Designing for learning mathematics through programming: A case study of pupils engaging with place value

Hoyles, 1992 Papert, 1991, Situating constructionism, Constructionism, 36, 1 Papert, 1980 Papert, 2000, What’s the big idea? Toward a pedagogy of idea power, IBM Syst. J., 39, 720, 10.1147/sj.393.0720 Lewis, 2010 Resnick, 2009, Scratch: Programming for all, Commun. ACM, 52, 60, 10.1145/1592761.1592779 Weintrop, 2015 Weintrop, 2015 Bagge, 2015 Förster, 2015 Gadanidis, 2015 NCTE/LERO scratch programming and numeracy in senior primary classes, 2012. Lewis, 2012, Building upon and enriching grade four mathematics standards with programming curriculum Ke, 2014, An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing, Comput. Educ., 73, 26, 10.1016/j.compedu.2013.12.010 S. Watt, Syntonicity and the psychology of programming, 1998. Perkins, 1988, Teaching for transfer, Educ. Leadership, 46, 22 Pea, 1983, On the cognitive effects of learning computer programming, New Ideas Psychol., 2, 137, 10.1016/0732-118X(84)90018-7 Lobato, 2006, Alternative perspectives on the transfer of learning: History, issues, and challenges for future research, J. Learn. Sci., 15, 431, 10.1207/s15327809jls1504_1 Clements, 2002, Computers in early childhood mathematics, 160 Clements, 1997, Research on logo: A decade of progress, Comput. Schools, 14, 9, 10.1300/J025v14n01_02 Noss, 1996 Delclos, 1985, Teaching thinking through logo: The importance of method, Roeper Rev., 7, 153, 10.1080/02783198509552879 Salomon, 1989, Rocky roads to transfer: Rethinking mechanism of a neglected phenomenon, Educ. Psychol., 24, 113, 10.1207/s15326985ep2402_1 Franklin, 2016 Gurtner, 1992 Fogarty, 1992 Jones, 2009, Teaching mathematics understandings for transfer, Teach. Math. Appl., 28, 145 Harel, 1990, Software design as a learning environment, Interact. Learn. Environ., 1, 1, 10.1080/1049482900010102 Calder, 2010, Using scratch: An integrated problem-solving approach to mathematical thinking, Austr. Primary Math. Classroom, 15, 9 Noss, 1986, Constructing a conceptual framework for elementary algebra through logo programming, Educ. Stud. Math., 17, 335, 10.1007/BF00311324 Cope, 1991, Children’s exploration of rotation and angle in limited logo microworlds, Comput. Educ., 16, 133, 10.1016/0360-1315(91)90019-N Akcaoglu, 2014, Learning problem-solving through making games at the game design and learning summer program, Educ. Technol. Res. Dev., 62, 583, 10.1007/s11423-014-9347-4 Council, 2001 DfE computing programmes of study: Key stages 1 and 2, in: National curriculum in England, 2013. Benton, 2016, Building mathematical knowledge with programming: insights from the scratchmaths project Benton, 2017, Bridging primary programming and mathematics: some findings of design research in England, Digital Exp. Math. Educ., 1 Thompson, 2000, Teaching place value in the UK: time for a reappraisal?, Educ. Rev., 52, 291, 10.1080/713664046 Hurst, 2014, Developing the big ideas of number, Int. J. Educ. Stud. Math., 1, 10.17278/ijesim.2014.02.001 Payne, 1993, Early number and numeration, 43 Major, 2012, The development of an assessment tool: student knowledge of the concept of place value Doabler, 2013, Explicit mathematics instruction what teachers can do for teaching students with mathematics difficulties, Intervention School Clinic, 48, 276, 10.1177/1053451212473151 Verschaffel, 1996 Kamii, 1986, Place value: An explanation of its difficulty and educational implications for the primary grades, J. Res. Childhood Educ., 1, 75, 10.1080/02568548609594909 Chandler, 2009, Giving change when payment is made with a dime: the difficulty of tens and ones, J. Res. Math. Educ., 40, 97 Fuson, 1990, Issues in place-value and multidigit addition and subtraction learning and teaching, J. Res. Math. Educ., 21, 273, 10.2307/749525 Kamii, 1998, The harmful effects of algorithms in grades 1-4, Teach. Learn. Algorithms School Math., 19, 130 Nunes, 2016 Pratt, 2012 Stemler, 2001, An overview of content analysis, Pract. Assess. Res. Eval., 7, 137 Maloney, 2010, The scratch programming language and environment, ACM Trans. Comput. Educ., 10, 16, 10.1145/1868358.1868363