Matematická výkonnost a metakognice žáků základních škol běžných, základních škol Montessori a žáků vyučovaných podle Hejného metody

Roč.24,č.1(2019)
Studia paedagogica

Abstrakt
Empirická sonda je věnována problematice metakognice a výkonnosti v matematice. Cílem příspěvku je porovnat úroveň metakognice a matematické výkonnosti v závislosti na preferovaném z působu vedení výuky (proklamované kurikulum) jako jednoho z možných faktorů ovlivňujících žákovu výkonnost a kompetence. Pro účely této empirické sondy byla zvolena metoda kvaziexperimentu, přičemž byly vybrány tři skupiny žáků: (i) žáci ZŠ Montessori (n = 49), (ii) žáci běžných nespecializovaných ZŠ (n = 63) a (iii) žáci, kteří jsou vyučováni podle Hejného metody (n = 77). Na základě induktivní statistiky byly prokázány jak statisticky významné rozdíly (metakognitivní znalost; bias index), tak i statisticky a zároveň věcně významné rozdíly (výkonnost v matematice; kalibrace). Příčiny těchto diferencí jsou v závěru textu diskutovány a zároveň je poukázáno na limity metodologického šetření.

Klíčová slova:
Hejného metoda; Montessori; matematika; metakognice; kvaziexperiment
Reference

[1] Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. US: Prentice-Hall, Inc.

[2] Bol, L., Hacker, D. J., O'Shea, P., & Allen, D. (2005). The influence of overt practice, achievement level, and explanatory style on calibration accuracy and performance. Journal of Experimental Education, 73(4), 269–290. | DOI 10.3200/JEXE.73.4.269-290

[3] Borkowski, J. G., Milstead, M., & Hale, C. (1988). Components of children's metamemory: Implications for strategy generalization. In F. E. Weinert & M. Perlmutter (Eds.), Memory development: Universal changes and individual differences (s. 73–100). Hillsdale, NJ: Erlbaum.

[4] Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

[5] Brown, A. L., & Palinscar, A. S. (1989). Guided, cooperative learning and individual knowledge acquisition. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (s. 393–451). Hillsdale, NJ: Erlbaum.

[6] Cermat (2006§§). Závěrečná z práva z projektu hodnocení výsledků vzdělávání žáků 5. ročníků základních škol 2006. [on-line]. Dostupné z http://www.cermat.cz/download.php?id_document=1404034181&at=1

[7] Cipro, M. (2002). Galerie světových pedagogů: encyklopedie Prameny výchovy. Praha: M. Cipro.

[8] Česká školní inspekce (2017). Výběrová z jištění výsledků žáků na úrovni 5. a 9. ročníků základních škol ve školním roce 2016/2017 – závěrečná z práva. Praha. Dostupné z http://www.csicr.cz/html/Vyberove_zjistovani_vysledku_zaku_2016_2017/resources/_pdfs_/Vyberove_zjistovani_2016_2017__.pdf

[9] Češková, T. (2016). Výukové situace rozvíjející kompetenci k řešení problémů: teoretický model jako východisko pro analýzu výuky. Pedagogika, 66(5), 530–548.

[10] Desoete, A., & Roeyers, H. (2006). Metacognitive macroevaluations in mathematical problem solving. Learning and Instruction, 16(1), 12–25. | DOI 10.1016/j.learninstruc.2005.12.003

[11] Desoete, A., Roeyers, H., & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities, 34(5), 435–449. | DOI 10.1177/002221940103400505

[12] Dignath, Ch., & Büttner, G. (2008). Components of fostering self-regulated learning among students. A meta-analysis on intervention studies at primary and secondary school level. Metacognition and Learning, 3, 231–264. | DOI 10.1007/s11409-008-9029-x

[13] Disman, M. (2005). Jak se vyrábí sociologická znalost. Praha: Karolinum.

[14] Dohrmann, K. R., Nishida, T. K., Gartner, A., Lipsky, D. K., & Grimm, K. J. (2007). High school outcomes for students in a public Montessori program. Journal of Research in Childhood Education, 22(2), 205–217. | DOI 10.1080/02568540709594622

[15] Dole, J. A., Nokes, J. D., & Drits, D. (2009). Cognitive strategy instruction. In S. E. Israel & G. G. Duffy (Eds.), Handbook of research on reading comprehension (s. 347–372). New York, NY: Routledge.

[16] Duchovičová, J. (2010). Neurodidaktický a psychodidaktický kontext edukácie. Nitra: UKF.

[17] Dunlosky, J., & Metcalfe, J. (2009). Metacognition. Thousand Oaks, CA: Sage Publications.

