FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING

Acta Didactica Universitatis Comenianae Mathematics, Issue 12, 2012, pp. 65-82 FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING VLADIMÍRA PETRÁŠKOVÁ, ROMAN HAŠEK Abstract. The authors did a research with the main aim to map out the structure of the financial literacy of first-year students in the Faculty of Education of the University of South Bohemia in 2011. Its purpose was to direct the adjustment of the content and methods of the subject An Introduction to Finance, which was established as a response to the governmental strategy for financial education in the Czech Republic in 2007. The research showed the expected change to the financial literacy of students and therefore it helped to direct future orientation of the financial education of both future and practising teachers. The paper presents a method of the research with the following recommendations and conclusions of the authors aimed at both secondary school financial education and the appropriate teacher training programs. Key words: financial literacy, mathematics, education, secondary school, teacher training 1 INTRODUCTION Government measures to improve financial literacy have been applied in basic and secondary education in the Czech Republic since 2007 (MF ČR, 2010), (MF MŠMT MPO ČR, 2007). Nowadays, after five years, we should experience the impact of these measures via the marked changes of the financial literacy of graduates from basic and secondary schools. Such movements in the financial literacy of graduates together with the natural development of the financial world should determine the up-to-date content of financial education and the methods that it uses. Bearing these facts in mind the authors did corresponding research on first-year students in the Faculty of Education of the University of South Bohemia. The main aim of the research was to map out the structure of the financial literacy of students for the purpose of the adjustment of the content and methods of the subject An Introduction to Finance (Petrášková,

66 V. PETRÁŠKOVÁ, R. HAŠEK Hašek, 2008), which was established as a response to the above mentioned governmental strategy for financial education in the Czech Republic (MF ČR, 2007) in 2007. The research really showed the expected change to the financial literacy of students and therefore it helped to direct future orientation of the financial education of both future and practising teachers. The paper presents a method of the research with the following recommendations and conclusions of the authors aimed at both secondary school financial education and the appropriate teacher training programs. 2 AIMS OF SECONDARY SCHOOL FINANCIAL EDUCATION IN THE CZECH REPUBLIC In the context of the demonstrably low level of financial literacy of citizens in countries around the world, which had been highlighted by the financial crisis, the OECD created an International Network for Financial Education (OECD, 2012) to facilitate the sharing of experience and expertise among worldwide public experts and to promote the development of both analytical work and policy recommendations (Atkinson, Messy, 2010). Among others are there displayed national strategies for the financial education of OECD member countries on this web portal. In the space devoted to the Czech Republic we can find the document Strategie finančního vzdělávání (Strategy of financial education) (MF ČR, 2007) (Its actualized version was issued under the title Národní strategie finančního vzdělávání (National strategy of financial education) in 2010). It was followed by the document Systém budování finanční gramotnosti na základních a středních školách (The system of establishment of financial literacy at primary and secondary schools) (MF MŠMT MPO ČR, 2007) in 2007 that defines the following three standards of financial literacy with respect to the target groups of affected pupils: Financial literacy standard of a first-grade pupil (ages 6-10 years), Financial literacy standard of a second-grade pupil (ages 11-15 years) and Financial literacy standard of a secondary school pupil (ages 16-19 years), which is equal to the financial literacy standard of an adult. All three standards include the areas of money, household management and financial products (Hašek, Petrášková, 2010a). The above standards were implemented into the so called General educational programs for gymnasiums and secondary schools, (MŠMT ČR, 2007), which play the role of curriculum texts in the Czech Republic. They figure in two so called educational areas: A man and the world of labour and Mathematics and its application. The area A man and the world of labour defines knowledge and skills related to the management of financial resources, to free market economy, national economy and the role of the State in the economy, which are to be mastered by secondary school students. The area

