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References
- Armanto, D. (2002). Teaching multiplication and division realistically in Indonesian primary schools: A prototype of local instructional theory. University of Twente. https://ris.utwente.nl/ws/portalfiles/portal/6085178/thesis_Armanto.pdf
- Ashcraft, M. H. (1985). Is it farfetched that some of us remember our arithmetic facts?. Journal for Research in Mathematics Education, 16(2), 99-105. https://doi.org/10.5951/jresematheduc.16.2.0099
- Ashcraft, M. H., & Fierman, B. A. (1982). Mental addition in third, fourth, and sixth graders. Journal of Experimental Child Psychology, 33(2), 216–234. https://doi.org/10.1016/0022-0965(82)90017-0
- Baroody, A. J. (1992). The development of kindergartners’ mental-addition strategies. Learning and Individual Differences, 4(3), 215–235. https://doi.org/10.1016/1041-6080(92)90003-W
- Beentjes, J. W. J., & Jonker, V. H. (1987). Inconsistency in addition and subtraction strategies. The Journal of Experimental Education, 56(1), 4–7. https://doi.org/10.1080/00220973.1987.10806459
- Beishuizen, M. (1993). Mental Strategies and Materials or Models for Addition and Subtraction up to 100 in Dutch Second Grades. Journal for Research in Mathematics Education, 24(4), 294-323. https://doi.org/10.2307/749464
- Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7(1), 87–106. https://doi.org/10.1016/S0959-4752(96)00012-6
- Callingham, R. (2005). Primary students’ mental computation: Strategies and achievement. Building Connections: Research, Theory and Practice, 193–200. https://hdl.handle.net/1959.11/11373
- Carpenter, T. P. (2013). Conceptual knowledge as a foundation for procedural knowledge. In Conceptual and procedural knowledge (pp. 113–132). Routledge. https://doi.org/10.4324/9780203063538
- Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3–20. https://doi.org/10.5951/jresematheduc.29.1.0003
- Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202. https://doi.org/10.5951/jresematheduc.15.3.0179
- Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87–115. https://doi.org/10.2307/30034843
- Clements, D. H., & Sarama, J. (2012). Learning trajectories in mathematics education. In Hypothetical Learning Trajectories (pp. 81–90). Routledge. https://doi.org/10.4324/9780203063279
- Cooke, H. (2001). Primary Mathematics (Vol. 2). SAGE.
- Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344–377. https://doi.org/10.1016/j.dr.2014.10.001
- Freudenthal, H. (2012). Mathematics as an educational task. Springer Science & Business Media. https://doi.org/10.1007/978-94-010-2903-2
- Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151. https://doi.org/10.1016/j.jecp.2004.03.002
- Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602_3
- Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Educational design research (pp. 29–63). Routledge. https://doi.org/10.4324/9780203088364
- Gravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777–796. https://doi.org/10.1080/00220270050167170
- Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524. https://doi.org/10.1086/596999
- Heirdsfield, A. (2011). Teaching mental computation strategies in early mathematics. YC Young Children, 66(2), 96–102. https://eprints.qut.edu.au/42451/1/42451.pdf
- Herman, T. (2001). Strategi mental yang digunakan siswa sekolah dasar dalam berhitung. Seminar Nasional Pendidikan Matematika di Universitas Negeri Yogyakarta, 1–7.
- Hiebert, J., & Lefevre, P. (2013). Conceptual and procedural knowledge in mathematics: An introductory analysis. In Conceptual and procedural knowledge (pp. 1–27). Routledge. https://doi.org/10.4324/9780203063538
- Hopf, C. (2004). Qualitative interviews: An overview. A Companion to Qualitative Research, 203(8), 100093.
