The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning

Affiliation(s)

Department of Elementary Mathematics Education, Faculty of Education, Adiyaman University, Adiyaman, Turkey.

Department of Elementary Mathematics Education, Faculty of Education, Adiyaman University, Adiyaman,Turkey.

Department of Computer Education and Instructional, Faculty of Education, Adiyaman University, Technology, Adiyaman, Turkey.

Department of Elementary Mathematics Education, Faculty of Education, Adiyaman University, Adiyaman, Turkey.

Department of Elementary Mathematics Education, Faculty of Education, Adiyaman University, Adiyaman,Turkey.

Department of Computer Education and Instructional, Faculty of Education, Adiyaman University, Technology, Adiyaman, Turkey.

ABSTRACT

This paper explores the effect of teaching mathematics performed with the help of Computer-Supported Concept Maps (CSCM) on the conceptual learning. To achieve this end, CSCM were developed and used in the process of teaching probability subject. Within the true-experimental research method, a pre- and post-test control groups study was conducted with 39 seventh graders—20 in experimental group, and 19 in the control group. Each group was taught three times/week, 40 min/session, for 4 weeks. A 12-item instrument was used to collect data. After the teaching intervention, the same instrument was re-administered to both groups as post-test. The results suggested that students in the experimental group performed significantly better than those in the control group, in terms of conceptual learning.

This paper explores the effect of teaching mathematics performed with the help of Computer-Supported Concept Maps (CSCM) on the conceptual learning. To achieve this end, CSCM were developed and used in the process of teaching probability subject. Within the true-experimental research method, a pre- and post-test control groups study was conducted with 39 seventh graders—20 in experimental group, and 19 in the control group. Each group was taught three times/week, 40 min/session, for 4 weeks. A 12-item instrument was used to collect data. After the teaching intervention, the same instrument was re-administered to both groups as post-test. The results suggested that students in the experimental group performed significantly better than those in the control group, in terms of conceptual learning.

Cite this paper

Gürbüz, R. , Erdem, E. & Fırat, S. (2012). The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning.*Creative Education, 3,* 1231-1240. doi: 10.4236/ce.2012.37182.

Gürbüz, R. , Erdem, E. & Fırat, S. (2012). The Effects of Teaching Mathematics Performed with the Help of CSCM on Conceptual Learning.

References

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[2] Anderson-Inman, L., & Horney, M. (1996). Computer-based concept mapping: Enhancing literacy with tools for visual thinking. Journal of Adolescent and Adult Literacy, 40, 302-306.

[3] Anderson-Inman, L., Ditson, L. A., & Ditson, M. T. (1998). Computerbased concept mapping: Promoting meaningful learning in science for students with disabilities. Information Technology and Disabilities, 5, 1-13.

[4] Anderson-Inman, L., & Ditson, L. (1999). Computer-based concept mapping: A tool for negotiating meaning. Learning and Leading with Technology, 26, 6-13.

[5] Ayres, P., Sawyer. W., & Dinham, S. (2004). Effective teaching in the context of a grade 12 high-stakes external examination in new south wales, Australia. British Educational Research Journal, 30, 141-165. doi:10.1080/01411920310001630008

[6] Baker, M., & Chick, H. L. (2007). Making the most of chance. Australian Primary Mathematics Classroom, 12, 8-13.

[7] Baki, A., & Mandaci-?ahin, S. (2004). Assessment of preservice teachers’ mathematical learning through computer aided concept mapping method. TOJET, 3, 91-104.

[8] Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished Ph.D. Thesis, East Lansing, MI: Michigan State University.

[9] Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449-466. doi:10.1086/461626

[10] Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30, 558-567. doi:10.2307/749774

[11] Bezzina, F. (2004). Pupils’ understanding of probabilistic & statistics (14-15+) difficulties and insights for instruction. Journal of Maltese Education Research, 2, 53-67.

[12] Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5, 7-74. doi:10.1080/0969595980050102

[13] Boaler, J. (1997). Experiencing school mathematics:Teaching styles, sex and setting. Buckingham: Open University Press.

[14] Brown, D. S. (2003). High school biology: A group approach to concept mapping. The American Biology Teacher, 65, 192-197.

[15] Chang, K. E., Sung, Y. T., & Chen, S. F. (2001). Learning through computer-based concept mapping with scaffolding aid. Journal of Computer Assisted Learning, 17, 21-33.

