Instr Sci (2010) 38:659–677 DOI 10.1007/s11251-009-9094-9

Boosting financial literacy: benefits from learning study Ming Fai Pang

Received: 30 September 2008 / Accepted: 23 March 2009 / Published online: 3 April 2009  Springer Science+Business Media B.V. 2009

Abstract This paper reports on a study that employed a theory-based approach in the form of a learning study to enhance a domain-specific generic capability, financial literacy, of Grade 12 students to empower them to make informed and independent financial decisions. Financial literacy is seen in this study as a function of student understanding of a limited set of interrelated economic concepts that can be used as tools to assess financial situations and make sound financial decisions. Twelve teachers participated in the study. Six worked together in a learning study group and drew on a particular theory of learning in planning and carrying out lessons designed to serve the learning aims, whereas the other six worked collaboratively in a lesson study group. To evaluate the effectiveness of the two learning conditions created by the two groups, 193 students answered questions on complex, everyday financial situations in four tests: a pretest, a posttest following the research lessons, and delayed posttests 6 weeks and 6 months after instruction. The results showed that students in the learning study group outperformed their counterparts in the lesson study group in all three post-lesson tests, and that the inter-group performance gap was maintained or widened over time. Keywords Learning study  Variation theory  Phenomenography  Student learning  Financial literacy

Introduction How learning is organized, whether students work individually, in groups, or together as a class, makes a difference. However, this is not the focus of the present paper. In previous research (e.g., Pang and Marton 2003, 2005; Marton and Pang 2006, 2008), we have shown that what students learn in different classes can differ radically, even if the same content is being taught, learning is organized in the same way, the students are equally capable and motivated, and the teachers are equally well educated and experienced. We have found that M. F. Pang (&) Faculty of Education, University of Hong Kong, Hong Kong SAR, China e-mail: [email protected]

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the differences in what students learn frequently originate from differences in how the learning content is handled and structured, and in the interaction between teachers and students. According to variation theory (see below), such differences have to do with what students can discern, notice, and become aware of through what is said and exemplified and the commonalities and differences that are brought out by means of the system of examples, problems, and illustrations in the class. The findings of the abovementioned studies suggest that variation theory could be a remarkably powerful tool in bringing about student learning of a specific concept. In these studies, some teachers made use of this theory whereas others did not. Differences in student learning appeared to correspond to differences in pedagogical approach (theory based or not), especially in terms of the relationships among the examples used to illustrate a specific concept or principle. To further examine whether variation theory can help students to appropriate a more complex object of learning, a study was conducted that attempts to break new ground by using this theory to develop generic capabilities, which have been emphasized in various educational reforms around the world. The study reported herein had two aims: to explore whether variation theory is effective in helping students to develop generic capabilities that go beyond a particular concept, and to identify ways to help students develop financial literacy.

Object of learning: financial literacy The specific aim of this study was to try out a theory-based approach to help Grade 12 students develop a domain-specific generic capability, namely, financial literacy, to enable them to make informed and independent financial decisions. The idea is that by developing a greater understanding of financial matters, students will become more capable of making decisions that better serve their aims. Financial literacy is defined as ‘‘the ability to make informed judgments and to make effective decisions regarding the use and management of money’’ (Australian Securities and Investments Commission 2005), and more specifically, as ‘‘the ability to read, analyze, manage, and communicate about the personal financial conditions that affect material well being. It includes the ability to discern financial choices, discuss money and financial issues without (or despite) discomfort, plan for the future and respond competently to life events that affect everyday financial decisions, including events in the general economy’’ (Policy Research Initiative 2004). To this end, one needs to learn how to analyze financial matters and interpret economic data by making use of relevant economic concepts and principles. However, according to a survey of adult financial literacy in Hong Kong commissioned by the Securities and Futures Commission in 2002, 64% of retail investors appeared to lack good financial understanding of certain financial issues, and 91% of potential investors considered their own understanding of investment dealings insufficient. It is ironic to find that there are rather low levels of financial literacy in Hong Kong, one of the world’s largest financial centers. In addition, university students in Hong Kong have commonly been found to manage their personal finances poorly, resulting in an ever-increasing number of bankruptcies over the last couple of years. In nationwide financial literacy surveys conducted in the US by Jumpstart in 2000, 2002, 2004, and 2006 with Grade 12 students, average scores were 51.9, 50.2, 52.3, and 52.4%, respectively, which indicates rather low levels of financial literacy among these students (see Jump Start Coalition for Personal Financial Literacy 2007). Not surprisingly, adults have also demonstrated low levels of financial understanding and performed poorly