- Karlsson, C., & Johansson, E. (2018). MATEMATIKUNDERVISNING I SUBTRAKTION: En litteraturstudie om undervisning, metoder och strategier i subtraktion. https://www.diva-portal.org/smash/get/diva2:1240818/FULLTEXT02
- Macintyre, T., & Forrester, R. (2003). Strategies for mental calculation. Proceedings of the British Society for Research into Learning Mathematics, 23(2), 49–54. https://www.nuffieldfoundation.org/wp-content/uploads/2019/11/Article_STRATEGIES20FOR20MENTAL20CALCULATION_2003.pdf
- Mariana, N. (2009). Design research in geometry education developing spatial abilities in first grade children. Utrecht University. https://www.fisme.science.uu.nl/en/impome/theses_group_2007/thesis_Neni.pdf
- Mariana, N. (2019). Transformation of research education at elementary school mathematics in the industry 4.0. International Journal of Innovation, Creativity and Change, 5(5), 1–10. https://www.ijicc.net/images/vol5iss5/Part_2/55223_Mariana_2020_E_R.pdf
- Mariana, N., Firmandani, F. A., & Indrawati, D. (2018). Labour Issues as a Context in Designing Mathematics Activity for Counting Strategy. MISEIC 2018.
- McIntosh, A., Reys, B. J., & Reys, R. E. (2005). A proposed framework for examining basic number sense. In Subject Learning in the Primary Curriculum (pp. 209–221). Routledge. https://doi.org/10.4324/9780203990247
- Moelong, L. J. (2012). Metode Penelitian Kualitatif. Remaja Rosda Karya.
- Nengsih, G. A., & Pujiastuti, H. (2021). Analisis kesulitan dalam menyelesaikan soal materi operasi bilangan cacah siswa sekolah dasar. JKPM (Jurnal Kajian Pendidikan Matematika), 6(2), 293-306. http://dx.doi.org/10.30998/jkpm.v6i2.9941
- Prahmana, R. C. I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar). Rajawali Press.
- Prahmana, R. C. I., & Kusumah, Y. S. (2017). Didactic trajectory of research in mathematics education using research-based learning. Journal of Physics: Conference Series, 893(1), 012001. http://dx.doi.org/10.1088/1742-6596/893/1/012001
- Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM, 47, 877–891. https://doi.org/10.1007/s11858-015-0722-3
- Principles, N. (2000). Standards for School Mathematics. NCTM.
- Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics, 84, 309–328. https://doi.org/10.1007/s10649-013-9480-8
- Proulx, J. (2019). Mental mathematics under the lens: Strategies, oral mathematics, enactments of meanings. The Journal of Mathematical Behavior, 56, 100725. https://doi.org/10.1016/j.jmathb.2019.100725
- Resnick, L. B. (1986). The development of mathematical intuition. Minnesota Symposia on Child Psychology, 19, 159–194.
- Reys, B. J. (1985). Mental computation. The Arithmetic Teacher, 32(6), 43–46. https://doi.org/10.5951/AT.32.6.0043
- Reys, B. J. (1986). Estimation and Mental Computation It’s “About” Time. The Arithmetic Teacher, 34(1), 22–23. https://doi.org/10.5951/AT.34.1.0022
- 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., 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/10.5951/jresematheduc.26.4.0304
- Risdiyanti, I., & Prahmana, R. C. I. (2020). The Learning Trajectory of Number Pattern Learning Using "Barathayudha" War Stories and Uno Stacko. Journal on Mathematics Education, 11(1), 157–166. https://doi.org/10.22342/jme.11.1.10225.157-166
- Simon, M. A., & Tzur, R. (2012). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. In Hypothetical learning trajectories (pp. 91–104). Routledge. https://doi.org/10.4324/9780203063279
- Siswono, T. Y. E. (2006). PMRI: Pembelajaran Matematika yang Mengembangkan Penalaran, Kreativitas dan Kepribadian Siswa. Makalah Workshop Pembelajaran Matematika di MI “Nuruh Rohmah”. Sidoarjo, 8.