[16] Chang, K. E., Sung, Y. T., & Chen, I. D. (2002). The effect of concept mapping to enhance text comprehension and summarization. The Journal of Experiment Education, 71, 5-23. doi:10.1080/00220970209602054

[17] Chernoff, E. J. (2009). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28, 19-29. doi:10.1016/j.jmathb.2009.03.002

[18] Chiu, C. H., & Hsiao, H. F. (2010). Group differences in computer supported collaborative learning: Evidence from patterns of Taiwanese students’ online communication. Computers & Education, 54, 427- 435. doi:10.1016/j.compedu.2009.08.026

[19] Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.

[20] Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61, 293-319. doi:10.1007/s10649-006-2372-4

[21] Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills. Unpublished M.A. Thesis, Ad?yaman: Ad?yaman University.

[22] Even, R., & Kvatinsky, T. (2010). What mathematics do teachers with contrasting teaching approaches address in probability lessons? Educational Studies in Mathematics, 74, 207-222. doi:10.1007/s10649-010-9234-9

[23] Fast, G. (1997). Using analogies to overcome student teachers’ probability misconceptions. Journal of Mathematical Behavior, 16, 325- 344. doi:10.1016/S0732-3123(97)90011-0

[24] F?rat, S. (2011). The effect of mathematics teaching performed through educational computer games on conceptual learning. Unpublished M.A. Thesis, Ad?yaman: Ad?yaman University.

[25] Fischbein, E., Nello, M. S. & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523-549. doi:10.1007/BF00312714

[26] Gürbüz, R. (2006a). Concept maps for the teaching of probability. 100th Year University Education Faculty Journal-Online, 3, 133- 151.

[27] Gürbüz, R. (2006b). Development of practice sheets for probability concept. Cukurova University Education Faculty Journal, 31, 111- 123.

[28] Gürbüz, R. (2007). The effects of computer aided instruction on students’ conceptual development: A case of probability subject. Eurasion Journal of Educational Research, 28, 75-87.

[29] Gürbüz, R. (2010). The effect of activity based instruction on conceptual development of seventh grade students in probability. International Journal of Mathematical Education in Science and Technology, 41, 743-767. doi:10.1080/00207391003675158

[30] Gürbüz, R., ?atl?o?lu, H., Birgin, O., & Erdem, E. (2010). An investigation of fifth grade students’ conceptual development of probability concepts based on activity based instruction: A quasi-experimental study. Educational Sciences: Theory & Practice, 10, 1053- 1068.

[31] Gürbüz, R., & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers & Education, 58, 931-941. doi:10.1016/j.compedu.2011.11.005

[32] Gürbüz, R., Birgin, O., & ?atl?o?lu, H. (2012). Comparing the probability-related misconceptions of pupils at different education levels. Croatian Journal of Education, 14, 307-357

[33] Heinze-Fry, J. A., & Novak, J. D. (1990). Concept mapping brings longterm movement towards meaningful learning. Science Education, 74, 461-472. doi:10.1002/sce.3730740406

[34] Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406. doi:10.3102/00028312042002371

[35] Huang, H. S., Chiou, C. C., Chiang, H. K., Lai, S. H., Huang, C. Y., Chou, Y. Y. (2012). Effects of multidimensional concept maps on fourth graders’ learning in web-based computer course. Computers & Education, 58, 863-873. doi:10.1016/j.compedu.2011.10.016

[36] Johnson, D. W., & Johnson, R. T. (1989). Cooperation and competition (2nd ed.). Edina, MI: Interaction.

[37] Jonassen, D. H. (1996). Computer in the classroom: Mindtools for critical thinking. Eaglewoods, NJ: Merill/Prentice Hall.

[38] Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, T. A. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101-125.

