Investigating differentiation: exploring the impact of task difficulty labelling on students’ mathematics performance
DOI:
https://doi.org/10.7146/nomad.v30i1.152734Keywords:
mathematicsAbstract
This study investigated the effect of task difficulty labelling on students’ mathematics performance. Lower secondary school students (n = 436) participated in an experimental study in which the control group received three similar tasks without labels and the experimental groups received the same tasks labelled as easy, medium and difficult. The findings indicate that the students in the control group outperformed the students assigned tasks labelled as difficult. Additionally, the students’ performance was worse when solving tasks labelled difficult compared to when they were given similar tasks labelled easy or medium, but the differences are not significant. We strongly advise exercising prudence when assigning tasks labelled difficult.
References
Anthony, G., Hunter, J. & Hunter, R. (2019). Working towards equity in mathematics education: Is differentiation the answer? Mathematics Education Research Group of Australasia.
Auliya, K. & Widjajanti, D. B. (2023). Singaporean and Japanese maths textbooks: character, structure, and content. Mosharafa. Jurnal Pendidikan Matematika, 12 (1), 155–168. https://doi.org/10.31980/mosharafa.v12i1.764
Bal, A. P. (2016). The effect of the differentiated teaching approach in the algebraic learning field on students’ academic achievements. Eurasian Journal of Educational Research, 16 (63), 185–204. http://dx.doi.org/ 10.14689/ejer.2016.63.11
Bandura, A. (1997). Self-efficacy: the exercise of control. W.H. Freeman.
Bannister, N. A. (2016). Breaking the spell of differentiated instruction through equity pedagogy and teacher community. Cultural Studies of Science Education, 11 (2), 335–347. https://doi.org/10.1007/s11422-016-9766-0
Björnsson, J. K. (2016). Metodegrunnlag for nasjonale prøver. Utdanningsdirektoratet. https://www.udir.no/globalassets/filer/vurdering/nasjonaleprover/metodegrunnlag-fornasjonale-prover-august-2018.pdf
Botten, G., Daland, E. & Dalvang, T. (2008). Tilpasset opplæring innenfor fellesskapet. Tangenten, 19 (2), 23–27.
Brändström, A. (2005). Differentiated tasks in mathematics textbooks. An analysis of the levels of difficulty [Unpublished licentiate thesis]. Luleå University of Technology.
Butz, A. R. & Usher, E. L. (2015). Salient sources of early adolescents’ self-efficacy in two domains. Contemporary Educational Psychology, 42, 49–61. https://doi.org/10.1016/j.cedpsych.2015.04.001
Chen, P. P. (2003). Exploring the accuracy and predictability of the self-efficacy beliefs of seventh-grade mathematics students. Learning and Individual Differences, 14 (1), 77–90. https://doi.org/ 10.3200/JEXE.75.3.221-244
Cohen, L., Manion, L. & Morrison, A. K. (2018). Research methods in education. Routledge.
Collins, J. L. (1984). Self-efficacy and ability in achievement behavior [Unpublished doctoral thesis]. Stanford University.
Creswell, J. W. & Creswell, J. D. (2018). Research design: quantitative, qualitative and mixed methods. Sage.
Csikszentmihalyi, M. (2005). Flow og engagement i hverdagen. Dansk Psykologisk Forlag.
Dolonen, J. A., Furberg, A., Gilje, O., Ingulfsen, L., Kluge, A. et al. (2016). Med ARK&APP. Bruk av læremidler og ressurser for læring på tvers av arbeidsformer. University of Oslo.
Doménech-Betoret, F., Abellán-Roselló, L. & Gómez-Artiga, A. (2017). Self-efficacy, satisfaction, and academic achievement: the mediator role of students’ expectancy-value beliefs. Frontiers in Psychology, 8, 1193. https://doi.org/10.3389/fpsyg.2017.01193
Eriksen, E., Solomon, Y., Bjerke, A. H., Gray, J. & Kleve, B. (2022). Making decisions about attainment grouping in mathematics: teacher agency and autonomy in Norway. Research Papers in Education, 1–21. https://doi.org/10.1080/02671522.2022.2135014
Everitt, B. S. (2002). The Cambridge dictionary of statistics. Cambridge University Press.
