Revised Bloom’s taxonomy and major theories and frameworks that influence the teaching, learning, and assessment of mathematics: a comparison

References

• Pegg J, Tall D. The fundamental cycle of concept construction underlying various theoretical frameworks. ZDM. 2005;37(6):468–475.
   Google Scholar
• Pegg J, Tall D. The fundamental cycle of concept construction underlying various theoretical frameworks. In: B Sriraman, L English, editor. Theories of mathematics education: seeking new frontiers. Berlin: Springer; 2010. p. 173–192.
   Google Scholar
• Biggs JB, Collis KF. Evaluating the quality of learning. New York (NY): Academic Press; 1982.
   Google Scholar
• Dubinsky E. Reflective abstraction in advanced mathematical thinking. In: DO Tall, editor. Advanced mathematical thinking. Dordrecht: Kluwer; 1991. p. 95–123.
   Google Scholar
• Arnon L, Cottrill J, Dubinsky E, et al. APOS theory: a framework for research and curriculum development in mathematics education. New York (NY): Springer; 2014.
   Google Scholar
• Anderson LW, Krathwohl DR, Airasian PW, et al. A taxonomy for learning, teaching, and assessing: a revision of bloom’s taxonomy of educational objectives. Complete edition. New York (NY): Longman; 2001.
   Google Scholar
• Stewart S. Understanding linear algebra concepts through the embodied, symbolic and formal worlds of mathematical thinking [Doctoral dissertation]. Auckland (NZ): The University of Auckland; 2008.
   Google Scholar
• Dubinsky E, McDonald M. APOS: A constructivist theory of learning in undergraduate mathematics education research. In: D Holton, M Artigue, U Kirchgräber, J Hillel, M Niss, A Schoenfeld, editor. The teaching and learning of mathematics at university level. New ICMI study series, vol. 7. Dordrecht: Springer; 2001. p. 275–282. doi:10.1007/0-306-47231-7_25.
   Google Scholar
• Lambdin D, Walcott C. Changes through the years: connections between psychological learning theories and the school mathematics curriculum. In: W Martin, M Strutchens, P Elliott, editor. The learning of mathematics: 67th yearbook. Reston (VA): National Council of Teachers of Mathematics; 2007. p. 3–25.
   Google Scholar
• Cobb P. Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educ Res. 1994;23(7):13–20. doi: 10.3102/0013189X023007013
   Google Scholar
• Radmehr F, Drake M. Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension. Int J Math Educ Sci Technol. 2017;48(8):1206–1224.
   Google Scholar
• Radmehr F. Exploring students' learning of integral calculus using revised Bloom's taxonomy [unpublished doctoral dissertation]. Wellington (New Zealand): Victoria University of Wellington; 2016.
   Google Scholar
• Bloom BS, Engelhart MD, Furst EJ, et al. Taxonomy of educational objectives: handbook I: cognitive domain. New York (NY): David McKay; 1956.
   Google Scholar
• Flavell JH. Metacognition and cognitive monitoring: a new area of cognitive–developmental inquiry. Am Psychol. 1979;34(10):906–911. doi: 10.1037/0003-066X.34.10.906
   Web of Science ®Google Scholar
• Krathwohl DR. A revision of bloom’s taxonomy: an overview. Theory Pract. 2002;41(4):212–218. doi: 10.1207/s15430421tip4104_2
   Web of Science ®Google Scholar
• Su WM, Osisek PJ. The revised bloom’s taxonomy: implications for educating nurses. J Contin Educ Nurs. 2011;42(7):321–327. doi: 10.3928/00220124-20110621-05
   PubMed Web of Science ®Google Scholar
• Näsström G. Interpretation of standards with bloom’s revised taxonomy: a comparison of teachers and assessment experts. Int J Res Method Educ. 2009;32(1):39–51. doi: 10.1080/17437270902749262
   Google Scholar
• Stewart J. Calculus: early transcendentals (6th ed). Australia: Thompson; 2008.