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 67 Mathematics and its application introduces students to the mathematical apparatus that gives them chance to grasp the basic laws of operation of financial relations and to examine the functioning of offered products. 3 FINANCIAL LITERACY OF UNIVERSITY APPLICANTS 3.1 FINANCIAL EDUCATION AT THE FACULTY OF EDUCATION Financial education at the Faculty of Education of the University of South Bohemia has been realized through the subject An Introduction to Finance since 2007. Its curriculum and methods reflect the definitions of financial education and financial literacy as they were laid out in the OECD materials (OECD, 2005), page 25: Financial education is the process by which individuals improve their understanding of financial products and concepts; and through information, instruction and/or objective advice develop the skills and confidence to become more aware of financial risks and opportunities, to make informed choices, to know where to go for help, and to take other effective actions to improve their financial well-being and protection. Financial literacy is the combination of consumers /investors understanding of financial products and concepts and their ability and confidence to appreciate financial risks and opportunities, to make informed choices, to know where to go for help, and to take other effective actions to improve their financial well-being. These definitions together with the consideration of the teacher s roles at different school levels became the starting point for design of the course. The main objective of this process was to develop special teaching and learning methods that would best suit the course s aim. An integral part of the process of the course s creation was its evaluation. The authors performed the corresponding evaluation research on the students of the 2 nd and 3 rd year of mathematics teaching who completed the course An Introduction to Finance. Results and conclusions of the research were published in (Hašek, Petrášková, 2010b).

68 V. PETRÁŠKOVÁ, R. HAŠEK 3.2 MEANS OF FINANCIAL EDUCATION The above mentioned teaching and learning methods are based on an interactive tool in the form of a web page that provides examples real life problems covering all up-to-date financial products. These problems are solved in a way that explains all aspects of the problem and uncovers possible risks which are mostly hidden from an uninformed user. For these purposes we use the tools of the software Maple 11. We especially take advantage of the features of interactive smart documents prepared in this software. The smart documents enable us to combine text, symbolic and numerical computation and graphs in one worksheet all focused on solving, explaining and modelling some particular phenomenon of financial mathematics (Hašek, Petrášková, 2010b). An advantage of this educational aid is the possibility of continuous updating according to the current condition of the financial products market. It reacts both to the creation of new products and to changes in the conditions (e.g. changes in interest rates, the creation of new products) of the banking and financial spheres. Its efficiency was verified by means of the above-mentioned research executed on the students of the Faculty of Education in 2010. 3.3 CURRENT SITUATION As explained in the introduction, we can expect apparent changes in the financial literacy of contemporary graduates from secondary schools when compared to their peers five years ago. The Faculty of Education should provide its students with a complete and up-to-date education in the field of financial literacy to enable them to better teach their pupils and students in basic and secondary schools. The main means of the financial education of future teachers is the above mentioned subject An Introduction to Finance. The authors decided to do research with the aim of mapping out the structure level of financial literacy of current university applicants and utilizing its results to actualize the content and educational methods of this subject. A similar research was also carried out in Slovakia and its results were published in (Regecová, Slavíčková, 2010). Our research questions were formulated as follows: What is the level of the newcomers financial literacy? Which components of financial literacy should be further developed in pre-service teacher training? The target group consisted of forty seven first-year students of mathematics teaching at the Faculty of Education. The survey was based on a questionnaire consisting of five questions:

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 69 TEST OF FINANCIAL LITERACY 1. Suppose you deposit CZK100 in a savings account with a guaranteed interest rate of 2 % per year. You neither deposit nor withdraw any money after that. How much will there be in your account in five years? The interest tax is not taken into account. (a) More than CZK110. (b) Exactly CZK110. (c) Less than CZK110. (d) I do not know. 2. Suppose that the interest rate in your savings account is 1 % per year and inflation is 2 % per year. How much will you be able to buy with the money in your account in one year s time? (a) More than today. (b) Exactly the same. (c) Less than today. (d) I do not know. 3. If interest rates rise, what will happen to bond prices? (a) Rise. (b) Fall. (c) Stay the same. (d) No relationship. (e) I do not know. 4. A 15-year mortgage typically requires higher monthly payments than a 30-year mortgage, but the total interest paid over the life of the loan will be less. (a) True. (b) False. (c) I don t know. 5. Buying a single company's stock usually provides a safer return than a mutual fund. (a) True. (b) False. (c) I don t know. These questions were adopted from the national survey of financial literacy in the USA (FINRA, 2011). Some of these questions were also used in national surveys of other OECD member countries. The questions are in the authors opinion well balanced with respect to current trends in the handling of personal finance. After the bank crisis revealed weak points of orientation to bank accounts only, more and more persons are trying to reduce risk by investing in shares and bonds. The quantitative evaluation of the survey is presented in Table 1. Here we can find numbers of correct, incorrect and undecided answers together with their percentages.

