An Exploration of Middle School Mathematics Teachers’ Beliefs and Goals regarding GeoGebra: Four Cases from the Turkish Republic

Author(s):

Ipek Saralar(presenting / submitting)Shaaron Ainsworth

Conference:

ECER 2017

Network:

24. Mathematics Education Research

Format:

Paper

Session Information

24 SES 10,

Paper Session

Time:

2017-08-24

15:30-17:00

Room:

K6.04

Chair:

Birgit Pepin

Contribution

Research evidence showing the benefits of effective technology integration into mathematics classes cannot be underestimated (e.g. Bu et al., 2011; Kim & Reeves, 2007; Mussoi et al., 2011). Researchers found out that some of the benefits are to facilitate learning and enhance understanding (Bu et al., 2011; Mussoi et al., 2011) and provide immediate feedback via different forms of assessments (Kim & Reeves, 2007). Considering these benefits, one of the projects regarding the technology integration into classrooms is FATIH Project in Turkey. One of the aims of this project is to plan in-service training sessions for teachers about new technologies. GeoGebra has been taught to middle school mathematics teachers as a part of FATIH Project since 2015. It is a dynamic mathematics software whose aim is to help learners discover relationships between different mathematical concepts by providing multiple representations such as algebraic, geometric and graphical representations (MoNE, 2010). Even though Turkish Ministry of National Education has adopted a policy to inform mathematics teachers about such software, teachers' beliefs in this regard have not been researched yet (Akgul, 2013; Ayvacı et al., 2014). This is an important omission as teachers’ beliefs and goals are not separable from their classroom practices (e.g., Cross, 2009; Nespor, 1987; Stipek et al., 2001; Zakaria & Maat, 2012). Thus, teachers’ individual interpretations and beliefs are likely to be integral parts of their teaching practices with GeoGebra. The present study attempts to determine the different categories of teacher beliefs regarding the utilisation of GeoGebra and its adequateness and practicality in middle school classes using TPACK Framework. This framework helps researchers to get more information about how teachers utilise technology while teaching by providing evidence on teachers’ technological competencies (Koehler & Mishra, 2005). It is also important to note that while most of the studies done on GeoGebra has been focused on the dynamic nature of GeoGebra (e.g. Aydin & Monaghan, 2011; Karaarslan et al., 2013) and the effects of GeoGebra on students’ learning (e.g. Bulut & Bulut, 2011; Edwards & Jones, 2006; Icel, 2011), this study explored teachers’ perspectives by describing their goals regarding the mathematics software GeoGebra and their beliefs about the utilisation of this software. Furthermore, instructional strategies and methods while integrating GeoGebra used by those teachers were investigated; and teachers’ favourite topics to integrate GeoGebra are further examined. Thus, the research questions are:

1. What are the middle school mathematics teachers' goals and beliefs about the use of GeoGebra in the seventh grade middle school mathematics classes in Turkey?

1.1. For what purposes do they use GeoGebra?

1.2. What do they believe about the effectiveness of using GeoGebra?

2. How do middle school mathematics teachers use GeoGebra in the seventh grade middle school mathematics classes in Turkey?

2.1. In which topics do they use GeoGebra?

2.2. Which instructional strategies and methods do they utilise to integrate it?

Method

A descriptive case study technique was chosen for this study to understand four participants’ views on their own use of GeoGebra in the middle school mathematics classes. Four different public middle schools were selected: two in villages and two in cities and they came from four different regions of Turkey: Aegean, Marmara, Mediterranean, and Central Anatolia Regions. Those schools were chosen from the schools in which the math teachers give technology-based classes; thus, they have necessary technology infrastructure. There were twenty to twenty-five students in each classroom. The mathematics teachers of these four classes had graduated from Elementary Mathematics Education programs of one of the universities in Ankara. They had at least three years classroom experience and they all had attended in-service training sessions of Ministry of National Education of the Turkish Republic, some of which are on GeoGebra and effective technology integration. The data were collected in the spring semester of the 2015-2016 academic year through observations, semi structured interviews and surveys. All of the participants were observed during their teaching with GeoGebra. Each teaching session was forty minutes. The participants were interviewed after their lesson implementations. Interviews took thirty minutes to forty-five minutes to complete. The interview questions focused upon the research questions such as whether participants experienced technological problems and their personal motivation to use GeoGebra. Finally, Bulut’s (2012) Perceived Techno-pedagogical Content Knowledge Survey was given to participants to triangulate data collected through interviews and observations. Open coding was used in data analyses. Separate sheets were created for each research question. Participants’ critical phrases and sentences directly related to the questions were determined. Specific examples and actions during the implementation process were identified. Those were combined on these sheets in order to see appeared themes clearly. Emerging themes were collected under three categories: beliefs and goals, challenges, and topics and methods. The data presented thematically under these three categories.