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on financial literacy examinations (see, for example, Mandell 2004; National Council on Economic Education 2005). This worrisome situation is not unique to the US, but is also found in many parts of the world. According to a review of financial literacy surveys conducted in twelve Organization for Economic Co-operation and Development (OECD) countries including Australia, Japan, Korea, the UK, and the US in 2005, financial understanding among citizens is low. It appears that there is an urgent need to raise financial literacy standards by integrating some form of personal finance education into school curricula. In response to this perceived need, measures have been taken by various governments to improve the level of financial literacy of students, based on the positive relationship found between financial understanding and financial outcomes (see, for example, Lusardi and Mitchell 2007; Bernanke 2006). Alan Greenspan (2002), Chairman of the Federal Reserve System in the US from 1987 to 2006, emphasized that improving financial education during secondary school years can provide a foundation for financial literacy, thereby helping high school graduates avoid poor financial decisions that can take years to overcome. In the UK, aspects of personal finance have been incorporated as a statutory part of the National Curriculum and included within national curriculum standards (Department for Education and Employment 2000), and the teaching of financial literacy, or financial capability, has been incorporated into a range of subject areas such as personal, social, and health education, citizenship, and mathematics. In the US, a white paper, ‘‘Integrating Financial Education into School Curricula,’’ has been issued that identifies ways in which such education can be incorporated into school curricula. Special funding has been allocated to ‘‘activities to promote consumer, economic, and personal finance education, such as disseminating information on and encouraging use of the best practices for teaching the basic principles of economics and promoting the concept of achieving financial literacy’’ (Office of Financial Education 2002). The President’s Advisory Council on Financial Literacy was established in 2008 to coordinate the efforts on financial education by different agencies and organizations, reaffirming the great importance of financial literacy to the US. Over the years, a large number of financial education and money management programs have been delivered to promote financial literacy, especially among high school students, with mixed results. It seems that these programs tend to be practically oriented and emphasize the development of practical money skills for well-specified situations. Take the teaching resource packs developed by the National Council for Economic Education (NCEE) in the US, ‘‘Financial Fitness for Life: Bringing Home the Gold—Grades 9–12,’’ as an example. The package features the following topics—‘‘evaluating career choices,’’ ‘‘making responsible spending decisions,’’ ‘‘applying for a job,’’ ‘‘using credit wisely,’’ ‘‘the cost of spending versus saving,’’ and ‘‘shopping for an auto loan,’’ which focus on the delivery of practical information and advice to students in the handling of day-to-day financial matters. However, it is doubtful that students are able to develop a deep understanding of the economic concepts or principles behind the financial decisions to be made so that they can apply these concepts to novel financial situations.

Conceptual approach to developing financial literacy As mentioned, the aim of developing the financial literacy of students is to enable them to make financial decisions and perform financial acts in a more considered and effective way. When students make decisions on financial matters, they need to choose one option among the different options available, based on relevant information in real-life situations. We

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reason that by helping students develop a good grasp of certain core economic concepts related to critical aspects that they need to take into account when dealing with financial matters, they will have a better chance of understanding financial phenomena and thus make more effective financial decisions. This conceptually oriented approach to developing student financial literacy was adopted by the teachers who participated in this study. Following this approach, financial literacy is seen as a function of student understanding of a limited set of interrelated economic concepts that can be used as tools for making sound financial decisions. Based on the discussions and deliberations among the teachers involved, a cluster of core economic concepts was identified that includes: the relations among saving, consumption, and investment, the opportunity cost of financial decisions, the relations among risk, return, and liquidity, inflation and the real value of return on investment, and present value and discounting. Understanding opportunity cost, for example, is fundamental to developing financial literacy, as people often need to choose among different financial options. When making a financial decision, they consider various alternatives, and the option taken is considered to be preferred in relation to the options forsaken. By taking into account the highest-valued option forgone (i.e., the opportunity cost of getting the chosen option), people are able to make a sound financial decision that minimizes the (opportunity) cost incurred, or in other words, maximizes the gain. In addition, when making financial decisions, people generally consider the expected values of the alternatives available rather than their actual values. This is because the world is full of uncertainty; many expected things will not be realized, whereas many unexpected things will occur. When people make financial decisions, they need to take risk into account when considering the return on an investment. In addition, they need to consider the availability of money or funds, rather than counting on an unlimited amount of liquid capital. These issues point to the relations among risk, return, and liquidity. People also need to consider general price level changes, that is, inflation and deflation and the real rate of return on investment. Inflation involves a general rise in prices, or fall in the real value of money. Provided that the nominal return on investment is not indexed with the inflation rate, the real return on investment will drop. In the real world, price levels constantly change. These fluctuations have huge implications for the real value of the return on an investment, especially when the investment requires an extended period of time to be capitalized. Finally, understanding present value and discounting is of paramount importance in the development of financial literacy, as people need to consider future income and payments made over a period of time. Financial decision making involves consideration of how much one receives in the present and how much one will receive in the future. It is thus very difficult, if not impossible, to make intertemporal choices among alternative financial options if one does not know how to use the discounting method to derive the present values of these options to compare their values and costs at the same point in time. Understanding of all of the above economic concepts is useful for financial acts such as saving, consumption, and investment. Hence, it is important to understand the relations among income, spending, saving, and investing in relation to the abovementioned core economic concepts in an integrated and organic manner. As noted, financial literacy is characterized by the ability to attend to, or take into consideration, intertwined critical aspects of financial situations when making financial decisions. Gaining an in-depth understanding of the abovementioned cluster of core economic concepts will help students develop an analytical framework based on the finance economics discipline. They will be able to develop a certain lens through which to evaluate

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financial problems, which will enable them to focus on those critical aspects that have not been discerned previously and/or taken for granted. As a result, students will be able to see financial problems and situations in a new light and learn how to make sound financial decisions. This approach to developing financial literacy is also related to work on threshold concepts (e.g., Meyer and Land 2003, 2006). For people to be able to ‘‘think’’ in a particular discipline, or to perceive, apprehend, or experience particular phenomena within that discipline, they need to develop a good understanding of the threshold concept of the discipline. This concept can be considered as ‘‘akin to a portal, opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something without which the learner cannot progress’’ (Meyer and Land 2006, p. 3). Following this line of reasoning, through acquiring certain core economic concepts, students will be able to develop an economic way of thinking, which will guide them in making finance-related decisions. In summary, to develop financial literacy, that is, a kind of domain-specific generic capability of handling financial affairs in a considered way, one needs to be able to discern the critical aspects of the economic concepts and principles relevant to the critical aspects of novel complex financial situations and contexts.