[39] Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454. doi:10.1016/0010-0285(72)90016-3

[40] Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist, 58, 697-720. doi:10.1037/0003-066X.58.9.697

[41] Keren, G. (1984). On the importance of identifying the correct “problem space”. Cognition, 16, 121-128. doi:10.1016/0010-0277(84)90002-7

[42] Kwon, S. Y., & Cifuentes, L. (2009). The comparative effect of individually-constructed vs. collaboratively-constructed computer-based concept maps. Computers & Education, 52, 365-375. doi:10.1016/j.compedu.2008.09.012

[43] Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557-568. doi:10.1007/BF00540060

[44] Ledesma, E. F. R. (2010). Using an interactive computer system to support the task of building the notions of ratio and proportion. Creative Education, 1, 115-120. doi:10.4236/ce.2010.12017

[45] Matin, M. A. (2012). Interactive computer-centered instructions for science and engineering education. Creative Education, 3, 375-379. doi:10.4236/ce.2012.33059

[46] Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66, 293-315. doi:10.1007/s10649-006-9062-0

[47] Nilsson. P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247-261. doi:10.1016/j.jmathb.2009.10.003

[48] Novak, J. D., & Gowin, B. (1984). Learning how to learn. New York: Cambridge University Press. doi:10.1017/CBO9781139173469

[49] Novak, J. D., & Ca?as, A. J. (2006). The origins of the concept mapping tool and the continuing evolution of the tool. Information Visualisation Journal, 5, 175-184. doi:10.1057/palgrave.ivs.9500126

[50] Polaki, M. V. (2002). Using instruction to identify key features of basotho elementary students’ growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285-313. doi:10.1207/S15327833MTL0404_01

[51] Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602-625. doi:10.2307/749889

[52] Rautama, E. (2000). Extending the delivery of concept maps. AAPS project, ITiCSE. The 5th Annual Conference on Innovation and Technolology in Computer Science Education.

[53] Royer, R., & Royer, J. (2004). Comparing hand drawn and computer generated concept mapping. Journal of Computers in Mathematics and Science Teaching, 23, 67-81.

[54] Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.

[55] Shulman, L. S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57, 1-22.

[56] Simone, C. D., Schmid, R. F., & McEwen, L. A. (2001). Supporting the learning process with collaborative concept mapping using computer-based communication tools and process. Educational Research and Evaluation, 7, 263-283 doi:10.1076/edre.7.2.263.3870

[57] Slavin, R. E. (1987). Cooperative learning and cooperative school. Educational Leadership, 45, 7-13.

[58] Slavin, R. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Educational Psychology, 21, 43-69. doi:10.1006/ceps.1996.0004

[59] Stoyanova, N., & Kommers, P. (2002). Concept mapping as a medium of shared cognition in computer-supported collaborative problem solving. Journal of Interactive Learning Research, 13, 111-133.

[60] Sturm, J. M., & Rankin-Erickson, J. L. (2002). Effects of hand-drawn and computer-generated concept mapping on the expository writing of middle students with learning disabilities. Learning Disabilities Research & Practice, 17, 124-139. doi:10.1111/1540-5826.00039

[61] Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76, 141-164. doi:10.1007/s10649-010-9269-y

[62] Tsai, C. C., Lin, S. S. J., & Yuan, S. M. (2001). Students’ use of webbased concept map testing and strategies for learning, Journal of Computer Assisted Learning, 17, 72-84. doi:10.1111/j.1365-2729.2001.00160.x

[63] Willerman, M., & Harg, R. A. (1991). The concept map as an advance organizer. Journal of Research in Science Teaching, 28, 705-711.

[64] Yavuz, A. (2005). Effectiveness of conceptual change instruction accompanied with demonstrations and computer assisted concept mapping on students’ understanding of matter concepts. Ph.D. Thesis, Ankara: Middle East Technical University. doi:10.1002/tea.3660280807

[1] Anderson-Inman, L., & Zeitz, L. (1993). Computer-based concept mapping: Active studying for active learners. Computing Teacher, 21, 6-11.

[2] Anderson-Inman, L., & Horney, M. (1996). Computer-based concept mapping: Enhancing literacy with tools for visual thinking. Journal of Adolescent and Adult Literacy, 40, 302-306.

[3] Anderson-Inman, L., Ditson, L. A., & Ditson, M. T. (1998). Computerbased concept mapping: Promoting meaningful learning in science for students with disabilities. Information Technology and Disabilities, 5, 1-13.

[4] Anderson-Inman, L., & Ditson, L. (1999). Computer-based concept mapping: A tool for negotiating meaning. Learning and Leading with Technology, 26, 6-13.

[5] Ayres, P., Sawyer. W., & Dinham, S. (2004). Effective teaching in the context of a grade 12 high-stakes external examination in new south wales, Australia. British Educational Research Journal, 30, 141-165. doi:10.1080/01411920310001630008

[6] Baker, M., & Chick, H. L. (2007). Making the most of chance. Australian Primary Mathematics Classroom, 12, 8-13.

