24 SES 11, ICT and Mathematics Education Part 1
Paper/Poster Session to be continued in 24 SES 14 JS
Technology is an integral part of almost every human activity in the current information age. It affects how people live, work, and, most importantly, how they learn and teach. The National Council of Teachers of Mathematics [NCTM] (2000) support that teachers’ knowledge about technology integration in the classroom is an important component of enhancing students’ knowledge in mathematics. Considering the significance of teaching with technology, researchers have concentrated on the consolidation of technology, content, and pedagogy. Based on Shulman’s pedagogical content knowledge, Mishra and Koehler (2006) established a theoretical framework called “Technological Pedagogical Content Knowledge (TPACK)” which combines three types of knowledge: pedagogical knowledge, content knowledge and technological knowledge. This framework −TPACK− explains how teachers understand technology and pedagogical content knowledge, and how they interact with each other to teach effectively via technology. TPACK is not just an awareness of technology, pedagogy and content separately; it focuses on “the connections, interactions, affordances and constraints between and among the three components” (Mishra & Koehler, 2006, p. 1025).
Niess, Sadri, and Lee (2007) suggested a model to identify how to develop mathematics teachers’ TPACK. According to this developmental model, TPACK moves through the stages of recognizing, accepting, adapting, exploring, and advancing. In the Recognizing stage, mathematics teachers are able to utilize technology and realize the potential of its use in mathematics, but they cannot integrate technology in their mathematics lessons (Niess et al., 2010). In the Accepting stage, teachers embark on a positive or negative attitude toward teaching and learning mathematics via technology (Niess et al., 2009). In the Adapting stage, they start to understand some advantages of using appropriate technologies as teaching tools (Niess et al., 2009). In the Exploring stage, teachers actively integrate technology in teaching and learning of mathematics and they redesign activities to align with the mathematics curriculum (Niess et al., 2010). Lastly, in the Advancing stage, teachers appraise the results of integration of appropriate technology in teaching and learning and make changes in the curriculum to benefit from technology affordances. In addition, this TPACK development model includes four major themes (curriculum and assessment, learning, teaching, and access) and eleven descriptors. One of these descriptors is barrier, which emphasizes how the teacher overcomes possible problems related to technology integration. In the present study, the aim is to analyze the development of middle school mathematics teachers’ TPACK according to levels of the TPACK Development Model of Niess et al. (2007) regarding the barrier descriptor of the access theme.
To improve teachers’ TPACK, teachers should be trained on how to use technology in the classroom. From this perspective, teacher professional development is crucial for improvement of TPACK. Teachers’ professional development programs should be well prepared to integrate technology in their classes. Since traditional professional development programs are kept independent of and disconnected from the classroom (Ball & Cohen, 1999, Knight, 2007), they are inadequate in improving teachers’ teaching knowledge and ability (Knight, 2007). For effective professional development, teachers should be provided with support and assistance in building their content and pedagogical content knowledge and it putting this into practice. According to Loucks-Horsley et al. (2003), coaching is an effective professional development strategy that provides one-on-one learning opportunities for teachers who are interested in improving their knowledge by means of self-reflection and by implementing their reflection in classroom practices. From this point of view, the current study investigated the development of teacher’s technological pedagogical content knowledge about how to address the barriers during coaching, which is regarded as a professional development.
