Mathematics from the Perceptions of Children and Teachers in Early Childhood Education

doi:10.21203/rs.3.rs-4445309/v2

This study was conducted to determine the perceptions of children in early childhood and teachers about mathematics. A basic qualitative research method was used. The study group consisted of 26 children attending kindergarten, 69 students attending primary school, and 13 teachers. The data of the study were obtained through semi-structured interview forms and were analyzed using descriptive analysis. Most children attending kindergarten expressed mathematics as numbers, operation, lesson, and homework; most primary school students expressed mathematics as number/counting, operation, lesson, calculation, and all of life. Most teachers defined mathematics as all life, number, reasoning skills, and logical thinking. While most children stated that they use mathematics at school, at home, while shopping, and in all areas of life, almost all the teachers stated that they use mathematics in all areas. While children generally stated that they use mathematics at home, at school, and while doing activities/homework/lessons, teachers stated that they use mathematics in all areas of life, always, and with the existence of human life.

Early childhood mathematics

children

teachers

perception

What is mathematics?

Mathematics has existed throughout history and is a vital and indispensable part of daily life (Nasibov & Kaçar, 2005; Nunes & Bryant, 1996; Tekkoyun, 2014). Mathematics is essential for children to understand the world in which they live. Children without sufficient mathematical knowledge and skills face various difficulties not only in mathematics lessons but also in daily life. It has been stated that mathematics is not only a subject but also a tool for thinking. Therefore, mathematics is used not only in schools but also outside of school (Nunes & Bryant, 1996). Various terms in mathematics, such as addition, counting, and calculation, are known and used by everyone, even those who are not experts in this branch of science (Nasibov & Kaçar, 2005). Mathematics is defined as a game played with numbers and symbols, a challenging yet beautiful endeavor, life’s riddles, and a necessary element (Tekkoyun, 2014). Mathematics is generally ubiquitous in children’s daily lives. For example, children encounter various situations, such as determining which of the two plates of cookies has more or thinking about the largest number. Mathematics is, therefore, an important part of children’s play. When playing with blocks or reading storybooks, children use informal mathematical knowledge and skills related to numbers, shapes, and patterns (Ginsburg, 2006).

The National Council of Teachers of Mathematics (NCTM, 2000) has published guidelines and standards for school mathematics. There are two types of standards: content and process standards. Content standards define the content areas that students should learn, including number and operations, algebra, geometry, measurement, data analysis, and probability. The process standards describe methods of acquiring and using content knowledge, including problem-solving, reasoning and proof, connections, communication, and representation (NCTM, 2000). From the first years of life, children recognize and explore their world mathematically by finding patterns, comparing quantities, and sharing crackers with friends (National Association for the Education of Young Children [NAEYC] and National Council of Teachers of Mathematics [NCTM], 2002). Furthermore, mathematics is a branch of science based on logic. For example, children count objects according to rules based on logic (Nunes & Bryant, 1996).

Importance of Mathematics in Early Childhood

Early childhood is a period during which children actively engage in acquiring basic concepts and learning essential process skills (Charlesworth & Lind, 2013). Children possess mathematical knowledge and skills from their early years (Anthony & Walshaw, 2009; Gelman & Gallistel, 1986; Nunes & Bryant, 1996). During this period, they begin to acquire various mathematical concepts and skills, such as matching, classification, comparison, sorting, counting, addition-subtraction, spatial location, and geometry. It is emphasized that the mathematical concepts and skills acquired in these early years form the foundation for mathematics education in subsequent years, enabling children to succeed in developing more advanced mathematical concepts and skills (Aubrey et al., 2006; Aunio & Niemivirta, 2010; Claessens & Engel, 2013; Clements & Sarama, 2007, 2009; Duncan et al., 2007; Ginsburg et al., 2008; Sammons et al., 2008). Given the importance of mathematics education in early childhood, various mathematics intervention programs, such as “Pre-K Mathematics” (Klein et al., 2002), “Big Math for Little Kids” (Ginsburg et al., 2003), “Number Worlds” (Griffin, 2004), and “Building Blocks” (Sarama & Clements, 2004), have been developed to enhance preschool children’s mathematics skills. These programs have been shown to be effective in fostering the development of children’s mathematic skills (Klein et al., 2008, 2011; Sarama et al., 2008; Starkey et al., 2004).

