Vliv procvičování na Khan Academy na znalosti a dovednosti žáků v matematice

Jiří Vančura

doi:10.14712/18047106.1520

Vol. 10 No. 2 (2019): SciED Research Reports

Vliv procvičování na Khan Academy na znalosti a dovednosti žáků v matematice

Jiří Vančura, ¹

KDM MFF UK

DOI: https://doi.org/10.14712/18047106.1520

pdf (Czech)

How to Cite

Vančura, J. (2020). Vliv procvičování na Khan Academy na znalosti a dovednosti žáků v matematice. Scientia in Educatione, 10(2), 103-126. https://doi.org/10.14712/18047106.1520

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Abstract

Two presented quantitative studies examine the effect of online practice on Khan Academy on knowledge and skills of grammar school students. The first study from year 2016/17 focused on the transfer of procedural knowledge acquired online in Khan Academy environment into Czech classroom context. The second study from year 2017/18 investigates the development of conceptual knowledge through online practice or procedural knowledge. Both studies worked with the same sample of 44 students of two same grade classes of a grammar (high) school in Prague. Collected data were subjected to a hypothesis testing with a 5% significance level. The researcher was (at the time of the research) mathematics teacher of the two classes. Whereas the first study arrived at statistically significant and strongly positive results, the second study didn’t show significant development of student’s conceptual knowledge. Secondarily, we investigated a student’s views on the benefits of online practice for their knowledge and skills.

