Review

Inquiry-based mathematics education: a call for reform in tertiary education seems unjustified


  • Received: 01 June 2022 Accepted: 01 August 2022 Published: 06 September 2022
  • In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting substantial funding from US government agencies. This resulted in the successful mobilization of regional consortia in many states, uniting over 800 mathematics education practitioners working to reform undergraduate education. Inquiry-based learning is characterized by the fundamental premise that learners should be allowed to learn 'new to them' mathematics without being taught. This progressive idea is based on the assumption that it is best to advance learners to the level of experts by engaging learners in mathematical practices similar to those of practicing mathematicians: creating new definitions, conjectures and proofs - that way, learners are thought to develop 'deep mathematical understanding'.

    However, concerted efforts to radically reform mathematics education must be systematically scrutinized in view of available evidence and theoretical advances in the learning sciences. To that end, this scoping review sought to consolidate the extant research literature from cognitive science and educational psychology, offering a critical commentary on the effectiveness of inquiry-based learning. Our analysis of research articles and books pertaining to the topic revealed that the call for a major reform by the IBME advocates is not justified. Specifically, the general claim that students would learn better (and acquire superior conceptual understanding) if they were not taught is not supported by evidence. Neither is the general claim about the merits of IBME for addressing equity issues in mathematics classrooms.

    Citation: Tanya Evans, Heiko Dietrich. Inquiry-based mathematics education: a call for reform in tertiary education seems unjustified[J]. STEM Education, 2022, 2(3): 221-244. doi: 10.3934/steme.2022014

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  • In the last decade, major efforts have been made to promote inquiry-based mathematics learning at the tertiary level. The Inquiry-Based Mathematics Education (IBME) movement has gained strong momentum among some mathematicians, attracting substantial funding from US government agencies. This resulted in the successful mobilization of regional consortia in many states, uniting over 800 mathematics education practitioners working to reform undergraduate education. Inquiry-based learning is characterized by the fundamental premise that learners should be allowed to learn 'new to them' mathematics without being taught. This progressive idea is based on the assumption that it is best to advance learners to the level of experts by engaging learners in mathematical practices similar to those of practicing mathematicians: creating new definitions, conjectures and proofs - that way, learners are thought to develop 'deep mathematical understanding'.

    However, concerted efforts to radically reform mathematics education must be systematically scrutinized in view of available evidence and theoretical advances in the learning sciences. To that end, this scoping review sought to consolidate the extant research literature from cognitive science and educational psychology, offering a critical commentary on the effectiveness of inquiry-based learning. Our analysis of research articles and books pertaining to the topic revealed that the call for a major reform by the IBME advocates is not justified. Specifically, the general claim that students would learn better (and acquire superior conceptual understanding) if they were not taught is not supported by evidence. Neither is the general claim about the merits of IBME for addressing equity issues in mathematics classrooms.



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    [1]

    Freeman, S., Eddy, S.L., McDonough, M., Smith, M.K., Okoroafor, N., Jordt, H., et al., Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 2014, 111(23): 8410‒8415. https://doi.org/10.1073/pnas.1319030111

    doi: 10.1073/pnas.1319030111
    [2]

    Marmur, O., Key memorable events: A lens on affect, learning, and teaching in the mathematics classroom. The Journal of Mathematical Behavior, 2019, 54: 100673. https://doi.org/10.1016/j.jmathb.2018.09.002

    doi: 10.1016/j.jmathb.2018.09.002
    [3]

    Pritchard, D., Where learning starts? A framework for thinking about lectures in university mathematics. International Journal of Mathematical Education in Science and Technology, 2010, 41(5): 609‒623. https://doi.org/10.1080/00207391003605254

    doi: 10.1080/00207391003605254
    [4]

    Deslauriers, L., McCarty L.S., Miller, K., Callaghan, K. and Kestin, G., Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom. Proceedings of the National Academy of Sciences, 2019, 116(39): 19251–19257. https://doi.org/10.1073/pnas.1821936116

    doi: 10.1073/pnas.1821936116
    [5]