Expected Outcomes

The first research question found that middle school mathematics teachers’ goals and beliefs concerning the use of GeoGebra in the seventh grade were that it would save time, decrease workload, facilitate students’ learning, increase their engagement, and provide visual representations. Even though all four teachers believed that it is effective to use GeoGebra in mathematics classes, they also reported significant challenges they faced while integrating GeoGebra into their classes including classroom management, lack of technology infrastructure, need for more time on lesson planning, and attitudes of students, parents and school administrators toward the use of technology in classrooms. This finding might have resulted from participants’ techno-pedagogical content knowledge. In particular, all four teachers have enough confidence to use GeoGebra; thus, this could be the reason why they continued using it despite all challenges. The second research question explored the instructional methods and strategies of teachers while using GeoGebra, and the most appropriate units from the seventh grade mathematics curriculum for integrating this software. Most of the teachers said they use inquiry learning and pause and think methods while integrating GeoGebra into their classrooms. Other methods named or implemented by participants were brainstorming, discovery learning, problem solving, reflecting the answer and comparison, and teamwork. This was consistent with the lesson observations where none of the teachers used direct teaching. The student centred environment which GeoGebra enables might be the reason for teachers to prefer these instructional methods and strategies. The units reported as the most appropriate to teach with GeoGebra appeared as Circle and Circular Region, Linearity and Analytic Geometry. To conclude, this study showed that middle school mathematics teachers in Turkey have positive attitudes toward the use of GeoGebra in math classes despite the challenges they faced. It seems that they will continue to use it in the near future.

References

Akgul, M. (2013). Fatih Projesi: Sorunlar, Riskler, Endişeler. BMO Dergisi, 2(1), 21-49. Aydin, H., & Monaghan, J. (2011). Bridging the divide-seeing mathematics in the world through dynamic geometry. Teaching Mathematics & Its Applications, 30(1), 1–9. Ayvacı, H., Bakırcı, H., & Başak, M. (2014). The Evaluation of Problems Emerging During the Implementation Process of Fatih Project by Administrators, Teachers and Students, YYÜ Journal of Education Faculty, 11(1), 20-46. Bu, L., Spector, M., & Hacıömeroğlu, E. S. (2011). Toward Model-Centered Mathematics Learning and Instruction Using GeoGebra: A Theoretical Framework for Learning Mathematics with Understanding. In Model Centred Learning (pp. 13–40). Bulut, A. (2012). Investigating Perceptions of Preservice Mathematics Teachers on their Technological Pedagogical Content Knowledge (TPACK) Regarding Geometry. (Unpublished Master’s Thesis). Middle East Technical University, Ankara, Turkey. Bulut, M., & Bulut, N. (2011). Pre-service teachers' usage of dynamic mathematics software. Turkish Online Journal of Educational Technology, 10(4), 294–299. Cross, D. I. (2009). Alignment, cohesions, and change: Examining mathematics teachers‟ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325–346. Edwards, J., & Jones, K. (2006). Linking geometry and algebra with GeoGebra. Mathematics Teaching, 194(1), 28-30. Icel, R. (2011). Bilgisayar destekli öğretimin matematik başarısına etkisi: GeoGebra örneği. (Doctoral Thesis). Selçuk University, Konya, Turkey. Karaarslan, E., Boz, B., & Yıldırım, K. (2013). Technology-based Approaches in Mathematics and Geometry Education. XVIII. Internet Conference in Turkey, 9–11. Kim, B., & Reeves, T. C. (2007). Reframing research on learning with technology: in search of the meaning of cognitive tools, Instructional Science, 35(3), 207–256. Koehler, M., & Mishra, P. (2005). What happens when teachers design educational technology? The development of technological pedagogical content knowledge. Journal of Educational Computing Research, 32(2), 131–152. Ministry of National Education. (2010). FATIH Project, Ankara: Milli Eğitim Bakanlığı, Turkey. Available from: http://fatihprojesi.meb.gov.tr/ Mussoi, E. M., Flores, M. L. P., Bulegon, A. M., & Tarouco, L. M. R. (2011). GeoGebra and eXe Learning: applicability in the teaching of Physics and Mathematics, Systemics, Cybernetics and Informatics, 9(2), 61–66. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19(4), 317–328. Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. Zakaria, E., & Maat, S. M. (2012). Mathematics Teachers’ Beliefs and Teaching Practices. Journal of Mathematics and Statistics, 8(2), 191–194.

Author Information

Ipek Saralar (presenting / submitting)

University of Nottingham

School of Education

Nottingham

Shaaron Ainsworth

University of Nottingham, United Kingdom

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