[18] Dunning, D., Johnson, K., Ehrlinger, J., & Kruger, J. (2003). Why people fail to recognize thein own incompetence. Current Directions in Psychological Science, 12, 83–87. | DOI 10.1111/1467-8721.01235

[19] Flannelly, L. T. (2001). Using feedback to reduce students' judgment bias on test questions. Journal of Nursing Education, 40, 10–16.

[20] Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (s. 231–236). Hillsdale, NJ: Erlbaum.

[21] Flavell, J. H., Miller, P. H., & Miller, S. A. (2002). Cognitive development. Upper Saddle River, NJ: Pearson Education.

[22] Garofalo, J., & Lester Jr, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176. | DOI 10.2307/748391

[23] Glenberg, A. M., & Epstein, W. (1985). Calibration of comprehension. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11(4), 702–718.

[24] Götz, L., Lingel, K., Artelt, C., & Schneider, W. (2013). Mathematisches Strategie wissen für 5. und 6. Klassen (MAESTRA 5-6). Göttingen: Hogrefe.

[25] Grizzle-Martin, T. (2014). The effect of cognitive- and metacognitive-based instruction on problem solving by elementary students with mathematical learning difficulties (Doctoral dissertation, Walden University, USA). Dostupné z http://elibraryusa.state.gov

[26] Hacker, D. J., Bol, L., & Keener, M. C. (2008). Metacognition in education: A focus on calibration. In J. Dunlosky & R. A. Bjork (Eds.), Handbook of metamemory and memory (s. 429–455), Los Angeles, CA: Taylor-Francis.

[27] Hejný, M., & Stehlíková, N. (1999). Číselné představy dětí. Praha: Univerzita Karlova.

[28] Hejný, M., Novotná, J., & Stehlíková, N. (Eds.). (2004). Dvacet pět kapitol z didaktiky matematiky. Praha: Pedagogická fakulta Univerzity Karlovy.

[29] Helmke, A. (2009). Unterrichtsqualität und Lehrerprofessionalität: Diagnose, Evaluation und Verbesserung des Unterrichts. Seelze-Velber: Klett.

[30] Helus, Z. (2006). Sociální psychologie pro učitele. Praha: Grada.

[31] Helvig, R., Rozek-Tedesco, M. A., Tindal, G., Heath, B., & Almond, P. J. (1999). Reading as an access to mathematics problem solving on multiple-choice tests for sixth-grade students. The Journal of Educational Research, 2(93), 113–125.

[32] Hoffman, B. (2010). "I think I can, but I'm afraid to try": The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency. Learning and Individual Differences, 20(3), 276–283. | DOI 10.1016/j.lindif.2010.02.001

[33] Hoffman, B., & Schraw, G. (2009). The influence of self-efficacy and working memory capacity on problem-solving efficiency. Learning and Individual Differences, 19(1), 91–100. | DOI 10.1016/j.lindif.2008.08.001

[34] Chmelicek, B. A. (1992). Impact of cognitive and metacognitive strategies on mathematical performance and attitudes of adolescent (Doctoral dissertation, The University of Iowa, USA). Dostupné z http://elibraryusa.state.gov

[35] Chytrý, V., Pešout, O., & Říčan J. (2014). Preference metakognitivních strategií na pozadí úkolových situací v matematice. Ústí nad Labem: PF UJEP.

[36] Ignacio, G. N., Nieto, B. J. L., & Barona, G. E. (2006). The affective domain in mathematics learning. International Electronic Journal of Mathematics learning, 1(1), 16–32.

[37] Jacobs, J. E., & Paris, S. G. (1987). Children's metacognition about reading: Issues in definition, measurement, and instruction. Educational Psychologist, 22, 255–278.

[38] Koriat, A., Goldsmith, M., Schneider, W., & Nakash-Dura, M. (2001). The credibility of children's testimony: Can children control the accuracy of their memory reports? Journal of Experimental Child Psychology, 79(4), 405–437. | DOI 10.1006/jecp.2000.2612

[39] Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310. | DOI 10.3102/00028312040001281

[40] Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250. | DOI 10.1023/A:1016282811724

[41] Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: How difficulties in recognizing one's own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6), 1121–1134. | DOI 10.1037/0022-3514.77.6.1121

[42] Lai, R. E. (2011). Metacognition: A literature review. Pearson. Dostupné z https://images.pearsonassessments.com/images/tmrs/Metacognition_Literature_Review_Final.pdf

[43] Lillard, A. S. (2012). Preschool children's development in classic Montessori, supplemented Montessori, and conventional programs. Journal of School Psychology, 50(3), 379–401. | DOI 10.1016/j.jsp.2012.01.001

[44] Lokajíčková, V. (2015). Příležitosti k rozvíjení kompetence k učení ve výuce zeměpisu (Doctoral dissertation). Dostupné z http://is.muni.cz/th/237142/pedf_d/

[45] Merenluoto, K., & Lehtinen, E. (2002). Conceptual change in mathematics: Understanding the real numbers. In M. Limón & L. Mason (Eds.), Reconsidering conceptual change: Issues in theory and practice (s. 232–257). Netherlands: Springer.