- Soedjadi, R. (2014). Inti Dasar – Dasar Pendidikan Matematika Realistik Indonesia. Jurnal Pendidikan Matematika, 1(2), 1–10. https://doi.org/10.22342/jpm.1.2.807.
- Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147–156. https://doi.org/10.3102/0013189X12442801
- Thevenot, C., Barrouillet, P., Castel, C., & Uittenhove, K. (2016). Ten-year-old children strategies in mental addition: A counting model account. Cognition, 146, 48–57. https://doi.org/10.1016/j.cognition.2015.09.003
- Thompson, I. (1999). Mental calculation strategies for addition and subtraction: Part 1. Mathematics in School, 28(5), 2–4. https://doi.org/10.1017/CBO9781107415324.004
- Thompson, I. (2000). Mental calculation strategies for addition and subtraction: Part 2. Mathematics in School, 29(1), 24–26. https://www.jstor.org/stable/30212066
- Thompson, I. (2010). 12 Getting your head around mental calculation. Issues in Teaching Numeracy in Primary Schools, 161-173.
- Treffers, A. (1991). Didactical background of a mathematics program for primary education. Realistic Mathematics Education in Primary School, 21–56.
- Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Educational Design Research. Routledge. https://doi.org/10.4324/9780203088364
- Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. Encyclopedia of Mathematics Education, 713–717. https://doi.org/10.1007/978-3-030-15789-0_170
- Van Nes, F., & De Lange, J. (2007). Mathematics education and neurosciences: Relating spatial structures to the development of spatial sense and number sense. The Mathematics Enthusiast, 4(2), 210–229. https://doi.org/10.54870/1551-3440.1072
- Varol, F., & Farran, D. (2007). Elementary school students’ mental computation proficiencies. Early Childhood Education Journal, 35, 89–94. https://doi.org/10.1007/s10643-007-0173-8
- Widaman, K. F., Geary, D. C., Cormier, P., & Little, T. D. (1989). A componential model for mental addition. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(5), 898-919. https://doi.org/10.1037/0278-7393.15.5.898
- Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.5951/jresematheduc.27.4.0458
References
Armanto, D. (2002). Teaching multiplication and division realistically in Indonesian primary schools: A prototype of local instructional theory. University of Twente. https://ris.utwente.nl/ws/portalfiles/portal/6085178/thesis_Armanto.pdf
Ashcraft, M. H. (1985). Is it farfetched that some of us remember our arithmetic facts?. Journal for Research in Mathematics Education, 16(2), 99-105. https://doi.org/10.5951/jresematheduc.16.2.0099
Ashcraft, M. H., & Fierman, B. A. (1982). Mental addition in third, fourth, and sixth graders. Journal of Experimental Child Psychology, 33(2), 216–234. https://doi.org/10.1016/0022-0965(82)90017-0
Baroody, A. J. (1992). The development of kindergartners’ mental-addition strategies. Learning and Individual Differences, 4(3), 215–235. https://doi.org/10.1016/1041-6080(92)90003-W
Beentjes, J. W. J., & Jonker, V. H. (1987). Inconsistency in addition and subtraction strategies. The Journal of Experimental Education, 56(1), 4–7. https://doi.org/10.1080/00220973.1987.10806459
Beishuizen, M. (1993). Mental Strategies and Materials or Models for Addition and Subtraction up to 100 in Dutch Second Grades. Journal for Research in Mathematics Education, 24(4), 294-323. https://doi.org/10.2307/749464
Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7(1), 87–106. https://doi.org/10.1016/S0959-4752(96)00012-6
Callingham, R. (2005). Primary students’ mental computation: Strategies and achievement. Building Connections: Research, Theory and Practice, 193–200. https://hdl.handle.net/1959.11/11373
Carpenter, T. P. (2013). Conceptual knowledge as a foundation for procedural knowledge. In Conceptual and procedural knowledge (pp. 113–132). Routledge. https://doi.org/10.4324/9780203063538
Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3–20. https://doi.org/10.5951/jresematheduc.29.1.0003
Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202. https://doi.org/10.5951/jresematheduc.15.3.0179
Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87–115. https://doi.org/10.2307/30034843
Clements, D. H., & Sarama, J. (2012). Learning trajectories in mathematics education. In Hypothetical Learning Trajectories (pp. 81–90). Routledge. https://doi.org/10.4324/9780203063279
Cooke, H. (2001). Primary Mathematics (Vol. 2). SAGE.
Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental Review, 34(4), 344–377. https://doi.org/10.1016/j.dr.2014.10.001
Freudenthal, H. (2012). Mathematics as an educational task. Springer Science & Business Media. https://doi.org/10.1007/978-94-010-2903-2
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151. https://doi.org/10.1016/j.jecp.2004.03.002
Gravemeijer, K. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602_3
Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Educational design research (pp. 29–63). Routledge. https://doi.org/10.4324/9780203088364
Gravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777–796. https://doi.org/10.1080/00220270050167170
Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524. https://doi.org/10.1086/596999
Heirdsfield, A. (2011). Teaching mental computation strategies in early mathematics. YC Young Children, 66(2), 96–102. https://eprints.qut.edu.au/42451/1/42451.pdf
Herman, T. (2001). Strategi mental yang digunakan siswa sekolah dasar dalam berhitung. Seminar Nasional Pendidikan Matematika di Universitas Negeri Yogyakarta, 1–7.
Hiebert, J., & Lefevre, P. (2013). Conceptual and procedural knowledge in mathematics: An introductory analysis. In Conceptual and procedural knowledge (pp. 1–27). Routledge. https://doi.org/10.4324/9780203063538
Hopf, C. (2004). Qualitative interviews: An overview. A Companion to Qualitative Research, 203(8), 100093.
Karlsson, C., & Johansson, E. (2018). MATEMATIKUNDERVISNING I SUBTRAKTION: En litteraturstudie om undervisning, metoder och strategier i subtraktion. https://www.diva-portal.org/smash/get/diva2:1240818/FULLTEXT02
Macintyre, T., & Forrester, R. (2003). Strategies for mental calculation. Proceedings of the British Society for Research into Learning Mathematics, 23(2), 49–54. https://www.nuffieldfoundation.org/wp-content/uploads/2019/11/Article_STRATEGIES20FOR20MENTAL20CALCULATION_2003.pdf
Mariana, N. (2009). Design research in geometry education developing spatial abilities in first grade children. Utrecht University. https://www.fisme.science.uu.nl/en/impome/theses_group_2007/thesis_Neni.pdf
Mariana, N. (2019). Transformation of research education at elementary school mathematics in the industry 4.0. International Journal of Innovation, Creativity and Change, 5(5), 1–10. https://www.ijicc.net/images/vol5iss5/Part_2/55223_Mariana_2020_E_R.pdf
Mariana, N., Firmandani, F. A., & Indrawati, D. (2018). Labour Issues as a Context in Designing Mathematics Activity for Counting Strategy. MISEIC 2018.
McIntosh, A., Reys, B. J., & Reys, R. E. (2005). A proposed framework for examining basic number sense. In Subject Learning in the Primary Curriculum (pp. 209–221). Routledge. https://doi.org/10.4324/9780203990247
Moelong, L. J. (2012). Metode Penelitian Kualitatif. Remaja Rosda Karya.
Nengsih, G. A., & Pujiastuti, H. (2021). Analisis kesulitan dalam menyelesaikan soal materi operasi bilangan cacah siswa sekolah dasar. JKPM (Jurnal Kajian Pendidikan Matematika), 6(2), 293-306. http://dx.doi.org/10.30998/jkpm.v6i2.9941
Prahmana, R. C. I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar). Rajawali Press.
