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    HISTORY-BASED ACCOUNTING REFORM:

    USING MATHEMATICS PERSPECTIVE TO IDENTIFY AND SOLVE SOME MAIN

    PROBLEMS IN ACCOUNTING EDUCATION AND STANDARDS

    Author:

    SONY WARSONO, PhD

    Email address:

    [email protected]; [email protected]

    Institution:

    Department of Accounting

    Faculty of Economics and Business

    Universitas Gadjah Mada

    Yogyakarta Indonesia

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    HISTORY-BASED ACCOUNTING REFORM:

    USING MATHEMATICS PERSPECTIVE TO IDENTIFY AND SOLVE SOME MAIN

    PROBLEMS IN ACCOUNTING EDUCATION AND STANDARDS

    ABSTRACT

    Manuscript Type: Perspective

    Research Issue: Perceived as a pure social science, prominent accounting scholars agree that thecurrent accounting development overemphasizes on rules, and this has wide negative impacts on

    accounting education and research. Thus, accounting reform is necessary even though it is still

    unclear the direction of the reform.

    Research Findings/Insights: The basic thesis of this study is that accounting is an application of

    mathematics because accounting was documented in the mathematics book and written by Luca

    Pacioli as a mathematics professor. Firstly, this study shows the inappropriateness of current

    accounting teaching methods. Specifically, this study shows that the use of debits and credits is

    purely the application of mathematics. Secondly, this study identifies the limitation of the

    definition of financial statement elements, and proposes the alternative redefinition of the

    elements. Thirdly, this study shows that the use of a mathematical perspective helps accountingprofession to solve current accounting issues. Finally, this study proposes the development of

    three pillars, i.e. mathematics, rules, and art, in a balanced manner to do accounting reform.

    Theoretical/Academic/Policy Implications: This study provides a new perspective that the

    accounting development is based on the history of accounting itself, i.e. accounting as an

    application of mathematics. Using the mathematical perspective, not only do accounting scholars

    improve the accounting education but also we innovate accounting research agenda. In addition,

    this study offers insights to accounting standard boards interested in developing a global uniform

    of financial accounting standard that effectively work.

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    HISTORY-BASED ACCOUNTING REFORM:

    USING MATHEMATICS PERSPECTIVE TO IDENTIFY AND SOLVE SOME MAIN

    PROBLEMS IN ACCOUNTING EDUCATION AND STANDARDS

    INTRODUCTION

    The 2001 and 2002 accounting scandals were considered the beginning of the wave of the global

    financial crisis. The wave of the scandals spread widely and resulted in significant damages.

    Many factors potentially contributed to the scandals (see Ball, 2009). The most recent wave of

    global financial crisis was the 2007 and 2008 financial crisis sometimes described as the most

    serious financial crisis since the Great Depression. The crisis was the result of frauds and

    mistakes committed by managers who were accountable to no one (Zingales, 2009:391).

    Association of Chartered Certified Accountants (ACCA, 2009) as the global body for

    professional accountants demands the accounting profession to learn from the year long financial

    crisis because it is clearly unacceptable that poor quality loans can be sliced, diced and parceled

    up with an AAA sticker and overvalued on banks balance sheets as a consequence.

    The magnitude of this worldwide financial crisis calls for a fundamental reassessment of

    all areas of business and economic scholarship, especially accounting because the main roles of

    accounting is to provide financial information. The better the accounting as a financial reporting

    system is, the higher the quality of financial information outcomes will be. It is expected that

    accounting provides information on what really happens both in micro- and macro-economic

    activities. In turn, accounting will detect and prevent the global financial crisis. Unfortunately,

    the accounting development is still far from the expectation. Accounting today is under pressure

    even from inside. Demski (2007) questions whether accounting is an academic discipline.

    Fellingham (2007) argues that accounting academicians tend to think in terms of contributions to

    the current generation of students, instead of to the academy or to future generations of students.

    Hopwood (2007) argues that accounting researchers increasingly focus on accounting research

    issues that are insufficiently innovative and increasingly detached from reality. Ball (2008)

    argues that an understanding of the actual economic role of financial reporting is important from

    both a positivist scientific perspective and a normative perspective. Recently Basu (2008:426)

    demanded several scholars to present the topic "What is the most important accounting issue

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    where we either think we understand it but in fact do not or have failed to consider the issue in

    anywhere near the depth it deserves?"