Variation theory Two groups of teachers participated in the study: a lesson study group and a learning study group. Teachers in the latter drew upon variation theory (see, for example, Marton and Booth 1997, Bowden and Marton 1998; Marton and Tsui 2004, Marton and Pang 2006) when designing instruction to help students appropriate the object of learning. Variation theory emphasizes the way in which one learns to discern various entities and their varying features. To be aware of something it must be discerned, and to discern something a learner has to experience how it differs from other things. How something is experienced by someone can be characterized in terms of what features the person manages to discern (i.e., what differences she/he notices) and focus on simultaneously (Pang 2003; Marton 2006). The presence of differences is a necessary, but not sufficient, condition for experiencing differences. To experience differences (variation) in certain respects, things have to remain invariant in other respects. The pattern of variation and invariance in a certain situation constrains, and opens up, what can possibly be learned. According to variation theory, the likelihood of learning something is a function of the particular pattern of variation and invariance in how learners encounter it. This relationship between learning and the pattern of variation and invariance inherent in the condition of learning has been demonstrated empirically in numerous studies (see, for example, Pang and Marton 2003, 2005; Marton and Pang 2006, 2008; Holmqvist 2006).

Method Design of the study In this study, groups of secondary school economics teachers worked together to develop instructional means for achieving an agreed-upon object of learning. The aim was to

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develop student financial literacy in terms of the capability of students to make use of the core economic concepts learned to make sound and well-reasoned financial decisions in certain novel situations. Two groups of teachers participated in the study, both of which adopted the abovementioned conceptual approach. One group followed the lesson study model (lesson study group), and the other followed the learning study model (learning study group). The procedures for planning, implementing, and evaluating the lessons, described below, were the same for both groups. The only critical difference between the groups was that teachers in the learning study group used variation theory, which they had learned from the researcher in a Master of Education program or other research projects in which they had participated, as a tool for designing the instruction to achieve the object of learning. The lesson study group thus served as a reference to show the possible effect of the instructional design based on variation theory. Each group comprised six teachers, who first discussed how the object of learning could best be handled. Subscribing to the conceptual approach to developing financial literacy, the teaching team tried to look for key economic concepts that are deemed crucial to the development of financial literacy from relevant literature in economics and finance as well as the teaching and learning resources produced by local and international organizations to promote financial literacy. After discussions and deliberations among the teachers involved in the first preparatory meeting, a cluster of core economic concepts was identified that includes: the relations among saving, consumption, and investment, the opportunity cost of financial decisions, the relations among risk, return, and liquidity, inflation and the real value of return on investment, and present value and discounting. To ascertain the existing understanding of students of the core economic concepts and their level of financial literacy, a pre-lesson test that included multiple-choice and shortanswer questions was administered to all of the students, in which they were asked to make financial decisions under different complex financial conditions and explain their answers. There were two sets of pretest questions: both sets contained the same 30 multiple-choice questions, but there were slight differences between them in the short-answer questions in terms of examples and wording. Their level of difficulty was considered to be more or less the same (details are given in the following section). Students in each class were divided randomly into two groups, with each group assigned to complete one or the other set of questions. In the posttest, students were asked to answer the set of pretest questions that they had not completed before. In addition, to understand better how they made sense of the questions in the pretest, the written task was supplemented by pretest interviews with 60 students (five students from each of the twelve classes involved) who were chosen randomly. The results of the written task and interviews were used by both groups of teachers in the course of planning the lessons. Combining their own experience of handling similar economic concepts and knowledge of other learning resources for developing financial literacy, the teachers developed a joint lesson plan for a series of 16 40-min lessons, which were then taught in the six different classrooms. To reiterate, the learning study group teachers used variation theory to guide their planning of the lessons, with a focus on the pattern of variation and invariance. The lesson plans and materials were collected, and all of the lessons were videotaped and then analyzed in terms of the enacted object of learning, that is, what actually happened in the classrooms. After the research lessons, to evaluate the development of the financial literacy of students and to understand their lived object of learning (i.e., what the students actually learned from the lessons in relation to the object of learning), all students were required to

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complete a posttest written task that was identical to that used in the pretest, but each student completed the version that he or she did not encounter in the pretest. The same 60 students who had attended the pretest interview were interviewed again to determine their progress in understanding. Six weeks later, the first delayed posttest and interviews were conducted to assess the level of retention of financial understanding. In the written task, in addition to the same 30 multiple-choice questions, new short-answer questions were asked, which were contextualized using some novel everyday financial situation and framed in such a way that required the use of one or more of the economic concepts learned to help explain the student’s decision. Approximately 6 months later, students were given a second delayed posttest, in which another set of short-answer questions set in everyday contexts was employed (no multiplechoice questions were used). This test served to determine whether the generic capability of students to deal with novel financial situations was sustained over a prolonged period of time. Based on the learning and teaching data obtained, inter- and intra-group comparisons were conducted.

