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

## 3.1. Views on what mathematics is

Within the scope of the study, children and teachers were first asked what mathematics is, and the distribution of the answers is presented in Table 3.

Table 3

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 3 2 2 2 2 2 1 1 |

1st grade | Number/counting Process Lesson Calculation Homework Measurement Science (geometry, arithmetic, physics, philosophy) Intelligence Entertainment | 10 10 7 5 2 2 2 2 1 |

2nd grade | Number All of life/indispensable/everything Operation Information Thinking differently Lesson Problem solving A tool to develop the mind Game-Entertainment | 8 7 6 4 4 3 3 2 2 |

3rd grade | Lesson All of life/indispensable/everything Operation Useful Number Intelligence Beautiful Fun Money Requires logic Difficult Creativity Success Information Question Learning | 14 12 9 9 5 5 3 2 1 1 1 1 1 1 1 |

Teachers | All of life/indispensable/everything Number Reasoning skills Logical thinking Science branch Concrete thinking The Game The foundation of all the sciences Symbol | 8 5 4 3 2 2 2 2 2 |

When children and teachers were asked what mathematics is and the answers given were analysed, preschool children mostly defined mathematics as number, operation, lesson, and homework; 1st grade students defined mathematics as number/counting, operation, lesson, and calculation; 2nd grade students defined mathematics as number, all of life/indispensable/everything, operation, and knowledge; and 3rd grade students defined mathematics as lesson, all of life/indispensable/everything, operation, useful, 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 maths 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.…*

C23: *“…To collect and remove things. One, two, three, four, five, six, seven, eight, nine, ten…”*

FG1: *“…Calculations…”*

FG2: *“…Mathematics is addition…”*

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 maths is everything, play, fun, logic…”*

SG7: *“…Numbers, addition, subtraction, multiplication, division…”*

SG10: *“…Mathematics is made up of numbers…”*

SG14: *“…Indispensable in our lives…”*

SG20: *“…Solving questions…”*

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

TG4: “…*In my opinion, mathematics is the numbers found by adding, subtracting, etc. with different numbers and the operations we use in our daily lives…”*

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

TG7: *“…I think mathematics is a little bit difficult, but very fun, consisting of numbers…”*

TG14: *“…I think maths is a profession, a mind…”*

T1: *“…A branch of science that includes numbers, shapes, logical problem solving, and reasoning skills..."*

T2: *“…The transformation of abstract concepts in the human mind into concrete forms is called mathematics. It is the science of numbers. The science enters our lives with numbers before we even start learning to read and accompanies us throughout our lives…”*

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. The infrastructure of life is built using mathematics. In short, the foundation stone of life is laid strongly with mathematics..."*

T13: *“…I think maths is playing with and loving numbers…”*

When early childhood children’s views on what mathematics is are evaluated, it is seen that they generally define mathematics as number, homework, lesson, operation, and calculation in all grade levels. However, it was also revealed that some preschool children expressed mathematics with unrelated expressions such as princess, my father’s police house, etc. This can be explain by the high imagination of preschool children. It was also found that children’s statements about what mathematics is changed from concrete to abstract as their grade level increased. In fact, the opinions of second- and third-grade children who expressed mathematics as the whole of life were encountered. Based on the views of the children, it can be said that they explain mathematics with more abstract expressions in higher grades. When the teachers’ views on what mathematics is are evaluated, it is seen that they generally express mathematics as the whole of life. However, it was revealed that teachers expressed their views on what mathematics is with concrete and abstract expressions. On the basis of the teachers’ views, it can be concluded that they express all of life as mathematics.

### 3. 2. Views on where mathematics is used

Children and teachers were asked where they used mathematics, and the distribution of the answers is presented in Table 4.

Table 4

Children’s and teachers’ views on where mathematics is used

Grades | Code | f |

Preschool Period | At school At home In the outside/Park Shopping Large classrooms In homework Counting When asked a question Playing toys Everywhere | 28 13 6 6 4 2 1 1 1 1 |

1st grade | During shopping In all areas of life/ everywhere At the bank In operation At school At home | 22 11 5 5 4 2 |

2nd grade | In all areas of life/ everywhere During shopping In lesson At the clock In construction Counting money In the measurement In commerce In operation | 17 5 4 3 3 2 2 2 2 |

3rd grade | In all areas of life/everywhere In operation In textile During shopping At school In examination When asked a question In the race At work In the measurement In the picture At home | 16 5 4 4 4 3 3 2 2 2 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 3 3 2 2 |