   Google Scholar
• Schneider W, Lockl K. The development of metacognitive knowledge in children and adolescents. In: TJ Perfect, BL Schwartz, editor. Applied metacognition. Cambridge: Cambridge University Press; 2002.
   Google Scholar
• Weinstein CE, Mayer RE. The teaching of learning strategies. In: M Wittrock, editor. Handbook of research on teaching, 3rd ed. New York (NY): Macmillan; 1986. p. 315–327.
   Google Scholar
• Tiong JYS. (2005). Top-down approach to teaching problem solving heuristics in mathematics. https://repository.nie.edu.sg/bitstream/10497/2928/1/CRP1_04JH_Conf05%28MES%29_Tiong.pdf.
   Google Scholar
• OECD. PISA 2012 results: ready to learn: students’ engagement, drive and self-beliefs (Vol III). Paris: Author; 2013.
   Google Scholar
• McLeod D. Research on affect in mathematics education: a reconceptualization. In: D Grouws, editor. Handbook of research on mathematics teaching and learning. New York (NY): McMillan; 1992. p. 575–596.
   Google Scholar
• Boaler J. When you believe in yourself your brain operates differently; 2015. https://www.youcubed.org/think-it-up/believe-brain-operates-differently.
   Google Scholar
• Anderson LW. Objectives, evaluation, and the improvement of education. Stud Educ Eval. 2005;31(2):102–113. doi: 10.1016/j.stueduc.2005.05.004
   Google Scholar
• Skemp R. The psychology of learning mathematics. Middlesex (England): Penguin; 1971.
   Google Scholar
• Skemp R. Relational understanding and instrumental understanding. In: DO Tall, MOJ Thomas, editor. Intelligence, learning and understanding in mathematics a tribute to Richard Skemp. Flaxton: Post Pressed; 1976. p. 1–16.
   Google Scholar
• Skemp R. Goals of learning and qualities of understanding. Proceedings of the 3rd conference of the international group for the psychology of mathematics education; 1979; 197–202, Warwick, UK.
   Google Scholar
• Rittle-Johnson B, Schneider M. Developing conceptual and procedural knowledge of mathematics. In: R Cohen Kadosh, A Dowker, editor. Oxford handbook of numerical cognition. Oxford: University Press; 2014.
   Google Scholar
• Radmehr F, Drake M. An assessment-based model for exploring the solving of mathematical problems: utilizing revised bloom's taxonomy and facets of metacognition. Stud Educ Eval. 2018;59:41–51. doi: 10.1016/j.stueduc.2018.02.004
   Web of Science ®Google Scholar
• Mahir N. Conceptual and procedural performance of undergraduate students in integration. Int J Math Educ Sci Technol. 2009;40(2):201–211. doi: 10.1080/00207390802213591
   Google Scholar
• Hiebert J, Lefevre P. Conceptual and procedural knowledge in mathematics: an introductory analysis. In: J Hiebert, editor. Conceptual and procedural knowledge: the case of mathematics. Hillsdale, New York: Erlbaum; 1986. p. 1–27.
   Google Scholar
• Baroody AJ, Feil Y, Johnson AR. An alternative reconceptualization of procedural and conceptual knowledge. J Res Math Educ. 2007;38(2):115–131.
   Web of Science ®Google Scholar
• Mish FC, editors. Merriam-Webster's collegiate dictionary. 10th ed. Springfield (MA): Merriam-Webster Inc.; 1999.
   Google Scholar
• Canobi KH. Concept-procedure interactions in children's addition and subtraction. J Exp Child Psychol. 2009;102(2):131–149. doi: 10.1016/j.jecp.2008.07.008
   PubMed Web of Science ®Google Scholar
• Gray EM, Tall DO. Duality, ambiguity, and flexibility: a “proceptual” view of simple arithmetic. J Res Math Educ. 1994;25(2):116–140. doi: 10.2307/749505
   Web of Science ®Google Scholar
• Silver E. Using conceptual and procedural knowledge: a focus on relationships. In: J Hiebert, editor. Conceptual and procedural knowledge, The case of mathematics. Hillsdale (NY): Erlbaum; 1986. p. 181–198.