70 V. PETRÁŠKOVÁ, R. HAŠEK Table 1 Test evaluation Question Correct answers Incorrect answers Do not know 1) Compound interest (a) 42 (89.4 %) 5 (10.6 %) 0 (0 %) 2) Inflation (c) 33 (70.2 %) 11 (23.4 %) 3 (6.4 %) 3) Bond price (b) 5 (10.6 %) 38 (80.9 %) 4 (8.5 %) 4) Mortgage credit (a) 33 (70.2 %) 13 (27.7 %) 1 (2.1 %) 5) Diversification of risk (b) 28 (59.6 %) 9 (19.1 %) 10 (21.3 %) 4 POSSIBLE REASONS OF THE TEST'S RESULTS To answer the questions correctly a respondent apparently has to have some insight into the functioning of relevant financial issues. In our opinion we can trace the evident connection of those issues to the curriculum in secondary school mathematics. Concretely problems related to the topics of questions number one, two and four are solved in detail in mathematics lessons devoted to arithmetical and geometrical progression. Let us show some of these problems with respect to the given questions: Question No. 1: Compound interest Compound interest appears in examples of the following type: At the beginning of 2009 Mr. Vávra deposited 50 000 CZK into a savings account that pays 2 % annual interest rate. What amount will he gain after three years (i.e. at the beginning of 2012), considering the annual interest period with interest added to the principal every year so that the next interest is computed from this increased basis and if the interest tax is 15 %?. The solving of such examples leads students naturally to the notion of compound interest and to the derivation of the general relation: ( ) Kn = K0 1 + (1 d) i, where i is the annual interest rate in its decimal form, K 0 is the initial deposit, K n is the total amount of savings after n years and d is a tax on the interest, again in its decimal representation. Question No. 2: Inflation vs. interest rate Students meet the notion of inflation regarding its influence on savings appreciation. First they solve simple problems, for example: We deposited 350 000 CZK in a saving account. After ten years the account debit amounted to 400 000 CZK. Was the corresponding annual interest rate higher than the average inflation rate during the last 10 years (2.71 %)?. Then they are exposed to more n

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 71 complex problems dealing with inflation, e.g. For one calendar year Mr. Nehoda deposited 100 000 CZK in a savings account that provides 2.15 % annual interest rate. At the beginning of the year, before depositing the money, he could have used it to buy exactly 20 lawn mowers for his gardening company. Could he buy the same number of mowers at the end of the year using the saved money? The inflation rate was 6.3 % in the relevant year. (Petrášková, Horváthová, 2010) Question No. 4: Mortgage credit The right answer to this question implies that a student understands the basic laws of mortgage credit functioning. He or she conceives relations between the pay-back period, the total amount of interest and the installment amount. A respective mathematical formula 1 (1 + i) n D = a, i where D means the total amount of a credit (debt), a is the installment amount, i is the interest rate and n is the number of payment periods, is derived in a natural way within the solving of examples of the following type: A young couple with sufficient income decided to built a small family house. According to a preliminary cost calculation they will need 3 170 000 CZK. They can cover 1 000 000 CZK from their savings and to get the remaining 2 170 000 they decided to use a mortgage credit. A bank offers the mortgage credit with the annual interest rate of 4.9 %, interest compounded annually, the pay-back period over 20 years and the installment amount of 172 653 CZK payable at the end of year. Create the installment schedule of this credit. Then students are prepared to solve an alternative task to the previous one: Determine the installment amount of the above mentioned mortgage credit considering the pay-back period of 10 years. What is the total interest paid over these 10 years. Compare this to the previous case of the pay-back period of 20 years. As the high success rate in the answering questions 1, 2 and 4 is in accordance with the content of the mathematics curriculum so is the low success rate in questions 3 and 5. Stock trade, which was the subject of these questions, is not generally used as a topic of any problem in secondary school mathematics. Within the educational area A man and the world of labour, which belongs to Civics, a student gains only basic information concerning financial transactions. Also the usual experience in finance of secondary school students does not contain stock trading but mainly issues of student s accounts, internet banking, selection of a mobile operator or the utilization of a credit or debit card.