    Perceived as pure social science, rules are fundamental in accounting (Penno, 2008), like

    in law and politics. However, in its development, prominent accounting scholars agree that the

    current accounting development overemphasizes on rules. Over time accounting profession tends

    to apply a rule-based approach which emphasizes compliance over substance to financial

    reporting rather than a principle-based approach which emphasizes substance over compliance

    (Ball, 2009:277). This development has wide and significant negative impacts on accounting

    education and research (Hopwood, 2007; Demski, 2007; Fellingham, 2007; Ball, 2008, 2009;

    Arnold, 2009).

    The current case is the adoption of IFRS (International Financial Reporting Standards).

    The objective of the IFRS adoption is that a uniform set of accounting standards will achieve the

    goals of comparability and consistency of financial reporting that applies throughout the world.

    On the one side, prior research studies find that the adoption of IFRS provides benefits on certain

    conditions (Daske, Hail, Leuz & Verdi, 2008; Li, 2010; Armstrong, Barth, & Riedl, 2010).

    Furthermore, the Financial Reporting Policy Committee of the Financial Accounting and

    Reporting Section of the American Accounting Association concludes that the adoption of IFRS

    is a desirable goal (AAA FRPC, 2010:117). On the other side, Holthausen (2009) argues that

    the objective of IFRS adoption would not be successful unless the underlying institutional and

    economic factors among countries were similar. Another committee in the American Accounting

    Association, the Financial Accounting Standards Committee favors allowing U.S. companies to

    choose use of U.S. GAAP or IFRS rather than mandating one global monopoly set of standards.

    (AAA FASC, 2010). In short, the effectiveness of the IFRS adoption is still debatable. This

    dilemma is not unusual in accounting standard setting. As a matter of fact, it is unlikely to find

    one industry, for example the telecommunication or computer industries, applies a single

    industry standard around the world. Interestingly, even though these telecommunication and

    computer industries use different standards but they still achieve the goals of comparability and

    interconnectivity.

    Accounting reform is necessary and starts running now. The reform is a main part of the

    enforcement of corporate governance initiatives. Demski (2007:156) challenges accounting

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    academicians to do good and redefine the game, and believes that the change will come from

    young accounting scholars who learn accounting with fun. Recently the former Vice-Chairman

    of the Financial Accounting Standards BoardDavid Mosso (2010) proposed a new accounting

    model that measured wealth and provided information about entitys financial health. The model

    was expected to discourage political tampering. This paper uses a mathematical perspective,

    especially the double entry system, to propose the accounting reform. The use of a mathematical

    perspective is appropriate and valid because accounting itself was academically documented in

    the mathematics book by Luca Pacioli as a mathematics professor (discussed in the second

    section). Moreover, using the mathematical perspective, this paper shows the inappropriateness

    of the present accounting education and proposes the solutions (third section), identifies the

    limitations of the current financial standards and proposes the solutions (fourth section), and

    proposes the solutions to solve two current accounting issues (fifth section). The final section

    concludes the discussion.

    ACCOUNTING AND MATHEMATICS

    As widely acknowledged, Luca Pacioli discussed accounting in his mathematics book

    Summa de Arithmetica, Geometria, Proportioni et Proportionalita (hereafter, Summa). Summas

    English title would be Collected Knowledge of Arithmetic, Geometry, Proportions and

    Proportionality (Weis & Tinius, 1991). The first time Summa was published, Luca Pacioli had

    been teaching mathematics courses in several universities for more than 20 years (Journal of

    Accountancy, 1987). Sangster, Stoner, & McCarthy (2007) mention that there were 10 chapters

    in the Summa: a) chapter 1 7 about Arithmetic, b) chapter 8 about Algebra, c) chapter 9 about

    Business, including, Particularis de Computis et Scripturis translated intoDetails of Accounting

    and Recording (Rabinowitz, 2009), and d) chapter 10 about Geometry and Trigonometry. The

    section of Particularis de Computis et Scripturis appears to be included for the sake of

    completeness to recognize the importance of arithmetic principles in the application of

    bookkeeping (Rabinowitz, 2009).

    Luca Pacioli was neither an accountant nor bookkeeper, but a university professor of

    mathematics (Peters & Emery, 1978; Weis & Tinius, 1991; Hernandez-Esteve, 1994;

    Rabinowitz, 2009), astrologer to Pope Leo X, and the author of a number of mathematics books

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    (Sangster et al., 2007). Pacioli cleverly explained mathematics in a clear and interesting way

    reflecting the state of mathematics during the early Renaissance (Weis & Tinius, 1991).

