Conceptual explanations and understanding fraction comparisons

Learning and Instruction

Volumn 52, Issue , 2017, Pages 122-129

  Geller, Emma H ^a   Son, Ji Y ^b   Stigler, James W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

Conceptual; Explanation; Fractions; Understanding

Indexed keywords

EID: 85020668667     PISSN: 09594752     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.learninstruc.2017.05.006     Document Type: Article

References (29)

1. Bonato, M., Fabbri, S., Umiltà, C., Zorzi, M., The mental representation of numerical fractions: Real or integer?. Journal of Experimental Psychology: Human Perception and Performance, 33(6), 2007, 1410.
2. Crooks, N.M., Alibali, M.W., Defining and measuring conceptual knowledge in mathematics. Developmental Review 34 (2014), 344–377.
3. Fuchs, L.S., Schumacher, R.F., Long, J., Namkung, J., Hamlett, C.L., Cirino, P.T., et al. Improving at-risk learners' understanding of fractions. Advance online publication Journal of Educational Psychology, 2013, 10.1037/a0032446.
4. Givvin, K.B., Stigler, J.W., Thompson, B.J., What community college developmental mathematics students understand about mathematics, part 2: The interviews. MathAMATYC Educator 2:3 (2011), 4–18.
5. Gray, E.M., Tall, D.O., Duality, ambiguity and flexibility. The Journal for Research in Mathematics Education 26:2 (1994), 115–141.
6. Hallett, D., Nunes, T., Bryant, P., Thorpe, C.M., Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology 113 (2012), 469–486.
7. Hecht, S.A., Vagi, K.J., Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology 102:4 (2010), 843–859.
8. Hecht, S.A., Vagi, K.J., Patterns of strengths and weaknesses in children's knowledge about fractions. Journal of Experimental Child Psychology 111 (2012), 212–229.
9. Hiebert, J., Lefevre, P., Conceptual and procedural knowledge in mathematics: An introductory analysis. Hiebert, J., (eds.) Conceptual and procedural knowledge: The case of mathematics, 1986, Lawrence Erlbaum, Hillsdale, NJ, 1–27.
10. Hiebert, J., Tonnessen, L.H., Development of the fraction concept in two physical contexts: An exploratory investigation. Journal for Research in Mathematics Education 9:5 (1978), 374–378.
11. Jordan, N.C., Hansen, N., Fuchs, L.S., Siegler, R.S., Gersten, R., Micklos, D., Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology 116 (2013), 45–58.
12. Mack, N.K., Whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education 26:5 (1995), 422–441.
13. Niemi, D., Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explanations. The Journal of Educational Research 89:6 (1996), 351–363.
14. Resnick, L.B., Nesher, P., Leonard, F., Magone, M., Omanson, S., Peled, I., Conceptual basis of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education 20:1 (1989), 8–27.
15. Rittle-Johnson, B., Alibali, M.W., Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology, 91(1), 1999, 175.
16. Rittle-Johnson, B., Siegler, R.S., The relation between conceptual and procedural knowledge in learning mathematics: A review. Donlan, Chris, (eds.) (1998). The development of mathematical skills. Studies in developmental psychology, 1998, Psychology Press/Taylor & Francis (UK), Hove, England, 75–110 xiv, 338.
17. Rittle-Johnson, B., Star, J.R., Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology 101:3 (2009), 529–544.
18. Schneider, M., Siegler, R.S., Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance 36:5 (2010), 1227–1238.
19. Siegler, R.S., Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117(3), 1988, 258.
20. Siegler, R.S., Strategy choice and strategy discovery. Learning and Instruction 1:1 (1991), 89–102.
21. Siegler, R.S., Fazio, L.K., Bailey, D.H., Zhou, X., Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences 17:1 (2013), 13–19.
22. Siegler, R.S., Pyke, A.A., Developmental and individual differences in understanding of fractions. Developmental Psychology 49:10 (2014), 1994–2004.
23. Siegler, R.S., Thompson, C.A., Schneider, M., An integrated theory of whole number and fractions development. Cognitive Psychology 62 (2011), 273–296.
24. Sprute, L., Temple, E., Representations of fractions: Evidence for accessing the whole magnitude in adults. Mind, Brain, and Education 5:1 (2011), 42–47.
25. Stafylidou, S., Vosniadou, S., The development of students' understanding of the numerical value of fractions. Learning and Instruction 14:5 (2004), 503–518.
26. Stigler, J.W., Givvin, K.B., Thompson, B.J., What community college developmental mathematics students understand about mathematics. The MathAMATYC Educator 10:3 (2010), 4–16.
27. Vamvakoussi, X., Vosniadou, S., Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction 14 (2004), 453–467.
28. Vamvakoussi, X., Vosniadou, S., How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation. Cognition and Instruction 28:2 (2010), 181–209.
29. th annual conference of the mathematics education research group of Australasia, 2007.