    Strelan, P., Osborn, A. and Palmer, E., The flipped classroom: A meta-analysis of effects on student performance across disciplines and education levels. Educational Research Review, 2020, 30: 100314. https://doi.org/10.1016/j.edurev.2020.100314

    doi: 10.1016/j.edurev.2020.100314
    [6]

    Laursen, S.L. and Rasmussen, C., I on the Prize: Inquiry Approaches in Undergraduate Mathematics. International Journal of Research in Undergraduate Mathematics Education, 2019, 5(1): 129–146. https://doi.org/10.1007/s40753-019-00085-6

    doi: 10.1007/s40753-019-00085-6
    [7]

    Melhuish, K., Fukawa-Connelly, T., Dawkins, P.C., Woods, C., and Weber, K., Collegiate mathematics teaching in proof-based courses: What we now know and what we have yet to learn. The Journal of Mathematical Behavior, 2022, 67: 100986. https://doi.org/10.1016/j.jmathb.2022.100986

    doi: 10.1016/j.jmathb.2022.100986
    [8]

    Laursen, S., Hassi, M.L., Kogan, M., Hunter, A.B. and Weston, T., Evaluation of the IBL mathematics project: Student and instructor outcomes of inquiry-based learning in college mathematics. Colorado University, 2011.

    [9]

    Katz, B.P. and Thoren, E., Introduction to the Special Issue on Teaching Inquiry (Part Ⅰ): Illuminating Inquiry. PRIMUS, 2017, 27(1): 1–7. https://doi.org/10.1080/10511970.2016.1252451

    doi: 10.1080/10511970.2016.1252451
    [10]

    Katz, B.P. and Thoren, E., Introduction to the Special Issue on Teaching Inquiry (Part Ⅱ): Implementing Inquiry. PRIMUS, 2017, 27(2): 165–170. https://doi.org/10.1080/10511970.2016.1252452

    doi: 10.1080/10511970.2016.1252452
    [11]

    Ernst, D.C., Hitchman, T., and Hodge, A., Bringing Inquiry to the First Two Years of College Mathematics. PRIMUS, 2017, 27(7): 641–645. https://doi.org/10.1080/10511970.2017.1393846

    doi: 10.1080/10511970.2017.1393846
    [12]

    Kirschner, P.A., Sweller, J. and Clark, R.E., Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching. Educational Psychologist, 2006, 41(2): 75–86. https://doi.org/10.1207/s15326985ep4102_1

    doi: 10.1207/s15326985ep4102_1
    [13]

    Sweller, J., Kirschner, P.A. and Clark, R.E., Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries. Educational Psychologist, 2007, 42(2): 115–121. https://doi.org/10.1080/00461520701263426

    doi: 10.1080/00461520701263426
    [14]

    Sweller, J., Why Inquiry-based Approaches Harm Students' Learning. The Centre for Independent Studies Analysis Paper, 2021, 24: 1‒10.

    [15]

    Dehaene, S., How We Learn: The New Science of Education and the Brain. 2020: Penguin Books Limited.

    [16]

    Moreno, R., Decreasing cognitive load for novice students: Effects of explanatory versus corrective feedback in discovery-based multimedia. Instructional science, 2004, 32(1): 99–113. https://doi.org/10.1023/B:TRUC.0000021811.66966.1d

    doi: 10.1023/B:TRUC.0000021811.66966.1d
    [17]

    Tuovinen, J.E. and Sweller, J., A comparison of cognitive load associated with discovery learning and worked examples. Journal of educational psychology, 1999, 91(2): 334. https://doi.org/10.1037/0022-0663.91.2.334

    doi: 10.1037/0022-0663.91.2.334
    [18]

    Hattie, J., Visible learning: A synthesis of over 800 meta-analyses relating to achievement. 2008: routledge.

    [19]

    Rousseau, J.J., Emile. Vol. 2. 1817: A. Belin.

    [20]

    Mayer, R.E., Should there be a three-strikes rule against pure discovery learning? American psychologist, 2004, 59(1): 14. https://doi.org/10.1037/0003-066X.59.1.14

    doi: 10.1037/0003-066X.59.1.14
    [21]

    Clark, R.E., Kirschner, P.A. and Sweller, J., Putting students on the path to learning: The case for fully guided instruction. American Educator, 2012, 36(1): 5–11.

