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The value of fixed versus faded self-regulatory scaffolds on fourth graders’ mathematical problem solving

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Abstract

Research has indicated that students can be taught self-regulated learning (SRL) in scaffolding programs focusing on a fixed continuous practice (e.g., metacognitive question prompts). However, the fading role of scaffolding to prepare autonomous learning is often an overlooked component. A unique approach for fading is suggested that offers a graduated reduction model of scaffolding prompts according to the SRL phases involved in the solution, which allows assimilation of processes to prepare learners for autonomous activity. This quasi-experimental study of fourth-graders (n = 134) examines the effectiveness of metacognitive self-question prompts in a Fixed (continuous) versus Faded (graduated reduction) scaffolds model during planning, monitoring and reflection phases, on the facilitation of students’ SRL (metacognition, calibration of confidence judgment, motivation), and sense making of mathematical problem solving at the end of the program (short-term effect) and 3 months later (long-term/lasting effect). Findings indicated that the Faded Group performed best in the metacognition knowledge aspect, motivation in the performance goal approach increased and, in the avoidance, goal decreased. No differences were found between the groups on the regulation aspect and calibration of confidence judgment in the solution success. Additionally, the Faded Group outperformed the Fixed Group on sense making of problem solving. These findings were manifested particularly in the long-term effect. The study supports theoretical claims relating the role of fading scaffolds to increase students’ autonomous SRL (metacognition, motivation) and improvements in sense making, particularly on the long-term retention effect.

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References

  • Abdullah, N., Halim, L., & Zakaria, E. (2014). VStops: A thinking strategy and visual representation approach in mathematical word problem solving toward enhancing STEM literacy. Eurasia Journal of Mathematics, Science & Technology Education, 10(3), 165–174.

    Google Scholar 

  • Adler, I., Schwartz, L., Madjar, N., & Zion, M. (2016). Reading between the lines: The effect of contextual factors on student motivation throughout an open inquiry process. Science Education, 102(4), 820–855.

    Article  Google Scholar 

  • Al-Harthy, I., & Was, C. (2010). Goals, efficacy and metacognitive self-regulation: A path analysis. International Journal of Education, 2(1), 1–2.

    Article  Google Scholar 

  • Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84(3), 261–271.

    Article  Google Scholar 

  • Ariës, R. J., Ghysels, J., Groot, W., & Van den Brink, H. M. (2015). Is working memory training effective in enhancing school based reasoning achievements? A systematic review. TIER working paper series.

  • Ariës, R. J., Groot, W., & Van den Brink, H. M. (2014). Improving reasoning skills in secondary history education by working memory training. British Educational Research Journal, 41(2), 210–228. https://doi.org/10.1002/berj.3142.

    Article  Google Scholar 

  • Azevedo, R. (2014). Issues in dealing with sequential and temporal characteristics of elf- and socially-regulated learning. Metacognition and Learning, 9(2), 217–228. https://doi.org/10.1007/s11409-014-9123-1.

    Article  Google Scholar 

  • Baddeley, A. (1992). Working memory. Science, 255(5044), 556–559.

    Article  Google Scholar 

  • Bannert, M., & Mengelkamp, C. (2013). Scaffolding hypermedia learning through metacognitive prompts. In R. Azevedo & V. Aleven (Eds.), International handbook of metacognition and learning technologies (pp. 171–186). New York: Springer. https://doi.org/10.1007/978-1-4419-5546-3_12.

    Chapter  Google Scholar 

  • Bannert, M., & Reimann, P. (2012). Supporting self-regulated hypermedia learning through prompts. Instructional Science, 40(1), 193–211. https://doi.org/10.1007/s11251-011-9167-4.

    Article  Google Scholar 

  • Bannert, M., Sonnenberg, C., Mengelkamp, C., & Pieger, E. (2015). Short- and long-term effects of students’ self-directed metacognitive prompts on navigation behavior and learning performance. Computers in Human Behavior, 52, 293–306.