    Most of accounting literature agrees that the double entry system is an application of

    mathematics. It was possible that the double entry system had existed hundreds of years before it

    was published in Summa (Yamey, 1994; Rabinowitz, 2009). Interestingly, the double entry

    system is one of few principles that stay unchanged for more than 500 years (Hatfield, 1924;

    Littleton, 1926; Rabinowitz, 2009). InMathematics Magazine, Ellerman (1985) confirms that the

    double entry system is purely the application of mathematics.

    The use of debits and credits in the double entry system is also an application of

    mathematics. Most of modern accounting textbooks define debits meaning the left side, and

    credits meaning the right side (e.g. Anthony, Hawkins, & Merchant, 2007; Williams, Haka, &

    Bettner, 2007; Weygandt, Kieso, & Kimmel, 2008). The definition indicates that the use of

    debits and credits is identical with algebra that has left and right sides.

    Peters & Emery (1978) believe that mathematicians did not use negative numbers when

    Pacioli published the Summa. In the contrary, Scorgie (1989) demonstrates that the negative

    numbers were known before the publication of the Summa. This study argues that the use of

    debits and credits in the double entry system is mainly because there is no negative numbers in

    financial unit. As we all know, accounting uses a monetary unit principle to measure the

    economic activities (Littleton, 1926). Mathematically, moving negative numbers (suppose minus

    5) from the left side of algebra to the right side will change the numbers into positive ones (plus

    5). Thus, the use of debits and credits in accounting that conveys financial information is purely

    an application of mathematics. This argument is important to explain the rules of debits and

    credits discussed in the next section.

    REFORMING THE ACCOUNTING EDUCATION

    Even though accounting has been taught for more than 500 years, discussions about

    accounting teaching methods are always appealing. The traditional teaching of accounting has

    been criticized in many countries (Duff & McKinstry, 2007). While business has experienced

    dynamic changes, the study of accounting remains essentially the same (Albrecht & Sack, 2000),

    passive (Bonner, 1999; Boyce, Williams, Kelly, & Yee, 2001), procedural (Dempsey &

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    Stegmann, 2001), inadequate in equipping the student with the necessary competencies

    (Mohamed & Lashine, 2003), and relying merely on a one-way direction of knowledge

    distribution (Williams, 1993; Saunders & Christopher, 2003). This traditional learning of

    accounting makes accounting textbooks look similar to one another (Sullivan & Benke, 1997)

    which in turn makes accounting less attractive to students.

    A great number of experts have been discussing the need of changes in the teaching

    methods of accounting (Rankin, Silvester, Vallely, & Wyatt, 2003; Hartnett, Romcke, & Yap,

    2004). Albrecht & Sack (2000) argue that the study of accounting needs to be transformed to

    catch up with changes in technology and globalization. Saudagaran (1996) and Springer &

    Borthick (2004) noted that the traditional curriculum of accounting, emphasizing memorizing

    skills, may actually hinder the students efforts to develop the requisite competence in

    accounting, such as critical thinking. Other researchers suggested the use of information

    technology to improve the effectiveness of accounting study (Elliott, 1992; Pincus, 1997;

    Mohamed & Lashine, 2003; David, Maccracken, & Reckers, 2003; Goldwater & Fogarty, 2007).

    Fordham & Hayes (2009) found that paper color may have significant contribution to student

    performance in the accounting principles courses.

    Our accounting textbooks typically consist of little other than a recitation of the more

    important standards (Ball, 2008:428); We teach the rules, and de-emphasize our

    contribution to the academy (Fellingham, 2007:160); and We have ceded to regulators the

    care, feeding, and deepening of our intellectual foundations. (Demski, 2007:156). Those three

    statements confirm that the teaching of accounting today overemphasizes standards. Some

    critical issues that might be questioned by students are answered based only on the rules. This

    paper discusses the two following basic issues problematic in accounting education.