    [22]

    Anthony, W., Learning to discover rules by discovery. Journal of Educational Psychology, 1973, 64(3): 325. https://doi.org/10.1037/h0034585

    doi: 10.1037/h0034585
    [23]

    Boud, D., Keogh, R. and Walker, D., Reflection: Turning experience into learning. 2013: Routledge. https://doi.org/10.4324/9781315059051

    [24]

    Kolb, D.A., Toward an Applied Theory of Experiental Learning. Theories of Group Processes, 1975: 33‒56.

    [25]

    Barrows, H.S. and Tamblyn, R.M., Problem-based learning: An approach to medical education. Vol. 1, 1980: Springer Publishing Company.

    [26]

    Papert, S., Mindstorms: Children, Computers, and Powerful Ideas. 1980, New York: Basic Books.

    [27]

    Jonassen, D.H., Objectivism versus constructivism: Do we need a new philosophical paradigm? Educational technology research and development, 1991, 39(3): 5–14. https://doi.org/10.1007/BF02296434

    doi: 10.1007/BF02296434
    [28]

    Bruner, J.S., The act of discovery. Harvard Educational Review, 1961, 31: 21–32.

    [29]

    Bruner, J.S., The art of dicovery, in Understanding Children, M. Sindwani, Editor. 2004, Australian Council for Educational Research: Andrews University.

    [30]

    Atkinson, R.C. and Shiffrin, R.M., Human memory: A proposed system and its control processes. Psychology of learning and motivation, 1968, 2: 89–195. https://doi.org/10.1016/S0079-7421(08)60422-3

    doi: 10.1016/S0079-7421(08)60422-3
    [31]

    Sweller, J., Human cognitive architecture. Handbook of research on educational communications and technology, 2008, 35: 369–381.

    [32]

    Sweller, J., van Merriënboer, J.J. and Paas, F., Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 2019, 31(2): 261–292. https://doi.org/10.1007/s10648-019-09465-5

    doi: 10.1007/s10648-019-09465-5
    [33]

    Inglis, M. and Mejía-Ramos, J.P., Functional explanation in mathematics. Synthese, 2021, 198(26): 6369–6392. https://doi.org/10.1007/s11229-019-02234-5

    doi: 10.1007/s11229-019-02234-5
    [34]

    Fiorella, L. and Mayer, R.E., Learning as a generative activity. 2015: Cambridge University Press. https://doi.org/10.1017/CBO9781107707085

    [35]

    Mayer, R.E. and Moreno, R., Nine ways to reduce cognitive load in multimedia learning. Educational psychologist, 2003, 38(1): 43–52. https://doi.org/10.1207/S15326985EP3801_6

    doi: 10.1207/S15326985EP3801_6
    [36]

    Peterson, L. and Peterson, M.J., Short-term retention of individual verbal items. Journal of experimental psychology, 1959, 58(3): 193. https://doi.org/10.1037/h0049234

    doi: 10.1037/h0049234
    [37]

    Chen, O., Castro-Alonso, J.C., Paas, F. and Sweller, J., Extending cognitive load theory to incorporate working memory resource depletion: evidence from the spacing effect. Educational Psychology Review, 2018, 30(2): 483–501. https://doi.org/10.1007/s10648-017-9426-2

    doi: 10.1007/s10648-017-9426-2
    [38]

    Miller, G.A., The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological review, 1956, 63(2): 81. https://doi.org/10.1037/h0043158

    doi: 10.1037/h0043158
    [39]

    Cowan, N., The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and brain sciences, 2001, 24(1): 87–114. https://doi.org/10.1017/S0140525X01003922

    doi: 10.1017/S0140525X01003922
    [40]

    Clark, J.M. and Paivio, A., Dual coding theory and education. Educational psychology review, 1991, 3(3): 149–210. https://doi.org/10.1007/BF01320076

    doi: 10.1007/BF01320076
    [41]

    Baddeley, A.D. and Hitch, G., Working memory. Psychology of learning and motivation, 1974, 8: 47–89. https://doi.org/10.1016/S0079-7421(08)60452-1

    doi: 10.1016/S0079-7421(08)60452-1
    [42]

