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References
- Adams, D. M., McLaren, B. M., Mayer, R. E., Goguadze, G., & Isotani, S. (2013). Erroneous Examples as Desirable Difficulty. In H. C. Lane, K. Yacef, J. Mostow, & P. Pavlik (Eds.), Artificial Intelligence in Education (pp. 803–806). Springer Berlin Heidelberg.
- Alacaci, C., & Pasztor, A. (2005). On People’s Incorrect Either-Or Patterns in Negating Quantified Statements: A Study. Proceedings of the Annual Meeting of the Cognitive Science Society, 27(27).
- Arslan, S. (2010). Traditional instruction of differential equations and conceptual learning. Teaching Mathematics and Its Applications, 29(2), 94–107. https://doi.org/10.1093/teamat/hrq001
- Bedros, V. (2003). An exploratory study of undergraduate students’ perceptions and understandings of indirect proofs [Doctoral dissertation, The University of Montana]. https://scholarworks.umt.edu/etd/9473
- Biggs, J., & Collis, K. (2014). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). Academic Press.
- Bisson, M.-J., Gilmore, C., Inglis, M., & Jones, I. (2016). Measuring Conceptual Understanding Using Comparative Judgement. International Journal of Research in Undergraduate Mathematics Education, 2(2), 141–164. https://doi.org/10.1007/s40753-016-0024-3
- Bloom, B. S., Engelhart, M. D., Furst, E. J., Hill, W. H., & Krathwohl, D. R. (1964). Taxonomy of educational objectives (Vol. 2). Longmans, Green New York.
- Buchbinder, O., & Zaslavsky, O. (2013). Inconsistencies in Students’ Understanding of Proof and Refutation of Mathematical Statements. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 129–136). 37th Annual Conference of the International Group for the Psychology of Mathematics Education, Kiel, Germany.
- Büchele, S., & Feudel, F. (2023). Changes in Students’ Mathematical Competencies at the Beginning of Higher Education Within the Last Decade at a German University. International Journal of Science and Mathematics Education, 21(8), 2325–2347. https://doi.org/10.1007/s10763-022-10350-x
- Burnett, P. C. (1999). Assessing the structure of learning outcomes from counselling using the SOLO taxonomy: An exploratory study. British Journal of Guidance & Counselling, 27(4), 567–580. https://doi.org/10.1080/03069889908256291
- Chan, C. C., Tsui, M. S., Chan, M. Y. C., & Hong, J. H. (2002). Applying the Structure of the Observed Learning Outcomes (SOLO) Taxonomy on Student’s Learning Outcomes: An empirical study. Assessment & Evaluation in Higher Education, 27(6), 511–527. https://doi.org/10.1080/0260293022000020282
- Claudia, L. F., Kusmayadi, T. A., & Fitriana, L. (2020). The SOLO taxonomy: Classify students’ responses in solving linear program problems. Journal of Physics: Conference Series, 1538(1), 012107. https://doi.org/10.1088/1742-6596/1538/1/012107
- 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
- Engelbrecht, J., Bergsten, C., & Kågesten, O. (2009). Undergraduate students’ preference for procedural to conceptual solutions to mathematical problems. International Journal of Mathematical Education in Science and Technology, 40(7), 927–940. https://doi.org/10.1080/00207390903200968
- Ferrini-Mundy, J., & Graham, K. G. (1991). An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development. The American Mathematical Monthly, 98(7), 627–635. https://doi.org/10.1080/00029890.1991.11995769
- Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher Questioning to Elicit Students’ Mathematical Thinking in Elementary School Classrooms. Journal of Teacher Education, 60(4), 380–392. https://doi.org/10.1177/0022487109339906
- Groves, S. (2012). Developing mathematical proficiency. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 119–145.
- Habre, S. (2002, July). Writing in a Reformed Differential Equations Class. International Conference on the Teaching of Mathematics.
- Hicks, T., & Bostic, J. D. (2021). Formative Assessment through Think Alouds. Mathematics Teacher: Learning and Teaching PK-12, 114(8), 598–606. https://doi.org/10.5951/MTLT.2020.0245
- Hillel, J. (2000). Modes of Description and the Problem of Representation in Linear Algebra. In J.-L. Dorier (Ed.), On the Teaching of Linear Algebra (pp. 191–207). Springer Netherlands. https://doi.org/10.1007/0-306-47224-4_7
- Kågesten, O., & Engelbrecht, J. (2006). Supplementary explanations in undergraduate mathematics assessment: A forced formative writing activity. European Journal of Engineering Education, 31(6), 705–715. https://doi.org/10.1080/03043790600911803
- Kani, N. H. A., & Shahrill, M. (2015). Applying the thinking aloud pair problem solving strategy in mathematics lessons. Asian Journal of Management Sciences and Education, 4(2), 20–28.