Ghalem, Â., Okar, C., Chroqui, R. & Semma, E. (2016). Performance: a concept to define. Logistica, 1–13. https://doi.org/10.13140/RG.2.2.24800.28165
Grave, I. & Pepin, B. (2015). Teachers’ use of resources in and for mathematics teaching. Nordic Studies in Mathematics Education, 20 (3-4), 199–222.
Hackett, G. & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education, 20 (3), 261–273. https://doi.org/10.2307/749515
Herset, M. & El Ghami, M. (2022). The effect of level-marking mathematical tasks on students’ time spent on such tasks and correct solutions: an experimental study. CERME12. https://hal.science/hal-03745597v1/file/TWG08_06_Herset.pdf
Herset, M., El Ghami, M. & Bjerke, A. H. (2023). The effect of level-marked mathematics tasks on students’ self-efficacy: an experimental study. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1116386
Joët, G., Usher, E. L. & Bressoux, P. (2011). Sources of self-efficacy: an investigation of elementary school students in France. Journal of Educational Psychology, 103 (3), 649–663. https://doi.org/10.1037/a0024048
Keane, G. & Heinz, M. (2019). Differentiated homework: impact on student engagement. Journal of Practitioner Research, 4 (2), 1–23.
https://doi.org/10.5038/2379-%20%099951.4.2.1111
Krauthausen, G. (2018). Natural differentiation – an approach to cope with heterogeneity. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited lectures from the 13th international congress on mathematical education (pp. 325–341). Springer.
Kristensen, T. E. (2008). Tilpasset opplæring innenfor fellesskapet. Tangenten, 19 (2), 9–14.
Lai, C. P., Zhang, W. & Chang, Y. L. (2020). Differentiated instruction enhances sixth-grade students’ mathematics self-efficacy, learning motives, and problem-solving skills. Social Behavior and Personality: an international journal, 48 (6), 1–13. https://doi.org/10.2224/sbp.9094
Little, C. A., Hauser, S. & Corbishley, J. (2009). Constructing complexity for differentiated learning. Mathematics Teaching in the Middle School, 15 (1), 34–42.
Liu, Q., Liu, J., Cai, J. & Zhang, Z. (2020). The relationship between domain- and task-specific self-efficacy and mathematical problem posing: a large-scale study of eighth-grade students in China. Educational Studies in Mathematics, 105 (3), 407–431. https://doi.org/10.1007/s10649-020-09977-w
Luster, R. (2008). A quantitative study investigating the effects of whole-class and differentiated instruction on student achievement [Unpublished doctoral thesis]. Walden University.
Mathiassen, K. (2009). Lektor – adjunkt – lærer: artikler for studiet i praktisk-pedagogisk utdanning. In I R. Mikkelsen & H. Flademoe (Eds.), Differensiert undervisning (pp. 123–136). Universitetsforlaget.
Olafsen, A. R. & Maugesten, M. (2022). Matematikkdidaktikk i klasserommet (3rd ed.). Universitetsforlaget.
Onyishi, C. N. & Sefotho, M. M. (2021). Differentiating instruction for learners’ mathematics self-efficacy in inclusive classrooms: Can learners with dyscalculia also benefit? South African Journal of Education, 41 (4), 1–15. https://doi.org/ 10.15700/saje.v41n4a1938
Özcan, Z. Ç., and Eren Gümüş, A. (2019). A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety. Australian Journal of Education, 63 (1), 116–134. https://doi.org/10.1177/000494411984007
Pajares, F. & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving. Contemporary Educational Psychology, 20 (4), 426–443. https://doi.org/10.1006/ceps.1995.1029
Pajares, F. & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: a path analysis. Journal of Educational Psychology, 86 (2), 193–203. https://doi.org/10.1037/0022-0663.86.2.193
Pajares, F. & Miller, M. D. (1995). Mathematics self-efficacy and mathematics performances: the need for specificity of assessment. Journal of counseling psychology, 42 (2), 190.