Participants Twelve teachers participated in the study, six of whom belonged to the learning study group and six of whom belonged to the lesson study group. The teachers in both groups had formal teacher training, and the average number of years of teaching experience was 10 for the former group and 13 years for the latter. One hundred and ninety-three students participated in this study. They ranged in age from 18 to 20 years, and all had studied economics as a school subject. In terms of academic attainment, no significant difference was observed between the students in the learning study group and those in the lesson study group.

Data collection Data for the study were collected through a pretest written task and interviews with students, class observation and video-recording of the lessons, and three post-lesson written tasks and interviews with students (i.e., immediately after, 6 weeks after, and 6 months after the lessons). (Note: All of the interview data are not used here.) Pretest written task and interviews A written test comprising multiple-choice and short-answer questions was employed to ascertain the understanding of students before the lessons and to form a basis to evaluate student learning outcomes after the lessons. There were 30 multiple-choice questions: some were extracted from financial literacy tests administered in the US and the UK (e.g., Q1), others came from the Hong Kong Advanced Level Examinations (e.g., Q11), and still others were set by the researcher to cater for the unique background and culture of Hong Kong students (e.g., Q25). Some questions were used to ascertain the understanding of students of the core economic concepts (for example, Q11 was used to assess student understanding of the concepts of present value and discounting), whereas others were used

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to evaluate the financial understanding of students (e.g., Q1 and Q25). One point was awarded for each correct answer. Sample questions follow. 1. Under which of the following circumstances would it be financially beneficial to you to borrow money to buy something now and repay it with future income? A. B. C. D.

When the interest on the loan is greater than the interest you get on your savings. When you really need a 2-week vacation. When the car you like becomes cheaper. When you need to buy a car to get a much better paying job.

11. Individual A chooses to be a medical doctor, with lower income in the early days but which rises later on. Individual B chooses to be an entertainer, with higher income in the early days but which falls later on. The total lifetime income of A is higher than that of B. Which of the following is correct? A. At no positive rate of interest will the wealth positions of A and B be equal. B. B is wealthier than A if the interest rate is low enough. C. A is wealthier than B regardless of the interest rate. D. None of the above. 25. In Hong Kong, your disposable income is less than the total amount you earn. Which of the following would MOST likely be taken out of your total pay? A. Salary tax and Mandatory Provident Fund. B. Profit tax and gasoline tax. C. Salary tax and property tax. D. Medicare contributions and insurance. Two sets of short-answer questions were designed, which to a large extent resembled each other in terms of the critical features of financial literacy to be examined. Most of the questions were situated in authentic complex contexts; to address the questions, students had to draw upon more than one of the economic concepts learned to deal with the financial situation. One pair of questions from sets A and B is given below. Set A: question 2b Each year you spend $100,000 for living at a constant price level. Suppose you plan to retire at the age of 55 and you expect you can live for 20 more years. If you have accumulated savings of HK$1,400,000 at the time of retirement, do you think you can maintain the same living standard for the following 20 years given an interest rate of 10% per annum and yearly inflation rate of 6% over this period? Why or why not? Explain. Mirror question in set B: question 1b Hong Kong Bank has just announced that all existing shareholders will be given one share as a dividend for every twenty shares 1 year later. Given that the unit price of a Hong Kong Bank share is currently $120 and the price of the share will follow the general price level, if the expected inflation rate is 6% and the interest rate of bank deposits is 10% per annum, will you buy the Hong Kong Bank share or deposit the money in the bank? Explain. Although the examples and wording of the questions are slightly different, the focus of the two questions is basically the same, as these questions aimed to assess whether students

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were able to use the given information to make sound and well-reasoned financial decision, with the help of related economic concepts such as the relationship between a change in the price level and real rate of return, present value and discounting, and, possibly, the relations among risk, return, and liquidity. For the pretest, half of the students in each class were asked to answer the questions in Set A and the other half was asked to complete those in Set B. In the posttest, each student was asked to answer the set of questions that he or she had not answered previously. Students were allowed 1 hour to answer the questions, and their answers were analyzed and rated in accordance with the level of understanding demonstrated (details are given in the data analysis section). Before the written test was administered, the researcher or his assistant gave each class instructions. Students were invited to elaborate on their ideas as much as possible and use whatever language or form of representation they desired to answer the question and articulate their understanding. They were strongly encouraged to show their steps and use diagrams to assist their explanations whenever possible. Interviews were conducted with individual students, who were mainly asked to elaborate their answers to the written task. In the posttest interviews, they were also asked to express their views about how the teachers had dealt with the object of learning. Each interview lasted from 25 to 40 min, with some spontaneous questions asked to allow the students to clarify or elaborate on the remarks that they had made earlier. All of the interviews were audio-recorded. In both the written task and interviews, the questions were open ended, which allowed the students to demonstrate their understanding of the cluster of core concepts and their financial understanding. Video-recording of lessons and post-lesson tests After devising a joint lesson plan, the teachers enacted it in their own classes with modifications and adaptations as they deemed necessary. To examine how the teachers enacted the object of learning in the actual classroom situation, all of the lessons were videorecorded. The lessons were transcribed verbatim by a research assistant and checked by the researcher to ensure accuracy. As noted, to ascertain the extent to which the students appropriated the object of learning, after the lessons all of the students were asked to complete a set of written tasks that aimed to measure their financial understanding (the questions were identical to those of the pretest), and the 60 students who were randomly chosen from each class for the pretest were interviewed. All of the interviews were audio-recorded and transcribed verbatim. A total of three post-lesson tests and interviews were conducted, that is, immediately after the completion of the series of lessons, 6 weeks later, and 6 months later. This served to determine the extent to which the generic capability, namely, financial literacy, had developed and was sustained over time. As mentioned, the pretest and first posttest questions were identical. However, to ascertain the extent to which the students had developed the ability to handle certain novel financial situations, a new set of questions was used in both the first and second delayed posttests. These questions were open ended and set in certain authentic contexts, and answering them required synthesis of the various economic concepts learned. The following question is an example drawn from the first delayed posttest (administered 6 weeks after the research lessons). It is based on current events reported in a local newspaper, and is closely related to the daily life experience of Grade 12 students who will

