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MATHEMATICS IMPORTANCE IN OUR LIFE

Jitka Hodaň ová , David Nocar

Palacký University in Olomouc (C ZECH REPUBLIC)

Abstract

Contemporary life demands the requirement to have good mathematical knowledge. Mathematics is

important for life and supports all-round personal development. Mathematics significantly influences

pupils' and students' education both in a special branch (mathematical knowledge) and in terms of

moral education.

We can find mathematical application in the nature, technology, architecture, machinery, building

industry, in the banking sector, in research, cartography etc. There are very interesting applications in

genetics and in using mathematics in the nature. Statistical methods are used in hypothesis testing in

genetics. By using mathematics, we can create statistical descriptions of quantitative relations. When

we process research data, we need arithmetical diameter, scattering, standard deviation etc.

In our paper we focus on the use of mathematics in human life. Our aim is to demonstrate that

mathematics is not only the basis in technical fields but is also applied in the nature (some

mathematical theories). Mathematics is the basis for research methods.

We can develop pupils' interest in mathematics with the help of quality education, because

mathematics is a part of our daily routine and influences the quality of our life and the quality of our

professional orientation.

We carried out a research with the aid of a questionnaire to find out the interest in mathematics in

pupils. We sent the questionnaires to selected schools. The questionnaire consists of 11 questions.

Four questions were closed and seven were open. Our goal was to increase the pupils' interest in

mathematics. We wanted to influence the professional orientation of pupils and students and make

them interested in technical fields, which are more useful in the labour market.

Keywords: mathematical application in our life, technical application of mathematics, mathematics in

nature, mathematics in research.

1 INTRODUCTION

The international TIMSS survey, which has taken place every four years since 1995, examines the

findings of mathematical education and education in natural science in 4th- and 8th-grade pupils.

Different countries participate in the research. Teachers of mathematics and natural science then use

the results of these surveys in the education of pupils and students. The Czech Republic took part in

the survey in the years 1995, 2007 and 2011. [2], [8].

In the years 2005 - 2007, a survey was conducted at selected schools. In this survey, the relationship

of the pupils to individual subjects and the popularity of the subjects were examined. Mathematics was

on the last places in the rankings in terms of popularity as well as in terms of the pupils' marks.

Mathematics was also designated as the second most difficult subject; however, in terms of

importance it was ranked third. [7] .

Also, under a grant STM-Morava at Palacký University in Olomouc , in the years 2006 – 2007, a

project called Playful Mathematics was carried out, whi ch was trying to implement the unconventional

activities from real life to math teaching at elementary school and to influence the attitudes and pupils'

interest about mathematics . [5].

2 THE RELATIONSHIP OF PUPILS TO MATHEMATICS - SURVEY

The objective of our survey was to find out the relationship of pupils to mathematics in different types

of schools. We also examined whether pupils and students realised that they would need mathematics

and natural science in practice. We also tried to identify the interest of pupils and students in the study

of technical fields.

Proceedings of INTED2016 Conference

7th-9th March 2016, Valencia, Spain

The total number of respondents was 115 pupils and students. The respondents included 61 girls and

54 boys aged 12-21. The questionnaire survey was conducted at the following schools: Tatenice

Primary School (Czech Republic), Lanškroun Grammar School (Czech Republic) and Lanškroun

Secondary Vocational School (Czech Republic). The questionnaire included 11 questions, of which 4

were closed (questions No. 2, 5, 8 and 10) and 7 were open. In the closed questions (No. 2, 5 and

10), the pupils and students could choose YES or NO. In question No. 8, they could choose from

EXCELLENT, COMMENDABLE, GOOD, SUFFICIENT and INSUFFICIENT.

The questionnaire included the following questions:

1. What do you imagine when you hear the word "mathematics"?

2. Is mathematics among your favourite subjects?

3. Which mathematical topics did you like?

4. Which mathematical topics did you fail to understand?

5. Which mathematical topics were the most difficult for you?

6. Do you solve tasks at school which you might encounter in practice?

7. What of mathematics do you use in everyday life?

8. What mathematics mark have you got on your school report most often?

9. Specify areas in which mathematics is used in practice.

10. Would you like to study a technical field? Which one?

11. What could change your relationship to mathematics?

In this paper, we include only some interesting findings that are the outcomes of the conducted

survey. In particular, we were interested in whether mathematics was popular in primary and

secondary schools. The research results are illustrated in chart 1 (Fig. 1) and chart 2 (Fig. 2). It can be

seen in Chart 1 that mathematics is not a popular subject in primary schools. Mathematics is a

favourite subject of only 31 % of the primary-school respondents. In comparing the responses of girls

and boys, we found out that the popularity of mathematics as a school subject was more or less the

same with both genders.