Children and teachers were asked where they used mathematics and when the answers were analysed, all of the preschool children stated that they used mathematics at school, half of them used mathematics at home; most of the first-grade students stated that they used mathematics while shopping; more than half of the second- and third-grade students stated that they used mathematics in all areas/everywhere in life; and almost all of the teachers stated that they used mathematics in all areas/everywhere in life. On the other hand, preschool children stated that they used mathematics mostly outside/in the park, in shopping, and in large classes; 1st graders in all areas of life/everywhere, at the bank, in operations/calculation, at school, and at home; 2nd graders in shopping, in lessons, at the clock, and in construction; 3rd graders in operations, in textiles, in shopping, at school, in exams, and when asked questions; and teachers in engineering, at school/in lessons, and in shopping. Some views of children and teachers on where mathematics is used are as follows:

*C3: “…At school, at home, when 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…”*

*C19: “…There’s a maths lesson at school. It happens in my sister’s maths lesson too. It is also done at home..."*

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

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

*FG7: “…Counting money, calculating the time, on the remote control, prices...”*

*FG20: “…At school and shopping..."*

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

*SG5: “…Coins, measuring, clocks, measuring liquids, etc...”*

*SG7: “…In lessons, in shopping, in professions...”*

*SG12: “…We use maths everywhere in our lives...”*

*SG16: “…In every corner of our lives..."*

*TG1: “...It is used everywhere in life, like the things we must have with us everywhere in life, like water...”*

*TG13: “...used at work, school, etc...”*

*TG18: “…Everywhere, everytime, 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 that human hands touch. The car we drive, the phone, etc...”*

*T5: “...We use mathematics in every field. We use it in science, in daily life, and in all fields of work. It is like there is no field in which mathematics does not enter. The functioning of machinery, the molecular components in medicine... it is endless. In the simplest sense, in clock calculations, we convert hours into minutes. The number of beats of our heart and length measurements. Wherever we look, there is maths at its foundation...”*

*T8: “...It is used in all fields of science. For example; to read the clock, to shop. When we build a building, when we park our car, etc...”*

When the views of early childhood children and teachers on where mathematics is used are evaluated, it is seen that all grade levels and teachers stated that mathematics is generally used at school, shopping, and at home. In addition, at higher grade levels, there was an increase in children’s responses that mathematics is used in all areas/everywhere in life. In addition, it was emphasised that almost all the teachers used mathematics in all areas/everywhere in life. Based on the opinions of the children, it is possible to say that the areas of use of mathematics diversify as children’s grade levels increase.

### 3. 3. Views on when mathematics is used

Children and teachers were asked when they used mathematics, and the distribution of the answers is presented in Table 5.

Table 5

Children’s and teachers’ views on when mathematics is used

Grades | Code | *f* |

Preschool Period | At home When performing activities/homework At school I do not use Outside When performing the operation When asked a question Sometimes In Ankara | 13 9 7 4 3 3 2 2 1 |

1st grade | When shopping When doing lesson/homework At school At home When playing games When counting money Every day When telling the clock When performing the operation When necessary | 16 11 8 6 3 3 2 2 2 2 |

2nd grade | When shopping Always When doing lesson/homework When problem solving In class When looking at the clock At all necessary times When playing games When measuring | 9 7 5 4 3 3 3 2 2 |

3rd grade | When shopping In class When necessary Questions related to mathematics In the classroom/school At home 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 | 8 7 5 3 3 4 3 3 2 2 2 1 1 1 1 1 |

Teachers | In all areas of life Always With the existence of human life At school When problem solving When necessary At outside | 6 6 5 2 2 2 1 |

When children and teachers were asked when they use mathematics and the answers were analysed, preschool children stated that they mostly use mathematics at home, when doing activities/homework, and at school; 1st grade students stated that they use mathematics when shopping, when doing lessons/homework, at school, and at home; 2nd grade students stated that they use mathematics when shopping, all the time, when doing lessons/homework, and when solving problems; 3rd grade students stated that they use mathematics when shopping, in lesson, and when necessary; and most teachers stated that they use mathematics in all areas of life, all the time, and with the existence of human life. Some views of children and teachers on where mathematics is used are as follows:

*C1: “…I use it at school. I use it at home. I perform multiplication. I encounter numbers in performances…”*

*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…”*

*C21: “…Only Saturday, then I love it very much…”*

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

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

*FG11: “…Sometimes I use them to collect things when I play games…”*

*FG15: “…When doing homework…”*

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

*SG15: “…In lesson, in the market, in the canteen and at play…”*

*TG4: “…When he appeared in front of me and the teacher asked…”*

*TG7: “…I use maths in maths lessons, when I do my maths homework, when I shop…”*