    The Rules of Debits and Credits

    The rules of debits and credits have been much debated by experts. On the one side,

    experts argue that the mechanism of debits and credits does not make sense (debits and credits

    are nothing more than pluses and minuses, Ingram, 1998:411), demands the student simply to

    memorize (Saudagaran, 1996; Pincus, 1997), is too narrowly procedural (Patten & Williams,

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    ----------------------------------------------

    Insert Figure 2 about here

    ------------------------------------------------

    Case B. Supposed, Assets = 10, Liabilities = 4, and Equity = 6. The basic accounting

    equation is 10 = 4 + 6. Next, the amount of liabilities is the difference between 18 and 14 (18

    14), and accounting does not recognize the negative number. Based on the ordered pairs of the

    group of differences construction (see Ellerman, 1985), the liabilities with the value of 4 can be

    recorded either on one side, i.e. 18 is recorded to the debit and 14 to the credit (alternative A) or

    14 to debit and 18 to the credit (alternative B). According to the mathematical formulation,

    however, the alternative B should be applied because the liabilities have a positive value and

    located on the right side of the accounting equation (see Figure 3). The interpretation is that

    number 14 on the debit deducts number 18 on the credit. As a result, the increase of liabilities is

    recorded on the credit while the decrease of liabilities is recorded on the debit (see Figure 4).

    ----------------------------------------------

    Insert Figure 3 about here

    ------------------------------------------------

    ----------------------------------------------

    Insert Figure 4 about here

    ------------------------------------------------

    Case C. Supposed, Assets = 10, Liabilities = 4, and Equity = 6. The basic accounting

    equation is 10 = 4 + 6. Next, the amount of equity is the difference between 36 and 30 (36 30),

    and accounting does not recognize the negative number. Based on the ordered pairs of the group

    of differences construction (see Ellerman, 1985), the equity with the value of 4 can be recorded

    either on one side, i.e. 36 is recorded to the debit and 30 to the credit (alternative A) or 30 to

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    debit and 36 to the credit (alternative B). According to the mathematical formulation, however,

    the alternative B should be applied because the equity has a positive value and located on the

    right side of the accounting equation (see Figure 5). The interpretation is that number 30 on the

    debit deducts 36 on the credit. As a result, the increase of equity is recorded on the credit while

    the decrease of equity is recorded on the debit (see Figure 6).

    ----------------------------------------------

    Insert Figure 5 about here

    ------------------------------------------------

    ----------------------------------------------

    Insert Figure 6 about here

    ------------------------------------------------

    In summary, the rules of debits and credits are based on a mechanism which entirely

    follows the mathematical logics. In our experience, students can understand and accept the rules

    more easily than if they have to memorize it. In other words, the use of the mathematical

    perspective has made irrelevant the assumption that the debit and credit rules are something that

    should be memorized. With a good reasoning, students may find it easier to apply the debit and

    credit rules to all kinds of algebraic equations, not just in relation to accounting equation.

    It is true that the rules of debits and credits tend to be mechanical but the rules are always

    relevant to be taught in accounting courses because of the following reasons. First, the debit and

    credit rules convey a picture to students that accounting is based on established knowledge,

    especially mathematics. Second, as computer science with its binary digits (0 and 1) and the

    science of electricity with its on and off, accounting is endowed with debits and credits as a

    unique knowledge, which is used only in accounting. Third, debits and credits can be used to

    enhance the concreteness of knowledge of accounting; the study of debits and credits tangibilizes

    the workings of accounting. Tangibilizing the accounting mechanism is important to help

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    students understand accounting topics related to keeping journals, posting, which are indeed in

    the heart of accounting as an academic discipline. Fourth, as accounting students are expected to

    compile or construct information, not just to use information, they must have acquired basic

    knowledge of data processing to present useful information (Vangermeersch, 1997). Fifth,

    knowledge of debits and credits encourages students to think systematically and logically, and to

    develop the knowledge about accounting dynamics as fast growing science through the

    implementation of mathematical knowledge.

    The Rationale of Accounting Equation

    In Summa, Luca Pacioli codified the double entry systems which are based on the basic

    accounting equation as: Assets = Liabilities + Equity (Equation 1). The rationale behind the

    equation is that assets are resources under the firms control, whose funds come from liabilities

    and equity (sources of funds). In other words, the rationale of the Equation 1 is that the resources

    must be always equal to the sources of funds. Then, the equation was expanded to include

    expense and revenue elements to represent firms economic activities. Expenses and revenues

    are part of the equity; revenues increase equity, while expenses decrease equity. Thus, the

    expanded accounting equation was written as: Assets = Liability + Equity + Revenues

    Expenses (Equation 2a). The rationale of the Equation 2a is that resources must be equal to

    sources of fund in which revenues and expenses are part of the equity. These rationales are

    primarily based on the balance-sheet approach so that other accounting variables (i.e. revenues

    and expenses) are considered secondary and derivative (Dichev, 2008:454). Many textbooks

    employ Equation 1 to analyze transactions which result in changes in the element of revenues

    and expenses (e.g., King, Lembke, & Smith, 2001; Porter and Norton, 2001; Warren, Reeve, &

    Fess, 2002; Libby, Libby, & Short, 2004; Williams et al., 2005; Anthony et al., 2007). Several of

    these textbooks write down the Equation 2a in their books (Horngren, Sundem, & Elliott, 2002;Weygandt et al., 2008).

