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Mathematical Values Conveyed by High School Mathematics Textbooks

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Mathematics is usually seen as a value-free field. This is the primary reason for the lack of values studies in mathematics education. However mathematics is related to various values and that must be seriously considered from this perspective.
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  Abstract Mathematics is usually seen as a value-free field. This is the primary reason for thelack of values studies in mathematics education. However mathematics is related tovarious values and that must be seriously considered from this perspective. Valuesare taught implicitly rather than explicitly in mathematics classes compared to otherfields. A similar trend can be found in mathematics textbooks. That is, mathematicstextbooks also convey various values. Thus, the presence of educational and mathe-matical values in the 9th, 10th and 11th Turkish high school mathematics textbookswas investigated in this paper. For this purpose, 12 textbooks were randomly chosenand were analyzed by semantic content analysis. Results showed that rationalism,control, and openness are emphasized more than complementary value pairs in the9th, 10th and 11th grade mathematics textbooks. Similarly, it has also been fixedthat formalistic view, theoretical knowledge; instrumental learning/ understanding,accessibility, and evaluation are conveyed more than complementary value pairs inthe 9th, 10th and 11th grade mathematics textbooks. Key Words Mathematical values, mathematics educational values, values, mathematics textbooks 118 Mathematical Values Conveyed by High School Mathematics Textbooks Yüksel DEDE *  © 2005 E¤itim Dan›flmanl›¤› ve Araflt›rmalar› ‹letiflim Hizmetleri Tic. Ltd. fiti. (EDAM) * Correspondence:  Assistant Prof. Dr. Yüksel DEDE, Cumhuriyet University, Faculty of EducationMathematics Education Department of Primary Education 58140 Sivas, Turkey.E-Mail: ydede@cumhuriyet.edu.tr & ydede2000@yahoo.com Educational Sciences: Theory & Practice 6  (1) • January 2006 • 118-132  Although affective or cognitive aims or cognitive factors contain af-fective factors, it is seen that cognitive aims usually take place a mo-re significant place in curriculum and textbooks. Yet, affective fac-tors have developed in the same way and shown their own effects inmen’s lives. So, this kind of negative point of view towards educati-on’s affective aspect is inconvenient. Studies that focus on mathe-matics education and effective usually focus on topics such as attitu-des, beliefs, and motivation while ignoring values (Seah & Bishop,2000). However, studies that focus on mathematics and values are li-mited. Nonetheless, values are the most important elements of mat-hematics learning and teaching (Seah, 2002). What are these values?According to Brown (2001), identifying values is hard. For this, weneed some concepts such as “good” and “bad” (Swadener & Soed- jadi, 1988). The word “value” has been used in different meanings.“The value” of unknown in an equation, the “value” of listening aconversation and a moral “value” of an individual can be given as anexample (Seah & Bishop, 2000). According to Swadener and Soed- jadi (1988), identify values as a concept or an idea about value of anything has been always difficult. Mattthews (2001) also sees themas leaders and means of behaviors. When looking these identificati-ons, it can be described as personnel choices considering value orimportance of a behavior or idea, or general aims that are adopted orfollowed by an individual as a member of a society. Therefore, valu-es have reflected concepts or ideas about anything. Values can be ca-tegorized into two as aesthetic and ethical. Aesthetic values are bea-uty concepts but ethical values are about concepts which can be ex-pressed as good or bad. Ethical values are interested especially in go-od and bad sides of a behavior. This part of values forms a whole-ness with education. They cooperate with education and so theymake society formation possible (Swadener & Soedjadi, 1988). Mathematics and Values  Modern mathematics has a deductive-axiomatic structure and gene-rally shows a hierarchical construction. So, it is hard to understand amathematical concept without being aware of its preliminary sub- jects. This structure of mathematics depends on undefined terms,definitions, and logical rules (Swadener & Soedjadi, 1988). Absolutistphilosophers who see mathematics from this perspective appreciateit as an abstract science and think that it is interested in generalizati- DEDE / Mathematical Values Conveyed by High School Mathematics Textbooks  • 119  on, theory, and abstractions. So, mathematics is seen as a field whichhas no social choice and with which only a few people concerns. Ac-cording to this view, mathematics is value-free; that it is neutral (Bis-hop, 1988; Bishop, 2002; Ernest, 1991). In fact, mathematics is loadedwith values. It is not neutral. Yet, values are generally taught impli-citly rather than explicitly in mathematics. However, values are rarelytaken seriously at mathematics-related educational discussions andmathematics teachers are generally interested in operations that ha-ve only one answer. They don’t believe values teaching in mathema-tics lessons (Clarkson et al., 2000). Sam and Ernest (1997) classify thevalues about mathematics education into three as: i) Epistemological Values:  They are values which are about theore-tical side of mathematics learning and teaching such as accuracy,systematicness, and rationalism and also characteristics, appreci-ation, and acquiring mathematical knowledge (e.g., accuracy, be-ing