72 V. PETRÁŠKOVÁ, R. HAŠEK 5 REMEDIAL MEASURES All discovered deficiencies in the financial literacy of first-year students gave important impulses for the immediate adjustment of the financial education of both future and present teachers at the Faculty of Education. There is no doubt that it should be faculties preparing the teachers that respond first to such actual demands on the content of education. Only a well prepared teacher can guarantee quality and topicality of schoolwork in basic and secondary schools. The adjustment was targeted on the subject An Introduction to Finance as mentioned above, particularly on actualization of its curriculum with respect to issues of the shares and bonds trading. The main steps of this actualization are the incorporation of real-world problems dealing with shares and bonds and the utilization of convenient software to visualize their solutions. In the authors opinion analogous actualization should be implemented within the secondary schools curriculum. Therefore the following passages are intended as the authors' concrete recommendations aimed at both secondary school financial education and the appropriate teacher training programs. 5.1 BONDS Students should be informed about two basic types of bonds: coupon bonds and zero-coupon bonds. Coupon bonds bring their holder a periodic interest payment, so called 'coupon' that is mostly defined as the percentage of the bond's face value. The bond's market price is derived from its theoretical fair value considering other not so rigorous criterions, as for example the creditworthiness of the issuer or the profit of other possible investment options. For the sake of simplicity let us consider the equality of the theoretical fair value of a bond and its market price in what follows. The theoretical fair value is given by the next formula, which is based on the discount of the future financial flows to get their present value: C C C NH P = + +... + + (1) 2 n n 1+ i 1+ i 1+ i 1+ i ( ) ( ) ( ) where P is the theoretical price of a bond, C is the annual coupon amount ( C = k NH, where k is the annual coupon rate in its decimal form), NH means the bond's face value, i is its market interest rate in its decimal form and n is the bond's maturity period in years. Given formula (1) represents a nice real-world example of the sum of the first n terms of a geometric progression. Its application leads to the formula: n ( 1 ) i ( 1+ i) C + i C + NH i P = n (2)

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 73 Both (1) and (2) formulas clearly presents the main risk of the coupon bonds: Sudden change of the market interest rate causes the immediate change of the bond's price. Example 1: Compute the theoretical value of a bond having the annual coupon rate 4 % p.a., face value 15 000 CZK and maturity period 3 years, considering the market annual interest rate: a) 2 %, b) 4 %, c) 5 %. Solution: It suffices to assign the given values to corresponding variables in (2). We can use a hand-held calculator or take advantage of a spreadsheet, for example Microsoft Office Excel, as shown in Figure 1. Resulting values indicate that if the market annual interest rate is 4 % the theoretical bond's value is equal to its face value. Then for the market interest rate 2 % p.a. and 5 % p.a. the theoretical value is higher and lower respectively. Figure 1. Solution to the Example 1 using Microsoft Office Excel To get a deeper insight into the laws of the functioning of formula (2) the experimentation with the values of its variables is very helpful. An appropriate means to do such experiments is any spreadsheet. Besides the already mentioned Microsoft Excel we can recommend free software GeoGebra (GeoGebra), which provides a user with an immediate graphical representation of the spreadsheet's content. Moreover GeoGebra enables the control of values of variables with the use of sliders. These qualities predetermine GeoGebra to become a means for the above desired experiments. Examples of such experimentations with the formula (2) are shown in Figures 2 and 3 respectively. In particular we can see two appearances of both the graphical and tabular representation of the dependence of P on i differing on the values of the maturity period n. Values of the bond's maturity period n, the annual coupon rate k, and the face value NH are controlled by sliders.

74 V. PETRÁŠKOVÁ, R. HAŠEK Figure 2. The dependence of the theoretical price P of the coupon bond on the market interest rate i. Maturity period n = 3 years Figure 3. The dependence of the theoretical price P of the coupon bond on the market interest rate i. Maturity period n = 9 years