   Google Scholar
• Inglis M. Review of APOS theory: a framework for research and curriculum development in mathematics education. Int J Res Under Math Educ. 2015;1(1):413–417. doi:10.1007/s40753-015-0015-9.
   Google Scholar
• Bayazit I. The influence of teaching on student learning: the notion of piecewise function. Int Electron J Math Educ. 2010;5(3):146–164.
   Google Scholar
• Dubinsky E, Wilson R. High school students’ understanding of the function concept. J Math Behav. 2013;32(1):83–101. doi: 10.1016/j.jmathb.2012.12.001
   Google Scholar
• Piaget J, Garcia R. Psychogenesis and the history of science. Feider H, translator. New York (NY): Columbia University Press; 1989.
   Google Scholar
• Asiala M, Brown A, DeVries D, et al. A framework for research and curriculum development in undergraduate mathematics education. In: Research in Collegiate mathematics education II. CBMS issues in mathematics education. Vol. 6. Providence (RI): American Mathematical Society; 1996. p. 1–32.
   Google Scholar
• Thomas MOJ, Hong YY. The Riemann integral in calculus: students' processes and concepts. Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA); 1996. p. 572–579. Available from: https://www.merga.net.au/documents/RP_Thomas_Hong_1996.pdf
   Google Scholar
• Sfard A. On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educ Stud Math. 1991;22(1):1–36. DOI:10.1007/BF00302715.
   Google Scholar
• de Boer H, Donker AS, Kostons DD, et al. Long-term effects of metacognitive strategy instruction on student academic performance: A meta-analysis. Educ Res Rev. 2018;24(6):98–115. doi: 10.1016/j.edurev.2018.03.002
   Web of Science ®Google Scholar
• Flavell JH, Miller PH, Miller SA. Cognitive development. (NJ): Prentice-Hall; 1993.
   Google Scholar
• Seufert T. The interplay between self-regulation in learning and cognitive load. Educ Res Rev. 2018;24(6):116–129. doi: 10.1016/j.edurev.2018.03.004
   Web of Science ®Google Scholar
• Jacobse AE, Harskamp EG. Towards efficient measurement of metacognition in mathematical problem solving. Metacogn Learn. 2012;7(2):133–149. doi: 10.1007/s11409-012-9088-x
   Web of Science ®Google Scholar
• Lester FK. Building bridges between psychological and mathematics education research on problem solving. In: FK Lester, J Garofalo, editor. Mathematical problem solving. Philadelphia (PA): The Franklin Institute Press; 1982. p. 55–85.
   Google Scholar
• Silver EA. Knowledge organization and mathematical problem solving. In: FK Lester, J Garofalo, editor. Mathematical problem solving. Philadelphia (PA): The Franklin Institute Press; 1982. p. 55–85.
   Google Scholar
• Verschaffel L. Realistic mathematical modelling and problem solving in the upper elementary school: analysis and improvement. In: JHM Hamers, JEH Van Luit, B Csapo, editor. Teaching and learning thinking skills: contexts of learning. Lisse: Swets & Zeitlinger; 1999. p. 215–240.
   Google Scholar
• Depaepe F, De Corte E, Verschaffel L. Teachers’ metacognitive and heuristic approaches to word problem solving: analysis and impact on students’ beliefs and performance. ZDM Math Educ. 2010;42:205–218. doi:10.1007/s11858-009-0221-5.
   Google Scholar
• Garofalo J, Lester FK Jr. Metacognition, cognitive monitoring, and mathematical performance. J Res Math Educ. 1985;16(3):163–176. doi: 10.2307/748391
   Google Scholar
• Efklides A. Metacognition and affect: what can metacognitive experiences tell us about the learning process? Educ Res Rev. 2006;1(1):3–14. doi: 10.1016/j.edurev.2005.11.001
   Google Scholar
• Efklides A. Metacognition: defining its facets and levels of functioning in relation to self-regulation and co-regulation. Eur Psychol. 2008;13(4):277–287. doi: 10.1027/1016-9040.13.4.277
   Web of Science ®Google Scholar
• Kim YR, Park MS, Moore TJ, et al. Multiple levels of metacognition and their elicitation through complex problem-solving tasks. J Math Behav. 2013;32(3):377–396. doi: 10.1016/j.jmathb.2013.04.002
   Google Scholar
• Tarricone P. The taxonomy of metacognition. Hove (East Sussex): Psychology Press; 2011.