[7] Baki, A., & Mandaci-?ahin, S. (2004). Assessment of preservice teachers’ mathematical learning through computer aided concept mapping method. TOJET, 3, 91-104.

[8] Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished Ph.D. Thesis, East Lansing, MI: Michigan State University.

[9] Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. Elementary School Journal, 90, 449-466. doi:10.1086/461626

[10] Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30, 558-567. doi:10.2307/749774

[11] Bezzina, F. (2004). Pupils’ understanding of probabilistic & statistics (14-15+) difficulties and insights for instruction. Journal of Maltese Education Research, 2, 53-67.

[12] Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5, 7-74. doi:10.1080/0969595980050102

[13] Boaler, J. (1997). Experiencing school mathematics:Teaching styles, sex and setting. Buckingham: Open University Press.

[14] Brown, D. S. (2003). High school biology: A group approach to concept mapping. The American Biology Teacher, 65, 192-197.

[15] Chang, K. E., Sung, Y. T., & Chen, S. F. (2001). Learning through computer-based concept mapping with scaffolding aid. Journal of Computer Assisted Learning, 17, 21-33.

[16] Chang, K. E., Sung, Y. T., & Chen, I. D. (2002). The effect of concept mapping to enhance text comprehension and summarization. The Journal of Experiment Education, 71, 5-23. doi:10.1080/00220970209602054

[17] Chernoff, E. J. (2009). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28, 19-29. doi:10.1016/j.jmathb.2009.03.002

[18] Chiu, C. H., & Hsiao, H. F. (2010). Group differences in computer supported collaborative learning: Evidence from patterns of Taiwanese students’ online communication. Computers & Education, 54, 427- 435. doi:10.1016/j.compedu.2009.08.026

[19] Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.

[20] Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61, 293-319. doi:10.1007/s10649-006-2372-4

[21] Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills. Unpublished M.A. Thesis, Ad?yaman: Ad?yaman University.

[22] Even, R., & Kvatinsky, T. (2010). What mathematics do teachers with contrasting teaching approaches address in probability lessons? Educational Studies in Mathematics, 74, 207-222. doi:10.1007/s10649-010-9234-9

[23] Fast, G. (1997). Using analogies to overcome student teachers’ probability misconceptions. Journal of Mathematical Behavior, 16, 325- 344. doi:10.1016/S0732-3123(97)90011-0

[24] F?rat, S. (2011). The effect of mathematics teaching performed through educational computer games on conceptual learning. Unpublished M.A. Thesis, Ad?yaman: Ad?yaman University.

[25] Fischbein, E., Nello, M. S. & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523-549. doi:10.1007/BF00312714

[26] Gürbüz, R. (2006a). Concept maps for the teaching of probability. 100th Year University Education Faculty Journal-Online, 3, 133- 151.

[27] Gürbüz, R. (2006b). Development of practice sheets for probability concept. Cukurova University Education Faculty Journal, 31, 111- 123.

[28] Gürbüz, R. (2007). The effects of computer aided instruction on students’ conceptual development: A case of probability subject. Eurasion Journal of Educational Research, 28, 75-87.

[29] Gürbüz, R. (2010). The effect of activity based instruction on conceptual development of seventh grade students in probability. International Journal of Mathematical Education in Science and Technology, 41, 743-767. doi:10.1080/00207391003675158

[30] Gürbüz, R., ?atl?o?lu, H., Birgin, O., & Erdem, E. (2010). An investigation of fifth grade students’ conceptual development of probability concepts based on activity based instruction: A quasi-experimental study. Educational Sciences: Theory & Practice, 10, 1053- 1068.

[31] Gürbüz, R., & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers & Education, 58, 931-941. doi:10.1016/j.compedu.2011.11.005

[32] Gürbüz, R., Birgin, O., & ?atl?o?lu, H. (2012). Comparing the probability-related misconceptions of pupils at different education levels. Croatian Journal of Education, 14, 307-357

[33] Heinze-Fry, J. A., & Novak, J. D. (1990). Concept mapping brings longterm movement towards meaningful learning. Science Education, 74, 461-472. doi:10.1002/sce.3730740406

[34] Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406. doi:10.3102/00028312042002371

[35] Huang, H. S., Chiou, C. C., Chiang, H. K., Lai, S. H., Huang, C. Y., Chou, Y. Y. (2012). Effects of multidimensional concept maps on fourth graders’ learning in web-based computer course. Computers & Education, 58, 863-873. doi:10.1016/j.compedu.2011.10.016

[36] Johnson, D. W., & Johnson, R. T. (1989). Cooperation and competition (2nd ed.). Edina, MI: Interaction.

