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Volume 11 Issue 10

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Volume 11 Issue 6

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## The Effects of GeoGebra On Third Grade Primary Students’ Academic Achievement in FractionsMehmet Bulut, Hanife Ünlütürk Akçakın, Gürcan Kaya & Veysel Akçakın
pp.
The aim of this study is to examine the effects of GeoGebra on third grade primary students’ academic achievement in fractions concept. This study was conducted with 40 students in two intact classes in Ankara. One of the classes was randomly selected as an experimental group and other for control group. There were 19 students in the experimental group, while 21 students in control group. The matching- only posttest- only control group quasi-experimental design was employed. As a pretest, student’s first term mathematics scores were used. Data were collected with post-test about fractions. The post-test consisted of 22 short ended questions. Thanks to the scores weren’t violated the normality, independent
Acar, N. (2010). Akın, P. (2009). Clements, D. H., Sarama, J., & DiBiase, A. M. (Eds.). (2004). Demirdöğen, N. (2007). Erdağ, S. (2011). Goodwin, K. (2008). The impact of interactive multimedia on kindergarten students’ representations of fractions. Gutiérrez, A., & Boero, P. (Eds.). (2006). Kayhan, H. C. (2010). Lee, H.J. & Boyadzhiev, I. (2013). Challenging Common Misconceptions of Fractions through GeoGebra. In R. McBride & M. Searson (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2013 (pp. 2893-2898). Chesapeake, VA: AACE. Martín-Caraballo, A. M., & Tenorio-Villalón, Á. F. (2015). Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities. McNamara, J., & Shaughnessy, M. M. (2010). Mısral, M. (2009). Moyer-Packenham, P. S., Ulmer, L. A., & Anderson, K. L. (2012). Examining Pictorial Models and Virtual Manipulatives for Third-Grade Fraction Instruction. Newstead, K. and Murray, H. (1998). Young students’ constructions of fractions. In A. Olivier & K. Newstead (Eds.), Pesen, C. (2007). Öğrencilerin kesirlerle ilgili kavram yanılgıları [Students’ Misconceptions About Fractions]. Pilli, O. (2008). Pitta-Pantazi, D., Gray, E., & Christou, C. (2004). Elementary school students’ mental representations of fractions. In Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Sözer, N. (2006). Suh, J., Moyer, P. S., & Heo, H. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. The National Council of Teachers of Mathematics [NCTM]. (2000). Thambi, N., & Eu, L. K. (2013). Effect of Students’ Achievement in Fractions using GeoGebra. Van de Walle, J.A., Karp, K.S. & Bay-Williams, J.M. (2010). Yazgan, Y. (2007). Yumuşak, E. Y. (2014). Yurtsever, N.T. (2012). |
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## Identity Development during Undergraduate Research in Mathematics EducationRandall E. Groth & Jenny McFadden
pp.
We describe a model that leverages natural connections between undergraduate research and mathematics teacher preparation. The model integrates teaching and research by prompting undergraduates to continuously reflect on classroom data from lessons they have taught. It is designed to help undergraduates build identities as teachers who base decisions on empirical data, and also to build identities as future graduate students in mathematics education. The identities that undergraduates participating in the first year of the project developed pertaining to these roles are described. Undergraduates generally identified with a problem-based approach to teaching and saw themselves as future graduate students in various fields, including mathematics education. Suggestions for improving and adapting the model for use in other settings are also provided.