   Google Scholar
• Schneider W, Artelt C. Metacognition and mathematics education. ZDM. 2010;42(2):149–161. doi: 10.1007/s11858-010-0240-2
   Google Scholar
• Kitchner KS. Cognition, metacognition, and epistemic cognition. Hum Dev. 1983;26(4):222–232. doi: 10.1159/000272885
   Web of Science ®Google Scholar
• Kuhn D. Theory of mind, metacognition, and reasoning: a life-span perspective. In: Mitchell P, Riggs KJ, editors, Children's reasoning and the mind. Hove: Psychology Press; 2000. p. 301–326.
   Google Scholar
• Bartsch K, Wellman HM. Children talk about the mind. New York (NY): Oxford University Press; 1995.
   Google Scholar
• Schraw G. Promoting general metacognitive awareness. Instr Sci. 1998;26:113–125. doi: 10.1023/A:1003044231033
   Web of Science ®Google Scholar
• Veenman M, Elshout JJ. Changes in the relation between cognitive and metacognitive skills during the acquisition of expertise. Eur J Psychol Educ. 1999;14(4):509–523. doi: 10.1007/BF03172976
   Web of Science ®Google Scholar
• Schöenfeld AH. Mathematical problem solving. New York (NY): Academic Press; 1985.
   Google Scholar
• Schöenfeld AH. What’s all the fuss about metacognitlon? In: AH Schoenfeld, editor. Cognitive science and mathematics education. New Jersey (NY): Lawrence Erlbaum; 1987. p. 189–215.
   Google Scholar
• Schöenfeld AH. Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: DA Grouws, editor. Handbook of research on mathematics teaching. New York (NY): McMilan Publishing; 1992. p. 224–270.
   Google Scholar
• Schöenfeld AH. How we think. A theory of goal-oriented decision making and its educational applications. New York (NY): Routledge; 2010.
   Google Scholar
• Schöenfeld AH. What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice, productively intertwined. Educ Res. 2014;43(8):404–412. doi: 10.3102/0013189X14554450
   Web of Science ®Google Scholar
• Chick H. Cognition in the formal modes: research mathematics and the SOLO taxonomy. Math Educ Res J. 1998;10(2):4–26. doi: 10.1007/BF03217340
   Google Scholar
• Jurdak M. Van Hiele levels and the SOLO taxonomy. Int J Math Educ Sci Technol. 1991;22(1): 57–60. doi: 10.1080/0020739910220109
   Google Scholar
• Özdemir AS, Göktepe Yildiz S. The analysis of elementary mathematics preservice teachers’ spatial orientation skills with SOLO model. Eurasian J Educ Res. 2015;15:217–236. doi: 10.14689/ejer.2015.61.12
   Google Scholar
• Hattie JA, Purdie N. The power of the solo model to address fundamental measurement issues. In Dart B, Boulton-Lewis G, editors, Teaching and learning in higher education. Victoria: ACER; 1998.
   Google Scholar
• Tall D. Building theories: the three worlds of mathematics. For Learn Math. 2004;24(1):29–32.
   Google Scholar
• Tall D. A theory of mathematical growth through embodiment, symbolism and proof. Annales de didactique et de sciences cognitives. 2006; 11: 195–215. Available from: https://mathinfo.unistra.fr/fileadmin/upload/IREM/Publications/Annales_didactique/vol_11_et_suppl/adsc11-2006_008.pdf
   Google Scholar
• Tall D. The transition to formal thinking in mathematics. Math Educ Res J. 2008;20(2):5–24. doi: 10.1007/BF03217474
   Google Scholar