analytical, rationalism and problem solving). ii) Social and Cultural Values:  They are values that indicate hu-man’s responsibilities about mathematics education for societysuch as compassion, integrity, moderation, and gratitude. iii) Personal Values:  Values that affect a person as an individual or alearner such as curiosity, thriftiness, patience, trust, and creativity.Bishop (1996) classifies values taught in mathematics into three dif-ferent types by making them more specialized than that of Sam andErnest. They are general educational values, mathematical values,and mathematics educational values (cited in Bishop et al., 1999). a) General Educational Values  General educational values are values that help teachers, schools,culture, society, and students to improve. Generally, they containethical values such as good behavior, integrity, obedience, kind-ness, and modesty (Bishop et al., 1999; FitzSimons et al., 2000).Warning a student who cheated during an exam can be an examp-le (Seah & Bishop, 2000). b) Mathematical Values  Mathematical values are those that reflect the nature of mathema-tical knowledge. They are produced by mathematicians who have 120 • EDUCATIONAL SCIENCES: THEORY&PRACTIGE  grown up in different cultures (Bishop et al., 1999). Proving Pytha-gorean Theorem in three different ways and their appreciation areexamples to mathematical values (Seah &Bishop, 2000). Culturestands as a powerful determiner of mathematical values. Researchshows that basis values of all cultures have not been shared. So,mathematics teachers work in different cultures do not teach the sa-me values, even if they have taught the same curriculum (Bishop etal., 2000). Bishop classifies mathematical values taught in Westernculture into three categories as complementary of each others(1988; cited in Seah & Bishop, 2000).These values are listed below: i) Rationalism-Objectivism:  Rationality indicates the values thatpeople have about mathematics. According to this value, mathe-matics has the ideas which depend on theory, logic, and hypot-hesis (Bishop et al., 2000). Shortly, rationalism value shows a de-ductive logic which concerns about only correctness of resultsand explanations. Objectivism value shows objects and symbolswhich are instruments to concretize mathematics that has an abs-tract language (Bishop et al., 1999; Seah & Bishop, 2000). ii) Control-Progress:  Control value shows that mathematics be app-lied, not only on phenomena about its nature but also on prob-lems and solutions in social areas (Seah & Bishop, 2000). Mathe-matics’ results have correct answers that can always be controlled(Bishop et al., 1999). However, mathematics with its other aspectis open to progress every time and it can be used in other fieldsespecially in school lessons. iii) Openness- Mystery:  Openness value shows discussing and analy-zing mathematical theorems, ideas, results, and argumentations.And such a situation leads us to reach corrects and to find newtheorems (Seah & Bishop, 2000). Mystery value indicates mathe-matics own relation, pattern and surprises in its own nature. Suchas; dividing every circle’s perimeter into its diameter gives thesame number ( π number) or Pythagorean triangles that have 3, 4,5 or 5, 12, 13 cm edge length gives always a multiple of 60 whenthey are multiplied with each other. Mathematics has alwayssuch kinds of mystery and surprise in itself (Bishop et al., 1999). DEDE / Mathematical Values Conveyed by High School Mathematics Textbooks  • 121  c) Mathematics Educational Values  Teaching mathematics educational values may show differences ac-cording to countries, cities, school types and grades. For example;choice of problem solving strategies may show differences accordingto the environment. So, the number of mathematics educational va-lues can increase to that rate. In this paper, five complementary mat-hematics educational values will be emphasized. These are; i) Formalistic view- Activist view:  Formalistic view value shows thedeductive and receptive learning values of mathematics, whileactivist view value shows its intuition and discovery learning;that is to say, its inductive sides. ii) Instrumental understanding/learning-Relational understan- ding/learning:  Instrumental learning indicates learning rules,operations and formulations in mathematics education and theirapplications to special questions. Relational learning shows disp-laying the relationships among concepts and forming appropria-te graphics. iii) Theoretical knowledge-Relevance:  Mathematical education’stheoretical value suggests teachings mathematics at theoreticalbasis and far from daily events. Relevance value shows the im-portance of mathematical knowledge in solving daily problems.Daily problems and demands show different at societies and cul-tures. Thus, mathematics can provide special solutions to cultu-ral needs and demands. iv) Accessibility -Special:  These values indicate doing and preparingmathematical activities by either everyone or just by people whohas talent in it. v) Evaluating - Reasoning:  Students are asked to realize the stepsof knowing, applying routine operations, searching solving prob-lem, reasoning and communicating in order to solve a problem.The first three of this five steps demonstrate using mathemati-cal knowledge about evaluating an unknown answer; while thelast two demonstrate the capability of using mathematical know-ledge, reasoning more and the ability of spreading the knowled-ge (Seah & Bishop, 2000).Mathematics textbooks are also main teaching tools. In some cases,mathematics textbooks are perceived as the mathematics curricu- 122 • EDUCATIONAL SCIENCES: THEORY&PRACTIGE
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