Fig. 1 Popularity of mathematics with primary-school pupils

In secondary schools, mathematics is a popular subject for 45 % of students. In comparison with

primary schools, we may say that mathematics is more popular in secondary schools.

Fig. 2 Popularity of mathematics with secondary-school students

Most of the pupils responded that they did not like any mathematical topics. Some of the pupils stated

that they liked only the topics which they understood.

In another question, we tried to identify the topics the primary-school pupils were not good at and the

topics which they did not understand. The responses are listed in the next table (Fig. 3).

Fig. 3 Mathematical topics which primary-school pupils do not understand

Primary-school pupils have most difficulties with geometry. Another difficult area for primary-school

pupils consists in equations. Next table (Fig. 4) lists the topics not understood by secondary-school

students.

Fig. 4 Mathematical topics which secondary-school students do not understand

The secondary-school students selected geometry as a difficult topic, just like the primary-school

pupils. Topics difficult for secondary-school students also include combinatorics and functions. In one

of the closed questions, we tried to identify whether the primary-school pupils and secondary-school

students solved practical tasks in their mathematics lessons. 69 % of all the primary-school

respondents stated that they solved practical tasks. Only 31 % of the pupils believe that they do not

solve tasks at school which they might encounter later in life.

Fig. 5 Solving practical tasks in mathematics in primary schools

55 % of the fourth-year secondary-school students believe that they solve practical tasks in

mathematics, which can be seen in next chart (Fig. 6).

Fig. 6 Solving practical tasks in mathematics in secondary schools

We examined what the pupils thought about using mathematics in practice. The primary-school pupils

and secondary-school students were supposed to state fields in which mathematics was used. The

responses of the primary-school pupils are listed in next table (Fig. 7) and the responses of the

secondary-school students are listed in other table (Fig. 8).

Most of the pupils stated that they used mathematics when shopping. Another field in which

mathematics is used is economy. The pupils also mentioned mathematics teachers, repairmen and

servicemen, builders and bankers.

Fig. 7 Use of mathematics in practice – the opinions of primary -school pupils

Fig. 8 Use of mathematics in practice – the opinions of secondary-school students

Adding, subtraction, multiplication, division

In the questionnaire, we also examined whether the primary-school pupils would like to study a

technical field. 59 % of the pupils responded that they did not want to study any technical field; 34 % of

the pupils want to study a technical field and 7 % have not decided yet. The pupils who responded that

they wanted to study a technical field mentioned architecture and civil engineering.

The same question was posed to the secondary-school students. 15 % of the students responded that

they wanted to study a technical field, 82 % of the students do not think of studying a technical field

and 3 % of the students have not decided yet. The students who are interested in technical fields want

to study chemistry, technology, mechanical engineering or informatics.

Fig. 9 Interest of secondary-school students in the study of technical fields

We also tried to identify what could change the relationship of a primary-school pupil and secondary-

school student to mathematics. Some of the respondents said that they would like playful

mathematics, logical games, origami and puzzles. Primary-school pupils and secondary-school

students are interested in mathematics lessons which are more entertaining, and they want to solve

easier tasks.

3 CONCLUSION

In conclusion, we can say that it is necessary to educate pupils and students for technical practice.

The knowledge of mathematics and the study of technical fields will enable students to find jobs and

be successful in the labour market. The interest of primary-school pupils and secondary-school

students in the study of mathematics and technical fields may be influenced by modern teaching

methods. This means using graphic programs in lessons and teaching mathematics by means of

discovering new concepts. It is necessary to involve primary-school pupils and secondary-school

students in mathematics lessons so that they actively participate in the process of learning. In the

teaching of mathematics, it is important to support an active approach of primary-school pupils and

secondary-school students in acquiring new knowledge. Pupils and students who participate in the

learning process will have a better knowledge of mathematics, which is the basis for the study of

technical fields.

REFERENCES

[1] BARTSCH, H. J. (1983). Matematické vzorce. 1st edition. Praha: SNTL. 832 p.