References

Alcock, L., Ansari, D., Batchelor, S., Bisson, M., Smedt, B. D., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2(1), 20-41. doi:10.5964/jnc.v2i1.10 Open DOI Search in Google Scholar
Anderson, L. W. & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives. New York: Longman. Search in Google Scholar
Attali, Y. (2015). Effects of multiple-try feedback and question type during mathematics problem solving on performance in similar problems. Computers & Education, 86, pp.260–267. doi: 10.1016/j.compedu.2015.08.011 Open DOI Search in Google Scholar
Bempechat, J., Li, J., Neier, S. M., Gillis, C. A. & Holloway S. D. (2011). The homework experience: Perceptions of low-income youth. Journal of Advanced Academics, 22(2), 250-278. doi: 10.1177/1932202X1102200204 Open DOI Search in Google Scholar
Berthold, K. & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of Educational Psychology, 101(1), 70–87. doi: 10.1037/a0013247 Open DOI Search in Google Scholar
Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. New York: Longmans, Green. doi: 10.1177/001316445601600310 Open DOI Search in Google Scholar
Bokhove, C. & Drijvers, P. (2012). Effects of a digital intervention on the development of algebraic expertise. Computers & Education, 58(1), 197–208. doi: 10.1016/j.compedu.2011.08.010 Open DOI Search in Google Scholar
Brunström, M. & Fahlgren, M. (2015). Designing prediction tasks in a mathematics software environment. International Journal for Technology in Mathematics Education, 22(1), 3–18. Search in Google Scholar
Cambridge Assessment, United Kingdom, 2019. https://www.cambridgeenglish.org/exams-and-tests/ Search in Google Scholar
Clarina, R. & Koul, R. (2003). Multiple-try feedback and higher-order learning outcomes. International Journal of Instructional Media, 32(3), 239–245. Search in Google Scholar
Crompton, H., Burke, D., & Lin, Y. C. (2019). Mobile learning and student cognition: A systematic review of PK‐12 research using Bloom’s Taxonomy. British Journal of Educational Technology, 50(2), 684-701. doi: 10.1111/bjet.12674 Open DOI Search in Google Scholar
Desmos, získáno 8. 5. 2019 z https://teacher.desmos.com Search in Google Scholar
Dettmers, S., Trautwein, U., Lüdtke, O., Kunter, M. & Baumert, J. (2010). Homework Works if Homework Quality Is High: Using Multilevel Modeling to Predict the Development of Achievement in Mathematics. Journal of Educational Psychology, 102, 467–482. doi: 10.1037/a0018453 Open DOI Search in Google Scholar
Dixon, J. A., Deets, J. K. & Bangert, A. (2001). The representations of the arithmetic operations include functional relationships. Memory and Cognition, 29(3), 462–477 Search in Google Scholar
Fan, H., Xu, J., Cai, Z., He, J. & Fan, X. (2017). Homework and students' achievement in math and science: A 30-year meta-analysis, 1986–2015. Educational Research Review, 20, 35–54. doi: 10.1016/j.edurev.2016.11.003 Open DOI Search in Google Scholar
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859. doi: 10.1037/a0019824 Open DOI Search in Google Scholar
Jupri, A., Drijvers, P. and van den Heuvel-Panhuizen, M. (2016). An instrumentation theory view on students’ use of an applet for algebraic substitution. International Journal for Technology in Mathematics Education, 23(2), 63–80. Search in Google Scholar
Kamii, C., & Dominick, A. (1997). To teach or not to teach algorithms. The Journal of Mathematical Behavior, 16(1), 51–61. doi: 10.1016/S0732-3123(97)90007-9 Open DOI Search in Google Scholar
Khan Academy, získáno 7. 12. 2018 z www.khanacademy.org Search in Google Scholar
Knuth, E. J., Stephens, A. C., McNeil, N. M. & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312. Search in Google Scholar
Lavigne, N. C. (2005). Mutually informative measures of knowledge: concept maps plus problem sorts in statistics. Educational Assessment, 10(1), 39–71. doi: 10.1207/s15326977ea1001_3 Open DOI Search in Google Scholar
Mueller, C. M. & Dweck, C. S. (1998). Praise for intelligence can undermine children's motivation and performance. Journal of Personality and Social Psychology, 75(1), 33–52 doi: 10.1037/0022-3514.75.1.33 Open DOI Search in Google Scholar
Murphy, R. et al. (2014). Research on the Use of Khan Academy in Schools. Menlo Park, CA: SRI Education. dostupné z https://www.sri.com/sites/default/files/publications/2014-03-07_implementation_briefing.pdf. Search in Google Scholar
Mustaffa, N., Ismail, Z., Said, M. N. H. M. and Tasir, Z. (2017). A Review on the Development of Algebraic Thinking Through Technology. Advanced Science Letters, 23, 2951–2953. doi: 10.1166/asl.2017.7615 Open DOI Search in Google Scholar
Rittle-Johnson, B. (2006). Promoting transfer: effects of self-explanation and direct instruction. Child Development, 77(1), 1–15. doi: 10.1111/j.1467-8624.2006.00852.x Open DOI Search in Google Scholar
Rittle-Johnson, B. & Schneider, M. (2016). Developing conceptual and procedural knowledge of mathematics. In The Oxford handbook of numerical cognition (pp. 1102–1118). Oxford, United Kingdom: Oxford University Press. doi: 10.1093/oxfordhb/9780199642342.013.014 Open DOI Search in Google Scholar
Rittle-Johnson, B., Schneider, M. & Star, J. R. (2015). Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics. Educational Psychology Review, 27(4), 587–597. doi: 10.1007/s10648-015-9302-x Open DOI Search in Google Scholar
Similar web, získáno 8. 5. 2019 z www.similarweb.com/website/khanacademy.org Search in Google Scholar
Star, J. R. & Rittle-Johnson, B. (2009). It pays to compare: an experimental study on computational estimation. Journal of Experimental Child Psychology, 102(2), 408–426. doi: 10.1016/j.jecp.2008.11.004 Open DOI Search in Google Scholar
Strandberg, M. (2013). Homework – is there a connection with classroom assessment? A review from Sweden. Educational Research, 55(4), 325–346. doi: 10.1080/00131881.2013.844936 Open DOI Search in Google Scholar
Trautwein, U., Lüdtke, O. (2009). Predicting homework motivation and homework effort in six school subjects: The role of person and family characteristics, classroom factors, and school track. Learning and Instruction, 19, 243–258. doi: 10.1016/j.learninstruc.2008.05.001 Open DOI Search in Google Scholar
Vančura, J. (2016). Využití Khan Academy pro výuku matematiky na střední škole. Setkání Učitelů Matematiky Všech Typů a Stupňů Škol 2016. Srní, Czech Republic: SUMA JČMF. Search in Google Scholar
Vančura, J. (2017). Research on the language barriers of students who use Khan Academy as a mathematics homework platform. CERME 10 Proceedings, 2660–2667, Dublin. https://keynote.conference-services.net/resources/444/5118/pdf/CERME10_0195.pdf Search in Google Scholar
Vančura, J. (2018a). Can students transfer their mathematical skills gained from their Khan Academy homework to other contexts? INTED2018 Proceedings, 2707–2714 Valencia. doi: 10.21125/inted.2018 Open DOI Search in Google Scholar
Vančura, J. (2018b). Využití Khan Academy pro zadávání a hodnocení domácích úkolů. Matematika, fyzika, informatika, 28(3), 169–180. Search in Google Scholar
Wilson, J., & Rhodes, J. (2010). Student perspectives on homework. Education, 131(2), 351-358. Search in Google Scholar
Zákon č. 561/2004 Sb., o předškolním, základním, středním, vyšším odborném a jiném vzdělávání, školský zákon. (2004). Praha: Tiskárna Ministerstva vnitra. Search in Google Scholar