    This study argues that the rationale employed to explain the basic accounting equation

    (Equation 1) is not consistent with those employed to explain the expanded accounting equation

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    equity, may result in their being less than optimal. Analogizing the approaches of data

    management in the computer system, the database approach provides information which is more

    up-to-date, standardized, and easier to access than the application-oriented approach because the

    database approach separate data from their application software (Romney & Steinhart, 2009).

    More than just offering consistent rationale, the use of mathematical rationale (Equation

    2b) will make it much simpler to explain why the elements of assets and expenses should receive

    the same treatment in relation to debits and credits even though by definition assets and expenses

    markedly differ from one another; assets represent sources which provide future benefits, while

    expenses represent a sacrifice of assets (FASB, 1985). Actually, assets and expenses have the

    same rules of debits and credits because both of them represent the uses of fund.

    REFORMING THE ACCOUNTING STANDARDS

    The International Accounting Standards Committee (IASC) issued the conceptual

    framework in 1989. It was based on FASB, which adopted the balance sheet model of financial

    reporting (Camfferman & Zeff, 2007). More specifically, the definition of the elements of

    financial statements was based on the perspective of assets (Alfredson, Leo, Picker, Pacter,

    Radford & Wise, 2007). This happened because the standards considered economic resources or

    assets as central to the existence and operations of an individual entity (FASB, 1985:Par. 11)

    and the lifeblood of a business enterprise (FASB, 1985:Par. 15). Furthermore, the IASC was

    replaced by the International Accounting Standards Board (IASB) in 2001.

    Currently the Joint Project IASB/FASB is redefining the elements of financial statements.

    The Joint Project IASB/FASB tentatively adopted the following working definitions of asset and

    liability as follows:

    An assetof an entity is a present economic resource to which the entity has a right

    or other access that others do not have. (IASB FASB, 2008:Asset Definition)

    A liability of an entity is a present economic obligation for which the entity is the

    obligor. (IASB FASB, 2008:Liability Definition)

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    Essentially the re-definition of the elements of assets and liabilities by the Joint Project

    IASB/FASB was still based on the same perspective, namely the balance sheet orientation

    (Dichev, 2008).

    So far the work of the Joint Project IASB/FASB is still continuing. The tentative

    definition of the elements of equity has not been issued. Taking a close look at the definition of

    assets and liabilities made by the Joint Project IASB/FASB, it is predicted that the Joint Project

    IASB/FASBs efforts to define equity and other elements, including revenues the IASB refers

    to them as income and expenses, would still be based on the perspective of assets, unless the

    Boards expand their effort to a more thorough reassessment of their conceptual framework

    (Dichev, 2008:454). In this case, it is very likely that equity will be defined as net assets, and

    revenues and expenses would be parts of the equity.

    The accounting standards actually employ mathematics in defining the elements of

    financial statements. Equity is defined as net assets, namely the arithmetic difference between

    assets and liabilities (Alfredson et al., 2007:76). Furthermore, revenues are conventionally

    defined as asset increases or liability decreases (or a combination of both). Such a definition of

    revenues is based purely on the accounting equation; increases in revenues (recognition of the

    occurrence of revenues) on the right side of the accounting equation should be followed by asset

    increases on the left side of the equation or followed by liability decreases on the right side of the

    equation (or a combination of both) so that a balance in the accounting equation would be

    maintained. Unfortunately, the elements of financial statements, especially for revenues and

    expenses, are not adequately defined to the effect that accounting runs the risk of providing

    financial information which does not correctly represent the reality of business. The limitation of

    accounting standards in defining the elements of financial statements and the alternative

    redefinition of the financial statement elements are discussed below.