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 75 Materials in figures 2 and 3, which differ on the values of n, clearly show how changes in the interest rate influence the bond's yield and that this influence is larger if the maturity period n is longer. The main message is that the bond's yield can be lower than expected. This possible risk of coupon bonds is more understandable owing to its visualization via GeoGebra or other software. On average the coupon bond is redeemed by its holder slightly sooner than determined by its maturity date. The average maturity period of a bond is called 'duration'. The increase/decrease of the interest rate has a deeper impact on the decrease/increase of the bond's market price when the bond is of a longer duration. On the other hand, higher risk corresponds to higher yield. Therefore if an investor expects a decrease in interest rates the sale of bonds with longer duration will bring him a higher profit than the sale of ones with shorter duration. Zero-coupon bonds do not bring their holder any interest during their maturity period. Their price constantly increases and achieves the face value at the end of the bond's term. The yield of the zero-coupon bond is given by the difference between its face value and its price at the moment of sale. Example 2: (Dvořáková a kol., 2011) An investment company issued zerocoupon bonds on 1 September 2010, the face value of which will reach 50 000 CZK per bond on 1 September 2020. The price of the bond increases uniformly every day and it is possible to purchase them at any time between the date of its issue and the date of its maturity. The annual discount rate of 5 % is guaranteed. a) Determine the price of the bond on 15 June 2011 and on 1 September 2010, the day of its issue, respectively. (To determine the number of days use the 30E/360 method (Wikipedia, 2012), (Radová a kol., 2011)). b) Compute the annual interest rate of the given bond. Solution: a) Let NH be the face value of the bond, SH to be its price on the day of purchase, d to be the annual discount rate and t to be the number of days remaining until the bond's maturity date. Then we can simply derive the formula: t t SH = NH d NH = NH 1 d (3) 360 360 There are t = 3316 days between 15 June 2011 and 1 September 2020 according to the 30E/360 method. After the assignment of these values to (3) we get: 3316 SH = 50000 1 0, 05 26972 CZK. 360

76 V. PETRÁŠKOVÁ, R. HAŠEK The bond s price on 15 June 2011 will be 26 972 CZK. At the moment of its issue the bond s price was 3600 SH 0 = 50000 1 0, 05 = 25000 CZK. 360 Figure 4. The dependence of the market price SH of the zero-coupon bond on the day of purchase b) To compute the annual interest rate i of the bond we use the simple interest formula: NH = SH + n i. ( ) 0 1 First we express the unknown i: NH SH i = n SH Then, after assigning the values to the remaining variables and simplification we get the result: 50000 25000 1 i = = = 0.1. 10 25000 10 Given bonds have the annual interest rate of 10 %. 0 0.

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 77 The growing importance of the understanding of bonds can be illustrated by the situation after the issue of the so called 'government saving bonds' by the Ministry of finance of the Czech Republic in November 2011. The issued bonds, which were destined for individuals and non-profit legal entities, were of three different types: One-year discount savings state bonds with the interest rate of 2 %, five-year savings coupon state bonds with a steadily increasing an interest rate and five-year reinvestment savings bonds. Since the majority of citizens did not have enough knowledge of the functioning of bonds and consequently were not able to consider all the pros and cons of the offered investment options the retail investors snapped up the bonds rather quickly without considering other possible financial products with the same return but better liquidity. 5.2 SHARES Example 3: In Figures 5 and 6 you can see the graphs of the share prices developments of the ČEZ company and the KB bank respectively within the time period from 1 December 2011 to 1 March 2012. Solve the following tasks concerning these share issues: a) When was the most advantageous to buy/sell the shares of ČEZ? b) Determine the highest profit of the purchase and sale of 100 stocks of the ČEZ company some time between 1 December 2011 and 1 March 2012. c) Suppose that you bought 100 shares of ČEZ at a price of 798 CZK per share on 10 January 2012. Fearing a bad investment you decided to sell them at price 751 CZK per share on 25 January 2012. What was the loss on this trade? d) To diversify the risk we also decided to buy several shares of the KB bank together with the shares of ČEZ. Again we invested about 77 000 CZK. We bought 36 shares of ČEZ at 798 CZK each and 15 shares of KB bank at 3 250 CZK each on 10 January 2012. Then we sold all the shares on 25 January 2012 at 751 CZK each of ČEZ and 3 560 CZK each of KB bank. How was the transaction? Did we make a profit or a loss?

