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
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.
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
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
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
Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. New York: Longmans, Green. doi: 10.1177/001316445601600310
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
Brunström, M. & Fahlgren, M. (2015). Designing prediction tasks in a mathematics software environment. International Journal for Technology in Mathematics Education, 22(1), 3–18.
Cambridge Assessment, United Kingdom, 2019. https://www.cambridgeenglish.org/exams-and-tests/
Clarina, R. & Koul, R. (2003). Multiple-try feedback and higher-order learning outcomes. International Journal of Instructional Media, 32(3), 239–245.
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
Desmos, získáno 8. 5. 2019 z https://teacher.desmos.com
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
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
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
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
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.
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
Khan Academy, získáno 7. 12. 2018 z www.khanacademy.org
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.
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
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
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.
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
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
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
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
Similar web, získáno 8. 5. 2019 z www.similarweb.com/website/khanacademy.org
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
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
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
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.
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
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
Vančura, J. (2018b). Využití Khan Academy pro zadávání a hodnocení domácích úkolů. Matematika, fyzika, informatika, 28(3), 169–180.
Wilson, J., & Rhodes, J. (2010). Student perspectives on homework. Education, 131(2), 351-358.
Zákon č. 561/2004 Sb., o předškolním, základním, středním, vyšším odborném a jiném vzdělávání, školský zákon. (2004). Praha: Tiskárna Ministerstva vnitra.