    Article  Google Scholar 

  • Belland, B. R., Walker, A. E., Kim, N. J., & Lefler, M. (2017). Synthesizing results from empirical research on computer-based scaffolding in STEM education: A Meta-Analysis. Review of Educational Research, 87(2), 309–344. https://doi.org/10.3102/0034654316670999.

    Article  Google Scholar 

  • Boekaerts, M., & Corno, L. (2005). Self-regulation in the classroom: A perspective on assessment and intervention. Applied Psychology: An International Review, 54, 199–231.

    Article  Google Scholar 

  • Brown, A. (1987). Metacognition, executive control, self-regulation, and other more mysterious mechanisms. In F. Weinert & R. Kluwe (Eds.), Metacognition, motivation and understanding (pp. 65–116). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Bulu, S., & Pedersen, S. (2010). Scaffolding middle school students’ content knowledge and ill-structured problem solving in a problem-based hypermedia-learning environment. Educational Technology Research and Development, 58, 507–529. https://doi.org/10.1007/s11423-010-9150-9.

    Article  Google Scholar 

  • Cabello, V. M., & Sommer Lohrmann, M. E. (2018). In T. Andre (Ed.), Advances in human factors in training, education, and learning sciences, advances in intelligent systems and computing 596 (pp. 350–360). https://doi.org/10.1007/978-3-319-60018-5_34.

    Chapter  Google Scholar 

  • Chatzistamatiou, M., Dermitzaki, I., Efklides, A., & Angeliki, L. (2015). Motivational and affective determinants of self-regulatory strategy use in elementary school mathematics. Educational Psychology, 35(7), 835–850. https://doi.org/10.1080/01443410.2013.822960.

    Article  Google Scholar 

  • Cleary, T. J., Velardi, B., & Schnaidman, B. (2017). Effects of the self-regulation empowerment program (SREP) on middle school students’ strategic skills, self-efficacy, and mathematics achievement. Journal of School Psychology, 64, 28–42. https://doi.org/10.1016/j.jsp.2017.04.004.

    Article  Google Scholar 

  • Davis, E. A. (2003). Prompting middle school science students for productive reflection: Generic and directed prompts. Journal of the Learning Sciences, 12(1), 91–142.

    Article  Google Scholar 

  • Devoldr, A., van Braak, J., & Tondeur, J. (2012). Supporting self-regulated learning in computer-based learning environments: systematic review of effects of scaffolding in the domain of science education. Journal of Computer Assisted Learning, 28(6), 557–573.

    Article  Google Scholar 

  • Dignath, C., Buettner, G., & Langfeldt, H. P. (2008). How can primary school students learn self-regulated learning strategies most effectively? : A meta-analysis on self-regulation training programmes. Educational Research Review, 3(2), 101–129.

    Article  Google Scholar 

  • Dweck, C. S. (1986). Motivational processes affecting learning. American Psychologist, 41, 1040–1048.

    Article  Google Scholar 

  • Dweck, C. S., & Leggett, E. L. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95, 256–272.

    Article  Google Scholar 

  • Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL Model. Educational Psychologist, 46(1), 6–25.

    Article  Google Scholar 

  • Elliot, A. (1997). Integrating the ‘‘classic’’ and ‘‘contemporary’’ approaches to achievement motivation: A hierarchical model of approach and avoidance achievement motivation. In M. L. Maehr & P. R. Pintrich (Eds.), Advances in motivation and achievement (Vol. 10, pp. 143–179). Greenwich, CT: JAI Press.

    Google Scholar 

  • Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34, 906–911. https://doi.org/10.1037/0003-066X.34.10.906.

    Article  Google Scholar 

  • Ge, X., Law, V., & Huang, K. (2012). Diagnosis, supporting, and fading: A scaffolding design framework for adaptive e-learning systems. In H. Wang (Ed.), Interactivity in E-learning: case studies and frameworks (pp. 116–142). Hershey, PA: IGI Global.

    Chapter  Google Scholar 

  • Gidalevich, S., & Kramarski, B. (2017). Metacognitive guidance for self-regulation judgements in various phases: A thinking aloud analysis in mathematics. Hellenic Journal of Psychology, 14, 88–113.

