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            <front>

                <journal-meta>
                                                                <journal-id>jcer</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Journal of Computer and Education Research</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2148-2896</issn>
                                                                                            <publisher>
                    <publisher-name>Tamer KUTLUCA</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.18009/jcer.1361502</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Mathematics Education</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Matematik Eğitimi</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <trans-title-group xml:lang="tr">
                                    <trans-title>Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function</trans-title>
                                </trans-title-group>
                                                                                                                                                                                                <article-title>Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function</article-title>
                                                                                                    </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0001-9349-4078</contrib-id>
                                                                <name>
                                    <surname>Gök</surname>
                                    <given-names>Mustafa</given-names>
                                </name>
                                                                    <aff>VAN YUZUNCU YIL UNIVERSITY</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-6553-8309</contrib-id>
                                                                <name>
                                    <surname>Erdoğan</surname>
                                    <given-names>Abdulkadir</given-names>
                                </name>
                                                                    <aff>ANADOLU UNIVERSITY</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20231027">
                    <day>10</day>
                    <month>27</month>
                    <year>2023</year>
                </pub-date>
                                        <volume>11</volume>
                                        <issue>22</issue>
                                        <fpage>1089</fpage>
                                        <lpage>1112</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20230916">
                        <day>09</day>
                        <month>16</month>
                        <year>2023</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20231023">
                        <day>10</day>
                        <month>23</month>
                        <year>2023</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 2013, Journal of Computer and Education Research</copyright-statement>
                    <copyright-year>2013</copyright-year>
                    <copyright-holder>Journal of Computer and Education Research</copyright-holder>
                </permissions>
            
                                                                                                <trans-abstract xml:lang="tr">
                            <p>This study investigates the praxeologies teachers use about the inverse function in the teaching process when the curriculum is changed. A case study, one of the qualitative research methods, was used in the study. The participants of the study were three experienced mathematics teachers. The data were collected by recording the teaching process of the teachers with a video camera and a voice recorder. The praxeological analysis method of the Anthropological Theory of Didactics (ATD) was used in the data analysis. The findings of the study show that teachers use two different praxeologies in the inverse function. The first one is praxeology based on informal mapping with the effect of the dominant definition of the concept of function in the curriculum, and this praxeology was used to introduce the concept of inverse function. The other praxeology, which shows the monoid structure more clearly, emerged due to both a necessity and the necessity to exhibit an approach appropriate to the curriculum in more complex tasks and was shaped as a mixed praxeology. It was determined that teachers did not structure both praxeologies well and made sudden transitions from one praxeology to another.</p></trans-abstract>
                                                                                                                                    <abstract><p>This study investigates the praxeologies teachers use about the inverse function in the teaching process when the curriculum is changed. A case study, one of the qualitative research methods, was used in the study. The participants of the study were three experienced mathematics teachers. The data were collected by recording the teaching process of the teachers with a video camera and a voice recorder. The praxeological analysis method of the Anthropological Theory of Didactics (ATD) was used in the data analysis. The findings of the study show that teachers use two different praxeologies in the inverse function. The first one is praxeology based on informal mapping with the effect of the dominant definition of the concept of function in the curriculum, and this praxeology was used to introduce the concept of inverse function. The other praxeology, which shows the monoid structure more clearly, emerged due to both a necessity and the necessity to exhibit an approach appropriate to the curriculum in more complex tasks and was shaped as a mixed praxeology. It was determined that teachers did not structure both praxeologies well and made sudden transitions from one praxeology to another.</p></abstract>
                                                            
            
                                                                                        <kwd-group>
                                                    <kwd>Anthropological theory of didactics</kwd>
                                                    <kwd>  praxeology</kwd>
                                                    <kwd>  teachers</kwd>
                                                    <kwd>  inverse function</kwd>
                                                    <kwd>  curriculum</kwd>
                                            </kwd-group>
                            
