References
- Alibali, M. W., Phillips, K. M. O., & Fischer, A. D. (2009). Learning new problem-solving strategies leads to changes in problem representation. Cognitive Development, 24(2), 89–101. https://doi.org/10.1016/j.cogdev.2008.12.005
- Ashlock, R. B. (2006). Error patterns in computation. Using error patterns to improve instruction. Pearson.
- Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24(4), 294–323. https://doi.org/10.5951/jresematheduc.24.4.0294
- Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7(1), 87–106. https://doi.org/10.1016/S0959-4752(96)00012-6
- Bennett, R. E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18(1), 5–25. https://doi.org/10.1080/0969594X.2010.513678
- Blazar, D. (2015). Effective teaching in elementary mathematics: Identifying classroom practices that support student achievement. Economics of Education Review, 48, 16–29. https://doi.org/10.1016/j.econedurev.2015.05.005
- Brown, J., & Burton, R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(2), 155–192. https://doi.org/10.1207/s15516709cog0202_4
- Brown, J., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379–426. https://doi.org/10.1207/s15516709cog0404_3
- Carless, D. (2007). Conceptualizing pre‐emptive formative assessment. Assessment in Education: Principles, Policy & Practice, 14(2), 171–184. https://doi.org/10.1080/09695940701478412
- Centraal Bureau voor de Statistiek, CBS [Statistics Netherlands] (2015). Demografische kerncijfers per gemeente [Demographic key figures per township 2015]. CBS. https://www.cbs.nl/-/media/imported/documents/2015/50/2015a414-demografische-kerncijfers-per-gemeente-2015_web.pdf?la=nl-nl
- Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1
- Fernández, R., & García, A. (2008). Evolutionary processes in the development of errors in subtraction algorithms. Educational Research and Reviews, 3(7), 229–235. http://www.researchgate.net/publication/242673416_Evolutionary_processes_in_the_development_of_errors_in_subtraction_algorithms/file/3deec5295a2a96c98f.pd
- Field, A. (2009). Discovering statistics using SPSS (3rd ed.). SAGE publications.
- Fuson, K. C., Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier, A. I., Carpenter, T. P., & Fennema, E. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28(2), 130–162. https://doi.org/10.5951/jresematheduc.28.2.0130
- Gravemeijer, K., Bowers, J., & Stephan, M. (2003). Chapter 4: A hypothetical learning trajectory on measurement and flexible arithmetic. Journal for Research in Mathematics Education, 12, 51–66. http://www.jstor.org/stable/30037721
- Hennessy, S. (1993). The stability of children’s mathematical behavior: When is a bug really a bug? Learning and Instruction, 3(4), 315–338. https://doi.org/10.1016/0959-4752(93)90022-R
- Hop, M. (2012). Balans (47) van het rekenwiskundeonderwijs halverwege de basisschool 5 [Fifth periodical assessment of mathematics education mid primary school] (PPON Report No. 47). Cito, Institute for Educational Measurement. https://www.cito.nl/-/media/files/kennis-en-innovatie-onderzoek/ppon/cito_ppon_balans_47.pdf?la=nl-nl
- Hox, J. (2002). Multilevel analysis. Techniques and applications. Lawrence Erlbaum Associates.
- Huff, K., & Goodman, D. P. (2007). The demand for cognitive diagnostic assessment. In J. P. Leighton & M. J. Gierl (Eds.), Cognitive diagnostic assessment for education: Theory and applications (pp. pp. 19–60). Cambridge University Press.
- IBM Corp. Released. (2017). IBM SPSS statistics for windows, version 25.0 [computer software]. IBM Corp.
- Janssen, J., Scheltens, F., & Kraemer, J. M. (2006). Primair onderwijs. Leerling- en onderwijsvolgsysteem. Rekenen-wiskunde groep 5 [Primary education. Pupil and educational monitoring system. Mathematics grade 3]. Cito.