    Google Scholar 

  • Goldberg, E. (2010). Het sturende brein: Onze hersenen in een complexe wereld [The new executive brain: Frontal lobes in a complex world]. Amsterdam: Wereldbibliotheek.

    Google Scholar 

  • Greene, J. A., & Azevedo, R. (2010). The measurement of learners’ self-regulated cognitive and metacognitive processes while using computer-based learning environments. Educational Psychologist, 45(4), 203–209. https://doi.org/10.1080/00461520.2010.515935.

    Article  Google Scholar 

  • Hoffman, B., & Spatariu, A. (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 33(4), 875–893.

    Article  Google Scholar 

  • Huff, J. D., & Nietfeld, J. L. (2009). Using strategy instruction and confidence judgments to improve metacognitive monitoring. Metacognition Learning, 4(2), 161–176. https://doi.org/10.1007/s11409-009-9042-8.

    Article  Google Scholar 

  • Ifenthaler, D. (2012). Determining the effectiveness of prompts for self-regulated earning in problem-solving scenarios. Educational Technology & Society, 15(1), 38–52.

    Google Scholar 

  • Israeli Ministry of Education. (2005). School efficiency and growth measures test for 4PthP graders—Version A. Jerusalem: Department of Assessment and Measurement. in Education.

    Google Scholar 

  • Jaakkola, T., & Veermans, K. (2018). Exploring the effects of concreteness fading across grades in elementary school science education. Instructional Science, 46(2), 185–207.

    Article  Google Scholar 

  • Kaplan, A., & Maehr, L. M. (2002). Adolescents’ achievement goals: situating motivation in socio-cultural contexts. In T. Urdan & F. Pajaers (Eds.), Academic motivation of adolescents. Adolescence and education (Vol. 2, pp. 125–167). Greenwich, CT: Iinformation Age.

    Google Scholar 

  • Kester, L., & Kirschner, P. A. (2009). Effects of fading support on hypertext navigation and performance in student-centered e-learning environments. Interactive Learning Environments, 17(2), 165–179. https://doi.org/10.1080/10494820802054992.

    Article  Google Scholar 

  • Kim, C., & Pekrun, R. (2014). Emotions and motivation in learning and performance. In J. M. Spector, M. D. Merrill, J. Elen, & M. J. Bishop (Eds.), Handbook of research on educational communications and technology (pp. 65–75). New York: Springer.

    Chapter  Google Scholar 

  • Kistner, S., Rakoczy, K., Otto, B., Dignath-van Ewijk, C., Büttner, G., & Klieme, E. (2010). Promotion of self-regulated learning in classrooms: Investigating fre-quency, quality, and consequences for student performance. Metacognition and Learning, 5(2), 157–171.

    Article  Google Scholar 

  • Koedinger, K. R., & Aleven, V. (2007). Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review, 19, 239–264.

    Article  Google Scholar 

  • Kramarski, B. (2017). Teachers as agents in promoting students' SRL and performance: Applications for teachers' dual-role training program. In D. H. Schunk & J.A. Greene (Eds.), Handbook of self-regulation of learning and performance (pp. 223–239). New York: Springer.

    Chapter  Google Scholar 

  • Kramarski, B., & Fridman, S. (2014). Solicited versus unsolicited metacognitive prompts for fostering mathematical problem-solving using multimedia. Journal of Educational Computing Research, 50(3), 285–314.

    Article  Google Scholar 

  • Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: Effects of cooperative learning and metacognitive training. American Educational Research Journal, 40, 281–310. https://doi.org/10.3102/00028312040001281.

    Article  Google Scholar 

  • Kramarski, B., & Revach, T. (2009). The challenge of self-regulated learning in mathematics teachers’ professional training. Educational Studies in Mathematics, 72(3), 379–399.

    Article  Google Scholar 

  • Kramarski, B., Weiss, I., & Sharon, S. (2013). Generic versus context-specific prompts for supporting self-regulation in mathematical problem solving among students with low or high prior knowledge. Journal of Cognitive Education and Psychology, 12, 197–214. https://doi.org/10.1891/1945-8959.12.2.97.