[37] Jonassen, D. H. (1996). Computer in the classroom: Mindtools for critical thinking. Eaglewoods, NJ: Merill/Prentice Hall.

[38] Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, T. A. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101-125.

[39] Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454. doi:10.1016/0010-0285(72)90016-3

[40] Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist, 58, 697-720. doi:10.1037/0003-066X.58.9.697

[41] Keren, G. (1984). On the importance of identifying the correct “problem space”. Cognition, 16, 121-128. doi:10.1016/0010-0277(84)90002-7

[42] Kwon, S. Y., & Cifuentes, L. (2009). The comparative effect of individually-constructed vs. collaboratively-constructed computer-based concept maps. Computers & Education, 52, 365-375. doi:10.1016/j.compedu.2008.09.012

[43] Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557-568. doi:10.1007/BF00540060

[44] Ledesma, E. F. R. (2010). Using an interactive computer system to support the task of building the notions of ratio and proportion. Creative Education, 1, 115-120. doi:10.4236/ce.2010.12017

[45] Matin, M. A. (2012). Interactive computer-centered instructions for science and engineering education. Creative Education, 3, 375-379. doi:10.4236/ce.2012.33059

[46] Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66, 293-315. doi:10.1007/s10649-006-9062-0

[47] Nilsson. P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247-261. doi:10.1016/j.jmathb.2009.10.003

[48] Novak, J. D., & Gowin, B. (1984). Learning how to learn. New York: Cambridge University Press. doi:10.1017/CBO9781139173469

[49] Novak, J. D., & Ca?as, A. J. (2006). The origins of the concept mapping tool and the continuing evolution of the tool. Information Visualisation Journal, 5, 175-184. doi:10.1057/palgrave.ivs.9500126

[50] Polaki, M. V. (2002). Using instruction to identify key features of basotho elementary students’ growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285-313. doi:10.1207/S15327833MTL0404_01

[51] Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602-625. doi:10.2307/749889

[52] Rautama, E. (2000). Extending the delivery of concept maps. AAPS project, ITiCSE. The 5th Annual Conference on Innovation and Technolology in Computer Science Education.

[53] Royer, R., & Royer, J. (2004). Comparing hand drawn and computer generated concept mapping. Journal of Computers in Mathematics and Science Teaching, 23, 67-81.

[54] Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.

[55] Shulman, L. S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57, 1-22.

[56] Simone, C. D., Schmid, R. F., & McEwen, L. A. (2001). Supporting the learning process with collaborative concept mapping using computer-based communication tools and process. Educational Research and Evaluation, 7, 263-283 doi:10.1076/edre.7.2.263.3870

[57] Slavin, R. E. (1987). Cooperative learning and cooperative school. Educational Leadership, 45, 7-13.

[58] Slavin, R. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Educational Psychology, 21, 43-69. doi:10.1006/ceps.1996.0004

[59] Stoyanova, N., & Kommers, P. (2002). Concept mapping as a medium of shared cognition in computer-supported collaborative problem solving. Journal of Interactive Learning Research, 13, 111-133.

[60] Sturm, J. M., & Rankin-Erickson, J. L. (2002). Effects of hand-drawn and computer-generated concept mapping on the expository writing of middle students with learning disabilities. Learning Disabilities Research & Practice, 17, 124-139. doi:10.1111/1540-5826.00039

[61] Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76, 141-164. doi:10.1007/s10649-010-9269-y

[62] Tsai, C. C., Lin, S. S. J., & Yuan, S. M. (2001). Students’ use of webbased concept map testing and strategies for learning, Journal of Computer Assisted Learning, 17, 72-84. doi:10.1111/j.1365-2729.2001.00160.x

[63] Willerman, M., & Harg, R. A. (1991). The concept map as an advance organizer. Journal of Research in Science Teaching, 28, 705-711.

[64] Yavuz, A. (2005). Effectiveness of conceptual change instruction accompanied with demonstrations and computer assisted concept mapping on students’ understanding of matter concepts. Ph.D. Thesis, Ankara: Middle East Technical University. doi:10.1002/tea.3660280807