Children’s and Teachers’ Perceptions of Mathematics in Early Childhood

Children’s interest and curiosity are crucial for learning. Increased interest and curiosity positively impact children’s mathematics achievement (Shah et al., 2018). Therefore, children’s enjoyment of mathematics activities and high intrinsic motivation boost their mathematics achievements (Collett, 2015). Vygotsky emphasized that adults significantly influence children’s mental development (Charlesworth & Lind, 2013). Early mathematics experiences shape children’s attitudes toward mathematics (Henniger, 1987). Teachers’ positive attitudes toward mathematics are a critical factor in children’s mathematical achievement (Zacharos et al., 2007). Conversely, teachers’ mathematics anxiety can negatively affect children’s mathematics anxiety and achievement (Beilock et al., 2010). It has been observed that the experiences and conversations teachers provide are influential in shaping children’s views on mathematics, with children often developing their perceptions of mathematics from social experiences. As a result, children can develop negative perceptions of mathematics from a very young age (Dağlı & Dağlıoğlu, 2018). Considering that children typically do not experience mathematics anxiety at an early age, it is vital to emphasize the importance of the preschool period and the significant role of educators’ thoughts and perceptions in preventing future mathematics anxiety. Therefore, teachers must possess strong mathematical knowledge and skills, along with positive attitudes and perceptions about mathematics, to foster a love for the mathematics and help children develop their mathematical knowledge and skills.

Importance and Purpose of the Research

In the national literature, there are studies aimed at determining the perceptions or opinions of preservice teachers in different branches (Büyükkarcı, 2023; Güner, 2013; Güveli et al., 2011; Kuzu et al., 2018; Şahin, 2013; Tarım et al., 2017); preservice preschool teachers (Çelik, 2021; Keleş et al., 2016; Yenigün et al., 2019); and parents (Ergel & Aydoğan, 2021; Öçal, 2019; Toptaş & Gözel, 2018) regarding the concept of mathematics. However, few studies have examined preschool teachers’ perceptions or attitudes towards mathematics (Aksoy, 2020; Tarım & Bulut, 2006) and preschool children’s views and perceptions of mathematics (Dağlı & Dağlıoğlu, 2018). Similarly, there are a limited number of international studies that explore early childhood educators’ perceptions of mathematics (Johnston & Bull, 2022; Thiel, 2010).

Upon reviewing the literature, no study was found that examines both the perceptions of children attending kindergarten and primary school in the 1st, 2nd, and 3rd grades, as well as teachers’ perceptions of mathematical concepts. Therefore, the purpose of this study is to determine the perceptions of kindergarten and primary school 1st, 2nd, and 3rd-grade children, as well as preschool and classroom teachers, regarding mathematics.

Research Questions

The question “What are the perceptions of early childhood children and teachers about mathematics?” constitutes the problem statement of this study. Accordingly, the subproblems of the research are as follows:

What does mathematics mean to children and teachers?
According to the children and teachers, where is mathematics used?
According to the children and teachers, when is mathematics used?

Research Design

In this study, the basic qualitative research method was used. Basic qualitative research involves understanding how people interpret their lives and experiences. The main purpose of basic qualitative research is to uncover and interpret these meanings (Merriam & Tisdell, 2016).

Participants

The study group consisted of children attending kindergarten and 1st, 2nd, and 3rd grades of primary school, along with their teachers in XXX Province, Türkiye. A convenience sampling method, which is selected based on factors such as time, money, location, and participant availability, was used (Merriam & Tisdell, 2016). The study group included 26 children attending MoNE kindergarten, 69 students attending MoNE primary school (24 1st grade students, 20 2nd grade students, and 25 3rd grade students), and 13 teachers (3 preschool teachers and 10 classroom teachers). Nine of the preschool children, 21 of the 1st grade children, 14 of the 2nd grade children, and 17 of the 3rd grade children had previously attended a preschool education institution. Almost half of the teachers who participated in the study had 26 years or more of occupational experience. Three teachers worked in kindergarten, three in 1st grade, four in 2nd grade, and three in 3rd grade.

