Readiness-based differentiation in primary school mathematics: expert recommendations and teacher self-assessment
Main Article Content
Abstract
The diversity of students’ achievement levels within classrooms has made it essential for teachers to adapt their lessons to the varying educational needs of their students (‘differentiation’). However, the term differentiation has been interpreted in diverse ways and there is a need to specify what effective differentiation entails. Previous reports of low to moderate application of differentiation underscore the importance of practical guidelines for implementing differentiation. In two studies, we investigated how teachers should differentiate according to experts, as well as the degree to which teachers already apply the recommended strategies. Study 1 employed the Delphi technique and focus group discussions to achieve consensus among eleven mathematics experts regarding a feasible model for differentiation in primary mathematics. The experts agreed on a five-step cycle of differentiation: (1) identification of educational needs, (2) differentiated goals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation of progress and process. For each step, strategies were specified. In Study 2, the Differentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate how teachers self-assess their use of the strategies recommended by the experts. While teachers (N = 268) were moderately positive about their application of the strategies overall, we also identified areas of relatively low usage (including differentiation for high-achieving students) which require attention in teacher professional development. Together, these two studies provide a model and strategies for differentiation in primary mathematics based on expert consensus, the DSAQ which can be employed in future studies, and insights into teachers’ self-assessed application of specific aspects of differentiation.
Article Details
How to Cite
Prast, E. J., Van de Weijer-Bergsma, E., Kroesbergen, E. H., & Van Luit, J. E. (2015). Readiness-based differentiation in primary school mathematics: expert recommendations and teacher self-assessment. Frontline Learning Research, 3(2), 90–116. https://doi.org/10.14786/flr.v3i2.163
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Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. New York: HarperPerennial.
De Corte, E., Geerligs, C., Lagerweij, N., Peters, J., & Vandenberghe, R. (1976). Beknopte didaxologie [Concise didaxology]. Groningen: Wolters-Noordhoff.
Deunk, M., Doolaard, S., Smale-Jacobse, A., & Bosker, R. J. (2015). Differentiation within and across classrooms: A systematic review of studies into the cognitive effects of differentiation practices. Groningen: GION.
Expertgroep doorlopende leerlijnen taal en rekenen (2008). Over de drempels met taal en rekenen: Consolideren, onderhouden, uitbreiden en verdiepen [Overcoming barriers in mathematics: Consolidating, maintaining, using and deepening]. Enschede, the Netherlands: Expertgroep doorlopende leerlijnen taal en rekenen. Retrieved from http://www.taalenrekenen.nl/referentiekader/rel_doc/downloads/Rekenrapport.pdf
Fuchs, L., & Fuchs, D. (2007). A model for implementing responsiveness to intervention. Teaching Exceptional Children, 39(5), 14-20. doi:10.1177/004005990703900503
Gelderblom, G. (2007). Effectief omgaan met verschillen in het rekenonderwijs [Dealing with differences in mathematics education effectively]. Amersfoort, the Netherlands: CPS.
Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202-1242. doi:10.3102/0034654309334431
Goei, S. L., Bekebrede, J., & Bosma, T. (2011). Teachers' Sense of Self Efficacy Scale: Meningen van leraren, experimentele versie [Teachers' Sense of Self Efficacy Scale: Teacher’s opinions, experimental version]. Amsterdam, the Netherlands: Onderwijscentrum Vrije Universiteit.
Hasson, F., Keeney, S., & McKenna, H. (2000). Research guidelines for the Delphi survey technique. Journal of Advanced Nursing, 32, 1008-1015. doi:10.1046/j.1365-2648.2000.t01-1-01567.x
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1-55. doi:10.1080/10705519909540118
Janson, D., & Noteboom, A. (2004). Compacten en verrijken van de rekenles voor (hoog)begaafde leerlingen in het basisonderwijs [Compacting and enrichment of the mathematics lesson for highly able students in primary education]. Enschede, the Netherlands: SLO.