*TG9: “…I use maths when I am bored. Because maths is like fun for me…”*

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

*T5: “…I have been using maths, in the simplest way, ever since I can remember when I was the youngest. It’s mathematical to know how old I am, it’s mathematical to see that I’m getting taller, it’s mathematical to know that when I have a fever, my temperature goes up to 39. I think we have been using maths since we know 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 that we cannot count…”*

When the opinions of early childhood children about when they use mathematics are evaluated, it can be said that mathematics is generally used at home, at school, and while doing activities/homework/lessons by all grade levels. However, while some preschool children stated that they did not use mathematics, some children in the 2nd and 3rd grades stated that they used mathematics always, most of the time, and all the time when necessary. When the teachers’ views on when mathematics is used are evaluated, it is possible to say that they use more abstract expressions.

## 3.4. Opinions on in which profession mathematics is used more

Children and teachers were asked in which profession mathematics is used more, and the distribution of the answers is presented in Table 6.

Table 6

Children’s and teachers’ views on professions in which mathematics is used more

Grades | Code | *f* |

Preschool Period | Teacher Doctor Police Nurse Firefighter Market employees Engineer Soldier Worker | 22 9 7 5 3 1 1 1 1 |

1st grade | Teacher Banker Market employees Engineer Accountant Salesman Architect Financier All professions Officer Police Farmer Pilot Builder Drivers Lawyer Doctor Scientist Electrician Statistics expert Mathematician Economist | 16 8 7 5 5 4 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |

2nd grade | Teacher Engineer Scientists Accountant Market/grocery store employees Architect Textile Manufacturer Salesman Marble maker Waiter All professions Tailor Cook Worker Financier Banker Pharmacist Doctor A person engaged in trade | 10 8 5 5 5 3 1 1 1 1 1 1 1 1 1 1 1 1 1 |

3rd grade | Teacher Market/grocery store employees Doctor Architect Engineer Tailor Textile Manufacturer All professions Carpenter Banker Athlete Pilot Courier Academician Baker | 16 11 8 5 5 4 4 3 3 2 2 1 1 1 1 |

Teachers | Engineer All professions Teacher Astronomy and space sciences Doctor Economist Statistician Architect Physicist Tailor Accountant Grocery Store Butcher Banker Financier Mathematician Map cadastre technician Chemist Philosopher Geophysicist | 10 7 6 5 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 |

Children and teachers were asked which professions use mathematics the most, and when the answers were analysed, preschool children stated that teachers, doctors, and police use mathematics the most; 1st grade students stated that teachers, bankers, market employees, engineers, and accountants use mathematics the most; 2nd grade students stated that teachers, engineers, scientists, and accountants use mathematics the most; and 3rd grade students stated that teachers, market/grocery store employees, doctors, architects, and engineers use mathematics the most.Teachers, on the other hand, stated that mathematics is used more in engineers, all professions, teachers, astronomy, and space sciences, respectively. Some opinions of children and teachers about the professions in which mathematics is used more are as follows:

*C4: “…Teacher, doctor, nurse…”*

*C6: “…Police, teachers…”*

*C20: “…Teacher. Other professions do not use...”*

*C19:” …A teacher uses it. My father is a police, he doesn't use maths…”*

*C24: “…Teachers, engineers, but no one else can use it...”*

*FG13: “…Teachers, electricians, bankers, engineers…”*

*SG4: “…In trade, accounting, stores, in fact in every profession there is maths…”*

*SG5: “…Engineering, architecture, cooking, tailoring, etc…”*

*SG8: “…Teachers, market workers use it more..."*

*SG19: “…Engineer, scientist, etc…”*

*TG1: “…I think it is used more in medicine and teaching..."*

*TG5: “…Teaching, carpentry and tailoring…”*

*TG8: “…I think it is used in countless professions…”*

*T2: “…Whatever we do, we use mathematics to a greater or lesser extent. In all branches such as teaching, engineering, tailoring, etc..."*

*T8: “…There are mathematics in every kind of engineering, teaching, grocery, butcher, in short, in every profession. When a doctor performs surgery, he calculates the place to cut millimetrically..."*

*T12: “…All professions involve mathematics. There must be. Mathematics is life..."*

When the opinions of early childhood children on the professions in which mathematics is used more were examined, it was revealed that children in all grade levels stated that mathematics is mostly used in the teaching profession. However, although children stated that mathematics is used in a wide variety of professions, it is possible to say that this diversity is higher in higher grades. There were also some 1st, 2nd, and 3rd grade students who stated that mathematics is used in all professions. When the opinions of the teachers were evaluated, they emphasised that mathematics is mostly used in engineering, all professions, teaching, astronomy, and space sciences.