International Electronic Journal of Mathematics Education

• Callingham, R. A., & Watson, J. (2008). Research in mental computation: Multiple perspectives. Brisbane: Post Pressed. ISBN: 978-1-921214-36-3.
• Callingham, R., & Mclntosh, A. (2001). A Developmental Scale of Mental Computation. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and Beyond: Proceedings of the 24th annual conference of the Mathematics Education Research Group of Australasia (pp. 137-146). Sydney: MERGA. Callingham. ISBM 1864873868
• Callingham, R., & Mclntosh, A. (2002). Mental Computation Competence Across Years 3 to 10. In: B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.) Mathematics Education in the South Pacific, Proceedings of the 25th Annual Conference of the Mathematics Education Research Group of Australasia, Auckland (pp. 155-162). Sydney: MERGA. ISBN: 0-86869-048-1
• Callingham, R., & Watson, J. M. (2004). A developmental scale of mental computation with part-whole numbers. Mathematics Education Research Journal, 16(2), 69-86. https://doi.org/10.1007/BF03217396
• Caney, A., & Watson, J. M. (2003). Mental computation for part-whole number operations. Paper presented at the joint conferences of the Australian Association for Research in Education and the New Zealand Association for Research in Education, Auckland. Retrieved from https://www.researchgate.net/publication/266359112_Mental_Computation_Strategies_for_Part-Whole_Numbers
• Carvalho, R., & da Ponte, J. P. (2013). Students’ Mental Computation Strategies with Fractions. In: B. Ubuz, C. Haser, & M. A. Mariotti (Eds.). Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (CERME 8, February 6 - 10, 2013) (pp. 283-292). Ankara, Turkey: Middle East Technical University and ERME.
• Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138. https://doi.org/10.1007/s10649-009-9198-9
• DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40(1), 71-82. https://doi.org/10.1037/a0032916
• Fazio, L., & Siegler, R. (2011). Teaching fractions. International Academy of Education. Vol. 22 of Educational practices series, Geneva: International Academy of Education - International Bureau of Education.
• Gay, Α. S., & Aichele, D. B. (1997). Middle School Students’ Understanding of Number Sense Related to Percent. School Science and Mathematics, 97(1), 27-36. https://doi.org/10.1111/j.1949-8594.1997.tb17337.x
• Hasemann, K. (1981). On difficulties with fractions. Educational Studies in Mathematics, 12(1), 71-87. https://doi.org/10.1007/BF00386047
• Hiebert, J. (1984). Children’ s Mathematics Learning: The Struggle to Link Form and Understanding. The Elementary School Journal, 84(5), 496-513. https://doi.org/10.1086/461380
• Iuculano, T., & Butterworth, B. (2011). Understanding the real value of fractions and decimals. Quarterly Journal of Experimental Psychology (2006), 64(11), 2088-2098. https://doi.org/10.1080/17470218.2011.604785
• Kalchman, M., Moss, J., & Case, R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. In S. M. Carver & D. Klahr (Eds.), Cognition and Instruction. Twenty- Five Years of Progress. (pp. 1-38). Lawrence Erlbaum Associates; ISBN 0-8058-3823-6
• Lembke, L. O., & Reys, B. J. (1994). The Development of, and Interaction between, Intuitive and School-Taught Ideas about Percent. Journal for Research in Mathematics Education, 25(3), 237-259. https://doi.org/10.2307/749337
• Lemonidis, C., Tsakiridou, H., & Meliopoulou, I. (2018). In-Service Teachers’ Content and Pedagogical Content Knowledge in Mental Calculations with Rational Numbers. International Journal of Science and Mathematics Education, 16(6), 1127-1145. https://doi.org/10.1007/s10763-017-9822-6
• Lemonidis, Ch. (2015). Mental Computation and Estimation: Implications for mathematics education research, teaching and learning. New York, NY: Routledge. ISBN 9781315675664. https://doi.org/10.4324/9781315675664
• Lemonidis, Ch., & Kaiafa, I. (2014). Fifth and sixth-grade students’ number sense in rational numbers and its relation with problem-solving ability. MENON: Journal of Educational Research. 1st Thematic Issue, 61-74.
• Markovits, Z., & Sowder, J. T. (1994). Developing Number Sense: An Intervention Study in Grade 7. Journal for Research in Mathematics Education, 25(1), 4-29. https://doi.org/10.2307/749290
• McIntosh, A. (2006). Mental computation of school-aged students: Assessment, performance levels and common errors. In: C. Bergsten, & B. Grevholm (Eds.) (2007). Developing and researching quality in mathematics teaching and learning. Proceedings of MADIF5, The 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006. (pp. 136-145). Linköping: SMDF.
• McIntosh, A. J., De Nardi, E., & Swan, P. (1994). Think mathematically. How to teach mental maths in the primary classroom. Melbourne: Longman Cheshire
• McIntosh, A., Reys, B., Reys, R., Bana, J., & Farrell, B. (1997). Number sense in school mathematics: Student performance in four countries. Perth: MASTEC, Edith Cowan University. ISBN 0-7298-0348-1