Data Collection Tools

The data for the study were obtained through semi-structured interview forms developed to determine the perceptions of early childhood children and teachers about mathematics. To achieve this, the researchers first prepared interview questions aligned with the study's purpose. The prepared questions were then sent to experts in the subject area. Based on expert feedback, the form items were revised and finalized. In addition to demographic questions, the interview forms included open-ended questions designed to explore children’s and teachers’ perceptions of mathematics.

Data Collection

During the research process, an ethics committee approval document was obtained from the XXX Human Research Ethics Committee (decision dated November 17, 2022, numbered 2022/200). Following this, the necessary official permission to collect data from the schools was obtained from the XXX Provincial Directorate of National Education (decision dated December 15, 2022, numbered E-65902639). The principal of the school where the data would be collected was interviewed, and permission was granted. The purpose of the study was explained to the children and teachers. Parents were informed about the study's purpose through a “Family Participation Research Consent Form” sent via the children, and only children whose parents consented participated in the study. Children and teachers who voluntarily and fully agreed to participate were included in the study group. The interviews were conducted one-on-one with the children and teachers by the first author, with responses recorded on the interview form. Additionally, the interview process was recorded using a voice recorder. The data used in the study were obtained through interviews, each lasting approximately 10 minutes.

Analysing the Data

The data were analyzed using a descriptive analysis approach. According to this approach, the data were organized and interpreted according to predetermined themes. The data can be organized based on the themes revealed by the research questions or presented according to the questions used during the interviews. The aim of descriptive analysis is to present the findings in an organized and interpreted form (Yıldırım & Şimşek, 2018). In this study, themes were formed according to the questions in the semi-structured interview form. For each question, the data were first coded, then organized and grouped according to the themes, and interpreted numerically. Participants often provided answers that included more than one code in the semi-structured interview form. As a result, the frequency counts for the codes obtained from the themes during the analysis were greater than the total number of participants.

Validity, Reliability, and Ethics

This study employed several methods to ensure internal validity (credibility) in qualitative research, including appropriate and adequate participation in the data collection processes, maximum diversity in the study group and purposive sampling, expert review, intercoder consistency, and a detailed description of participants (Merriam & Tisdell, 2016). Appropriate and sufficient participation was ensured by the large number of children and teachers who voluntarily participated in the study. Maximum diversity was achieved by including children from different grade levels and teachers from different branches. The study group was also defined in detail.

Expert opinion and consistency reviews were conducted to assess the alignment between the questions in the semi-structured interview form, the data collected, and the coding performed during analysis. The interview questions were reviewed by three experts from different universities specializing in preschool mathematics education. Additionally, another researcher, an expert in preschool education, coded the data. The other coders were the researchers themselves. The participants' responses to the semi-structured interview questions were coded by both the researchers and the expert.

To ensure external validity (transferability), the study used methods such as rich and dense descriptions and maximum diversity in the study group (Merriam & Tisdell, 2016). Detailed and intensive descriptions were provided for the participants' demographic characteristics, research design, data collection tools, data analysis process, and findings, which were supported by quotations from participant interviews. Maximum diversity in the study group was also ensured, and quotations from children’s and teachers’ perspectives were frequently included. In line with ethical principles, code names were used instead of actual names to maintain anonymity. For example, preschool children were coded as C1, C2, ..., C26; 1st-grade students as FG1, FGS2, ..., FGS24; 2nd-grade students as SG1, SG2, ..., SG20; 3rd-grade students as TG1, TG2, ..., TG25; and teachers as T1, T2, ..., T13.

The expert review and supervision technique (Merriam & Tisdell, 2016), which is used to ensure consistency (reliability) in qualitative research, was also employed in this study. Reliability was ensured by clearly defining the study group and providing detailed explanations of the data collection and analysis processes. The data were coded and analyzed by the researchers, and also by another researcher who is an expert in preschool education. These analyses were then compared, and a consensus was reached.

Regarding ethics, official permission was first obtained from the XXX Human Research Ethics Committee (decision dated November 17, 2022, numbered 2022/200) and then from the XXX Provincial Directorate of National Education (decision dated December 15, 2022, numbered E-65902639). Furthermore, the teachers and children participated voluntarily and willingly in the study.