In this study, researchers collected qualitative data from a middle school mathematics teacher to determine the development of his TPACK in geometry before, during and after the coaching sessions. The in-service teacher is determined as the case of the study. The mathematics teacher’s TPACK constitutes the unit of analysis. The participant of the study, Esen (Pseudonym), was in her sixth year of teaching, and she had graduated from the department of mathematics education. In her mathematics class there were 28 students. She was not good at integrating technology effectively into her mathematics classroom. Mathematics coaching sessions, based on an actual lessons, allow content-focused coaches to meet with individual teachers or small groups of teachers to plan for, teach, and debrief a lesson (West & Staub, 2003). According to mathematics coaching, there are three phases in a coaching session: pre-conferencing, teaching the lesson (observation), and post-conferencing. In the present study, the teacher designed mathematics lessons with the guidance of a coach (the first author) at the pre-conference. Additionally, the coached helped teacher to show how to use dynamic geometry environments, how to address the barriers and how to deal with management issues in technology-enhanced classrooms. In the observation session, the researcher observed the teacher to determine how the teacher integrated technology and how the problems faced in the technology-enhanced lesson were handled. Furthermore, the researcher took some notes to discuss in the post-conference. In the post conference, the teacher reflected on himself, identifying the strengths and weaknesses of the lessons. Every week researchers identified the teacher’s technological pedagogical content knowledge during mathematics coaching –the preconference-observation-post conference cycle- to assess the development of the teacher’s technological pedagogical content knowledge, and this coaching cycle was repeated four times. The progress in the teacher’s knowledge about barriers in technology-enhanced lessons was determined by means of the barrier descriptor in the TPACK Development Model by Niess et al. (2007). The barrier descriptor in this model entails teachers’ worries about access and management issues in a technology-enhanced lesson, recognizing challenges with technology in the mathematics classroom and resolving the challenges through extended planning with enrichment of technological resources and tools. As for data analysis, the deductive analysis method was utilized to analyze the data by considering the barrier descriptor of the TPACK Development Model. Deductive analysis is appropriate “where the data are analyzed according to an existing framework” (Patton, 2002, p. 453).
In the lesson before mathematics coaching, Esen implemented technology as a supplement to regular classroom activities. Thus, she had concerns about the usage of technology. In the pre-conference, Esen remarked that some students would fall behind due to technology. Furthermore, she stated that she had concerns regarding management issues while integrating Geogebra. To control student behavior, she wanted to access and use Geogebra in limited time period after teaching geometrical concepts as indicated in the lowest level (recognizing) of TPACK for the barriers descriptor. At the beginning of mathematics coaching, Esen started to make use of technology for the students’ exploration; however, she was worried about classroom management. Subsequently, Esen sought for ways to obtain technology for classroom use and began creating methods for technology management issues. Through mathematics coaching, Esen made progress in the barrier descriptor in the TPACK Development Model. She viewed technology as an opportunity for the students to master geometrical concepts in an innovative way. This situation also helped management issues. After mathematics coaching, she emphasized the importance of preparing and planning lessons to expand the use of available resources and tools, such as using different activities with different perspectives. She recognized challenges in teaching geometry via technology and resolved the challenges through the technological resources as indicated in the highest level (advancing) of the barrier descriptor. To sum up, Esen faced the challenges that emerged in her implementation of a technology-enhanced lesson and then she resolved these challenges during this study. Mathematics coaching based on the process of the teacher’s implementations might have helped the teacher to face and realize her strengths and weaknesses. In other words, this professional development program might have helped her to transform her ideas and teaching ability via technology and allowed her time to practice it.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional educa-tion. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey-Bass. Knight, J. (2007). Instructional coaching: A partnership approach to improving instruction. Thousand Oaks, CA: Corwin Press. Loucks-Horsley, S., Love, N., Stiles, K. E., Mundry, S., & Hewson, P. W. (2003). Designing professional development for teachers of science and mathematics (2nd ed.). Thousand Oaks, CA: Corwin Press. Mishra, P., & Koehler, M. (2006). Technological Pedagogical Content Knowledge: A framework for teacher knowledge. Teachers College Record, 108 (6), 1017–1054. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Niess, M. L., Sadri, P., & Lee, K. (2007). Dynamic spreadsheets as learning technology tools: Developing teachers’ technology pedagogical content knowledge (TPCK) . Paper presentation at the annual meeting of the American Education Research Association, Chicago. Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage Publications. West, L., & Staub, F. (2003). Content focused coaching: transforming mathematics lessons. Portsmouth: Heinemann.
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