                                                <kwd-group xml:lang="tr">
                                                    <kwd>Anthropological theory of didactics</kwd>
                                                    <kwd>  praxeology</kwd>
                                                    <kwd>  teachers</kwd>
                                                    <kwd>  inverse function</kwd>
                                                    <kwd>  curriculum</kwd>
                                            </kwd-group>
                                                                                                                                    <funding-group specific-use="FundRef">
                    <award-group>
                                                    <funding-source>
                                <named-content content-type="funder_name">Anadolu University</named-content>
                            </funding-source>
                                                                            <award-id>1408E364</award-id>
                                            </award-group>
                </funding-group>
                                </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">Artigue, M., &amp; Winsløw, C. (2010). International comparative studies on mathematics education: A viewpoint from the anthropological theory of didactics. Recherches en didactiques des mathématiques, 30(1), 47-82.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">Barbe´, J., Bosch, M., Espinoza, L., &amp; Gascón, J. (2005). Didactic restrictions on the teacher’s practice: The case of limits of functions in Spanish high schools. Educational Studies in Mathematics, 59, 235–268. https://doi.org/10.1007/0-387-30451-7_9</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">Barquero, B., Jessen, B.E., Ruiz-Hidalgo, J.F., &amp; Goldin, J. (2023). What theories and methodologies are appropriate for studying phenomena related to mathematics curriculum reforms?. In Y. Shimizu, R. Vithal, (eds.) Mathematics Curriculum Reforms Around the World (pp. 193-217). New ICMI Study Series. Cham: Springer.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 51–69). Springer.</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., &amp; Demirel, F. (2017). Bilimsel araştırma yöntemleri [Scientific research methods]. Ankara: Pegem Akademi.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">Cha, I. S. (1999). Mathematical and pedagogical discussions of the function concept. Research in Mathematical Education, 3(1), 35-56.</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (1997). Familière et problématique, la figure du professeur. Recherches en Didactique Des Mathématiques, 17(3), 17–54.</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (1998) Analyse des pratiques enseignantes et didactique des mathématiques: L’approche anthropologique. Recherches en Didactique des Mathématiques, 19(2), 221-266.</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (pp. 21–30). Fundemi IQS.</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6(2), 131-134.</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima journal of mathematics education, 12, 71-114. https://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">Chevallard, Y. (2022). Challenges and advances in teacher education within the ATD. In Y. Chevallard et al. (Eds.), Advances in the anthropological theory of the didactic (pp. 81-89). Springer. https://doi.org/10.1007/978-3-030-76791-4_7</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">Chevallard, Y., &amp; Bosch, M. (2020). Didactic transposition in mathematics education. In: S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 53-61). Springer.</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">Chevallard, Y., &amp; Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 38-43). Springer.</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">Erdogan, A. (2014). Conditions épistémiques de l’étude autonome des élèves relativement à l’algèbre et aux fonctions, en classe de Seconde française [Epistemological condition of the study of functions and algebra, in France]. Recherche en didactique des mathmématiques, 34(2/3), 201-238.</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">Even, R. Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21, 521–544 (1990). https://doi.org/10.1007/BF00315943</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">Fraleigh, J. B. (2014). A first course in abstract algebra (7th ed.). London: Pearson.</mixed-citation>
                    </ref>
                                    <ref id="ref18">
                        <label>18</label>
                        <mixed-citation publication-type="journal">Garcia, F. J., Pérez, J. G., Higueras, L. R., &amp; Casabó, M. B. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM, 38(3), 226-246.</mixed-citation>
                    </ref>
                                    <ref id="ref19">
                        <label>19</label>
                        <mixed-citation publication-type="journal">Gellert, U., Barbé, J., &amp; Espinoza, L. (2013). Towards a local integration of theories: Codes and praxeologies in the case of computer-based instruction. Educational Studies in Mathematics, 82, 303–321.</mixed-citation>
                    </ref>
                                    <ref id="ref20">
                        <label>20</label>
                        <mixed-citation publication-type="journal">Gök, M., Erdoğan, A., &amp; Özdemir Erdoğan, E. (2019). Transpositions of function concept in mathematics curricula and textbooks from the historical development perspective. International Journal of Instruction, 12(1), 1189-1206.</mixed-citation>
                    </ref>
                                    <ref id="ref21">
                        <label>21</label>
                        <mixed-citation publication-type="journal">Ikram, M., Purwanto, Parta, I.N., &amp; Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591-611.</mixed-citation>
                    </ref>
                                    <ref id="ref22">
                        <label>22</label>
                        <mixed-citation publication-type="journal">Merriam, S. B., &amp; Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. San Francisco, CA: John Wiley &amp; Sons.</mixed-citation>
                    </ref>
                                    <ref id="ref23">
                        <label>23</label>
                        <mixed-citation publication-type="journal">Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8, 1-14.</mixed-citation>
                    </ref>
                                    <ref id="ref24">
                        <label>24</label>
                        <mixed-citation publication-type="journal">Putra, Z. H. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365-394.</mixed-citation>
                    </ref>
                                    <ref id="ref25">
                        <label>25</label>
                        <mixed-citation publication-type="journal">Strømskag, H., &amp; Chevallard, Y. (2023). Breaches of the didactic contract as a driving force behind learning and non-learning: A story of flaws and wants. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(1), 52-64.</mixed-citation>
                    </ref>
                                    <ref id="ref26">
                        <label>26</label>
                        <mixed-citation publication-type="journal">The Ministry of National Education [MoNE]. (2005). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.</mixed-citation>
                    </ref>
                                    <ref id="ref27">
                        <label>27</label>
                        <mixed-citation publication-type="journal">The Ministry of National Education [MoNE]. (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.</mixed-citation>
                    </ref>
                                    <ref id="ref28">
                        <label>28</label>
                        <mixed-citation publication-type="journal">The Ministry of National Education [MoNE]. (2018). Ortaöğretim fen lisesi matematik dersi (9, 10, 11 ve 12. Sınıflar) öğretim programı [Secondary education science high school mathematics course (Grades 9, 10, 11 and 12) curriculum]. Ankara: MoNE.</mixed-citation>
                    </ref>
                                    <ref id="ref29">
                        <label>29</label>
                        <mixed-citation publication-type="journal">Topphol, V. (2023). The didactic transposition of the fundamental theorem of calculus. REDIMAT – Journal of Research in Mathematics Education, 12(2), 144-172.</mixed-citation>
                    </ref>
                                    <ref id="ref30">
                        <label>30</label>
                        <mixed-citation publication-type="journal">Wasserman, N. H. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understandings of inverse functions in relation to its group structure. Mathematical Thinking and Learning, 19(3), 181-201.</mixed-citation>
                    </ref>
                                    <ref id="ref31">
                        <label>31</label>
                        <mixed-citation publication-type="journal">Weber, K., Mejía-Ramos, J. P., Fukawa-Connelly, T., &amp; Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 100752.</mixed-citation>
                    </ref>
                                    <ref id="ref32">
                        <label>32</label>
                        <mixed-citation publication-type="journal">Zazkis, R., &amp; Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263-281.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