In this section, the views of preschool children, primary school children in the first, second, and third grades, and their teachers on what mathematics is, as well as where and when mathematics is used, are presented.

Views on What Mathematics Is

As part of the study, children and teachers were first asked to describe what mathematics is. The distribution of their answers is presented in Table 1.

Table 1. Children’s and Teachers’ Views on What Mathematics Is

Grades

Code

f

Preschool Period

Number

Operation

Lesson

Homework

Symbol (+, -)

Question

Don’t answer, I don’t know

Learning

Teaching

Letter

Writing

Reading

My father’s police house

Princess

11

7

6

5

4

3

2

1

1st grade

Number/counting

Operation

Lesson

Calculation

Homework

Measurement

Science (geometry, arithmetic, physics, philosophy)

Intelligence

Entertainment

10

7

5

2

1

2nd grade

Number

All of life

Operation

Knowledge

Thinking differently

Lesson

Problem solving

A tool to develop the mind

Game-Entertainment

8

7

6

4

3

2

3rd grade

Lesson

All of life

Operation

Useful

Number

Intelligence

Beautiful

Fun

Money

Requires logic

Difficult

Creativity

Success

Knowledge

Question

Learning

14

12

9

5

3

2

1

Teachers

All of life

Number

Reasoning skills

Logical thinking

Science branch

Concrete thinking

The game

The foundation of all the sciences

Symbol

8

5

4

3

2

When children and teachers were asked what mathematics is, and the answers given were analyzed, preschool children mostly defined mathematics as number, operation, lesson, and homework. First-grade students defined mathematics as number/counting, operation, lesson, and calculation. Second-grade students defined mathematics as number, all of life, operation, and knowledge. Third-grade students defined mathematics as lesson, all of life, operation, usefulness, number, and intelligence. Teachers, on the other hand, mostly defined mathematics as all life/indispensable/everything, number, reasoning skills, and logical thinking. Some views of children and teachers on what mathematics is are as follows:

C1: “…It is a lesson. It is learning. Letters and numbers. Addition, subtraction, division, and multiplication…”

C5: “…1 and 2 come to mind…”

C7: “…I think math is adding apples. We’re doing addition…”

C11: “…Questions coming up. What is 2+2? There are numbers. We learn numbers and become great men…”

C16: “…I don’t know. Is she like a princess or something? …”

C19: “…My father’s police house. It means studying.…”

FG1: “…Calculations…”

FG22: “…Mathematics is a subject where we add and subtract numbers…”

SG1: “…Operations that we encounter in every part of our lives…”

SG2: “…I think math is everything, play, fun, logic…”

SG14: “…Indispensable in our lives…”

SG20: “…Solving questions…”

TG1: “…Something made of numbers and operations that fundamentals the world…”

TG5: “…Mathematics is a beautiful subject that requires logic and is useful in every subject…”

T6: “…Mathematics is not just numbers, symbols, and formulas taught in schools. It is the reasoning and logic that we are born with and in every aspect of our lives. Mathematics is also an important field in the development of science and technology…”

T9: “…It is essential to life. It is play…”

T10: “…Mathematics is the cornerstone of human life. Mathematics and spatial relations form the foundation of human life, and vital relations strengthen human reasoning. Life infrastructure is built using mathematics. In short, the foundation stone of life is laid strongly with mathematics...”

When early childhood children’s views on what mathematics is are evaluated, they generally define mathematics as number, homework, lesson, operation, and calculation across all grade levels. However, it was also revealed that some preschool children described mathematics using unrelated expressions, such as “princesses” and “my father’s police house.” This can be explained by the high level of imagination typical of preschool children. Additionally, it was found that children’s statements about what mathematics is tend to shift from concrete to abstract as their grade level increases. For instance, the opinions of second- and third-grade children who defined mathematics as “the whole of life” were noted. Based on these views, it can be said that children in higher grades explain mathematics with more abstract concepts. When teachers’ views on what mathematics is are evaluated, they generally express mathematics as “the whole of life.” However, it was revealed that teachers described mathematics using both concrete and abstract expressions. Based on the teachers’ views, it can be concluded that they perceive all of life as being intertwined with mathematics.