    The Limitation of the Accounting Standards

    The use of the asset perspective to define the other elements of financial statements may

    result in an incomplete definition. In turn, accounting may provide financial information which

    does not faithfully represent the firms real condition. Many experts have revealed the

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    Illustrative Case. Business event A: Merchandising firm Q, which is in the business of

    selling computers, and merchandising firm R, which is in the business of selling furniture, barter

    their merchandise. According to the standards, both merchandising firms Q and R recognize this

    business event as a revenue transaction, as in this event there is an increase of assets into each

    firm.

    Business event B: Service firm S, which is in the information technology consulting

    business, and service firm T, which is in the accounting consulting business, barter their main

    service. According to the standards, both firms S and T should not recognize this business event

    as a revenue transaction because there is no increase of assets or decrease of liabilities in each of

    these firms. Accordingly this business event cannot be classified as a revenue transaction by

    either firm.

    Business event C: Service firm S, which is in the accounting consulting business, is

    conducting barter with merchandising firm Q, which is in the business of selling computers.

    According to the standards, firm S should recognize this business event as a revenue transaction

    because there is an increase in assets in the form of computers. Firm Q, however, should not

    recognize this business event as a revenue transaction because there is neither an increase in

    assets nor decrease in liabilities even though firm Q delivers its services. This business event,

    therefore, is recognized as a transaction by firm S but cannot be recognized as such by firm Q.

    Business event D: Service firm V, which is in the business of advertisement, purchases a

    number of firm Ws shares (with the intention to own them). The payment is made directly and

    fully in the form of advertising services delivered by firm V. Firm V should recognize this

    business event as a revenue transaction because there is an increase in assets in the form of

    shared investment. According to the standards, however, firm W should not recognize this

    business event as an expense transaction because there is neither a decrease in assets nor an

    increase in liabilities as a result of this business event; what results is an increase in equity.

    Business event E: Service firm X, which is in the business of TV advertising, distributes

    revenue dividends in the form of services to firm Y, which owns more than 20 percent of the

    company shares. On the announcement date, firm Y immediately utilizes the revenue dividends.

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    According to the standards, firm X should not recognize this business event as a revenue

    transaction because there is neither an increase in assets nor a decrease in liabilities; what results

    is an increase in dividends distribution. On the other hand, firm Y should recognize this business

    event as an expense transaction because the firm receives advertising services and there is a

    decrease in assets in the form of shared investment (equity method). Therefore, this business

    event should be recognized as an expense transaction by firm Y but should not be recognized as

    a transaction by firm X.

    The illustrative cases above are simulations of transactions that may happen in business

    on the basis of the expanded accounting equation. In short, the recognition of revenues can be

    balanced not only by increases in assets or decreases in liabilities, but also by increases in

    expenses or decreases in equity. Likewise, the recognition of expenses can be balanced by

    decreases in assets, increases in liabilities, increases in equity, or increases in revenues.

    Therefore, the current definitions of the elements of revenues (income) and expenses are

    incomplete. This occurs because the standards argue that revenues and expenses should make a

    direct impact on the assets and/or liabilities. The inadequacy of the definitions of revenues and

    expenses is also due to the placement of revenues and expenses under the category of equity.

    The Redefinition of the Elements of Financial Statements

    One of the topics currently discussed in earnest by accounting experts is the approach that

    should be adopted in constructing financial statements (Haka, 2009). Current standards have

    opted for the balance sheet approach, while some accounting scholars suggest the use of income

    statement approach (see Dichev, 2008; AAA FASC, 2007). First and foremost, financial

    accounting should provide financial information, not just the balance sheet and income

    statement. Therefore, standards determined by the use of one perspective are likely to

    underestimate the importance of other perspectives. As demonstrated above, the use of the

    balance sheet perspective has rendered as un-coverable a large number of business events

    significantly related to revenues and expenses. Likewise, the use of the income statement

    approach is likely to underestimate the importance of business events related to assets, liabilities,

    and equity.

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    To solve the problems related to the use of appropriate approaches in the definition of the

    elements of financial statements, we can take a lesson from the approach employed in data

    management. Early in the development of the computer, data management employed a file-

    oriented approach, which tied the data to the application that produced them. As a consequence,

    in order to access particular data with other applications the data must be converted first. The

    conversion process may cause changes to the original data. This file-oriented system was

    considered inefficient, highly susceptible to errors, redundant, etc (Wilkinson, Cerullo, Raval, &

    Wong-on-Wing, 2000). Modern data management uses a database approach, which separates

    data from the application that produced them. The database approach makes it possible to

    produce data which are standardized, consistent, and integrated (Romney & Steinhart, 2009). An

    analogy can be made between the use of the balance sheet or income statement approach and the

    file-oriented approach.