• Mclntosh, A. (2002). Common Errors in Mental Computation of Students in Grades 3 - 10. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.), Mathematics Education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia) (pp. 457-464). Sydney. MERGA.
• Mclntosh, A., Nobuhiko, N., Reys, B. J., & Reys, R. E. (1995). Mental computation performance in Australia, Japan and the United States. Educational Studies in Mathematics, 29(3), 237-258. https://doi.org/10.1007/BF01274093
• Mclntosh, A., Reys, B. J., & Reys, R. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8.
• Nunes, T., & Bryant, P. (2009). Paper 3: Understanding rational numbers and intensive quantities. In T. Nunes, P. Bryant, & A. Watson (Eds.), Key understandings in mathematics learning. London: Nuffield Foundation.
• Pagni, D. (2004). Fractions and Decimals. Australian Mathematics Teacher, 60(4), 28-30.
• Post, T., Cramer, K., Behr, M., Lesh, R., & Harel, G. (1993). Curriculum implications of research on the learning, teaching and assessing of rational number concepts. In T. Carpenter, E. Fennema, & T. Romberg (Eds.), Rational numbers: An integration of research (pp. 327-361). Hillsdale, NJ: Lawrence Erlbaum.
• Reys, B. J., Reys, R., E. & Hope, J. A. (1993). Mental Computation: A Snapshot of Second, Fifth and Seventh Grade Student Performance. School Science and Mathematics, 93(6), 306-315. https://doi.org/10.1111/j.1949-8594.1993.tb12251.x
• Reys, R. E. (1984). Mental computation and estimation: Past, present, and future. The Elementary School Journal, 84(5), 546-557. https://doi.org/10.1086/461383
• Reys, R. E., & Yang, D. C. (1998). Relationship between Computational Performance and Number Sense among Sixth- and Eighth-Grade Students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225-237. https://doi.org/10.2307/749900
• Reys, R. E., Reys, B. J., Nohda, N., & Emori, H. (1995). Mental Computation Performance and Strategy Use of Japanese Students in Grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26(4), 304-326. https://doi.org/10.2307/749477
• Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
• Sowder, J. T. (1990). Mental computation and number sense. Arithmetic Teacher, 37(7), 18-20.
• Sowder, J. T., & Schappelle, B. P. (1989). Establishing Foundations for Research on Number Sense and Related Topics: Report of a Conference (San Diego, California, February 16-17, 1989).
• Sowder, J. Τ. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371-389). New York: Macmillan.
• Sweeney, E. S., & Quinn, R. J. (2000). Concentration: Connecting fractions, decimals & percents. Mathematics Teaching in the Middle School, 5(5), 324-328. https://doi.org/10.1108/17506200710779521
• Trafton, P. R. (1992). Using number sense to develop mental computation and computational estimation. In C. J. Irons (Ed.), Challenging children to think when they compute (pp. 78-92). Brisbane: Center for Mathematics and Science Education.
• Yang, D. C. (2003). Teaching and learning number sense—an intervention study of fifth grade students in Taiwan. International Journal of Science and Mathematics Education, 1(1), 115-134. https://doi.org/10.1023/A:1026164808929
• Yang, D. C. (2005). Number sense strategies used by sixth grade students in Taiwan. Educational Studies, 31(3), 317-334. https://doi.org/10.1080/03055690500236845
• Yang, D. C. (2007). Investigating the strategies used by preservice teachers in Taiwan when responding to number sense questions. School Science and Mathematics, 107, 293-301. https://doi.org/10.1111/j.1949-8594.2007.tb17790.x
• Yang, D. C., Reys, R. E., & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7(2), 383-403. https://doi.org/10.1007/s10763-007-9124-5

APA

Lemonidis, C., & Pilianidis, N. (2020). The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers. International Electronic Journal of Mathematics Education, 15(3), em0587. https://doi.org/10.29333/iejme/7865

Vancouver

Lemonidis C, Pilianidis N. The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers. INT ELECT J MATH ED. 2020;15(3):em0587. https://doi.org/10.29333/iejme/7865

AMA

Lemonidis C, Pilianidis N. The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers. INT ELECT J MATH ED. 2020;15(3), em0587. https://doi.org/10.29333/iejme/7865

Chicago

Lemonidis, Charalampos, and Nikos Pilianidis. "The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0587. https://doi.org/10.29333/iejme/7865

Harvard

Lemonidis, C., and Pilianidis, N. (2020). The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers. International Electronic Journal of Mathematics Education, 15(3), em0587. https://doi.org/10.29333/iejme/7865

MLA

Lemonidis, Charalampos et al. "The 8^th Grade Students’ Competencies in Alternating Different Symbolic Representations of Rational Numbers". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0587. https://doi.org/10.29333/iejme/7865