[46] Mihalca, L., Mengelkamp, C., Schnotz, W., & Paas, F. (2015). Completion problems can reduce the illusions of understanding in a computer-based learning environment on genetics. Contemporary Educational Psychology, 41, 157–171. | DOI 10.1016/j.cedpsych.2015.01.001

[47] Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with disabilities. Journal of Learning Disabilities, 25(4), 230–248. | DOI 10.1177/002221949202500404

[48] Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31(1), 37–44. | DOI 10.2307/30035524

[49] Nelson, L. L. (2012). The effectiveness of metacognitive strategies on 8th grade students in mathematical achievements and problem solving skills (Doctoral dissertation, Southern University and A & M College, USA). Dostupné z http://elibraryusa.state.gov

[50] Nelson, T. O. (1996). Gamma is a measure of the accuracy of predicting performance on one item relative to another item, not the absolute performance on an individual item: comments on Schraw (1995). Applied Cognitive Psychology, 10(3), 257–260. | DOI 10.1002/(SICI)1099-0720(199606)10:3<257::AID-ACP400>3.0.CO;2-9

[51] Nelson, T. O., & Narens, L. (1994). Why investigate metacognition? In J. Metcalfe & A. P. Shimamura (Eds.), Metacognition: Knowing about knowing (s. 1–25). Cambridge, MA: The MIT Press.

[52] Neuenhaus, N., Artelt, C., Lingel, K., & Schneider, W. (2011). Fifth graders metacognitive knowledge: general or domain-specific? European Journal of Psychology of Education, 26(2), 163–178. | DOI 10.1007/s10212-010-0040-7

[53] Nietfeld, J. L., Cao, L., & Osborne, J. W. (2005). Metacognitive monitoring accuracy and student performance in the classroom. Journal of Experimental Education, 74(1), 7–28.

[54] Opravilová, E. (2016). Předškolní pedagogika. Praha: Grada.

[55] Ozsoy, G. (2012). Investigation of Fifth Grade Students' Mathematical Calibration Skills. Educational Sciences: Theory and Practice, 12(2), 1190–1194.

[56] Pappas, S., Ginsburg, H. P., & Jiang, M. (2003). SES differences in young children's metacognition in the context of mathematical problem solving. Cognitive Development, 18(3), 431–450. | DOI 10.1016/S0885-2014(03)00043-1

[57] Paris, S. G., & Winograd, P. (1990). How metacognition can promote academic learning and instruction. In B. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction (s. 15–51). Hillsdale, NJ: Erlbaum.

[58] Pilegard, C., & Mayer, R. E. (2015). Adding judgments of understanding to the metacognitive toolbox. Learning and Individual Differences, 41, 62–72. | DOI 10.1016/j.lindif.2015.07.002

[59] Pintrich, P. R. (2000). The role of goal orientation in self-regulated learning. In M. Boekarts & P. R. Pintrich (Eds.), Handbook of self-regulation (s. 451–502). San Diego, CA: Academic Press.

[60] Polya, G. (1973). How to solve it. Princeton, NJ: Princeton University Press.

[61] Pravdová, B. (2013). Podpora metakognice v pregraduální přípravě studentů učitelství. In J. Duchovičová, Z. Babulicová, & H. Zelená (Eds.), Medzinárodný dialóg o pedagogických a psychologických aspektoch edukácie (s. 60–68). Nitra: PF.

[62] Prins, F. J., Veenman, M. V. J., & Elshout, J. J. (2006). The impact of intellectual ability and metacognition on learning: New support for the threshold of problematicity theory. Learning and Instruction, 16(4), 374–387. | DOI 10.1016/j.learninstruc.2006.07.008

[63] Rawson, K. A., & Dunlosky, J. (2012). When is practice testing most effective for improving the durability and efficiency of student learning? Educational Psychology Review, 24(3), 419–435. | DOI 10.1007/s10648-012-9203-1

[64] Rendl, M., & Vondrová, N. (2014). Kritická místa v matematice u českých žáků na základě výsledků šetření TIMSS 2007. Pedagogická orientace, 24(1), 22–57. | DOI 10.5817/PedOr2014-1-22

[65] Risemberg, R., & Zimmerman, B. J. (1992). Self-regulated learning in gifted students. Roeper Review, 15(1), 225–230. | DOI 10.1080/02783199209553476

[66] Robinson, D. H., & Levin, J. R. (1997). Reflections on statistical and substantive significance, with a slice of replication. Educational Researcher, 26, 21–26.