    Baddeley, A., Working memory. Science, 1992, 255(5044): 556–559. https://doi.org/10.1126/science.1736359

    doi: 10.1126/science.1736359
    [43]

    Sweller, J., Cognitive load theory. Psychology of learning and motivation, 2011, 55: 37–76. https://doi.org/10.1016/B978-0-12-387691-1.00002-8

    doi: 10.1016/B978-0-12-387691-1.00002-8
    [44]

    Chase, W.G. and Simon, H.A., Perception in chess. Cognitive psychology, 1973, 4(1): 55–81. https://doi.org/10.1016/0010-0285(73)90004-2

    doi: 10.1016/0010-0285(73)90004-2
    [45]

    De Groot, A., Perception and memory versus thought: Some old ideas and recent findings. Problem solving, 1966: 19–50.

    [46]

    Chiesi, H.L., Spilich, G.J. and Voss, J.F., Acquisition of domain-related information in relation to high and low domain knowledge. Journal of verbal learning and verbal behavior, 1979, 18(3): 257–273. https://doi.org/10.1016/S0022-5371(79)90146-4

    doi: 10.1016/S0022-5371(79)90146-4
    [47]

    Larkin, J., McDermott, J., Simon, D.P. and Simon, H.A., Expert and novice performance in solving physics problems. Science, 1980, 208(4450): 1335–1342. https://doi.org/10.1126/science.208.4450.1335

    doi: 10.1126/science.208.4450.1335
    [48]

    Egan, D.E. and Schwartz, B.J., Chunking in recall of symbolic drawings. Memory & cognition, 1979, 7(2): 149–158. https://doi.org/10.3758/BF03197595

    doi: 10.3758/BF03197595
    [49]

    Jeffries, R., The processes involved in designing software. Cognitive skills and their acquisition, 1981: 255–283.

    [50]

    Sweller, J. and Cooper, G.A., The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra. Cognition and Instruction, 1985, 2(1): 59–89. https://doi.org/10.1207/s1532690xci0201_3

    doi: 10.1207/s1532690xci0201_3
    [51]

    Tobias, S. and Duffy, T.M., Constructivist instruction: success or failure. 2009. https://doi.org/10.4324/9780203878842

    [52]

    Alcock, L., Tilting the classroom. 2018.

    [53]

    Luke, A., Direct Instruction is not a solution for Australian schools. EduResearch Matters; AARE blog: a voice for Australian educational researchers, 2014.

    [54]

    Bature, I.J., The Mathematics Teachers Shift from the Traditional Teacher-Centred Classroom to a More Constructivist Student-Centred Epistemology. OALib, 2020, 7(5): 1–26. https://doi.org/10.4236/oalib.1106389

    doi: 10.4236/oalib.1106389
    [55]

    Ashman, G., The truth about teaching: An evidence-informed guide for new teachers. 2018: Sage.

    [56]

    Mayo, P., Gramsci and the politics of education. Capital & Class, 2014, 38(2): 385–398. https://doi.org/10.1177/0309816814533170

    doi: 10.1177/0309816814533170
    [57]

    Sweller, J., Cognitive load during problem solving: Effects on learning. Cognitive science, 1988, 12(2): 257–285. https://doi.org/10.1207/s15516709cog1202_4

    doi: 10.1207/s15516709cog1202_4
    [58]

    Rittle-Johnson, B., Promoting Transfer: Effects of Self-Explanation and Direct Instruction. Child Development, 2006, 77(1): 1–15. https://doi.org/10.1111/j.1467-8624.2006.00852.x

    doi: 10.1111/j.1467-8624.2006.00852.x
    [59]

    Quilici, J.L. and Mayer, R.E., Role of examples in how students learn to categorize statistics word problems. Journal of Educational Psychology, 1996, 88(1): 144. https://doi.org/10.1037/0022-0663.88.1.144

    doi: 10.1037/0022-0663.88.1.144
    [60]

    Chandler, P. and Sweller, J., Cognitive load theory and the format of instruction. Cognition and instruction, 1991, 8(4): 293–332. https://doi.org/10.1207/s1532690xci0804_2

    doi: 10.1207/s1532690xci0804_2
    [61]