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[1] Alcock, L., Ansari, D., Batchelor, S., Bisson, M., Smedt, B. D., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2(1), 20-41. doi:10.5964/jnc.v2i1.10 Open DOI Search in Google Scholar

[2] Anderson, L. W. & Krathwohl, D. R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives. New York: Longman. Search in Google Scholar

[3] Attali, Y. (2015). Effects of multiple-try feedback and question type during mathematics problem solving on performance in similar problems. Computers & Education, 86, pp.260–267. doi: 10.1016/j.compedu.2015.08.011 Open DOI Search in Google Scholar

[4] Bempechat, J., Li, J., Neier, S. M., Gillis, C. A. & Holloway S. D. (2011). The homework experience: Perceptions of low-income youth. Journal of Advanced Academics, 22(2), 250-278. doi: 10.1177/1932202X1102200204 Open DOI Search in Google Scholar

[5] Berthold, K. & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of Educational Psychology, 101(1), 70–87. doi: 10.1037/a0013247 Open DOI Search in Google Scholar

[6] Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. New York: Longmans, Green. doi: 10.1177/001316445601600310 Open DOI Search in Google Scholar

[7] Bokhove, C. & Drijvers, P. (2012). Effects of a digital intervention on the development of algebraic expertise. Computers & Education, 58(1), 197–208. doi: 10.1016/j.compedu.2011.08.010 Open DOI Search in Google Scholar

[8] Brunström, M. & Fahlgren, M. (2015). Designing prediction tasks in a mathematics software environment. International Journal for Technology in Mathematics Education, 22(1), 3–18. Search in Google Scholar

[9] Cambridge Assessment, United Kingdom, 2019. https://www.cambridgeenglish.org/exams-and-tests/ Search in Google Scholar

[10] Clarina, R. & Koul, R. (2003). Multiple-try feedback and higher-order learning outcomes. International Journal of Instructional Media, 32(3), 239–245. Search in Google Scholar

[11] Crompton, H., Burke, D., & Lin, Y. C. (2019). Mobile learning and student cognition: A systematic review of PK‐12 research using Bloom’s Taxonomy. British Journal of Educational Technology, 50(2), 684-701. doi: 10.1111/bjet.12674 Open DOI Search in Google Scholar

[12] Desmos, získáno 8. 5. 2019 z https://teacher.desmos.com Search in Google Scholar

[13] Dettmers, S., Trautwein, U., Lüdtke, O., Kunter, M. & Baumert, J. (2010). Homework Works if Homework Quality Is High: Using Multilevel Modeling to Predict the Development of Achievement in Mathematics. Journal of Educational Psychology, 102, 467–482. doi: 10.1037/a0018453 Open DOI Search in Google Scholar

[14] Dixon, J. A., Deets, J. K. & Bangert, A. (2001). The representations of the arithmetic operations include functional relationships. Memory and Cognition, 29(3), 462–477 Search in Google Scholar

[15] Fan, H., Xu, J., Cai, Z., He, J. & Fan, X. (2017). Homework and students' achievement in math and science: A 30-year meta-analysis, 1986–2015. Educational Research Review, 20, 35–54. doi: 10.1016/j.edurev.2016.11.003 Open DOI Search in Google Scholar

[16] Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859. doi: 10.1037/a0019824 Open DOI Search in Google Scholar

[17] Jupri, A., Drijvers, P. and van den Heuvel-Panhuizen, M. (2016). An instrumentation theory view on students’ use of an applet for algebraic substitution. International Journal for Technology in Mathematics Education, 23(2), 63–80. Search in Google Scholar

[18] Kamii, C., & Dominick, A. (1997). To teach or not to teach algorithms. The Journal of Mathematical Behavior, 16(1), 51–61. doi: 10.1016/S0732-3123(97)90007-9 Open DOI Search in Google Scholar

[19] Khan Academy, získáno 7. 12. 2018 z www.khanacademy.org Search in Google Scholar