American Association of Colleges for Teacher Education & Stanford Center for Assessment, Learning, and Equity. (2015). Ball, D. L. (2003). Beijaard, D. (1995). Teachers’ prior experiences and actual perceptions of professional identity. Beijaard, D., Meijer, P. C., & Verloop, N. (2004). Reconsidering research on teachers’ professional identity. Chong, S., Low, E. L., & Goh, K. C. (2011). Emerging professional identity of pre-service teachers. Clift, R. T., & Brady, P. (2005). Research on methods courses and field experiences. In M. Cochran-Smith & K.M. Zeichner (Eds.), Common Core State Standards Writing Team. (2011). Confrey, J., Maloney, A. P., Nguyen, K. H., Mojica, G., & Myers, M. (2012). Council on Undergraduate Research. (2015). Dewey, J. (1933). Educational Testing Service. (2015). Ellemor-Collins, D. L., & Wright, R. J. (2008). Student thinking about arithmetic: Videotaped interviews Ferrini-Mundy, J. (2011). Forbes, C. T., & Davis, E. A. (2008). The development of pre-service elementary teachers’ curricular role identity for science teaching. Girod, M., & Pardales, M. (2001, April). Harrison, R. L. (2008). Scaling the ivory tower: Engaging emergent identity as a researcher. Hu, S., Scheuch, K., Schwartz, R., Gaston-Gayles, J., & Li, S. (2008). Reinventing undergraduate education: Engaging college students in research and creative activities. Hunter, A. -B., Laursen, S. L., & Seymour, E. (2006). Becoming a scientist: The role of undergraduate research in students’ cognitive, personal, and professional development. Ingersoll, R. M., & Perda, D. (2010). Is the supply of mathematics and science teachers sufficient? Jenkins, O. F. (2010). Developing teachers’ knowledge of students as learners of mathematics through structured interviews. Kilpatrick, J., Swafford, J. and Findell, B. (Eds.). (2001). McDonough, A., Clarke, B., & Clarke, D. M. (2002). Understanding, assessing and developing children’s mathematical thinking: The power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., Phillips, E. D. (2009). Learn NC & Wheatley, G. (2001). National Governors Association for Best Practices & Council of Chief State School Officers. (2010). Pillen, M., Beijaard, D., & den Brok, P. (2013). Tensions in beginning teachers’ professional identity development, accompanying feelings and coping strategies. Ponte, J. P., & Chapman, O. (2008). Preservice mathematics teachers’ knowledge and development. In L.D. English & D. Kirshner (Eds.), Reys, B. J., & Reys, R. E. (2004). Recruiting mathematics teachers: Strategies to consider. Reys, R. E., Reys, B., & Estapa, A. (2013). An update on jobs for doctorates in mathematics education at institutions of higher education in the United States. Ricks, T. E. (2011). Process reflection during Japanese Lesson Study experiences by prospective secondary mathematics teachers. Russell, S. H., Hancock, M. P., & McCullough, J. (2007). Benefits of undergraduate research experiences. Sammons, P., Day, C., Kington, A., Gu, Q., Stobart, G., & Smees, R. (2007). Exploring variations in teachers’ work, lives and their effects on pupils: Key findings and implications from a longitudinal mixed-methods study. Schön, D. A. (1983). Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Stigler, J. W., & Hiebert, J. (1999). Weiland, I. S., Hudson, R. A., & Amador, J. M. (2014). Preservice formative assessment interviews: The development of competent questioning. Wenger, E. (1999). |
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## Mental Constructions for The Group Isomorphism TheoremArturo Mena-Lorca & Astrid Morales Marcela Parraguez
pp.
The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets) to the particular (e.g., groups) might not always the best strategy, but in some cases we may just be turning to more familiar settings.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa, S., Trigueros, M. & Weller, K. (2014). Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. In J. Kaput, A. H. Schoenfeld & E. Dubinsky (Eds.), Asiala, M., Dubinsky, E., Mathews, D., Morics, S., & Oktaç, A. (1997). Development of students’ understanding of cosets, normality, and quotient groups. Baker, B., Trigueros, M. & Hemenway, C. (2001). On transformations of functions. In Bourbaki, N. (1999). Brousseau, G. (1997). Brown, A., De Vries, D., Dubinsky, E., & Thomas, K. (1997). Learning binary operations, groups and subgroups. Burnside, W. (1897). Clark, J., De Vries, D., Hemenway, C., St. John, D., Tolia, G., & Vakil, R. (1997). An Investigation of students’ understanding of abstract algebra (binary operations, groups and subgroups) and the use of abstract structures to build other structures (through cosets, normality and quotient groups). Dubinsky, E. (1986). Reflective abstraction and computer experiences: A new approach to teaching theoretical mathematics. In G. Lappan & R. Even (Eds.), Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall, (Ed.), Dubinsky, E., Dauterman, J., Leron, U. & Zazkis, R. (1994). On learning fundamental concepts of group theory. Dubinsky, E., & Leron, U. (1994). Dubinsky, E., & Lewin P. (1986). Reflective abstraction and mathematics education. Dubinsky, E., & McDonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), Dubinsky, E., & Zazkis, R. (1996). Dihedral groups: A tale of two interpretations. Dummit, D., & Foote, R. (2011). Fraleigh, J. B. (2003). Galois, E. (1897). Godfrey, D., & Thomas, M. O. J. (2008). Student perspectives on equation: The transition from school to university. Goetz, J. P., & Le Compte, M. D. (1988). Hamdan, M. (2006). Equivalent Structures on Sets: Equivalence Classes, Partitions and Fiber Structures of Functions. Herstein, I. N. (1999). Hazzan, O., & Leron, U. (1996). Students’ use and misuse of mathematical theorems: the case of Lagrange’s theorem. Hungerford, T. W. (2003). Iannone, P., & Nardi, E. (2002). A group as a ‘special set’? Implications of ignoring the role of the binary operation in the definition of a group. In A. D. Cockburn & E. Nardi (Eds.), Ioannou, M. & Iannone, P. (2011). Students' affective responses to the inability to visualise cosets. Ioannou, M., & Nardi, E. (2009). Engagement, abstraction and visualisation: Cognitive and emotional aspects of Year 2 mathematics undergraduates’ learning experience in abstract algebra. Jordan, C. (1869). Mémoire sur les groupes de mouvements, Jordan, C. (1870). Lajoie, C. (2001). Students’ difficulties with the concept of group, subgroup and group isomorphism. In H. Chick, K. Stacey, Jill Vincent & John Vincent (Eds.): Lang, S. (2005). Larsen, S. (2009). Reinventing the concepts of group and isomorphism: The case of Jessica and Sandra. Larsen, S. (2013a). A local instructional theory for the guided reinvention of the group and isomorphism concepts. Larsen, S. (2013b). A local instructional theory for the guided reinvention of the quotient group concept. Le Compte, M. D., Millroy, W.L., & Preissle, J. (Eds.) (1992). Leron, U., & Dubinsky, E. (1995). An abstract algebra story. Leron, U., Hazzan, O., & Zazkis, R. (1994). Student’s constructions of group isomorphisms Leron, U., Hazzan, O., & Zazkis, R. (1995). Learning group isomorphism: A crossroads of many concepts. Mena-Lorca, A. (2010). Nardi, E. (1996). Nardi, E. (2000). Mathematics undergraduate’s responses to semantic abbreviations, ’geometric’ images and multi-level abstractions in group theory. Neubrand, M. (1981). The homomorphism theorem within a spiral curriculum. Novotná, J., & Stehlíková, N., & Hoch, M. (2006). Structure sense for university algebra. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Piaget, J., & García, R. (1982). Roa-Fuentes, S., & Oktaç, A. (2010). Construcción de una descomposición genética: Análisis teórico del concepto transformación lineal. Stadler, E. (2011). The same but different – novice university students solve a textbook exercise. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Thomas, M.; de Freitas, I.; Huillet, D.; Ju, M.-K.; Nardi, E.; Rasmussen, C.; & Xie, J. (2015). Key mathematical concepts in the transition from secondary school to university. In Sung Je Cho (Ed.), Trigueros, M., & Oktaç, A. (2005). La théorie APOS et l’enseignement de l’algèbre linéaire. Vergnaud, G. (1981). Quelques orientations théoriques et méthodologiques des recherches françaises en didactique des mathématiques. Weber, K (2002). The role of instrumental and relational understanding in proofs about group isomorphisms. Proceedings of the Second International Conference for the Teaching of Mathematics. Weber, K., & Larsen, S. (2008). Teaching and learning group theory. In M. Carlson and C. Rasmussen, (Eds.), |
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## Teachers’ Beliefs about the Discipline of Mathematics and the Use of Technology in the ClassroomMorten Misfeldt, Uffe Thomas Jankvist & Mario Sánchez Aguilar
pp.