Views on Where Mathematics Is Used

Children and teachers were asked where they use mathematics, and the distribution of their answers is presented in Table 2.

Table 2

Children’s and Teachers’ Views on Where Mathematics Is Used

Grades

Code

f

Preschool Period

At school

At home

Outside/Park

Shopping

Large classes

In homework

Counting

When asked a question

Playing with toys

Everywhere

28

13

6

4

2

1

1st grade

During shopping

In all areas of life/everywhere

At the bank

In operation

At school

At home

22

11

5

4

2

2nd grade

In all areas of life/everywhere

During shopping

In lesson

Using the clock

In construction

Counting money

In measurement

In commerce

In operation

17

5

4

3

2

3rd grade

In all areas of life/everywhere

In operation

In textile

During shopping

At school

In exams

When asked a question

In the race

At work

In measurement

In the picture

At home

16

5

4

3

2

1

Teachers

In all areas of life/everywhere

In engineering

At school/class

During shopping

Calculations (age, money, hours)

At home

In statistics

12

5

3

2

The children and teachers were asked where they used mathematics. When the answers were analyzed, it was found that all preschool children stated they used mathematics at school, while half of them mentioned using it at home. Most first-grade students reported using mathematics while shopping. More than half of the second- and third-grade students stated they used mathematics in all areas/everywhere in life, and almost all the teachers indicated that they used mathematics in all areas/everywhere in life. Preschool children also mentioned using mathematics mostly outside/in the park, during shopping, and in large classes. First graders reported using mathematics in all areas of life/ everywhere, at the bank, in operations/calculations, at school, and at home. Second graders noted using mathematics while shopping, in lessons, when using the clock, and in construction. Third graders stated they used mathematics in operations, textiles, shopping, at school, during exams, and when asked questions. Teachers indicated they used mathematics in engineering, at school/in lessons, and while shopping. Some views of children and teachers on where mathematics is used are as follows:

C3: “…At school, at home, whenever our mother bought us hats…”

C14: “…In schools, big schools; it is not used anywhere else…”

C17: “…We use it at school until the age of 25…”

C21: “…In 1st grade, 2nd grade, at home, at school, on the street. Sometimes my sister takes her homework and does it on a picnic…”

FG2: “…We use it in markets, in banks, in meteorology, and in many areas of our lives…”

FG7: “…Counting money, calculating time, using the remote control, determining prices…”

SG1: “…It is present in all areas of life…”

SG12: “…We use math everywhere in our lives…”

TG18: “…Everywhere, all the time, in life, in questions, in exams…”

TG24: “…Whenever you need it…”

T2: “…Sometimes more, sometimes less, but we always need and use mathematics in our lives. We can find traces of mathematics in everything human hands touch- the car we drive, the phone we use, etc…”

T5: “…We use mathematics in every field. We use it in science, daily life, and all areas of work. It seems there is no field where mathematics does not play a role. The functioning of machinery, molecular components in medicine- it is endless. In its simplest form, clock calculations involve converting hours into minutes. The number of heartbeats and length measurements are all based on math. Wherever we look, math is at its foundation…”

When the views of early childhood children and teachers on where mathematics is used are evaluated, it was found that across all grade levels and among teachers, mathematics is generally used at school, while shopping, and at home. Additionally, as children advance to higher grade levels, there is an increase in the number of students who recognize that mathematics is used in all areas or everywhere in life. It was also emphasized that almost all teachers reported using mathematics in all areas or everywhere in life. Based on the opinions of the children, it can be concluded that the areas where mathematics is used become more diverse as children progress to higher grade levels.

Views on When Mathematics is Used

Children and teachers were asked about when they use mathematics. The distribution of their responses is presented in Table 3.