- Janssen, J., Verhelst, N., Engelen, R., & Scheltens, F. (2010). Wetenschappelijke verantwoording van de toetsen LOVS Rekenen-Wiskunde voor groep 3 tot en met 8. [Scientific validation report for the LOVS mathematics test for grades 3 through 6]. Resource document. Cito. http://www.toetswijzer.nl/html/tg/14.pdf
- Keeley, P., & Tobey, C. R. (2011). Mathematics formative assessment- 75 Practical strategies for linking assessment, instruction, and learning. Corwin Press.
- Klein, A. S., Beishuizen, M., & Treffers, A. (1998). The empty number line in Dutch second grades: Realistic versus gradual program design. Journal for Research in Mathematics Education, 29(4), 443. https://doi.org/10.2307/749861
- Kraemer, J. M. (2009). Balans (40) over de strategieën en procedures bij het hoofdrekenen halverwege de basisschool. [Periodical assessment of strategies and procedures in mental arithmetic mid primary school] (PPON Report No. 40). Cito, Institute for Educational Measurement. https://www.cito.nl/-/media/files/kennis-en-innovatie-onderzoek/ppon/cito_ppon_balans_40.pdf?la=nl-nl
- Kraemer, J. M. (2011). Oplossingsmethoden voor aftrekken tot 100 [solution methods for subtraction up to 100] [Doctoral dissertation]. Technical University Eindhoven. https://doi.org/10.6100/IR721544
- Ledoux, G., Blok, H., Boogaard, M., & Krüger, M. (2009). Opbrengstgericht werken; over waarde van meetgestuurd onderwijs. [Data based decision-making: About the value of measurement driven education] (SCO-Rapport 812). SCO-Kohnstamm Instituut.
- Leighton, J. P., & Gierl, M. J. (2007a). Why cognitive diagnostic assessment. In J. P. Leighton & M. J. Gierl (Eds.), Cognitive diagnostic assessment for education: Theory and applications (pp. pp. 3–18). Cambridge University Press.
- Leighton, J. P., & Gierl, M. J. (2007b). Defining and evaluating models of cognition used in educational measurement to make inferences about examinees’ thinking processes. Educational Measurement: Issues and Practice, 26(2), 3–16. https://doi.org/10.1111/j.1745-3992.2007.00090.x
- Leighton, J. P., Gokiert, R. J., Cor, M., & Heffernan, C. (2010). Teacher beliefs about the cognitive diagnostic information of classroom versus large scale tests: Implications for assessment literacy. Assessment in Education: Principles, Policy & Practice, 17(1), 7–21. https://doi.org/10.1080/09695940903565362
- Murchan, D. (2011). The formative use of diagnostic assessment to support teaching and learning in mathematics. In G. Mickovska, M. Ceslarov, K. Binceva, T. Mitrevska, & K. Poposki (Eds.), Assessment for learning in the 21st century (pp. pp. 147–156). United States Angency for International Development (USAID).
- Murchan, D., Oldham, E., & O’Sullilvan, C. (2013). Applying CBA technology to traditional error analysis in elementary mathematics. lessons from maths assist. Paper presented at the annual meeting of the American Educational Research Association, San Fransisco, CA. http://www.tara.tcd.ie/bitstream/handle/2262/68337/Murchan, Oldham & O’Sullivan (2013).pdf?sequence=1
- Narciss, S., & Huth, K. (2006). Fostering achievement and motivation with bug-related tutoring feedback in a computer-based training for written subtraction. Learning and Instruction, 16(4), 310–322. https://doi.org/10.1016/j.learninstruc.2006.07.003
- Opgenoort, L. (2014). Ondersteunend leertraject. Splitsvaardigheid Groep 5 [Supportive learning trajectory. Decomposition skills third grade]. Cito. https://diagnostischetoetsvooraftrekken.files.wordpress.com/2017/01/ondersteunend-leertraject1.pdf
- Rasbash, J., Charlton, C., Browne, W. J., Healy, M., & Cameron, B. (2009). MLwiN Version 2.10. [Computer software]. Centre for Multilevel Modelling, University of Bristol.