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soon enter university. Students are asked to make a decision about how to finance their university education and repay the loans after graduation, which goes beyond the application of a single economic concept learned. In this way, students are given the opportunity to demonstrate their level of financial literacy by justifying their choices made with the use of the relevant economic concepts. Q2. (Sing Tao Daily) The government is considering including the income from a parttime job or internship in tertiary students’ family income, but a survey shows that 65% of tertiary students believe that the amount in grants and loans offered by the government is not enough to cover tuition fees and living expenses. About half of them were offered less than $10,000, far below the annual tuition fee of about $40,000. Ms. Wong Fung Chu, a member of the Youth Committee of the Democratic Party, who was responsible for the survey, said that over 15% of students were offered neither grants nor low-interest loans under the Local Student Finance Scheme (LSFS), and could obtain only a high-interest loan under the Non-means Tested Loan Scheme (NLS). She took a family with four members having a monthly income of $15,000 as an example and said, ‘‘The tuition fee of about $40,000 is already equivalent to the family’s total income for 3 months. However, the student is offered grants and a loan totaling only $20,000, which is definitely not enough to cover the tuition fee. Is the scheme set only for impoverished families?’’ She said the assessment criteria for grants and low-interest loans were too stringent. Given: • tuition fee of local universities is $42,100 per annum (to be paid at the beginning of the year); • NLS loan is interest bearing, at a rate of 7.36% per annum; • savings rate is 2.5% per annum over the entire 2006–2014 period; • your living expenses are $20,000 per year during your studies and rise to $30,000 after graduation; • your annual income after graduation is $150,000 over the entire 2009–2014 period and you have no income during your  studies;  Y 1  1  ð1þr%Þ • formula of present value: r% n : a. Suppose you are offered a place in one of the local universities that offers 3-year bachelor’s degree programs: i. How much do you need to have NOW to finance the 3-year program? ii. Based on the financial condition of yourself and your family, do you think that you have other ways to finance your studies without borrowing from the government? If so, what are they? What would be the costs and benefits of these other options compared with borrowing from the government? b. Now suppose your family is not able to finance your studies and you have no savings. Alternatively, you may borrow from the government under the NLS any amount not exceeding $42,100, while you are also provided with financial assistance in the form of grants* of $22,100 per year under the LSFS. (*LSFS grants do not require repayment) i. How much do you need to borrow each year during the 3-year program? ii. If you want to repay the loan in five equal installments after graduation in 2009, how much will you pay at the beginning of each year starting in 2010? (See the table below)

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Year

2006

2007

2008

Borrow

?

?

?

Repayment

2009

2010

2011

2012

2013

2014

$X

$X

$X

$X

$X

iii. Suppose you find a 3-year bond (starting in 2010) that yields 10% per annum. How will you rearrange your repayment schedule in (bii), given that you still have to repay the loan within 5 years after graduating? (Note: You may answer this part by intuition or calculation.) iv. Considering your annual income, living expenses, and repayments in (bii), how much will you give your family per month to cover these expenses after graduation? How will you invest the remaining amount of income? What factors will you consider when making such a financial decision? The questions in the second delayed posttest, administered 6 months after the research lessons, contain salient features that are similar to those of the first delayed posttest. This is illustrated by the following question, which invites students to make a financial decision about investing, specifically, about the repayment of a mortgage. Although this scenario may appear somewhat beyond the life experience of students of this age, this kind of financial decision is considered important for a citizen in his or her lifetime. 1. Suppose you buy an apartment by hire purchase. You get a bank loan of $2 million now from Hong Kong Bank, which is to be repaid by 120 monthly installments. The mortgage interest rate is set at 2% below the prime rate (P-2%), where the   prime rate is Y 1  1  ð1þr%Þ 10% per annum. Formula to find the present value: r% n a. Suppose the Bank of East Asia offers you a lower rate of (P-2.5%) right after you have signed the mortgage deed. All other things remaining constant, calculate how much you can save every month in your mortgage repayment by changing your mortgage bank. b. However, to accept the offer by the Bank of East Asia, you need to pay a surcharge of $10,000 to Hong Kong Bank and a legal fee of $5,000. Will you decide to change your mortgage bank? Show your calculation to support your decision. (Hint: The market interest rate is 5% per annum.) c. It has been observed that some people prefer to hold a substantial amount of cash rather than using all of the money they have to partially repay their mortgage loan. Why?