Johnsen, S. K., Haensly, P. A., Ryser, G. A. R., & Ford, R. F. (2002). Changing general education classroom practices to adapt for gifted students. Gifted Child Quarterly, 46, 45-63. doi:10.1177/001698620204600105
Kulik, J. A., & Kulik, C. C. (1992). Meta-analytic findings on grouping programs. Gifted Child Quarterly, 36, 73-77. doi:10.1177/001698629203600204
Landeta, J. (2006). Current validity of the delphi method in social sciences. Technological Forecasting and Social Change, 73, 467-482. doi:10.1016/j.techfore.2005.09.002
Latz, A. O., Speirs Neumeister, K. L., Adams, C. M., & Pierce, R. L. (2009). Peer coaching to improve classroom differentiation: Perspectives from project CLUE. Roeper Review, 31, 27-39. doi:10.1080/02783190802527356
Liamputtong, P. (2011). Focus group methodology: Principles and practice. London, UK: Sage.
Lou, Y., Abrami, P. C., Spence, J. C., Poulsen, C., Chambers, B., & D'Appolonia, S. (1996). Within-class grouping: A meta-analysis. Review of Educational Research, 66, 423-458. doi:10.3102/00346543066004423
McDonald Connor, C., Morrison, F. J., Fishman, B., Giuliani, S., Luck, M., Underwood, P. S., . . . Schatschneider, C. (2011a). Testing the impact of child characteristics x instruction interactions on third graders' reading comprehension by differentiating literacy instruction. Reading Research Quarterly, 46, 189-221. doi:10.1598/RRQ.46.3.1
McDonald Connor, C., Morrison, F. J., Fishman, B. J., Schatschneider, C., & Underwood, P. (2007). Algorithm-guided individualized reading instruction. Science, 315, 464-465. doi:10.1126/science.1134513
McDonald Connor, C., Morrison, F. J., Schatschneider, C., Toste, J. R., Lundblom, E., Crowe, E. C., & Fishman, B. (2011b). Effective classroom instruction: Implications of child characteristics by reading instruction interactions on first graders’ word reading achievement. Journal of Research on Educational Effectiveness, 4, 173-207. doi:10.1080/19345747.2010.510179
McDonald Connor, C., Piasta, S. B., Fishman, B., Glasney, S., Schatschneider, C., Crowe, E., . . . Morrison, F. J. (2009). Individualizing student instruction precisely: Effects of child x instruction interactions on first graders' literacy development. Child Development, 80, 77-100. doi:10.1111/j.1467-8624.2008.01247.x
McLeskey, J., & Waldron, N. L. (2002). Inclusion and school change: Teacher perceptions regarding curricular and instructional adaptations. Teacher Education and Special Education, 25, 41-54. doi:10.1177/088840640202500106
McLeskey, J., & Waldron, N. L. (2011). Educational programs for elementary students with learning disabilities: Can they be both effective and inclusive? Learning Disabilities Research & Practice, 26, 48-57. doi:10.1111/j.1540-5826.2010.00324.x
Megay-Nespoli, K. (2001). Beliefs and attitudes of novice teachers regarding instruction of academically talented learners. Roeper Review, 23, 178-182. doi:10.1080/02783190109554092
Moon, T. R., Callahan, C. M., Tomlinson, C. A., & Miller, E. M. (2002). Middle school classrooms: Teachers' reported practices and student perceptions (No. RM02164). Storrs, CT: The National Research Center on the Gifted and Talented.
Muthén, L. K., & Muthén, B. O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
Nationaal Expertisecentrum Leerplanontwikkeling (2010). Professionele ontwikkeling: Tussenmeting project 'Als je merkt dat het werkt' [Professional development: Midtime measurement project 'When you notice it works']. Enschede, the Netherlands: SLO.