[20] Knuth, E. J., Stephens, A. C., McNeil, N. M. & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312. Search in Google Scholar

[21] Lavigne, N. C. (2005). Mutually informative measures of knowledge: concept maps plus problem sorts in statistics. Educational Assessment, 10(1), 39–71. doi: 10.1207/s15326977ea1001_3 Open DOI Search in Google Scholar

[22] Mueller, C. M. & Dweck, C. S. (1998). Praise for intelligence can undermine children's motivation and performance. Journal of Personality and Social Psychology, 75(1), 33–52 doi: 10.1037/0022-3514.75.1.33 Open DOI Search in Google Scholar

[23] Murphy, R. et al. (2014). Research on the Use of Khan Academy in Schools. Menlo Park, CA: SRI Education. dostupné z https://www.sri.com/sites/default/files/publications/2014-03-07_implementation_briefing.pdf. Search in Google Scholar

[24] Mustaffa, N., Ismail, Z., Said, M. N. H. M. and Tasir, Z. (2017). A Review on the Development of Algebraic Thinking Through Technology. Advanced Science Letters, 23, 2951–2953. doi: 10.1166/asl.2017.7615 Open DOI Search in Google Scholar

[25] Rittle-Johnson, B. (2006). Promoting transfer: effects of self-explanation and direct instruction. Child Development, 77(1), 1–15. doi: 10.1111/j.1467-8624.2006.00852.x Open DOI Search in Google Scholar

[26] Rittle-Johnson, B. & Schneider, M. (2016). Developing conceptual and procedural knowledge of mathematics. In The Oxford handbook of numerical cognition (pp. 1102–1118). Oxford, United Kingdom: Oxford University Press. doi: 10.1093/oxfordhb/9780199642342.013.014 Open DOI Search in Google Scholar

[27] Rittle-Johnson, B., Schneider, M. & Star, J. R. (2015). Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics. Educational Psychology Review, 27(4), 587–597. doi: 10.1007/s10648-015-9302-x Open DOI Search in Google Scholar

[28] Similar web, získáno 8. 5. 2019 z www.similarweb.com/website/khanacademy.org Search in Google Scholar

[29] Star, J. R. & Rittle-Johnson, B. (2009). It pays to compare: an experimental study on computational estimation. Journal of Experimental Child Psychology, 102(2), 408–426. doi: 10.1016/j.jecp.2008.11.004 Open DOI Search in Google Scholar

[30] Strandberg, M. (2013). Homework – is there a connection with classroom assessment? A review from Sweden. Educational Research, 55(4), 325–346. doi: 10.1080/00131881.2013.844936 Open DOI Search in Google Scholar

[31] Trautwein, U., Lüdtke, O. (2009). Predicting homework motivation and homework effort in six school subjects: The role of person and family characteristics, classroom factors, and school track. Learning and Instruction, 19, 243–258. doi: 10.1016/j.learninstruc.2008.05.001 Open DOI Search in Google Scholar

[32] Vančura, J. (2016). Využití Khan Academy pro výuku matematiky na střední škole. Setkání Učitelů Matematiky Všech Typů a Stupňů Škol 2016. Srní, Czech Republic: SUMA JČMF. Search in Google Scholar

[33] Vančura, J. (2017). Research on the language barriers of students who use Khan Academy as a mathematics homework platform. CERME 10 Proceedings, 2660–2667, Dublin. https://keynote.conference-services.net/resources/444/5118/pdf/CERME10_0195.pdf Search in Google Scholar

[34] Vančura, J. (2018a). Can students transfer their mathematical skills gained from their Khan Academy homework to other contexts? INTED2018 Proceedings, 2707–2714 Valencia. doi: 10.21125/inted.2018 Open DOI Search in Google Scholar

[35] Vančura, J. (2018b). Využití Khan Academy pro zadávání a hodnocení domácích úkolů. Matematika, fyzika, informatika, 28(3), 169–180. Search in Google Scholar

[36] Wilson, J., & Rhodes, J. (2010). Student perspectives on homework. Education, 131(2), 351-358. Search in Google Scholar

[37] Zákon č. 561/2004 Sb., o předškolním, základním, středním, vyšším odborném a jiném vzdělávání, školský zákon. (2004). Praha: Tiskárna Ministerstva vnitra. Search in Google Scholar

Scientia in educatione

Vliv procvičování na Khan Academy na znalosti a dovednosti žáků v matematice

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