table 5 were examined in detail (see Table 6).

From Table 7 it is clear that the majority of pre-service pre-school teachers (n= 9) used materials in mathematics activities. The pre-service pre-school teachers' opinions on the results in Table 7 were examined in detail (see Table 8).

 

 

From Table 9 one can see that the pre-service pre-school teachers stated that they integrated mathematics activities mostly with games (f = 10), art (f = 2), science (f = 1) and Turkish (f = 1). It is clear that pre-service teachers have never integrated mathematics activities with music, preparation for reading and writing, movement and field trips. The pre-service pre-school teachers' opinions on the results in Table 9 were examined in detail (see Table 10).

From Table 11 it is clear that pre-service pre-school teachers stated that they mostly used the mathematics activities of narration (f = 4), gamification (f = 4), demonstration (f = 2), drama (f = 1) and question-answer (f = 1). The pre-service pre-school teachers' opinions on the results in Table 11 were examined in detail (see Table 12).

Table 13 shows that pre-service pre-school teachers mostly use ready-made activities in mathematics activities (n = 7), although some of them (n = 3) wrote their own activities. The pre-service pre-school teachers' opinions on the results in Table 13 were examined in detail (see Table 14).

 

 

When Table 15 is examined, all pre-service pre-school teachers (n = 10) stated that they had difficulties in using mathematics activities with children of 36 to 48 months old. The pre-service pre-school teachers' opinions on the results in Table 15 were examined in detail (see Table 16).

 

Conclusion and Discussion

When the results of the research are examined, it is determined that pre-service pre-school teachers used more than one-to-one correspondence, classification and geometrical figures in mathematics activities. They used concepts like creating graphics and patterns very little and they did not use time and measuring concepts. Similarly, they stated that they had difficulty in using concepts such as classification, creating graphics, time, and measurement. The results of a study conducted by Orçan (2013) supports this view in that teachers did not have sufficient information related to content of the programme and did not include mathematics activities adequately. Furthermore, classroom size, overcrowding and problems such as training qualified teachers, inadequate concrete materials and training toys also contributed to the problem. Similarly, the results of an OECD (2018) report show that educational materials in Turkey are insufficient or absent compared with the OECD.

One might think that this situation originated from the fact that pre-service teachers did not have sufficient knowledge about the concepts of measuring, patterns, time and how to do the activities. The findings of this research are supported in literature. Öçal (2015) states that senior year pre-service teachers emphasise number concepts, correspondence, operation concepts, sorting and geometry in pre-school level mathematics teaching. Hachey (2013) states that pre-school teachers regard numbers and arithmetical skills as the most important focus. Aslan, Günay Bilaloglu and Aktas Arnas (2006) state that teachers spend most of their time on numbers. Based on this information, it can be said that teachers and pre-service teachers do not have enough knowledge about other mathematical concepts.

From the research results it is clear that pre-service pre-school teachers use integrated activities in mathematics activities. Köksal, Balaban Dagal and Duman (2016) found that 50% of pre-school teachers used integrated activities. However, no evidence was found in the literature on the integration of mathematics activities. The results of this research clarify this situation and show that teacher candidates integrate mathematics activities mostly with the gaming activities. Alat (2019) reports that integrated activities were not used and that not enough effort was put into relating mathematics to real life for children. It was determined that mathematics activities were limited in terms of the discussed skills and concepts and were carried out as extremely structured, teacher-focused, large-group events that required children to sit at their desks for long periods of time without individual differences among children being taken into account. Kesicioglu (2018) found similar results in his research on the analysis of pre-school teachers' educational activities and stated that preschool teachers integrated their mathematics activities mostly with gaming activities. From the literature it is clear that academic skills such as mathematics in pre-school programmes would be more beneficial if presented together with games, drama, music, language and science activities (Aktas Arnas, 2009; Dere & Ömeroglu, 2001; Eliason & Jenkins, 2003; Güven, 2000; Uyanik & Kandir, 2010). Many opportunities exist each day that may allow students to have mathematical experiences. Mathematics skills can be supported both formally during events and informally at any hour of the day and during any other activity. The teacher can consolidate mathematics skills whenever suitable, even if the children have not yet attained the gains and indicators regarding mathematics education in the flow of daily education (Aktas Arnas, 2009). Aktas Arnas (2009) indicates that the mathematical concepts could be supported with studies like comparing the dimensions of paper during artistic activities and ranking them from large to small, classification based on the colours of paint, and the lengths of the materials used. Fleming, Merrell and Tymms (2004) specify that many mathematical concepts could be made concrete and entertaining for children through drama activities. That is why it can be said that pre-service teachers insufficiently integrate mathematical activities with other activities.