    Mathematically, the expanded accounting equations (Equation 2a and Equation 2b) show

    that the elements of assets, expenses, liabilities, equity, and revenues are on the same level. The

    placement of one element above another is inconsistent with the accounting equation. Therefore,

    we argue that the approach employed in the definitions of the elements of financial statements

    should be on the basis of an infobase (another word for database, which is already common

    in the literature of information systems), instead of using either the balance sheet or the income

    statement approach. With the infobase approach, the elements of financial statements are not

    tied to the financial information which has been produced. It is only at the end of the accounting

    period that these elements are designed to produce financial statements.

    The current definition of the elements of financial statements is mechanistic rather than

    substantive, especially for the definitions of the elements of equity, revenues (income) and

    expenses. The mechanistic definition is not flexible enough for future development, and is

    incapable of providing any information about the subject to be defined. The equation of Assets +

    Expenses = Liabilities + Equity + Revenues indicates that the left side of the equation reflects the

    uses of funds, while the right side of the equation reflects the sources of funds. That rationale

    should, therefore, be employed in defining each element of financial statements.

    Using the infobase approach, the alternative definitions of the elements of financial

    statements are as follow. First, assets are uses of fund in the form of resources whose economic

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    value can still be utilized in the future. Second, expenses are uses of fund in the form of

    resources whose economic value has been utilized for the firms activities within a particular

    period. Third, liabilities are sources of fund from third parties acting as creditors. Fourth, equity

    is sources of fund from the companys owner, retained earnings (accumulated profits), and

    sources other than creditors. Fifth, revenues are sources of fund from the firms activities within

    a particular period. This infobase-based definition of elements of financial statements is more

    abstract, and covers many more business events than the current mechanistic definition allows

    for.

    MATHEMATICAL PERSPECTIVE TO SOLVE THE CURRENT ISSUES

    Written documents show that accounting was included in Luca Paciolis mathematic

    book (Sangster et al., 2007). In its historical progress, however, accounting has developed a

    focus on rules (Penno, 2008). A large number of rules have been issued to the effect that

    accounting was well-known as a regulatory enterprise (AAA FASC, 2007). Nevertheless, the

    development of rules cannot completely protect the users of accounting information (Scott,

    2009). Besides focusing on the development of rules, accounting has also developed an emphasis

    on vocational skills. The teaching of accounting, as a result, has focused largely on vocational

    skills (Demski, 2007), with little contribution to the academic world (Fellingham, 2007).

    Financial reporting is not an end in itself. It is a means of communicating to the users of

    financial reports information that is useful in making choices among alternative uses of scarce

    resources (FASB, 2006:OB6) and The objective of general purpose financial reporting is to

    provide financial information . . . (FASB, 2008:OB2). Thus, financial accounting is a tool to be

    used to provide financial information. As a tool, accounting should be of the same nature as

    computing, aircraft technology, etc. All these technologies require established knowledge in

    order to function effectively; to give the best possible contribution to humanity, and to allow for

    continuous development. This study argues that three major pillars should be developed in a

    balanced manner to enable accounting to become an academic discipline, namely mathematics,

    rules, and art.

    The Joint Project IASB/FASB has been developing the Conceptual Framework for

    Financial Reporting that underlies financial reporting. Several topics are still debated up to the

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    present. These debated topics usually become problematic when we have to choose between two

    extreme points which appear utterly irreconcilable but which eventually must be accommodated

    in order to serve the interests of all parties involved. For example, the Joint Project IASB/FASB

    originally stated in the Preliminary Views of the Conceptual Framework for Financial Reporting

    that the potential users of financial reports include equity investors, creditors, suppliers,

    employees, customers, governments and their agencies and regulatory bodies, and the public

    (FASB, 2006:OB6). Later, the Joint Project IASB/FASB revised the objective of external

    financial reporting as to provide information that is useful for capital providers including equity

    investors, lenders, and other creditors (FASB, 2008:OB6).

    Below are two Joint Project IASB/FASBs objectives as mentioned in the Preliminary

    Reviews of the Conceptual Framework (FASB, 2006) that can be achieved through the

    development of the accounting equation.