    Paas, F., Renkl, A. and Sweller, J., Cognitive load theory and instructional design: Recent developments. Educational psychologist, 2003, 38(1): 1–4. https://doi.org/10.1207/S15326985EP3801_1

    doi: 10.1207/S15326985EP3801_1
    [62]

    Sweller, J., Cognitive load theory, learning difficulty, and instructional design. Learning and instruction, 1994, 4(4): 295–312. https://doi.org/10.1016/0959-4752(94)90003-5

    doi: 10.1016/0959-4752(94)90003-5
    [63]

    Case, R., The development of conceptual structures, in Handbook of child psychology: Cognition, perception, and language, W. Damon (Ed. ), 1998, 2: 745–800.

    [64]

    Alfieri, L., Brooks, P.J. and Aldrich, N.J., Does discovery-based instruction enhance learning? Journal of Educational Psychology, 2011, 103(1): 1–18. https://doi.org/10.1037/a0021017

    doi: 10.1037/a0021017
    [65]

    Slamecka, N.J. and Graf, P., The generation effect: Delineation of a phenomenon. Journal of experimental Psychology: Human learning and Memory, 1978, 4(6): 592. https://doi.org/10.1037/0278-7393.4.6.592

    doi: 10.1037/0278-7393.4.6.592
    [66]

    Geary, D., Principles of evolutionary educational psychology. Learning and Individual Differences, 2002, 12(4): 317–345. https://doi.org/10.1016/S1041-6080(02)00046-8

    doi: 10.1016/S1041-6080(02)00046-8
    [67]

    Geary, D.C., An evolutionarily informed education science. Educational psychologist, 2008, 43(4): 179–195. https://doi.org/10.1080/00461520802392133

    doi: 10.1080/00461520802392133
    [68]

    Wittwer, J. and Renkl, A., Why instructional explanations often do not work: A framework for understanding the effectiveness of instructional explanations. Educational Psychologist, 2008, 43(1): 49–64. https://doi.org/10.1080/00461520701756420

    doi: 10.1080/00461520701756420
    [69]

    Lachner, A., Weinhuber, M. and Nückles, M., To teach or not to teach the conceptual structure of mathematics? Teachers undervalue the potential of Principle-Oriented explanations. Contemporary Educational Psychology, 2019, 58: 175–185. https://doi.org/10.1016/j.cedpsych.2019.03.008

    doi: 10.1016/j.cedpsych.2019.03.008
    [70]

    Wittwer, J. and Renkl, A., How Effective are Instructional Explanations in Example-Based Learning? A Meta-Analytic Review. Educational Psychology Review, 2010, 22(4): 393–409. https://doi.org/10.1007/s10648-010-9136-5

    doi: 10.1007/s10648-010-9136-5
    [71]

    Evans, T., Mejía-Ramos, J.P. and Inglis, M., Do mathematicians and undergraduates agree about explanation quality? Educational Studies in Mathematics, 2022: 1‒23. https://doi.org/10.1007/s10649-022-10164-2

    doi: 10.1007/s10649-022-10164-2
    [72]

    Lawson, A.P. and Mayer, R.E., Benefits of Writing an Explanation During Pauses in Multimedia Lessons. Educational Psychology Review, 2021, 33(4): 1859‒1885. https://doi.org/10.1007/s10648-021-09594-w

    doi: 10.1007/s10648-021-09594-w
    [73]

    Hodds, M., Alcock, L. and Inglis, M., Self-explanation training improves proof comprehension. Journal for Research in Mathematics Education, 2014, 45(1): 62–101. https://doi.org/10.5951/jresematheduc.45.1.0062

    doi: 10.5951/jresematheduc.45.1.0062
    [74]

    Rittle-Johnson, B., Loehr, A.M. and Durkin, K., Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM, 2017, 49(4): 599–611. https://doi.org/10.1007/s11858-017-0834-z

    doi: 10.1007/s11858-017-0834-z
    [75]

    Renkl, A., Learning mathematics from worked-out examples: Analyzing and fostering self-explanations. European Journal of Psychology of Education, 1999, 14(4): 477–488. https://doi.org/10.1007/BF03172974

    doi: 10.1007/BF03172974
    [76]