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). The Strands of Mathematical Proficiency. In N. R. Council, Adding It Up: Helping Children Learn Mathematics. The National Academies Press. https://doi.org/10.17226/9822
- Knuth, E., Zaslavsky, O., & Ellis, A. (2019). The role and use of examples in learning to prove. The Journal of Mathematical Behavior, 53, 256–262. https://doi.org/10.1016/j.jmathb.2017.06.002
- Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 159–174.
- Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020). Applying the SOLO taxonomy in assessing and fostering students’ mathematical problem-solving abilities. Problems of Education in the 21st Century, 77(6), 13.
- Mulbar, U., Rahman, A., & Ahmar, A. (2017). Analysis of the ability in mathematical problem-solving based on SOLO taxonomy and cognitive style. World Transactions on Engineering and Technology Education, 15(1).
- Niemi, D. (1996). Assessing Conceptual Understanding in Mathematics: Representations, Problem Solutions, Justifications, and Explanations. The Journal of Educational Research, 89(6), 351–363. https://doi.org/10.1080/00220671.1996.9941339
- Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15–30. https://doi.org/10.1080/0020739X.2017.1340679
- Pasani, C. F., Kusumawati, E., & Suryaningsih, Y. (2021). The ability of mathematics education students to build counterexamples in solving cyclic group problems. AIP Conference Proceedings, 2330(1), 040023. https://doi.org/10.1063/5.0043223
- Putri, U. H., Mardiyana, M., & Saputro, D. R. S. (2017). How to Analyze the Students’ Thinking Levels Based on SOLO Taxonomy? Journal of Physics: Conference Series, 895, 012031. https://doi.org/10.1088/1742-6596/895/1/012031
- Radmehr, F., & Drake, M. (2019). Revised Bloom’s taxonomy and major theories and frameworks that influence the teaching, learning, and assessment of mathematics: A comparison. International Journal of Mathematical Education in Science and Technology, 50(6), 895–920. https://doi.org/10.1080/0020739X.2018.1549336
- Ramos, R. A., Gutierrez, M. C., Carang, E. S. P., & Caguete, R. R. (2024). Measuring Student Performance in Mathematics in the Modern World Course Using Bloom’s and Solo Taxonomies. International Journal of Management and Accounting, 78–84. https://doi.org/10.34104/ijmms.024.078084
- Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
- Santos-Trigo, M., Camacho-Machín, M., & Barrera-Mora, F. (2024). Focusing on foundational Calculus ideas to understand the derivative concept via problem-solving tasks that involve the use of a Dynamic Geometry System. ZDM – Mathematics Education, 56(6), 1287–1301. https://doi.org/10.1007/s11858-024-01607-6
- Stålne, K., Kjellström, S., & Utriainen, J. (2016). Assessing complexity in learning outcomes – a comparison between the SOLO taxonomy and the model of hierarchical complexity. Assessment & Evaluation in Higher Education, 41(7), 1033–1048. https://doi.org/10.1080/02602938.2015.1047319
- Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. https://doi.org/10.1016/S0742-051X(00)00052-4
- Stovner, R. B., Klette, K., & Nortvedt, G. A. (2021). The instructional situations in which mathematics teachers provide substantive feedback. Educational Studies in Mathematics, 108(3), 533–551. https://doi.org/10.1007/s10649-021-10065-w
- Sudihartinih, E. (2019). Facilitating Mathematical Understanding in Three-Dimensional Geometry Using the Solo Taxonomy. Erudio Journal of Educational Innovation, 6(1), 11–18. https://doi.org/10.18551/erudio.6-1.2
- Suh, J. M. (2007). Tying It All Together: Classroom Practices That Promote Mathematical Proficiency for All Students. Teaching Children Mathematics, 14(3), 163–169. https://doi.org/10.5951/TCM.14.3.0163
- Wilson, M. (2009). Measuring progressions: Assessment structures underlying a learning progression. Journal of Research in Science Teaching, 46(6), 716–730. https://doi.org/10.1002/tea.20318
References
Adams, D. M., McLaren, B. M., Mayer, R. E., Goguadze, G., & Isotani, S. (2013). Erroneous Examples as Desirable Difficulty. In H. C. Lane, K. Yacef, J. Mostow, & P. Pavlik (Eds.), Artificial Intelligence in Education (pp. 803–806). Springer Berlin Heidelberg.