    Article  Google Scholar 

  • Kuhn, D., & Dean, D. (2004). A bridge between cognitive psychology and educational practice. Theory into Practice, 43(4), 268–273.

    Article  Google Scholar 

  • Labuhn, A. S., Zimmerman, B. J., & Hasselhorn, M. (2010). Enhancing students’ self-regulation and mathematics performance: the influence of feedback and self-evaluative standards. Metacognition and Learning, 5(2), 173–194. https://doi.org/10.1007/s11409-010-9056-2.

    Article  Google Scholar 

  • Lee, H. & Songer, N. B. (2004). Expanding an understanding of scaffolding theory using an inquiry-fostering science program. Understanding scafolding. The Journal of the Learning Sciences, October.

  • Mayer, R. E. (2009). Multimedia learning (2nd ed.). New York: Cambridge University Press.

    Book  Google Scholar 

  • McNeill, K. L., Lizotte, D. J., Krajcik, J., & Marx, R. W. (2006). Supporting students’ construction of scientific explanations by fading scaffolds in instructional materials. Journal of the Learning Sciences, 15(2), 153–191.

    Article  Google Scholar 

  • Meece, J. L. (1994). Individual and classroom differences in students’ achievement goal patterns. In D. Schunk & B. Zimmerman (Eds.), Self-regulated learning: Definitions and issues (pp. 25–44). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classroom. American Educational Research Journal, 34, 365–395. https://doi.org/10.3102/0028312034002365.

    Article  Google Scholar 

  • Mevarech, Z. R., & Kramarski, B. (2014). Critical maths for innovative societies: The role of meta-cognitive pedagogies. Paris: OECD. https://doi.org/10.1787/9789264223561-en.

    Book  Google Scholar 

  • Midgley, C., Maehr, M., Hruda, L., Anderman, E., Anderman, L., Freeman, K., …Urdan, T. (2000). Manual for the patterns of adaptive learning scales. Ann Arbor, MI: University of Michigan.

  • Mihalca, L., Mengelkamp, C., & Schnotz, W. (2017). Accuracy of metacognitive judgments as a moderator of learner control effectiveness in problem-solving tasks. Metacognition and Learning, 12(3), 357–379. https://doi.org/10.1007/s11409-017-9173-2.

    Article  Google Scholar 

  • Moos, D. C., & Ringdal, A. (2012). Self-regulated learning in the classroom: A literature review on the teacher’s role. Education Research International. https://doi.org/10.1155/2012/423284.

    Article  Google Scholar 

  • Müller, N. M., & Seufert, T. (2018). Effects of self-regulation prompts in hypermedia learning on learning performance and self-efficacy. Learning and Instruction, 58, 1–11. https://doi.org/10.1016/j.learninstruc.2018.04.011.

    Article  Google Scholar 

  • Narciss, S., Proske, A., & Koerndle, H. (2007). Promoting self-regulated learning in webbased learning environments. Computers in Human Behavior, 23, 1126–1144.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM). (2009). Focus on HIGH SCHOOL MATHEMATICS: Reasoning and sense making. Reston, VA: NCTM.

    Google Scholar 

  • Nelson, T. O., & Narens, L. (1994). Why investigate metacognition?. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Nolen, S. B. (1988). Reasons for studying: Motivational orientation and strategies. Cognition and Instruction, 5, 269–287.

    Article  Google Scholar 

  • Panadero, E., Tapia, J. A., & Huertas, J. A. (2012). Rubrics and self-assessment scripts effects on self-regulation, learning and self-efficacy in secondary education. Learning and Individual Differences, 22(6), 806–813.

    Article  Google Scholar 

  • Patrick, H., Ryan, A. M., & Kaplan, A. (2007). Early adolescents’ perceptions of the classroom social environment, motivational beliefs, and engagement. Journal of Educational Psychology, 99, 83–98.

    Article  Google Scholar 

  • Pea, R. D. (2004). The social and technological dimensions of scaffolding and related theoretical concepts for learning, education, and human activity. The Journal of the Learning Sciences, 13(3), 423–451.

    Article  Google Scholar 

  • Pintrich, P. R. (2000). The role of goal orientation in self-regulated learning. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 451–502). San Diego: Academic.