One of the results of the research shows that pre-service pre-school teachers have difficulty in capturing the children's attention in mathematics activities. From the literature it is clear that one of the most important tasks of a teacher is to offer children different methods, techniques, strategies and options to keep them actively involved (Kirova & Bhargava, 2002; MEB, 2013; Tarim, K & Bulut, 2006). As mathematics development involves complex processes, it is known that mathematical concepts, skills to be acquired and the methods and techniques used in teaching these concepts depend on the teacher (Uyanik & Kandir, 2010). One of the results of this study is that pre-service pre-school teachers prefer the most direct instruction method to traditional methods in mathematics activities. It can be said that pre-service teachers' inability to use different methods/techniques results in them not being able to draw and hold children' s attention. Another reason for pre-service teachers having difficulty in implementing mathematics activities is that the physical environment is not suitable and the classes are crowded. From many studies (Kiwanuka, Van Damme, Van den Noortgate, Anumendem & Namusisi, 2015) where pre-schools were involved, it was clear that inadequate physical conditions and the large number of children in one class make it difficult to apply different activities. It is seen that another method used by pre-service teachers is gamification. Literature shows that the gamification of the mathematical skills is effective in drawing children' s attention and materialising abstract concepts (Tucker, 2014).

The findings of the research show that the majority of pre-service pre-school teachers use materials in mathematics activities. When the opinions of pre-service teachers are examined, it is clear that they prefer more open-ended, real-life activities in which they often apply waste materials. From the literature it is clear that the materials used should be more social, support learners' communication skills, increase their creativity, support their imagination, develop their ability to produce solutions to the problems, affect life skills positively, and to colour, shape, manipulate and use every-day materials (Firat & Dinçer, 2018; Kavak & Coskun, 2016). In this respect, it can be said that pre-service teachers' material choices are positive. The materials used during the activities are important for the success of pre-school education which has an important place in children' s lives (Durmuçoglu, 2013). Previous research has reported that classes taught with traditional rather than alternative methods and the use of concrete materials negatively affect students' learning of mathematics (Harper & Daane, 1998; Sloan, 2010).

Participant in this research stated that they had difficulty in using mathematics activities with children of 36 to 48 months old. From the literature it is clear that working with young children causes difficulties in some of the basic subjects of classroom management, such as taking instructions in accordance with the developmental characteristics, which result in teachers struggling with classroom management (Dinçer & Akgün, 2015). The rates of schooling in Turkey are 38% for age 3 to 5, 50% for age 4 to 5, and 66% for age 5. The low rate of schooling at a young age reveals that teachers and teaching candidates have fewer opportunities to experience teaching children in younger age groups. It can be said that they struggle to convey the instructional experiences they experience with children in older age groups to younger ages (MEB, 2019). As pre-service teachers struggle with classroom management with children in the younger age groups, they also struggle with mathematics activities. In the light of this information, the following are suggested:

• To conduct studies that will increase the theoretical and practical knowledge on the concepts that prospective teachers struggle with in mathematics activities, such as classification, geometrical figures, sorting, creating graphics, time, and measuring.

• To determine the shortcomings of pre-service teachers in contemporary teaching methods and techniques and to inform them about how to adapt these methods and techniques for pre-school education activities.

• To provide pre-service teachers with information about the preparation and application of integrated activities for the teaching of mathematics.

• That pre-service teachers are provided with information and knowledge on class management in less conducive physical environments and crowded classes.

 

Notes

i. Published under a Creative Commons Attribution Licence.

ii. DATES: Received: 23 December 2018; Revised: 13 December 2019; Accepted: 30 January 2020; Published: 28 February 2021.

 

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