[2] BASL, J., KRAM PLOVÁ, I., TOMÁŠEK , V., VERNEROVÁ, M. (2013). PIRLS 2011 and TIMSS

2011: Vybraná zjiš t ě ní . 1st issue. [online]. Praha: Česká školní inspekce, Available at:

http://www.csicr.cz/getattachment/a9eb6f08-d83e-4169-8a37-51098e93102d

[3] CRILLY, A. (2012). Velké otázky: matematika. 1st edition. Translated by Jiří Jarník. Praha:

Kniž ní klub. 208 p. ISBN 978-80-242-3596- 7.

[4] DEVLIN, K. J. (2003). Jazyk matematiky: jak zviditelnit neviditelné. 1st edition in Czech.

Translated by Jan Š vábenický . Praha: Argo. 343 p., ISBN 80-86569-09- 8.

[5] DOFKOVÁ, R. (2008). Two Years with „Different " Mathematics. In Sborník recenzovaných

př íspěvků k projektu STM- Morava . 1. vyd. pp. 33 - 34. Olomouc: Univerzita Palackého v

Olomouci. ISBN 978 -80-244-2127- 8.

[6] HENDL, J. (2012). Přehled statistických metod: analý za a metaanalýza dat. 4th extended

edition, Praha: Portál. 764 p. ISBN 978-80-262-0200- 4.

[7] HRABAL, V., PAVELKOVÁ, I. (2010). Jaký jsem učitel. 1st edition. Praha: Portál . 239 p. ISBN

978-80-7367-755- 8.

[8] KRAMPLOVÁ, I., TOMÁŠEK, V., VERNEROVÁ , M. (2012). Národní zpráva PIRLS 2011, 1st

edition. [online]. Praha: Česká školní inspekce. 32 p. ISBN 978-80-905370-3-3. Available at:

http://www.csicr.cz/getattachment/53120d54-47da-4a68-9452-12c44b0e3aab/narodni -zprava-

PIRLS_2011_WEB.pdf

[9] STEWART, I. (2014). Matematika života: odkr ývání tajemství bytí. 1st edition. Galileo, Vol. 58.

Translated by Jiří Rákosník, Marie Rákosníková. Praha: Academia. 391 p. ISBN 978-80-200-

2360- 5.

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... al., 2016). It is the foundation of all designs and inventions for without which the world cannot move even a little (Hodaňová & Nocar, 2016). Some attributes that include ability of reasoning, creativity, hypothetical and critical thinking, ability in solving problem and even operative communication skills are fostered by mathematics (Kusmaryono, 2014). ...

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هدفت هذه الدراسة إلى التعرّف على نمط التعلّم الأكثر شيوعاً لدى الطلبة الموهوبين في مدارس الملك عبد الله الثاني للتميّز وعلاقتها بالاتجاهات نحو المباحث العلمية. كما هدفت إلى معرفة الفروق في أنماط التعلّم والاتجاهات نحو المباحث العلمية وفقاً لمتغيّري (الجنس والصف)، ومن أجل تحقيق أهداف هذه الدراسة، تم اختيار عينة مكوّنة من (268) طالب وطالبة من الصفين السابع والثامن الأساسي في مدارس الملك عبد الله الثاني للتميّز، وتم تطبيق مقياس أنماط التعلّم واستبيان الاتجاهات نحو المباحث العلمية إلكترونياً عليهم. أشارت نتائج هذه الدراسة إلى أنّ أكثر أنماط التعلّم شيوعاً عند طلبة مدارس الملك عبد الله الثاني للتميّز هو نمط التعلّم الخارجي الخطي. كما أشارت نتائج هذه الدراسة إلى وجود فروق دالة إحصائيا في نمط التعلّم التفاعلي الشمولي لصالح الإناث، ونمط التعلّم الخارجي الخطي لصالح طلبة الصف السابع الأساسي. بالإضافة إلى أنّ اتجاهات طلبة مدارس الملك عبد الله الثاني للتميّز نحو المباحث العلمية كانت إيجابية بشكل كبير، وأنّه لا توجد فروق في هذه الاتجاهات تعزى لمتغيّري الجنس والصف. وأشارت النتائج أيضاً إلى وجود علاقة ارتباطية موجبة دالة إحصائياً بين أنماط التعلّم وبين الاتجاهات نحو المباحث العلمية، وكانت العلاقة الأقوى هي بين الاتجاهات ونمط التعلّم الخارجي الخطي. الكلمات المفتاحية: أنماط التعلّم، الاتجاهات نحو المباحث العلمية، الموهوبين، طلبة مدارس الملك عبد الله الثاني للتميّز.