Prahmana, R. C. I., & Kusumah, Y. S. (2017). Didactic trajectory of research in mathematics education using research-based learning. Journal of Physics: Conference Series, 893(1), 012001. http://dx.doi.org/10.1088/1742-6596/893/1/012001
Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM, 47, 877–891. https://doi.org/10.1007/s11858-015-0722-3
Principles, N. (2000). Standards for School Mathematics. NCTM.
Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics, 84, 309–328. https://doi.org/10.1007/s10649-013-9480-8
Proulx, J. (2019). Mental mathematics under the lens: Strategies, oral mathematics, enactments of meanings. The Journal of Mathematical Behavior, 56, 100725. https://doi.org/10.1016/j.jmathb.2019.100725
Resnick, L. B. (1986). The development of mathematical intuition. Minnesota Symposia on Child Psychology, 19, 159–194.
Reys, B. J. (1985). Mental computation. The Arithmetic Teacher, 32(6), 43–46. https://doi.org/10.5951/AT.32.6.0043
Reys, B. J. (1986). Estimation and Mental Computation It’s “About” Time. The Arithmetic Teacher, 34(1), 22–23. https://doi.org/10.5951/AT.34.1.0022
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., 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/10.5951/jresematheduc.26.4.0304
Risdiyanti, I., & Prahmana, R. C. I. (2020). The Learning Trajectory of Number Pattern Learning Using "Barathayudha" War Stories and Uno Stacko. Journal on Mathematics Education, 11(1), 157–166. https://doi.org/10.22342/jme.11.1.10225.157-166
Simon, M. A., & Tzur, R. (2012). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. In Hypothetical learning trajectories (pp. 91–104). Routledge. https://doi.org/10.4324/9780203063279
Siswono, T. Y. E. (2006). PMRI: Pembelajaran Matematika yang Mengembangkan Penalaran, Kreativitas dan Kepribadian Siswa. Makalah Workshop Pembelajaran Matematika di MI “Nuruh Rohmah”. Sidoarjo, 8.
Soedjadi, R. (2014). Inti Dasar – Dasar Pendidikan Matematika Realistik Indonesia. Jurnal Pendidikan Matematika, 1(2), 1–10. https://doi.org/10.22342/jpm.1.2.807.
Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147–156. https://doi.org/10.3102/0013189X12442801
Thevenot, C., Barrouillet, P., Castel, C., & Uittenhove, K. (2016). Ten-year-old children strategies in mental addition: A counting model account. Cognition, 146, 48–57. https://doi.org/10.1016/j.cognition.2015.09.003
Thompson, I. (1999). Mental calculation strategies for addition and subtraction: Part 1. Mathematics in School, 28(5), 2–4. https://doi.org/10.1017/CBO9781107415324.004
Thompson, I. (2000). Mental calculation strategies for addition and subtraction: Part 2. Mathematics in School, 29(1), 24–26. https://www.jstor.org/stable/30212066
Thompson, I. (2010). 12 Getting your head around mental calculation. Issues in Teaching Numeracy in Primary Schools, 161-173.
Treffers, A. (1991). Didactical background of a mathematics program for primary education. Realistic Mathematics Education in Primary School, 21–56.
Van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Educational Design Research. Routledge. https://doi.org/10.4324/9780203088364
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. Encyclopedia of Mathematics Education, 713–717. https://doi.org/10.1007/978-3-030-15789-0_170
Van Nes, F., & De Lange, J. (2007). Mathematics education and neurosciences: Relating spatial structures to the development of spatial sense and number sense. The Mathematics Enthusiast, 4(2), 210–229. https://doi.org/10.54870/1551-3440.1072
Varol, F., & Farran, D. (2007). Elementary school students’ mental computation proficiencies. Early Childhood Education Journal, 35, 89–94. https://doi.org/10.1007/s10643-007-0173-8
Widaman, K. F., Geary, D. C., Cormier, P., & Little, T. D. (1989). A componential model for mental addition. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(5), 898-919. https://doi.org/10.1037/0278-7393.15.5.898
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.5951/jresematheduc.27.4.0458