Data analysis The student learning data were analyzed using a new approach inspired by phenomenography, focusing on the number of critical aspects of a certain phenomenon discerned (i.e., quantitative) as well as the different meanings of the phenomenon (i.e., qualitative) that can be found in students’ answers. The main reason of using this way of analyzing data was that unlike our previous studies in economics (e.g., Pang and Marton 2003, 2005; Marton and Pang 2006, 2008), there is no single, definitive way of understanding the authentic, ill-defined financial problems that the

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students were invited to handle in this study. As one may understand from the financial tsunami nowadays, it is extremely difficult to evaluate whether a certain way of understanding or handling a certain financial situation is definitely better than the other, particularly in view of a high level of uncertainty and people’s different value systems. In this connection, the number of critical aspects which are deemed relevant to the problem to be handled and which are identified from the data and not pre-determined was considered. The more dimensions considered of variations corresponding to the critical features of the phenomenon, the more sophisticated the answer is and the higher the level of understanding demonstrated; as a result, more points are awarded to answers that belong to this category. Furthermore, in order to derive an aggregate level of financial literacy for the students concerned which is derived from their answers to a series of financial problems with different focus, it is important to establish a consistent way of analyzing the data generated from each question. By examining the number of critical aspects relevant to each question consistently, the scores obtained from each of the different questions in the preand posttests are made comparable, and subsequently the aggregate score can be used to show students’ level of financial literacy. To demonstrate how student answers were analyzed, the following two questions about investing, found in both the pre- and posttests, are presented. Although the two questions involve different financial instruments, such as bonds, shares, or time deposits, they both evaluate the ability of students to make sound well-reasoned financial decisions; hence, the category of description is the same. Set A: question 2 Suppose you have $100,000 to invest. Which of the following investment options will you choose: (i) buying the share of one listed company in the Hong Kong Stock Exchange (e.g., Cheung Kong Holding Ltd.), (ii) putting money in 6-month time deposits with a local bank, or (iii) investing in a tracker fund (which is based on the Hang Seng Index)? Why? What factors will you consider when making such a financial decision? Set B: question 1 Suppose you have $1,000,000 to invest. Which of the following investment options will you choose: (i) investing in a global fund that invests in different markets around the world, (ii) purchasing a 5-year US treasury bill, or (iii) investing in foreign currencies (e.g., Australian dollars)? Why? What factors will you consider when making such a financial decision? Category A Focus only on one critical feature of the phenomenon such as the expected profitability of the investment itself or the stability of returns. Students expressing this conception discerned and focused only on one critical feature such as the expected profitability of the investment or the stability of return when they made the financial decision to invest. The following excerpts from students C103 and D321 show that the students considered only the expected profitability or the stability of returns and tended to ignore other critical aspects such as liquidity and inflation rate. This level of understanding is considered to be the lowest. Option (ii), because the economy of the US is good and the company will pay me. I will consider the gain before making a decision (C103, pretest).

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I will invest in US Treasury Bill. It is because I do not know much about investment. What I know is that it has the most stable returns and best protects my money. Of course, I will ask for advice from my friends or the brokers (D321, pretest). Category B Focus simultaneously on two critical features of the phenomenon, such as the level of risk or liquidity, the expected profitability of the investment and the change in price levels. Students expressing this conception discerned and focused on two critical features. Usually, they focused either on how the risk of and return on investment could go in the opposite direction; that is, the higher the risk, the higher is the expected return, and vice versa, or on how liquidity affects the profitability or return on investment, that is, the higher the liquidity of the investment, the lower is the rate of return, and vice versa. This level of understanding is deemed higher than Category A, and the answers of the following two students are a good illustration of this conception. I will choose putting money in 6-month time deposits with a local bank. I make this choice because I will not suffer from loss on this investment and the return is relatively stable. If investing in the shares of a local company, HK$100,000 is not a big sum; you cannot buy that much and earn that much. With regard to investing in the tracker fund, the risk tends to be higher because the daily price fluctuation is quite big. I therefore choose to put my money into time deposit with a local bank which offers higher interest rate or has good reputation (C107, pre-test). I will choose option (ii) because from option (ii) I can receive constant interest but for option (i) and (iii) the interest I receive is not fixed. In other words, options (i) and (iii) contain higher risk. Of course, I will consider the saving interest rate and whether there is inflation or inflation now and in the near future as well as economic growth (A319, pre-test). Category C Focus simultaneously on three or more critical aspects of the phenomenon, such as the level of liquidity and expected profitability of the investment and other critical features such as the inflation rate, exchange rate fluctuations, and so forth. Students expressing this conception discerned and focused on more critical features simultaneously compared to those in categories A or B. This level of understanding is the highest among the three categories identified. For instance, some students were able to show good understanding of the relations among the risk, liquidity, and profitability of the various investment options. In addition, some even considered an additional critical aspect—how transaction costs can affect their choice of financial assets. The following quotes from two students clearly demonstrate this level of understanding. I will consider the risk of investment in the sense that I should be aware of the possible profit or loss from each investment option. Also, I will consider the liquidity of my investment. This means whether I can get back my money whenever I want. Finally, the returns from the investment also need to be considered. If I invest, I would try to get the highest possible returns from my limited amount of capital and I would choose to invest in (i). Firstly, the rate of return of buying shares is higher whereas the time deposit rate is usually lower. Even though you put your money in the 6-month time deposit, the interest earned is not that much. Furthermore, the rate of return for buying shares issued by the giant corporations listed in the Hong Kong Stock Exchange is relatively higher and the price fluctuation tends to be lower.