Alacaci, C., & Pasztor, A. (2005). On People’s Incorrect Either-Or Patterns in Negating Quantified Statements: A Study. Proceedings of the Annual Meeting of the Cognitive Science Society, 27(27).
Arslan, S. (2010). Traditional instruction of differential equations and conceptual learning. Teaching Mathematics and Its Applications, 29(2), 94–107. https://doi.org/10.1093/teamat/hrq001
Bedros, V. (2003). An exploratory study of undergraduate students’ perceptions and understandings of indirect proofs [Doctoral dissertation, The University of Montana]. https://scholarworks.umt.edu/etd/9473
Biggs, J., & Collis, K. (2014). Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome). Academic Press.
Bisson, M.-J., Gilmore, C., Inglis, M., & Jones, I. (2016). Measuring Conceptual Understanding Using Comparative Judgement. International Journal of Research in Undergraduate Mathematics Education, 2(2), 141–164. https://doi.org/10.1007/s40753-016-0024-3
Bloom, B. S., Engelhart, M. D., Furst, E. J., Hill, W. H., & Krathwohl, D. R. (1964). Taxonomy of educational objectives (Vol. 2). Longmans, Green New York.
Buchbinder, O., & Zaslavsky, O. (2013). Inconsistencies in Students’ Understanding of Proof and Refutation of Mathematical Statements. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 129–136). 37th Annual Conference of the International Group for the Psychology of Mathematics Education, Kiel, Germany.
Büchele, S., & Feudel, F. (2023). Changes in Students’ Mathematical Competencies at the Beginning of Higher Education Within the Last Decade at a German University. International Journal of Science and Mathematics Education, 21(8), 2325–2347. https://doi.org/10.1007/s10763-022-10350-x
Burnett, P. C. (1999). Assessing the structure of learning outcomes from counselling using the SOLO taxonomy: An exploratory study. British Journal of Guidance & Counselling, 27(4), 567–580. https://doi.org/10.1080/03069889908256291
Chan, C. C., Tsui, M. S., Chan, M. Y. C., & Hong, J. H. (2002). Applying the Structure of the Observed Learning Outcomes (SOLO) Taxonomy on Student’s Learning Outcomes: An empirical study. Assessment & Evaluation in Higher Education, 27(6), 511–527. https://doi.org/10.1080/0260293022000020282
Claudia, L. F., Kusmayadi, T. A., & Fitriana, L. (2020). The SOLO taxonomy: Classify students’ responses in solving linear program problems. Journal of Physics: Conference Series, 1538(1), 012107. https://doi.org/10.1088/1742-6596/1538/1/012107
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
Engelbrecht, J., Bergsten, C., & Kågesten, O. (2009). Undergraduate students’ preference for procedural to conceptual solutions to mathematical problems. International Journal of Mathematical Education in Science and Technology, 40(7), 927–940. https://doi.org/10.1080/00207390903200968
Ferrini-Mundy, J., & Graham, K. G. (1991). An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development. The American Mathematical Monthly, 98(7), 627–635. https://doi.org/10.1080/00029890.1991.11995769
Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher Questioning to Elicit Students’ Mathematical Thinking in Elementary School Classrooms. Journal of Teacher Education, 60(4), 380–392. https://doi.org/10.1177/0022487109339906
Groves, S. (2012). Developing mathematical proficiency. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 119–145.
Habre, S. (2002, July). Writing in a Reformed Differential Equations Class. International Conference on the Teaching of Mathematics.