    Chapter  Google Scholar 

  • Pintrich, P. R. (2002). The role of metacognitive knowledge in learning, teaching, and assessing. Theory Into Practice, 41(4), 219–225.

    Article  Google Scholar 

  • Pintrich, P. R., Wolters, C., & Baxter, G. (2000). Assessing metacognition and self-regulated learning. In G. Schraw & J. Impara (Eds.), Issues in the measurement of metacognition (pp. 43–97). Lincoln, NE: Buros Institute of Mental Measurements.

    Google Scholar 

  • Puntambekar, S., & Hubscher, R. (2005). Tools for scaffolding students in a complex learning environment: What have we gained and what have we missed? Educational Psychologist, 40(1), 1–12. https://doi.org/10.1207/s15326985ep4001_1.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561–574.

    Article  Google Scholar 

  • Roderer, T., & Roebers, C. M. (2010). Explicit and implicit confidence judgments and developmental differences in metamemory: An eye-tracking approach. Metacognition and Learning, 5(3), 229–250. https://doi.org/10.1007/s11409-010-9059-z.

    Article  Google Scholar 

  • Roebers, C. M., Krebs, S. S., & Roderer, T. (2014). Metacognitive monitoring and control in elementary school children: Their interrelations and their role for test performance. Learning and Individual Differences, 29, 141–149.

    Article  Google Scholar 

  • Salomon, G., & Perkins, D. N. (1989). Rocky roads to transfer: Rethinking mechanism of a neglected phenomenon. Educational Psychologist, 24(2), 113–142. https://doi.org/10.1207/s15326985ep2402_1.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 165–197). New York: MacMillan.

    Google Scholar 

  • Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1–2), 113–125.

    Article  Google Scholar 

  • Schraw, G. (2009). A conceptual analysis of five measures of metacognitive monitoring. Metacognition Learning, 4(1), 33–45. https://doi.org/10.1007/s11409-008-9031-3.

    Article  Google Scholar 

  • Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19, 460–475.

    Article  Google Scholar 

  • Schunk, D. H. (1991). Self-efficacy and academic motivation. Educational Psychologist, 26, 207–232.

    Article  Google Scholar 

  • Seo, D., & Kim, J. (2001). Expanding a goal mediational model: The Korean elementary school math class. Academic Exchange Quarterly, 5, 177–183.

    Google Scholar 

  • Shin, H., Bjorklund, D. F., & Beck, E. F. (2007). The adaptive nature of children’s overestimation in a strategic memory task. Cognitive Development, 22, 197–212.

    Article  Google Scholar 

  • Sperling, R. A., Howard, B. C., Miller, L. A., & Murphy, C. (2002). Measures of children’s knowledge and regulation of cognition. Contemporary Educational Psychology, 27(1), 51–79. https://doi.org/10.1006/ceps.2001.1091.

    Article  Google Scholar 

  • Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognition and Science, 12, 257–285.

    Article  Google Scholar 

  • Tawfik, A. A., Law, V., Ge, X., Xing, W., & Kim, K. (2018). The effect of sustained versus faded scaffolding on students’ argumentation in ill-structured problem solving. Computers in Human Behavior. https://doi.org/10.1016/j.chb.2018.01.035.

    Article  Google Scholar 

  • Tomlinson, C. A. (2005). Quality curriculum and instruction for highly able students. Theory into Practice, 44(2), 160–166.

    Article  Google Scholar 

  • Trends in International Mathematics and Science Study—TIMSS. (2011). Mathematics Frameworks, 2011. Retrieved from http://timss.bc.edu/index.html. Accessed 28 Nov 2018.

  • Tzohar-Rozen, M., & Kramarski, B. (2014). Metacognition, motivation and emotions: Contribution of self-regulated learning to solving mathematical problems. Global Education Review, 1(4), 76–95.

    Google Scholar 

  • Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1, 3–14.

    Article  Google Scholar 

  • Veenman, M. V. J., Wilhelm, P., & Beishuizen, J. J. (2004). The relation between intellectual and metacognitive skills from a developmental perspective. Learning and Instruction, 14(1), 89–109. https://doi.org/10.1016/j.learninstruc.2003.10.004.