Nurmi, J., Kiuru, N., Lerkkanen, M., Niemi, P., Poikkeus, A., Ahonen, T., . . . Lyyra, A. (2013). Teachers adapt their instruction in reading according to individual children's literacy skills. Learning and Individual Differences, 23, 72-79. doi:http://dx.doi.org/10.1016/j.lindif.2012.07.012
Reis, S. M., Gubbins, E. J., Richards, S., Briggs, C. J., Jacobs, J. K., Eckert, R. D., . . . Schreiber, F. J. (2004). Reading instruction for talented readers: Case studies documenting few opportunities for continuous progress. Gifted Child Quarterly, 48, 315-338. doi:10.1177/001698620404800406
Reis, S. M., McCoach, D. B., Little, C. A., Muller, L. M., & Kaniskan, R. B. (2011). The effects of differentiated instruction and enrichment pedagogy on reading achievement in five elementary schools. American Educational Research Journal, 48, 462-501. doi:10.3102/0002831210382891
Rogers, K. B. (2007). Lessons learned about educating the gifted and talented: A synthesis of the research on educational practice. Gifted Child Quarterly, 51, 382-396. doi:10.1177/0016986207306324
Roy, A., Guay, F., & Valois, P. (2013). Teaching to address diverse learning needs: Development and validation of a differentiated instruction scale. International Journal of Inclusive Education, 17, 1186-1204. doi:10.1080/13603116.2012.743604
Schram, E., Van der Meer, F., & Van Os, S. (2013). Omgaan met verschillen: (G)een kwestie van maatwerk [Responding to differences: (Not) a matter of customisation] (No. AN2.6547.542). Enschede, the Netherlands: SLO.
Scott, B. J., Vitale, M. R., & Masten, W. G. (1998). Implementing instructional adaptations for students with disabilities in inclusive classrooms: A literature review. Remedial and Special Education, 19, 106-119. doi:10.1177/074193259801900205
Skaalvik, E. M., & Skaalvik, S. (2007). Dimensions of teacher self-efficacy and relations with strain factors, perceived collective teacher efficacy, and teacher burnout. Journal of Educational Psychology, 99, 611-625. doi:10.1037/0022-0663.99.3.611
Slavin, R. E. (1987). Ability grouping and student achievement in elementary schools: A best evidence synthesis. Review of Educational Research, 57, 293-336. doi:10.3102/00346543057003293
Streiner, D. L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal consistency. Journal of Personality Assessment, 80, 99-103. doi:10.1207/S15327752JPA8001_18
Teddlie, C., Creemers, B., Kyriakides, L., Muijs, D., & Yu, F. (2006). The international system for teacher observation and feedback: Evolution of an international study of teacher effectiveness constructs. Educational Research & Evaluation, 12, 561-582. doi:10.1080/13803610600874067
Tieso, C. L. (2003). Ability grouping is not just tracking anymore. Roeper Review, 26, 29-36. doi:10.1080/02783190309554236
Tieso, C. L. (2005). The effects of grouping practices and curricular adjustments on achievement. Journal for the Education of the Gifted, 29, 60-89.
Tomlinson, C. A. (2005). How to differentiate instruction in mixed-ability classrooms (2nd ed.). Upper Saddle River, NJ: Pearson Education.
Tomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., . . . Reynolds, T. (2003). Differentiating instruction in response to student readiness, interest and learning profile in academically diverse classrooms: A review of literature. Journal for the Education of the Gifted, 27, 119-145. doi:10.1177/016235320302700203
Tschannen-Moran, M., & Woolfolk Hoy, A. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17, 783-805. doi:10.1016/S0742-051X(01)00036-1
Van de Weijer-Bergsma, E., & Prast, E. J. (2013). Gedifferentieerd primair rekenonderwijs volgens experts: De resultaten uit een Delphi-onderzoek [Differentiated primary math education according to experts: Results from a Delphi study]. Orthopedagogiek: Onderzoek en Praktijk, 52, 336-349.
Van den Broek-d’Obrenan, V., Van Cauwenberghe, C., Van Dongen, D., Drewes, I., Knuver, A., Lincklaen Arriëns, K., . . . De Vries, B. (2012). De staat van het onderwijs: Onderwijsverslag 2010-2011 [The state of education: Educational report 2010-2011]. Utrecht, the Netherlands: Inspectie van het Onderwijs. Retrieved from http://www.onderwijsinspectie.nl/binaries/content/assets/Onderwijsverslagen/2012/onderwijsverslag_2010_2011_printversie.pdf
Van Gelder, L., Oudkerk Pool, T., Peters, J., & Sixma, J. (1973). Didactische analyse [Didactical analysis]. Groningen, The Netherlands: Wolters-Noordhoff.
Van Groenestijn, M., Borghouts, C., & Janssen, C. (2011). Protocol ernstige rekenwiskunde-problemen en dyscalculie [Protocol severe mathematics difficulties and dyscalculia]. Assen, the Netherlands: Van Gorcum.
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