Hicks, T., & Bostic, J. D. (2021). Formative Assessment through Think Alouds. Mathematics Teacher: Learning and Teaching PK-12, 114(8), 598–606. https://doi.org/10.5951/MTLT.2020.0245
Hillel, J. (2000). Modes of Description and the Problem of Representation in Linear Algebra. In J.-L. Dorier (Ed.), On the Teaching of Linear Algebra (pp. 191–207). Springer Netherlands. https://doi.org/10.1007/0-306-47224-4_7
Kågesten, O., & Engelbrecht, J. (2006). Supplementary explanations in undergraduate mathematics assessment: A forced formative writing activity. European Journal of Engineering Education, 31(6), 705–715. https://doi.org/10.1080/03043790600911803
Kani, N. H. A., & Shahrill, M. (2015). Applying the thinking aloud pair problem solving strategy in mathematics lessons. Asian Journal of Management Sciences and Education, 4(2), 20–28.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). The Strands of Mathematical Proficiency. In N. R. Council, Adding It Up: Helping Children Learn Mathematics. The National Academies Press. https://doi.org/10.17226/9822
Knuth, E., Zaslavsky, O., & Ellis, A. (2019). The role and use of examples in learning to prove. The Journal of Mathematical Behavior, 53, 256–262. https://doi.org/10.1016/j.jmathb.2017.06.002
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 159–174.
Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020). Applying the SOLO taxonomy in assessing and fostering students’ mathematical problem-solving abilities. Problems of Education in the 21st Century, 77(6), 13.
Mulbar, U., Rahman, A., & Ahmar, A. (2017). Analysis of the ability in mathematical problem-solving based on SOLO taxonomy and cognitive style. World Transactions on Engineering and Technology Education, 15(1).
Niemi, D. (1996). Assessing Conceptual Understanding in Mathematics: Representations, Problem Solutions, Justifications, and Explanations. The Journal of Educational Research, 89(6), 351–363. https://doi.org/10.1080/00220671.1996.9941339
Norqvist, M. (2018). The effect of explanations on mathematical reasoning tasks. International Journal of Mathematical Education in Science and Technology, 49(1), 15–30. https://doi.org/10.1080/0020739X.2017.1340679
Pasani, C. F., Kusumawati, E., & Suryaningsih, Y. (2021). The ability of mathematics education students to build counterexamples in solving cyclic group problems. AIP Conference Proceedings, 2330(1), 040023. https://doi.org/10.1063/5.0043223
Putri, U. H., Mardiyana, M., & Saputro, D. R. S. (2017). How to Analyze the Students’ Thinking Levels Based on SOLO Taxonomy? Journal of Physics: Conference Series, 895, 012031. https://doi.org/10.1088/1742-6596/895/1/012031
Radmehr, F., & Drake, M. (2019). Revised Bloom’s taxonomy and major theories and frameworks that influence the teaching, learning, and assessment of mathematics: A comparison. International Journal of Mathematical Education in Science and Technology, 50(6), 895–920. https://doi.org/10.1080/0020739X.2018.1549336
Ramos, R. A., Gutierrez, M. C., Carang, E. S. P., & Caguete, R. R. (2024). Measuring Student Performance in Mathematics in the Modern World Course Using Bloom’s and Solo Taxonomies. International Journal of Management and Accounting, 78–84. https://doi.org/10.34104/ijmms.024.078084
Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. https://doi.org/10.1037/0022-0663.91.1.175
Santos-Trigo, M., Camacho-Machín, M., & Barrera-Mora, F. (2024). Focusing on foundational Calculus ideas to understand the derivative concept via problem-solving tasks that involve the use of a Dynamic Geometry System. ZDM – Mathematics Education, 56(6), 1287–1301. https://doi.org/10.1007/s11858-024-01607-6
Stålne, K., Kjellström, S., & Utriainen, J. (2016). Assessing complexity in learning outcomes – a comparison between the SOLO taxonomy and the model of hierarchical complexity. Assessment & Evaluation in Higher Education, 41(7), 1033–1048. https://doi.org/10.1080/02602938.2015.1047319
Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. https://doi.org/10.1016/S0742-051X(00)00052-4
Stovner, R. B., Klette, K., & Nortvedt, G. A. (2021). The instructional situations in which mathematics teachers provide substantive feedback. Educational Studies in Mathematics, 108(3), 533–551. https://doi.org/10.1007/s10649-021-10065-w
Sudihartinih, E. (2019). Facilitating Mathematical Understanding in Three-Dimensional Geometry Using the Solo Taxonomy. Erudio Journal of Educational Innovation, 6(1), 11–18. https://doi.org/10.18551/erudio.6-1.2
Suh, J. M. (2007). Tying It All Together: Classroom Practices That Promote Mathematical Proficiency for All Students. Teaching Children Mathematics, 14(3), 163–169. https://doi.org/10.5951/TCM.14.3.0163
Wilson, M. (2009). Measuring progressions: Assessment structures underlying a learning progression. Journal of Research in Science Teaching, 46(6), 716–730. https://doi.org/10.1002/tea.20318