In the article, three Danish secondary level mathematics teachers’ beliefs about the use of technological tools in the teaching of mathematics and their beliefs about mathematics as a scientific discipline are identified and classified - and the process also aspects of their beliefs about the teaching and learning of mathematics. The potential relationships between these sets of beliefs are also explored. Results show that the teachers not only manifest different beliefs about the use of technology and mathematics as a discipline, but that one set of beliefs can influence the other set of beliefs. The article concludes with a discussion of the research findings and their validity as well as their implications for both practice and research in mathematics education.
Artigue, M. (2002). Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Blömeke, S. & Kaiser, G. (2015). Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective. In B. Pepin & B. Roesken-Winter (Eds.), Buchberger, B. (2002). Computer algebra: the end of mathematics? Carter, G. & Norwood, K.S. (1997). The relationship between teacher and student beliefs about mathematics. Cooney, T.J., Shealy, B.E. & Arvold, B. (1998). Conceptualizing belief structures of preservice secondary mathematics teachers. De Guzman, M., Hodgson, B.R., Robert, A. & Villani, V. (1998). Difficulties in the passage from secondary to tertiary education. 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Leder, E. Pehkonen and G. Törner (Eds.), Fullan, M.G. (1991). Gill, M.G., Ashton, P.T. & Algina, J. (2004). Changing preservice teachers’ epistemological beliefs about teaching and learning in mathematics: An intervention study. Georgsen, M., Fougt, S.S., Mikkelsen, S.L.S. & Lorentzen, R.F. (2014). Green, T.F. (1971). Goos, M. (2014). Technology integration in secondary school mathematics: the development of teachers’ professional identities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), Hanzsek-Brill, M.B. (1997). Jankvist, U.T. (2015). Changing students’ images of “mathematics as a discipline”. Jankvist, U.T., Misfeldt, M. & Iversen, S.M. (preprint). When students are subject to various teachers’ varying policies: A bricolage framework for the case of CAS in teaching. Kuhs, T. M., & Ball, D. L. (1986). Kvale, S. (1996). Lagrange, J. (2005). Using symbolic calculators to study mathematics: the case of tasks and techniques. The case of tasks and techniques. In D. Guin, K. Ruthven & L. Trouche (Eds.), Lavicza, Z. (2010). Integrating technology into mathematics teaching at the university level. Leatham, K.R. (2006). Viewing mathematics teachers’ beliefs as sensible systems. Leatham, K.R. (2007). Pre-service secondary mathematics teachers’ beliefs about the nature of technology in the classroom. Leder, G.C. (2015). Foreword. In B. Pepin & B. Roesken-Winter (Eds.), Liljedahl, P. (2009). Teachers’ insights into the relationship between beliefs and practice. In J. Maaß & W. Schlöglmann (Eds.), McCulloch, A.W. (2011). Affect and graphing calculator use. Nabb, K.A. (2010). CAS as a restructuring tool in mathematics education. Op’t Eynde, P., de Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Pajares, M.F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. Partnership For 21st Century Skills (2011). Partnership For 21st Century Skills (2004). Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F.K. Lester Jr. (Ed.), Rokeach, M. (1960). Schmidt, M.E. (1999). Middle grade teachers’ beliefs about calculator use: pre-project and two years later. Schoenfeld, A.H. (2007). Method. In F.K. Lester, Jr. (Ed.), Skott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: a design research study. Tharp, M.L., Fitzsimmons, J.A. & Ayers, R.L.B. (1997). Negotiating a technological shift: teacher perception of the implementation of graphic calculators. Thomas, M.O.J. & Palmer, J.M. (2014). Teaching with digital technology: obstacles and opportunities. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), Thompson, A.G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D.A. Grouws (Ed.), Van Zoest, L.R., Jones, G.A., & Thornton, C.A. (1994). Beliefs about mathematics teaching held by pre-service teachers involved in a first grade mentorship program. Walen, S.B., Williams, S.R. & Garner, B.E. (2003). Pre-service teachers learning mathematics using calculators: a failure to connect current and future practice. Wilkins, J.L.M & Brand, B.R. (2004). Change in preservice teachers’ beliefs: an evaluation of a mathematics methods course. Winsløw, C. (2003). Semiotic and discursive variables in CAS-based didactical engineering. |
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