78 V. PETRÁŠKOVÁ, R. HAŠEK Figure 5. Shares price development ČEZ company (Akcie, 2012a) Figure 6. Shares price development KB bank (Akcie, 2012b)

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 79 Solution: a) Buying shares was at the most advantageous when the price was at its lowest. For example on 7 December 2011 shares were at a price of 734 CZK each or on 25 January 2012 they were at a price of 751 CZK each. Selling of shares was most advantageous on 4 January 2012 at a price of 805 CZK each or on 8 February 2012 at a price of 837 CZK each. b) The share price was lowest on 7 January 2012, 736 CZK each. One hundred shares costs 73 600 CZK. If we sell them on 22 February 2012 at a price of 837.5 CZK each our income will be 83 750 CZK. The yield of this trade will be 83 750 CZK 73 600 CZK = 10 150 CZK. It is necessary to pay a tax of 15 % from the yield because of holding the shares for less than 6 months. Therefore the net profit of the transaction will be 0.85 10 150 CZK = 8 627.5 CZK, i.e. 11.72 % of the invested amount. Such a profit over one and a half months sounds attractive but do not forget that in a normal situation it is not possible to know the development of the share price in advance. c) You lost 4 700 CZK, i.e. 5.89 % of the invested money. The detailed solution is given in Table 2. Table 2 Trading with shares of ČEZ Purchase 10 January 2012 Sale 25 January 2012 Price per share 798 CZK 751 CZK Number of shares 100 100 Total price 100 798 = 79 800 CZK 100 751 = 75 100 CZK Loss = sale purchase 75 100 CZK 79 800 CZK = - 4 700 CZK d) We earned 2 260.5 CZK, i.e. 2.92 % of the investment. The loss on ČEZ was exceeded by the profit from KB. It shows the importance of risk diversification in share trading. Table 3 Purchase of shares Purchase / 10 January 2012 ČEZ company KB bank Price per share 798 CZK 3 250 CZK Number of shares 36 15 Total price 36 798 = 28 728 CZK 15 3 250 = 48 750 CZK Total costs 28 728 CZK + 48 750 CZK = 77 478 CZK

80 V. PETRÁŠKOVÁ, R. HAŠEK Table 4 Sale of shares Sale / 25 January 2012 ČEZ company KB bank Price per share 751 CZK 3 560 CZK Number of shares 36 15 Total price 36 751 = 27 036 CZK 15 3 560 = 53 400 CZK Loss = sale purchase 27 036-28 728 = -1 692 CZK 53 400 48 750 = 4 650 CZK Profit tax 0 CZK 0.15 4 650 = 697.5 CZK Net profit 4 650 CZK 697.5 1 692 CZK = 2 260.5 CZK 6 CONCLUSION The average citizen is traditionally conservative in the handling of his money. To revalue it he or she mostly chooses standard options such as saving accounts, term deposits or a building society account. A considerable number of people even allow their money to lie in a common account with an interest rate of hundredths or, at best, tenths of a percent. They justify this money-losing saving method by in fact the incorrect argument that only the common account enables them immediate access to their money. Not many people use unit investment trusts to invest their money. These trusts can have different investment strategies but they have a common aim to diversify the risk. The weak point of this investment option lies in the fact that the investor can not control the portfolio. Thus the worst scenario can lead to the accidental loss of the investment. To avoid the impossibility of portfolio control a citizen can enter the capital market himself. Unfortunately for the majority of people it is an inconceivable act because they do not have enough information about the functioning of the capital market. It should be secondary schools that provide citizens with knowledge of bonds and shares because of the importance of the proper handling of personal money to both citizens and the economic health of society. The above mentioned research, in our opinion, pointed out the essential role of mathematics education in the formation process of the financial literacy of secondary school students. We recommend taking advantage of the topic arithmetical and geometrical progression in secondary school mathematics to solve real-world problems dealing with shares and bonds. The pattern examples were presented in this paper. The same method should be used within mathematics teacher training courses.