Table 3: Views of Children and Teachers on When Mathematics is Used

Grades

Code

f

Preschool Period

At home

When doing activities/homework

At school

I do not use

Outside

When performing the operation

When asked a question

Sometimes

13

9

7

4

3

2

1st grade

When shopping

When doing lesson/homework

At school

At home

When playing games

When counting money

Every day

When telling the time

When performing the operation

When necessary

16

11

8

6

3

2

2nd grade

When shopping

Always

When doing lesson/homework

When problem solving

At school

When looking at the clock

At all necessary times

When playing games

When measuring

9

7

5

4

3

2

3rd grade

At school

When shopping

When necessary

At home

Questions related to mathematics

On the street

Most of the time

Always

In the races

When at work

When measuring

While playing a match

When I am bored

When performing the operation

I don’t use it much

10

8

5

4

3

2

1

Teachers

In all areas of life

Always

With the existence of human life

At school

When problem solving

When necessary

Outside

6

5

2

1

When children and teachers were asked about when they use mathematics and their responses were analyzed, preschool children primarily use mathematics at home, when doing activities/homework, and at school. 1st grade students reported using mathematics when shopping, doing lesson/homework, at school, and at home. 2nd grade students indicated they use mathematics when shopping, always, when doing lesson/ homework, and when solving problems. 3rd grade students mentioned using mathematics at school, when shopping, and as needed. Teachers generally use mathematics in all areas of life, always, and in relation to the existence of human life. Some views of children and teachers on when mathematics is used are as follows:

C2: “…I will use it when I grow up…”

C7: “…When I do my activities…”

C11: “…I use it when my sister asks me questions. I use it at home…”

FG2: “…When telling the time, shopping, and counting…”

FG8: “…When I go to the market, when I calculate the hours, and when I figure out how many days are left until my birthday…”

SG6: “…I use it when I buy bread and when I shop…”

SG15: “…In lessons, at the market, in the canteen, and while playing…”

TG7: “…I use math in math lessons, when I do my math homework, and when I shop…”

TG9: “…I use math when I am bored because it’s fun for me…”

T3: “…It is used whenever and wherever it is needed in our lives…”

T5: “…I have been using math in the simplest ways since I can remember. It”s mathematical to know how old I am, to see that I’m getting taller, and to understand that my temperature increases to 39 when I have a fever. I think we’ve been using math since we’ve known ourselves…”

T6: “…We use mathematics constantly in our daily lives. For example, while looking at the clock, shopping, solving problems, thinking, in lessons, and in various areas we cannot even count…”

When evaluating early childhood children's opinions about when they use mathematics, it is observed that mathematics is generally used at home, at school, and during activities, homework, or lessons across all grade levels. However, while some preschool children reported not using mathematics, many 2nd and 3rd grade students indicated that they use mathematics constantly, most of the time, or whenever necessary. In contrast, when assessing teachers’ views on when mathematics is used, it is possible to say that they use more abstract expressions.

Most preschool children expressed their understanding of mathematics in terms of number, operation, lessons, and homework. Most first- grade studenrs viewed mathematics as number/counting, operation, lesson, and calculation. Second-grade students described mathematics as number, all of life, operation, and knowledge. Third-grade students associated mathematics with lesson, all of life, operation, useful, number, and intelligence. Teachers generally described mathematics as encompassing all of life, number, logical thinking, and reasoning skills. Dağlı and Dağlıoğlu (2018) investigated children’s perceptions of mathematics and found that children mostly recognized numbers, geometry, and grouping materials. The study revealed that children most commonly associated mathematics with numbers and defined it as “studying”. However, while children often viewed mathematics as “a difficult lesson”, “something challenging”, “homework for older sisters and brothers”, some children admitted they did not know what mathematics was. Only one child described it as “learning about shapes” and very few associated it with operations like “addition-subtraction”. The study concluded that children’s perceptions of mathematics are largely influenced by their environment and social experiences, that children perceive mathematics as difficult and complex. According to the NCTM (2000), numbers are fundamental to mathematics curricula. Supporting this, Baroody (2004) noted that children frequently encounter numbers in their daily lives. Therefore, it is expected and natural that children and teachers in the current study associate mathematics with number-counting. Öçal (2019) explored parents’ perceptions of mathematics and found that parents generally view it as involving numbers and operations, while also emphasizing its connection to daily life. Öçal’s study highlighted parental perceptions of mathematical skills used in everyday life, such as counting, operations, symbols, early mathematical skills (e.g., sorting, comparing, matching, classifying), geometry, and measurement. This finding aligns with the children’s use of various mathematical concepts and skills in the present study. Ergel and Aydoğan (2021) revealed that parents view mathematics as being related to all areas of life. Toptaş and Gözel (2018) found that metaphors related to life, play, and air-water were especially prominent in parents’ perceptions of mathematics. These findings are consistent with the views of children and teachers in the present study, who stated that mathematics encompasses all of life and forms the basis of all sciences. Similarly, Markovits (2011) emphasized that mathematics is a major part of daily life. Umay (1996) noted that despite its importance, mathematics is generally perceived as difficult by society. Ginsburg (2006) highlighted that play can facilitate mathematical learning and is crucial for children’s cognitive development. Therefore, it is not surprising that some children in the present study referred to mathematics as a game. Additionally, very few children in the study stated that they did not know what mathematics was. Although most preschool children in the study had not previously received formal preschool education, they offered various comments on mathematics. In contrast, Collett (2015) reported that most kindergarten students were unclear about the meaning of mathematics.