[67] Roebers, C. M., Moga, N., & Schneider, W. (2001). The role of accuracy motivation on children's and adults' event recall. Journal of Experimental Child Psychology, 78, 313–329. | DOI 10.1006/jecp.2000.2577

[68] Ronzano, S. (2010). Effectiveness of metacognitive strategies for improving reading comprehension in secondary students (Doctoral dissertation). Dostupné z http://elibraryusa.state.gov

[69] Rusek, M., Stárková, D., Chytrý, V., & Bílek, M. (2017). Adoption of ICT innovations by secondary school teachers and pre-service teachers within education. Journal of Baltic Science Education, 16(4), 510–523.

[70] Rýdl, K. (2006). Metoda Montessori pro naše dítě: inspirace pro rodiče a další zájemce. Pardubice: Filozofická fakulta Univerzity Pardubice.

[71] Sarver, M. E. (2006). Metacognition and mathematical problem solving: Case studies for six seventh grade students (Doctoral dissertation, Montclair State University, NJ, USA). Dostupné z http://elibraryusa.state.gov/

[72] Sedláková, M. (2004). Vybrané kapitoly z kognitivní psychologie: Mentální reprezentace a mentální modely. Praha: Grada.

[73] Schneider, W., Schlagmüller, M., & Visé, M. (1998). The impact of metamemory and domain-specific knowledge on memory performance. European Journal of Psychology of Education, 13(1), 91–103. | DOI 10.1007/BF03172815

[74] Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

[75] Schoenfeld, A. H. (1987). What's all the fuss about metacognition. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (s. 189–215). Hillsdale, NJ: Lawrence Erlbaum Associates.

[76] Schraw, G. (1998). Promoting general metacognitive awereness. Instructional Science, 26(1–2), 113–125. | DOI 10.1023/A:1003044231033

[77] Schraw, G. (2009). A conceptual analysis of five measures of metacognitive monitoring. Metacognition and Learning, 4(1), 33–45. | DOI 10.1007/s11409-008-9031-3

[78] Schraw, G., Kuch, F., & Gutierrez, A. P. (2013). Assessing the dimensionality of calibration measures used in monitoring research. Learning and Instruction, 24, 48–57.

[79] Siegler, R. S. (1999). Strategic development. Trends in Cognitive Sciences, 3(11), 430–435. | DOI 10.1016/S1364-6613(99)01372-8

[80] Slezáková, J., & Šubrtová, E. (2015). Matematika všemi smysly aneb Hejného metoda v MŠ, pokus o malou příručku pro kreativní pedagogy. Praha: Step by step ČR.

[81] 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. | DOI 10.1006/ceps.2001.1091

[82] Swanson, H. L. (1992). The relationship between metacognition and problem solving in gifted children. Roeper Review, 15, 43–48. | DOI 10.1080/02783199209553457

[83] Tavakol, M., & Dennick, R. (2011). Making sense of Cronbach's alpha. International Journal of Medical Education, 2, 53–55. | DOI 10.5116/ijme.4dfb.8dfd

[84] Thiede, K. W., Griffin, T. D., & Wiley, J. (2011). Test expectancy affects metacomprehension accuracy. British Journal of Educational Psychology, 81(2), 264–273. | DOI 10.1348/135910710X510494

[85] Tobias, S., & Everson, H. T. (2002). Knowing what you know and what you don't: Further research on metacognitive knowledge monitoring. New York: College Entrace Examination Board.

[86] Veenman, M. V. J., & Spaans, M. A. (2005). Relation between intellectual and metacognitive skills: Age and task differences. Learning and Individual Differences, 15, 159–176. | DOI 10.1016/j.lindif.2004.12.001

[87] Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Affenbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition and Learning, 1, 3–14. | DOI 10.1007/s11409-006-6893-0

[88] Walsh, B. A., & Petty, K. (2007). Frequency of six early childhood education approaches: A 10-year content analysis of early childhood education journal. Early Childhood Education Journal, 34(5), 301–305. | DOI 10.1007/s10643-006-0080-4

[89] Wang, M., Haertel, G., & Walberg, J. H. (1990). What influences learning? A content analysis of review literature. Journal of Educational Psychology, 84, 30–43.

[90] Wirth, J., & Leutner, D. (2008). Self-regulated learning as a competence. Zeitschrift für Psychologie/Journal of Psychology, 216(2), 102–110. | DOI 10.1027/0044-3409.216.2.102

[91] Zimmerman, B. J. (1990). Self-regulated learning and academic achievement: An overview. Educational Psychologist, 25(1), 3–17. | DOI 10.1207/s15326985ep2501_2

[92] Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory into Practice, 41(2), 64–70. | DOI 10.1207/s15430421tip4102_2

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