Pierce, R. L. & Adams, C. M. (2005). Using tiered lessons in mathematics. Mathematics Teaching in the Middle School, 11 (3), 144–149. https://doi.org/10.5951/MTMS.11.3.0144
Pozas, M., Letzel, V. & Schneider, C. (2020). Teachers and differentiated instruction: exploring differentiation practices to address student diversity. Journal of Research in Special Educational Needs, 20 (3), 217–230. https://doi.org/10.1111/1471-3802.12481
Schöber, C., Schütte, K., Köller, O., McElvany, N. & Gebauer, M. M. (2018). Reciprocal effects between self-efficacy and achievement in mathematics and reading. Learning and Individual Differences, 63, 1–11. https://doi.org/10.1016/j.lindif.2018.01.008
Scott, B. E. (2012). The effectiveness of differentiated instruction in the elementary mathematics classroom [Unpublished doctoral thesis]. Ball State University.
Singh, O. (2017). Danningsperspektiver på utforming av lærersubjektet i læreverket i matematikk. Norsk Pedagogisk Tidsskrift, 101 (3), 266–277. https://doi.org/10.18261/issn.1504-2987-2017-03-07
Skaalvik, E. M., Federici, R. A. & Klassen, R. M. (2015). Mathematics achievement and self-efficacy: relations with motivation for mathematics. International Journal of Educational Research, 72, 129–136. https://doi.org/10.1016/j.ijer.2015.06.008
Skaalvik, E. M. & Skaalvik, S. (2015). Motivasjon for læring: teori og praksis. Universitetsforlaget.
Smale-Jacobse, A. E., Meijer, A., Helms-Lorenz, M. &Maulana, R. (2019). Differentiated instruction in secondary education: a systematic review of research evidence. Frontiers in Psychology, 10, 2366. https://doi.org/10.3389/fpsyg.2019.02366
Spielberg, Y. & Azaria, A. (2021). Revelation of task difficulty in AI-aided education. In Proceedings of ICTAI (pp. 1403–1408). IEEE.
Street, K. E. S., Malmberg, L.-E. & Stylianides, G. J. (2017). Level, strength, and facet-specific self-efficacy in mathematics test performance. ZDM, 49 (3), 379–395. https://doi.org/10.1007/s11858-%20%09017-0833-0
Street, K. E., Stylianides, G. J. & Malmberg, L. E. (2022). Differential relationships between mathematics self-efficacy and national test performance according to perceived task difficulty. Assessment in Education: Principles, Policy & Practice, 29 (3), 288–309.
https://doi.org/10.1080/0969594X.2022.2095980
Suarez, D. (2007). Differentiation by challenge: using a tiered program of instruction in mathematics. In W. Powel & O. K. Powel (Eds), Making the difference: differentiation in international schools (pp. 199–227). CreateSpace Independent Publishing Platform.
Tomlinson, C. A. (2014). The differentiated classroom: responding to the needs of all learners. ASCD.
Tomlinson, C. A. & Imbeau, M. B. (2010). Leading and managing a differentiated classroom. ASCD.
Usher, E. L. & Pajares, F. (2009). Sources of self-efficacy in mathematics: a validation study. Contemporary Educational Psychology, 34 (1), 89–101. https://doi.org/ 10.1016/j.cedpsych.2008.09.002
Winther, K. (1965). Oppgavesamling i regning og matematikk: for 8. skoleår i den niårige folkeskolen. H. Aschehoug & Co.
Zakariya, Y. F. (2022). Improving students’ mathematics self-efficacy: a systematic review of intervention studies. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.986622
Zakariya, Y. F. (2021). Self-efficacy between previous and current mathematics performance of undergraduate students: an instrumental variable approach to exposing a causal relationship. Frontiers in Psychology, 11, 1–11.
https://doi.org/10.3389/fpsyg.2020.556607
Zuffianò, A., Alessandri, G., Gerbino, M., Kanacri, B. P. L., Di Giunta, L. et al. (2013). Academic achievement: the unique contribution of self-efficacy beliefs in self-regulated learning beyond intelligence, personality traits, and self-esteem. Learning and Individual Differences, 23, 158–162. https://doi.org/10.1016/j.lindif.2012.07.010
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Maria Herset, Mohamed El Ghami, Annette Hessen Bjerke
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