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Lastly, for option (iii), the Hang Seng Index may fluctuate from time to time and the extent of fluctuation tends to be bigger. The risk of investing in (iii) is therefore higher. So I choose to invest in option (i) (A323, pre-test). I will choose option (i). This is because the risk of investment is relatively lower since it diversifies to different markets in the world. Options (ii) and (iii) will bear a larger risk. Besides, option (i) can enjoy a higher liquidity. When making a financial decision, I will consider the possible return, risk of investment, liquidity, terms, and transaction costs involved (B308, posttest). These categories of description can then be organized in an outcome space, according to the level of inclusiveness and complexity. In this case, there is a hierarchical relationship among the categories. The greater is the number of relevant dimensions of variation in relation to the critical aspects of the object of learning that are opened up in the answer, the higher is the level of understanding of that way of experiencing the object. Thus, Category C represents the most complex and inclusive way of experiencing the object as it includes three or more dimensions of variation corresponding to the critical features of understanding the phenomenon. Accordingly, the number of points awarded to answers belonging to categories A, B, and C was one, two, and three, respectively, and corresponds to the level of understanding of the conception. The teaching data were analyzed using the framework based on variation theory (see, for example, Pang and Marton 2003, 2005). The focus was on the enacted object of learning, that is, how teachers handled the same object of learning in the actual classroom context. Rather than providing a comprehensive account of the teaching process, the main focus of the analysis of the classroom data was on the patterns of variation and invariance constituted by students and teachers in the lessons, specifically, those aspects that varied and those that did not. Similarities and differences were identified in terms of the patterns of variation and invariance in the critical features of the object of learning that were found between and within groups in the lessons. As in our earlier reported studies, teachers in both groups worked collaboratively to maximize the learning conditions to enable their students to appropriate the agreed-upon object of learning. Both groups made use of the results obtained from the pretest of their own students, together with their own teaching experience and expertise as well as other learning resources that they could locate, to best deal with the object of learning. The critical difference between the two groups was as follows: teachers in the lesson study group planned lessons and designed the instruction without using a specific theoretical framework, whereas teachers in the learning study group designed their lessons based on variation theory. Based on the answers of students to the pretest questions, teachers in both groups tried their best to extract the critical features that defined the concepts in question, which not all of the students had mastered previously. According to variation theory, critical features, that is, critical pedagogical features, are critical to the mastery and understanding of the concept in question by students, and may not be identical to those critical disciplinary features that are derived from the subject discipline to which the concept belongs. In considering the prior learning and understanding of students, the former features can be of greater importance than the latter when student understanding is hampered by features other than those derived from the discipline. Conversely, the former can be less important than the latter, on the condition that students may have discerned some of the critical disciplinary aspects before teaching starts.

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After the teachers identified the critical pedagogical aspects related to their own students, they tried their best to design a learning environment that would help students appropriate the object of learning, that is, develop financial literacy. The salient feature of the learning study group was that the teachers, using variation theory, juxtaposed systems of examples to introduce variation in the dimensions of variation corresponding to the critical features identified, against the backdrop of other critical features that were invariant. They made more systematic use of patterns of variation and invariance, varying one critical feature at a time while keeping others constant, and subsequently bringing together the critical features. The differences in teaching and their relation to differences in learning will be reported in coming papers.

Results and findings As different questions were used in the first and second delayed posttests, a comparison of the mean scores across all four tests was conducted between the two groups for different occasions, to evaluate the effectiveness of the instructional designs for these groups. To better understand student performance in the different components of the tests, the results of the multiple-choice and short-answer questions are reported separately. Table 1 shows that in the pretest, the mean score of the learning study (lesson study) group was 56.97 (55.93). Although the performance of students in the former group was slightly better than that of students in the latter, the difference was not statistically significant (t = 0.794, df = 191, p = 0.428 ([0.01), effect size = 0.115). However, in the posttest, a statistically significant difference between the two groups in terms of mean score was observed. The learning study group had a mean score of 67.89, whereas that of the lesson study group was 62.56 (t = 2.966, df = 191, p = 0.003 (\0.01), effect size = 0.429). In the first delayed posttest, the difference between the two groups in terms of mean score persisted. The mean scores of the learning study and lesson study groups were 69.59 Table 1 Mean scores of multiple-choice questions The learning study group (98 students)

The lesson study group (95 students)

t

df

Sig.

Effect sizes

Pretest

56.97

55.93

0.794

191

0.428

0.115

Posttest

67.89

62.56

2.966

191

0.003

0.429

First delayedposttest

69.59

62.53

4.087

191

0.000

0.592

df

Sig.