    Stakeholder vs. Stockholder Approaches

    The objective of external financial reporting is directed to the needs of a wide range of

    users (stakeholder approach). However, as long as all sources of funds other than liabilities are

    contained in one element, namely the equity, it will be difficult for financial reporting to provide

    information which is useful to users other than equity investors and creditors (stockholder

    approach). As the equity contains various sources of funds the quality of information coming

    from the element may decrease. For example, current financial reporting is unable to provide a

    representative picture of the long-term contribution of the management to the company because

    their performance is periodically moved into the equity. This study argues that this could be the

    reason for the emergence of conflicts between principals and agents. Likewise, current financial

    reporting is unable to provide information which is specific about governmental subsidies,

    donations or facilities received by the firm, as the information about governmental support is

    mixed up with information about other sources of funds in one big basket called equity.

    In this information era firms need information that is more detailed and comprehensive in

    order to make informed decisions. Had the accounting equation consisted of elements that

    represented specific types of users, information that is useful to a wide range of users might have

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    been produced. The accounting equation could be developed along the line of, for instance,

    Asset + Expenses = Liabilities + Owners Capital + Revenues + Management Contribution

    + Governmental Fund + Residual Sources.

    Relevance vs. Reliability

    The qualitative characteristics of financial reporting information should be relevant,

    faithful, comparable, and understandable. However, as long as the elements of accounting

    equation consist of financial information employing various measurements, it will be difficult to

    fulfill these qualitative requirements. For example, when assets cover several accounts that

    employ some measures, the assets are unable to fully meet both the characteristics of relevance

    and faithful representation. Likewise, the use of various measurements in one element may

    weaken the comparability and understandability of the financial reporting. This also applies to

    other elements in the accounting equation, both in the element of balance sheet and income

    statements.

    Had the accounting equation consisted of various elements containing information

    measured with the same (homogenous) measuring tool, the accounting information produced

    would have acquired the long-awaited characteristics of relevance, faithful representation,

    comparability, and understandability. For instance, the elements of assets are divided into two,

    namely value-based assets and historical-cost assets, and the elements of expenses are divided

    into two, namely accrual-based expenses and cash-based expenses. Elements of the value-based

    assets reflect the provision of information which is relevant for decision-making, while the

    elements of historical-cost assets reflect information which is relevant for faithful representation.

    THE TRIANGLE OF ACCOUNTING DEVELOPMENT

    Accounting is a tool to attain a particular aim (Ingram 1998). In other words, accounting

    should be treated like technology. As a technology, accounting can be made analogous to

    aircrafts, computers, or any other technological products. Those technologies are developed

    systematically, logically, and on the basis of sciences whose validity has been so well established

    that they are capable of growing even further and giving a vast contribution to the humankind.

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    accounting knowledge, rather than to be content with understanding accounting simply as a rule

    of play established by the business game. The use of the mathematical perspective can also be an

    initial step toward the development of new models of determining monetary values in financial

    statements, which up to now have been considered within the competence of other fields.

    CONCLUSION

    The development of financial accounting overemphasizing rules has limited accounting

    simply to the rules of the game. The use of a mathematical perspective identifies the

    inappropriateness of current accounting teaching methods and reveals the limitations of the

    current standard boards in defining elements of financial statements. This study also briefly

    discusses the use of the mathematical perspective to achieve the ideal objectives expected by the

    Joint Project IASB/FASB.

    Accounting should apply mathematical theorems widely. As a preliminary step, we

    should identify and discuss several persistent questions and problems, including standards, by

    using the mathematical perspective. Subsequently, developing accounting along the line of the

    three main pillars, namely mathematics, rules, and arts, should be undertaken in a balanced

    manner. Like in computer and telecommunication technologies, accounting should be able not

    only to function as a supporting tool to portray the reality of business, but also to function as a

    transformer in the future. The use of mathematical perspective in the development of accounting

    will convey financial information that is useful to prevent, detect, and correct global financial

    crisis.

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    APPENDIX

    FIGURE 1

    The Mathematics of Numbers Debit/Left Side

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    25 15

    FIGURE 2

    The Rule of Debits and Credits Assets

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    + -

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    FIGURE 3

    The Mathematics of Number Credit/Right Side

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    14 18

    FIGURE 4

    The Rule of Debits and Credits Liabilities

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    - +

    FIGURE 5

    The Mathematics of Number Credit/Right Side

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    30 36

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    FIGURE 6

    The Rule of Debit and Credit Equity

    Debit/Left Side Credit/Right Side

    10 = 4 + 6

    - +