- Resnick, L. B. (1982). Syntax and semantics in learning to subtract. Learning Research and Development Center, University of Pittsburgh. https://eric.ed.gov/?id=ED221386
- Resnick, L. B. (1984). Beyond error analysis: The role of understanding in elementary school arithmetic. Learning Research and Development Center, University of Pittsburgh. http://eric.ed.gov/ERICWebPortal/recordDetail?accno=ED248099
- Riccomini, P. J. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 28(3), 233–242. https://doi.org/10.2307/1593661
- Rittle-Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives, 11(3), 184–190. https://doi.org/10.1111/cdep.12229
- Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic measurements. Theory, methods, and applications. The Guilford Press.
- Schildkamp, K., & Kuiper, W. (2010). Data-informed curriculum reform: Which data, what purposes, and promoting and hindering factors. Teaching and Teacher Education, 26(3), 482–496. https://doi.org/10.1016/j.tate.2009.06.007
- Shepard, L. A. (2009). Commentary: Evaluating the validity of formative and interim assessment. Educational Measurement: Issues and Practice, 28(3), 32–37. https://doi.org/10.1111/j.1745-3992.2009.00152.x
- Stobart, G. (2008). Testing times: The uses and abuses of assessment. Routledge.
- Torbeyns, J., De Smedt, B., Ghesquière, P., & Verschaffel, L. (2008). Acquisition and use of shortcut strategies by traditionally schooled children. Educational Studies in Mathematics, 71(1), 1–17. https://doi.org/10.1007/s10649-008-9155-z
- Torbeyns, J., Hickendorff, M., & Verschaffel, L. (2017). The use of number-based versus digit-based strategies on multi-digit subtraction: 9–12-year-olds’ strategy use profiles and task performance. Learning and Individual Differences, 58(June 2016), 64–74. https://doi.org/10.1016/j.lindif.2017.07.004
- Treffers, A., van den Heuvel-panhuizen, M., & Buys, K. (2000). Jonge kinderen leren rekenen. Tussendoelen annex leerlijnen. Hele getallen onderbouw basisschool [Young children learn mathematics. Intermediate goals annex learning trajectories. Whole numbers in lower grades of primary school]. Wolters-Noordhoff.
- van der Kleij, F. M., & Eggen, T. J. H. M. (2013). Interpretation of the score reports from the computer program LOVS by teachers, internal support teachers and principals. Studies in Educational Evaluation, 39(3), 144–152. https://doi.org/10.1016/j.stueduc.2013.04.002
- van der Kleij, F. M., Eggen, T. J. H. M., & Engelen, R. J. H. (2014). Towards valid score reports in the computer program LOVS: A redesign study. Studies in Educational Evaluation, 43(1), 24–39. https://doi.org/10.1016/j.stueduc.2014.04.004
- van der Kleij, F. M., Vermeulen, J. A., Schildkamp, K., & Eggen, T. J. H. M. (2015). Integrating data-based decision making, assessment for learning and diagnostic testing in formative assessment. Assessment in Education: Principles, Policy & Practice, 22(3), 324–343. https://doi.org/10.1080/0969594X.2014.999024
- van der Linden, W. J., & Hambleton, R. K. (1997). Handbook of modern item response theory. Springer.
- VanLehn, K. (1990). Mind Bugs. The origins of procedural misconceptions. MIT Press.
- Veldhuis, M. (2015). Improving classroom assessment in primary mathematics education [Doctoral dissertation]. Utrecht University. https://dspace.library.uu.nl/handle/1874/313660
- Veldhuis, M., van den Heuvel-panhuizen, M., Vermeulen, J. A., & Eggen, T. J. H. M. (2013). Teachers’ use of classroom assessment in primary school mathematics education in the Netherlands. CADMO, 21(2), 35–53. https://doi.org/10.3280/CAD2013-002004
- Vermeulen, J. A., Béguin, A., Scheltens, F., & Eggen, T. J. H. M. (2020). Evaluating the characteristics of diagnostic items for bridging errors in multi-digit subtraction. Frontiers in Education, 5. https://doi.org/10.3389/feduc.2020.537531
- Young, R. M., & O’Shea, T. (1981). Errors in children’s subtraction. Cognitive Science, 5(2), 177–153. https://doi.org/10.1207/s15516709cog0502_3