    Lachner, A., Backfisch, I., Hoogerheide, V., van Gog, T. and Renkl, A., Timing matters! Explaining between study phases enhances students' learning. Journal of Educational Psychology, 2020, 112(4): 841. https://doi.org/10.1037/edu0000396

    doi: 10.1037/edu0000396
    [77]

    Ashman, G., Kalyuga, S. and Sweller, J., Problem-solving or Explicit Instruction: Which Should Go First When Element Interactivity Is High? Educational Psychology Review, 2020, 32(1): 229–247. https://doi.org/10.1007/s10648-019-09500-5

    doi: 10.1007/s10648-019-09500-5
    [78]

    Lachner, A. and Nückles, M., Tell me why! Content knowledge predicts process-orientation of math researchers' and math teachers' explanations. Instructional Science, 2016, 44(3): 221–242. https://doi.org/10.1007/s11251-015-9365-6

    doi: 10.1007/s11251-015-9365-6
    [79]

    Chi, M.T., Feltovich, P.J. and Glaser, R., Categorization and representation of physics problems by experts and novices. Cognitive science, 1981, 5(2): 121–152. https://doi.org/10.1207/s15516709cog0502_2

    doi: 10.1207/s15516709cog0502_2
    [80]

    Lachner, A. and Nückles, M., Bothered by abstractness or engaged by cohesion? Experts' explanations enhance novices' deep-learning. Journal of Experimental Psychology: Applied, 2015, 21(1): 101. https://doi.org/10.1037/xap0000038

    doi: 10.1037/xap0000038
    [81]

    Kalyuga, S., Renkl, A. and Paas, F., Facilitating flexible problem solving: A cognitive load perspective. Educational Psychology Review, 2010, 22(2): 175–186. https://doi.org/10.1007/s10648-010-9132-9

    doi: 10.1007/s10648-010-9132-9
    [82]

    Piaget, J., Piaget's theory. In P.H. Mussen (Ed. ), Carmichael's manual of child psychology (Vol. 1). NY: Wiley, 1970.

    [83]

    Bredderman, T., Effects of activity-based elementary science on student outcomes: A quantitative synthesis. Review of Educational research, 1983, 53(4): 499–518. https://doi.org/10.3102/00346543053004499

    doi: 10.3102/00346543053004499
    [84]

    McDaniel, M.A. and Schlager, M.S., Discovery learning and transfer of problem-solving skills. Cognition and Instruction, 1990, 7(2): 129–159. https://doi.org/10.1207/s1532690xci0702_3

    doi: 10.1207/s1532690xci0702_3
    [85]

    Bisson, M.J., Cilmore, C., Inglis, M. and Jones, I., Measuring Conceptual Understanding Using Comparative Judgement. International Journal of Research in Undergraduate Mathematics Education, 2016, 2(2): 141–164. https://doi.org/10.1007/s40753-016-0024-3

    doi: 10.1007/s40753-016-0024-3
    [86]

    Klahr, D. and Nigam, M., The equivalence of learning paths in early science instruction: Effects of direct instruction and discovery learning. Psychological science, 2004, 15(10): 661–667. https://doi.org/10.1111/j.0956-7976.2004.00737.x

    doi: 10.1111/j.0956-7976.2004.00737.x
    [87]

    Chen, Z. and Klahr, D., All other things being equal: Acquisition and transfer of the control of variables strategy. Child development, 1999, 70(5): 1098–1120. https://doi.org/10.1111/1467-8624.00081

    doi: 10.1111/1467-8624.00081
    [88]

    Klahr, D., Chen, Z. and Toth, E.E., From cognition to instruction to cognition: A case study in elementary school science instruction. 2001.

    [89]

    Kapur, M. and Bielaczyc, K., Designing for productive failure. Journal of the Learning Sciences, 2012, 21(1): 45–83. https://doi.org/10.1080/10508406.2011.591717

    doi: 10.1080/10508406.2011.591717
    [90]

    Kapur, M., Examining productive failure, productive success, unproductive failure, and unproductive success in learning. Educational Psychologist, 2016, 51(2): 289–299. https://doi.org/10.1080/00461520.2016.1155457

    doi: 10.1080/00461520.2016.1155457
    [91]

    Schwartz, D.L., Lindgren, R. and Lewis, S., Constructivism in an age of non-constructivist assessments, in Constructivist instruction: Success or failure, S. Tobias and T.M. Duffy (Eds. ). 2009: 34–61.