Güveli et al. (2011) highlighted that preservice primary school teachers perceived mathematics as an exciting, difficult, and boring lesson, consisting of many subjects. Güner (2013) found that most preservice mathematics teachers stated that mathematics is life itself and that it is an enjoyable endeavor. Tarim et al. (2017) found that preservice primary school teachers frequently used metaphors such as “life, intelligence cube, game, puzzle, computer” to describe the concept of mathematics. Büyükkarcı (2023) found that preservice primary school teachers created metaphors like “puzzle” and “life” to describe the concept of mathematics. Çelik (2021) emphasized that the categories of “necessity” and “difficulty” stand out in preservice preschool teachers’ perceptions of mathematics. The most frequently used metaphor for mathematics was “life”. and metaphors like “water, nightmare, puzzle, space, universe, maze” were also common. Tarım and Bulut (2006) found that most preschool teachers described mathematical concepts as numbers and shapes, enjoyed incorporating mathematics into activities, and used “games”, “concrete materials”, and “activities” in their teaching. Thiel (2010) stated that preschool teachers recognized the benefits of mathematics for daily life, but most perceived it only as numbers and shapes. Johnston and Bull (2022) emphasized that educators consider mathematics necessary and important for children from birth to the age of five.

According to current research, all preschool children reported using mathematics at school, half reported using it at home, and most first-grade students mentioned using mathematics while shopping. More than half of the second and third-grade students indicated that they use mathematics in all areas of life, and nearly all teachers stated that they use mathematics everywhere in life. Preschool children specifically noted using mathematics mostly outside/in park, while shopping, and in large classes; first graders in all areas of life/everywhere, at the bank, in operations, and at school; second graders during shopping and in lessons; third graders in operations, textiles, shopping, at school, during exams, and when asked questions; and teachers in engineering, at school/class, and while shopping. Güven (2005) emphasized that both home and school environments are crucial for the development of children’s mathematical skills. Starkey et al. (2004) highlighted the importance of a systematic mathematics program in preschools and at home to develop children’s mathematical abilities. Libertus (2023) underscored the significant role of the home learning environment in the development of children’s mathematical skills, noting that mathematics is used in daily activities such as cooking and shopping. Sonnenschein et al. (2012) and Jay et al. (2018) demonstrated the importance of incorporating daily life activities at home to support children’s mathematical skills. Nunes and Bryant (1996) emphasized the importance of mathematics in social environments. Ergel and Aydoğan (2006) found that the kitchen, living room, and children's rooms were typically used for activities supporting mathematical skills, whereas outdoor spaces like parks, gardens, streets, and avenues were not commonly mentioned. Ginsburg (2006) stated that mathematics is present in all aspects of children’s daily lives and is an integral part of their play. Ergel and Aydoğan (2021) revealed that parents view play as the most important factor in supporting children’s math skills. The fact that some children in the present study reported using mathematics while playing with toys aligns with the association of mathematics with play, as seen in the studies by Ginsburg (2006) and Ergel and Aydoğan (2021). The statements by teachers and children in this study, indicating that mathematics is used at school, at home, on the street, outdoors, and everywhere, are consistent with the findings in the literature.