FINANCIAL EDUCATION DEMANDS CONCERNING TEACHER TRAINING 81 REFERENCES Akcie (2012a). [cit. 2012-04-30) ]. Available at http://www.akcie.cz/kurzy-cz/graf/akcie-11392- cez/. Akcie (2012b). [cit. 2012-04-30) ]. Available at http://www.akcie.cz/kurzy-cz/graf/akcie-717- komercni-banka/. Atkinson, A., Messy, F.A. (2010) Assessing financial literacy in 12 countries an OECD Pilot Exercise [online]. Financial Literacy Center. [cit. 2012-04-30]. Available at http://www. financialliteracyfocus.org/files/flatdocs/oecd%20paper.pdf. Dvořáková, Z., Smrčka, L. a kol. (2011). Finanční vzdělávání pro střední školy. Se sbírkou řešených příkladů na CD. C. H. Beck, Praha 2011, 1. vyd., ISBN 978-80-7400-008-9. FINRA (2011). Financial capability study [online]. [cit. 2012-04-30]. Available at http://www. usfinancialcapability.org. GeoGebra [cit. 2012-04-30]. Available at: http://www.geogebra.org Hašek, R., Petrášková, V. (2010). A Way to Improve Financial Literacy of Future Teachers. Mathematics Education with Technology - Experiences in Europe. Tamara Bianco, Volker Ulm (Ed.). Augsburg. 2010. ISBN 978-3-00-032628-8. pp. 199-218. Hašek, R., Petrášková, V. (2010). Issue of Financial Capability. The International Journal for Technology in Mathematics Education. Research Information Ltd., Burnham, UK. Volume 17, Number 4, 2010. ISSN 1744-2710. pp. 183-190. OECD (2005). Improving Financial Literacy: Analysis of Issues and Policies. Paris: OECD Publishing. 2005. 177 p. ISBN 9264012567. OECD (2012). International Gateway for Financial Education [online]. [cit. 2012-04-30]. Available at http://www.financial-education.org MF ČR. (2007). Strategie finančního vzdělávání [online]. Praha: Ministerstvo financí ČR (Ministry of finance of the Czech Republic). [cit. 2012-04-30]. Available at http://www. mfcr.cz/cps/rde/xchg/mfcr/xsl/ft_strategie_financniho_vzdelavani.html. MF ČR (2010). Národní strategie finančního vzdělávání (National strategy of financial education) [online]. Praha: Ministerstvo financí ČR (Ministry of finance of the Czech Republic). [cit. 2012-4-30]. Available at http://www.mfcr.cz/cps/rde/xchg/mfcr/xsl/ft_ strategie_financniho_vzdelavani.html?year=present. MF MŠMT MPO ČR (2007). Systém budování finanční gramotnosti na základních a středních školách. Common document of MF, MŠMT a MPO ČR, actualized. [cit. 2010-10-30]. Available at http://www.msmt.cz/vzdelavani/system-budovani-financni-gramotnosti-na-zakladnich-astrednich-skolach. MŠMT ČR (2007). Rámcové vzdělávací programy oborů středního vzdělání [online]. Praha: Ministry of education, youth and sports of the Czech Republic. [cit. 2012-04-30]. Available at http://www.msmt.cz/vzdelavani/ramcove-vzdelavaci-programy-zaslani-dovnejsiho-pripominkoveho-rizeni. Petrášková, V., Hašek, R. (2008) Úvod do financí (Introduction to finance) [online]. České Budějovice: Pedagogická fakulta JU. 2008. [cit. 2010-04-30]. Available at http://www.pf. jcu.cz/stru/katedry/m/uf. Petrášková, V. Horváthová, Z. (2010). Vybrané kapitoly z finanční gramotnosti. 1. vyd. České Budějovice: Jihočeská univerzita v Č. B. 2010. 134 s. ISBN 978-80-7394-233-5. Radová, J.a kol. (2011) Finanční matematika pro každého: příklady. 2., přeprac. vyd. Praha: Grada, 2011. 249 s.isbn 978-80-247-3584-9. Regecová, M., Slavíčková, M. (2010). Financial literacy of graduated students. Acta Didactica Universitatis Comenianae - Mathematics. Volume 10, 2010. ISSN 1210-3608. pp. 121-147.

82 V. PETRÁŠKOVÁ, R. HAŠEK Wikipedia: the free encyclopedia (2012) [online]. Day count convention. [cit. 2012-04-29] Available at http://en.wikipedia.org/wiki/day_count_convention. VLADIMÍRA PETRÁŠKOVÁ, Department of Mathematics, Faculty of Education, University of South Bohemia, Jeronýmova 10, 371 15 České Budějovice, Czech Republic E-mail: petrasek@pf.jcu.cz ROMAN HAŠEK, Department of Mathematics, Faculty of Education, University of South Bohemia, Jeronýmova 10, 371 15 České Budějovice, Czech Republic E-mail: hasek@pf.jcu.cz