Effect sizes

Table 2 Mean scores of short-answer questions The learning study group (98 students)

The lesson study group (95 students)

t

Pretest

19.39

21.78

-1.595

191

0.112

-0.231

Posttest

49.06

29.85

7.580

191

0.000

1.097

First delayed-posttest

39.98

23.92

6.347

191

0.000

0.919

Second delayed-posttest

42.40

24.21

9.389

191

0.000

1.359

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and 62.53, respectively, and the difference was statistically significant (t = 4.087, df = 191, p = 0.000, effect size = 0.592). The data indicate that the students belonging to the learning study group outperformed their counterparts in the multiple-choice questions, and that the difference, in terms of their mean scores, widened over time. Table 2 shows that for the short-answer questions, in the pretest the mean score of the learning study group was higher than that of the lesson study group, but the difference was not statistically significant (t = -1.595, df = 191, p = 0.112 ([0.01), effect size = -0.231). In the posttest, however, the performance of students in the former group surpassed that of their counterparts, and the difference was statistically significant (t = 7.580, df = 191, p = 0.000, effect size = 1.097). In the first delayed posttest, the performance gap between the two groups remained, and the difference was statistically significant (t = 6.347, df = 191, p = 0.000, effect size = 0.9185). In the second delayed posttest, the gap between the two groups grew larger, and the difference was also statistically significant (t = 9.389, df = 191, p = 0.000, effect size = 1.359). Although questions were set in the two delayed posttests that were different from those in the pre- and posttests, the intergroup difference between the two groups was found to remain or increase over time.

Discussion and conclusion The findings indicate that variation theory is a powerful tool for developing not only the understanding of students of a specific concept (as reported in previous studies) but also their financial literacy, a kind of domain-specific generic capability, in terms of their ability to handle complex, everyday financial situations. Students belonging to the learning study group outperformed their counterparts in the lesson study group in all three post-lesson tests conducted, and the differences in the learning outcomes of the students were found to be statistically significant. There appears to be an association between student learning performance and the conscious and intentional structuring of lessons by teachers in accordance with a framework grounded in variation theory, that is, lessons created using a certain pattern of variation and invariance that corresponds to the critical features of the phenomenon in question or the object of learning identified. Furthermore, a persistent and even widening performance gap was observed between the learning study and lesson study groups over time. Regarding the short-answer questions, the difference in mean scores between the two groups first increased from -1.39 (pretest) to 19.21 (posttest), dropped slightly to 16.06 (first delayed posttest), and then increased to 18.19 (second delayed posttest). With regard to the multiple-choice questions, the intergroup differences in mean score in the pretest, posttest, and first delayed posttest were 1.04, 5.53, and 7.06, respectively. Figure 1 shows that the difference between the two groups in terms of effect size also remained or increased over time. With regard to the multiple-choice questions, the effect sizes showed an upward trend (i.e., pretest = 0.115, posttest = 0.429, first delayed posttest = 0.592). A similar trend was observed for the short-answer questions. The effect size was negative (-0.231) in the pretest, increased to 1.097 in the posttest, dropped slightly to 0.9185 in the first delayed posttest, and increased to 1.359 in the second delayed posttest. Apparently, students in the learning study group were comparatively more able to sustain their ability to handle financial problems in novel situations over time than those in the lesson study group, or at least the fading-out effect was less pronounced. The former

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1.6 1.4

Effect Sizes

1.2 1 0.8 0.6 0.4

Multiple-choice Questions

0.2

Short-answer Questions

0 -0.2 -0.4

Pre-test

Post-test

First Delayedpost-test

Test

Second Delayed-posttest

Fig. 1 The effect sizes for multiple-choice questions and short-answer questions in the four tests

appeared to have developed the ability to transfer a domain-specific generic capability, financial literacy, from one context to another over time. This lends support to the notion of generative learning; that is, the learning of students went ‘‘beyond the learning situation itself and [students] developed a way of seeing the learning object in forthcoming situations that deepens the knowledge further in every new situation’’ (Holmqvist et al. 2007, p. 188). In many parts of the world, curriculum reforms emphasize the development of the generic capabilities of students, such as critical thinking, problem-solving ability, and so forth, to help them learn how to learn in knowledge-based economies. Undoubtedly such capabilities are of paramount importance, but they cannot be developed in a vacuum. These capabilities, we believe, are often contextualized and closely related to the various domains of knowledge. Throughout history, people have learned how to handle their everyday matters successfully by drawing on resources from various disciplines or fields, which has led to the crystallization of and theories on the essence of human experience. People use conceptual resources from a certain domain of knowledge to help them identify the critical features of a novel situation or problem in order to make sound decisions and act effectively. Rather than being content free, generic capability tends to be domain specific, and thus can be promoted by developing an in-depth understanding of the content, or concepts, of a certain domain, which becomes the skeleton of a particular generic capability. The findings also support the conceptual approach adopted in this study for developing student financial literacy. According to Marton and Pang (2006), powerful ways of acting originate from powerful ways of seeing. To acquire a more powerful way of seeing, one needs to develop the ability to attend to the critical features of a given phenomenon or situation, and the critical features identified hinge on the lens of the experiencer, which is influenced by his or her own domains of knowledge or understanding. In other words, a domain of knowledge will provide people with a certain lens through which to interpret and analyze the phenomena around them and thus enable them to focus upon different critical aspects of the situation or phenomenon. Pang and Marton (2003) argue that it is the way of experiencing or seeing that matters, and which influences what and how people act. In summary, to help students develop a domain-specific generic capability, namely financial literacy, it is important for teachers to help students develop a good understanding of core economic concepts through the systematic use of variation and invariance in the

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dimensions that correspond to the critical aspects of the object of learning and the contexts. These core economic concepts learned will empower students by providing them with the conceptual tools to make sense of novel financial situations, which will allow them to be more sensitive to the critical features of such situations and enable them to make sound and effective financial decisions. Acknowledgments The study described in this paper was supported by funding from the Hong Kong Research Grants Council.

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