    [92]

    Hirshman, E. and Bjork, R.A., The generation effect: Support for a two-factor theory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 1988, 14(3): 484. https://doi.org/10.1037/0278-7393.14.3.484

    doi: 10.1037/0278-7393.14.3.484
    [93]

    Chen, O., Kalyuga, S. and Sweller, J., The expertise reversal effect is a variant of the more general element interactivity effect. Educational Psychology Review, 2017, 29(2): 393–405. https://doi.org/10.1007/s10648-016-9359-1

    doi: 10.1007/s10648-016-9359-1
    [94]

    Kalyuga, S., Chandler, P., Tuovinen, J. and Sweller, J., When problem solving is superior to studying worked examples. Journal of educational psychology, 2001, 93(3): 579. https://doi.org/10.1037/0022-0663.93.3.579

    doi: 10.1037/0022-0663.93.3.579
    [95]

    Chen, O., Kalyuga, S. and Sweller, J., Relations between the worked example and generation effects on immediate and delayed tests. Learning and Instruction, 2016, 45: 20–30. https://doi.org/10.1016/j.learninstruc.2016.06.007

    doi: 10.1016/j.learninstruc.2016.06.007
    [96]

    Tang, G., Ei Turkey, H., Cilli-Turner, E., Savic, M., Karakok, G. and Plaxco, D., Inquiry as an entry point to equity in the classroom. International Journal of Mathematical Education in Science and Technology, 2017, 48: S4–S15. https://doi.org/10.1080/0020739X.2017.1352045

    doi: 10.1080/0020739X.2017.1352045
    [97]

    Hassi, M.L. and Laursen, S.L., Transformative learning: Personal empowerment in learning mathematics. Journal of Transformative Education, 2015, 13(4): 316–340. https://doi.org/10.1177/1541344615587111

    doi: 10.1177/1541344615587111
    [98]

    Laursen, S.L., Hassi, M.L., Kogan, M., Weston, T.J., Benefits for women and men of inquiry-based learning in college mathematics: A multi-institution study. Journal for Research in Mathematics Education, 2014, 45(4): 406–418. https://doi.org/10.5951/jresematheduc.45.4.0406

    doi: 10.5951/jresematheduc.45.4.0406
    [99]

    Johnson, E., Andrews-Larson, C., Keene, K., Melhuish, K., Keller, R. and Fortune, N., Inquiry and gender inequity in the undergraduate mathematics classroom. Journal for Research in Mathematics Education, 2020, 51(4): 504–516. https://doi.org/10.5951/jresematheduc-2020-0043

    doi: 10.5951/jresematheduc-2020-0043
    [100]

    Reinholz, D., Johnson, E., Andrews-Larson, C., Stone-Johnstone, A., Smith, J., Mullins, B., et al., When Active Learning Is Inequitable: Women's Participation Predicts Gender Inequities in Mathematical Performance. Journal for Research in Mathematics Education, 2022, 53(3): 204–226. https://doi.org/10.5951/jresematheduc-2020-0143

    doi: 10.5951/jresematheduc-2020-0143
    [101]

    Chall, J.S., The academic achievement challenge: What really works in the classroom? 2002: Guilford Press.

    [102]

    Van Alten, D.C., Phielix, C., Janssen, J. and Kester, L., Effects of flipping the classroom on learning outcomes and satisfaction: A meta-analysis. Educational Research Review, 2019, 28: 100281. https://doi.org/10.1016/j.edurev.2019.05.003

    doi: 10.1016/j.edurev.2019.05.003
    [103]

    Lindsay, E. and Evans, T., The use of lecture capture in university mathematics education: a systematic review of the research literature. Mathematics Education Research Journal, 2021: 1‒21. https://doi.org/10.1007/s13394-021-00369-8

    doi: 10.1007/s13394-021-00369-8
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