Mathematics has always been a fundamental part of human life (Nasibov & Kaçar 2005). According to current research, most preschool children reported using mathematics primarily at home, during activities/ homework, and at school. Most first-grade students stated that they used mathematics while shopping, during lessons/ homework, at school, and at home. Second-grade students reported using mathematics while shopping, alwyas, during lessons/ homework, and when solving problems. Most third-grade students indicated they used mathematics at school, while shopping, when necessary, and at home. Additionally, the majority of teachers stated that they used mathematics in all areas of life, always, and with the existence of human life. Ergel and Aydoğan (2021) revealed that parents believe that games play with peer in children’s daily activities, at home, during outdoor play, reading time, music and art activities, trips and visits, and caring for plants and animals, especially on the street, are effective factors in developing children’s mathematical skills. Nunes and Bryant (1996) noted that, in addition to using mathematics at school, low-income children often use mathematics outside of school, such as on the streets, by selling fruit, candy, drinks, and other items. Kennedy et al. (2008) emphasized that people use spatial perception in their daily lives, such as organizing furniture, parking cars, and applying geometric relations to measure distances and estimate length and area. The NAEYC-NCTM (2002) stated that mathematics helps children understand life outside of school. Children need mathematics not only in primary and secondary education but also in science, social studies, and other subjects. Consequently, people use mathematics at work, at home, in society, and when making various decisions in their lives. Markovits (2011) noted that mathematics is used in almost all aspects of daily life, including shopping, calculations, operations, telling and calculating time, and measuring. Umay (1996) emphasized that mathematics is used throughout the day, such as when calculating time, at home, on the road, shopping, solving problems, watching TV, counting, and performing operations. In the present study, the finding that teachers and children stated that mathematics is used in various contexts aligns with the existing literature. Another significant finding of this study is that teachers mentioned using mathematics since the beginning of their lives. This observation is supported by Nasibov and Kaçar (2005), who noted that mathematics has existed for as long as human history.

Jean Piaget significantly contributed to our understanding of children’s cognitive development. Piaget analyzed cognitive development across four stages. In early childhood, educators focus on the sensorimotor period, the entire preoperational period, and part of the concrete operational period. During the preoperational period, children’s thinking is more limited, and they tend to think in one dimension (Charlesworth & Lind 2013). Additionally, children in this stage have limited reasoning skills (Buldu, 2019).

The study’s results revealed that most children, particularly the younger ones, perceived mathematics as a subject or a lesson-related activity, associating it with school and home, and recognizing its use by teachers. This observation aligns with Piaget’s theory of cognitive development, as most children in this study were in the preoperational stage. According to Piaget’s theory, it is expected that younger children’s perceptions of mathematics are more concrete and limited, but as they grow older, their perceptions evolve, expand, and become more abstract. Supporting this conclusion, Nunes and Bryant (1996) noted that as children age, their mathematical concepts, knowledge, and experiences increase, leading to a shift in their understanding of mathematics. Similarly, Charlesworth and Lind (2013) emphasized that as children develop physically, socially, and cognitively, their concepts also evolve. Akman (2002) pointed out that preschool children do not fully grasp the abstract aspects of mathematics, which supports the finding that preschool children’s perceptions of mathematics are primarily concrete, as indicated in the present study.

Given that early mathematics education significantly impacts students’ later achievement in mathematics, it is crucial to explore both children’s and teachers’ perceptions of mathematics during these formative years. Since teachers’ perceptions shape their attitudes and behaviors, which in turn influence children’s perceptions, it is essential to foster positive perceptions of mathematics among teachers. To address these issues, future research should focus on introducing mathematics to children through engaging and enjoyable methods, such as games, which may help alter any negative perceptions children might have. Additionally, it is important to increase awareness among families and teachers about the significance of integrating mathematics into everyday life.

Disclosure statement

The authors report there are no competing interests to declare.

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The authors declare no competing interests.

Mathematics from the Perceptions of Children and Teachers in Early Childhood Education

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Abstract

Introduction

Method

Findings

Conclusions and Discussion

Future Research

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Additional Declarations

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