    Article  Google Scholar 

  • Vrugt, A., & Oort, F. J. (2008). Metacognition, achievement goals, study strategies and academic achievement: Pathways to achievement. Metacognition & Learning, 30, 123–146.

    Article  Google Scholar 

  • Watts, T. W., Clements, D. H., Sarama, J., Wolfe, C. B., Spitler, M. E., & Bailey, D. H. (2016). Does early mathematics intervention change the processes underlying children’s learning? Journal of Research on Educational Effectiveness. https://doi.org/10.1080/19345747.2016.1204640.

    Article  Google Scholar 

  • Weinstein, C. E., Acee, T. W., & Jung, J. (2011). Self-regulation and learning strategies. New Directions for Teaching and Learning, 126, 45–53.

    Article  Google Scholar 

  • Winne, P. H. (1996). A metacognitive view of individual differences in self-regulated learning. Learning and Individual Differences, 8, 327–353.

    Article  Google Scholar 

  • Winne, P., & Perry, N. (2000). Measuring self-regulated learning. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 531–566). San Diego, CA: Academic Press.

    Chapter  Google Scholar 

  • Wolters, C. A. (2004). Advancing achievement goal theory: Using goal structures and goal-orientations to predict students’ motivation, cognition and achievement. Journal of Educational Psychology, 96, 236–250.

    Article  Google Scholar 

  • Zheng, L. (2016). The effectiveness of self-regulated learning scaffolds on academic performance in computer-based learning environments: a meta-analysis. Asia Pacific Education Review, 17(2), 187–202.

    Article  Google Scholar 

  • Zimmerman, B. J. (2000). Attaining self-regulation: A social cognitive perspective. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 13–39). San Diego: Academic Press.

    Chapter  Google Scholar 

  • Zimmerman, B. J. (2008). Investigating self-regulation and motivation: Historical background, methodological developments, and future prospects. American Educational Research Journal, 45(1), 166–183. https://doi.org/10.3102/0002831207312909.

    Article  Google Scholar 

  • Zimmerman, B. J., Moylan, A., Hudesman, J., White, N., & Flugman, B. (2011). Enhancing self-reflection and mathematics achievement of at-risk urban technical college students. Psychological Test and Assessment Modeling, 53(1), 108–127.

    Google Scholar 

  • Zusho, A., & Edwards, K. (2011). Self-regulation and achievement goals in the college classroom. New Directions for Teaching and Learning, 126, 117–124.

    Google Scholar 

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Acknowledgements

We confirm that we have reported all measures, conditions, data exclusions, and how we determined our sample sizes. This research was supported by Oranim Academic College of Education.

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Correspondence to Stella Gidalevich.

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Appendices

Appendix A

See Appendix Tables 3 and 4.

Table 3 Means (and SD) of the dependent variables by class at each time point in the Fixed group
Table 4 Means (and SD) of the dependent variables by class at each time point in the Faded group

Appendix B

  1. 1.

    Confidence Judgments—CJ: Assessing the correctness of one’s performance after the solution.

    figure a
  2. 2.

    Sense making of problem solving task

    figure b

Expected answer

Grading

106 students

Path of the solution:

12 × 6 + 8 × 4 + 2 = 106

Or according to the phases:

12 X 6 = 72

8 X 4 = 32

72 + 32 + 2 = 106

100 pts—correct answer and correct presentation of the solution path

50 pts—correct presentation of the solution path but wrong answer, or correct final answer without presentation of the solution path or a wrong presentation of the solution path

0 pts—wrong answer without presenting the solution path or with presenting a wrong solution path

Appendix C: Pearson correlation coefficients between the three aspects of the SRL (N = 134)

See Appendix Tables 5, 6 and 7.

Table 5 T1
Table 6 T2
Table 7 T3

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Gidalevich, S., Kramarski, B. The value of fixed versus faded self-regulatory scaffolds on fourth graders’ mathematical problem solving. Instr Sci 47, 39–68 (2019). https://doi.org/10.1007/s11251-018-9475-z

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