Thevarasa Mukunthan

Children"s achievements in mathematics is not at satisfactory level in elementary and secondary schools in Sri Lanka. Children"s mathematical errors, is one of the main reason for this low achievements. The main objective of this study is to identify the error-patterns made in multiplication by the elementary school children. Apaper-pencil test was administered to 980 children from 24 schools in Colombo District, studying in Grades 4 and 5. Each paper consisted of 50 questions. The answer scripts were marked and the responses were analyzed. 300 children were selected randomly from the 980 children and interviewed, for an in-depth study in order to identify theerror-patterns. The errors identified were classified as Careless Errors, Random Errors and Systematic Errors. Most of the errors identified were Systematic Errors. The study categorized the Systematic Errors (56.21%), further, as errors in detail: Recalling Error(9.11%),Operation Sign related Error(17.66%), Zero related Error(11.76%),Direction of Operation Error(12.46%),Answer in Reverse Order (5.36), Errors related to Carrying Digit related Errors (28.03) and Place Value related Error (15.4%). This study suggests that, teachers have to enhancetheir teaching methodologies when they teach mathematics. They have to use the relevant teaching-learning materials to explain the basic concepts of multiplications.

Hans-Jochen Bartsch

Vyd. 4., V nakl. Academia 1. (reprint) Na obálce označení: studentské vydání V tiráži: sazba reprint 3. vyd.

Matematické vzorce Velké otázky: matematika

H J Bartsch
J Basl
I Kramplová
V Tomášek
M Vernerová
A Crilly

[1] BARTSCH, H. J. (1983). Matematické vzorce. 1st edition. Praha: SNTL. 832 p. [2] BASL, J., KRAMPLOVÁ, I., TOMÁŠEK, V., VERNEROVÁ, M. (2013). PIRLS 2011 and TIMSS 2011: Vybraná zjištění. 1st issue. [online]. Praha: Česká školní inspekce, Available at: http://www.csicr.cz/getattachment/a9eb6f08-d83e-4169-8a37-51098e93102d [3] CRILLY, A. (2012). Velké otázky: matematika. 1st edition. Translated by Jiří Jarník. Praha: Knižní klub. 208 p. ISBN 978-80-242-3596-7.

Two Years with "Different" Mathematics

R Dofková

DOFKOVÁ, R. (2008). Two Years with "Different" Mathematics. In Sborník recenzovaných příspěvků k projektu STM-Morava. 1. vyd. pp. 33 -34. Olomouc: Univerzita Palackého v Olomouci. ISBN 978-80-244-2127-8.

Národní zpráva PIRLS Praha: Česká školní inspekce. 32 p. ISBN 978-80-905370-3-3 Available at Matematika života: odkrývání tajemství bytí

I Kramplová
V Tomášek
M Vernerová

[8] KRAMPLOVÁ, I., TOMÁŠEK, V., VERNEROVÁ, M. (2012). Národní zpráva PIRLS 2011, 1st edition. [online]. Praha: Česká školní inspekce. 32 p. ISBN 978-80-905370-3-3. Available at: http://www.csicr.cz/getattachment/53120d54-47da-4a68-9452-12c44b0e3aab/narodni-zprava- PIRLS_2011_WEB.pdf [9] STEWART, I. (2014). Matematika života: odkrývání tajemství bytí. 1st edition. Galileo, Vol. 58. Translated by Jiří Rákosník, Marie Rákosníková. Praha: Academia. 391 p. ISBN 978-80-200- 2360-5.

V Hrabal
I Pavelková

HRABAL, V., PAVELKOVÁ, I. (2010). Jaký jsem učitel. 1st edition. Praha: Portál. 239 p. ISBN 978-80-7367-755-8.

Praha: Česká školní inspekce

I Kramplová
V Tomášek
M Vernerová

KRAMPLOVÁ, I., TOMÁŠEK, V., VERNEROVÁ, M. (2012). Národní zpráva PIRLS 2011, 1st edition. [online]. Praha: Česká školní inspekce. 32 p. ISBN 978-80-905370-3-3. Available at: http://www.csicr.cz/getattachment/53120d54-47da-4a68-9452-12c44b0e3aab/narodni-zprava-PIRLS_2011_WEB.pdf

Translated by Jiří Jarník. Praha: Knižní klub