Using tasks that cognitively challenge students is essential, particularly in mathematics, in order to promote students’ mathematical thinking and achieve meaningful understanding (Clarke et al., 2014). Cognitive activation should, however, apply to all students, regardless of their readiness level (Tekkumru-Kisa et al., 2020). Even in mixed ability classrooms, all students can productively engage with cognitive demanding tasks, if provided with necessary scaffolds (Russo et al., 2019). Doing so requires differentiating teaching to meet students where they are and support their learning accordingly; yet, to customize teaching based on students’ needs, interests, and readiness level, teachers need to collect information on students’ current status and learning to make informed decisions on how to better support them (Black & William, 1998). Therefore, as argued by Fault and colleagues (2024), the starting point for linking cognitive activation with differentiation is formative assessment.

Several scholars (e.g., Eysink & Schildkamp, 2021; Fauth et al., 2024) have emphasized the multiple benefits of combining the three teaching dimensions—cognitive activation, differentiation, and formative assessment—in practice. These dimensions’ close interdependence and complementarity and their potential to promote effective learning and deep understanding have been emphasized, at least at a theoretical level (Moon, 2005). Moreover, it has even been argued that the confluence of the three dimensions in teaching is necessary, as one cannot stand without the others (Fauth et al., 2024). Nonetheless, despite the theoretical research interest in the interplay of these dimensions, teaching that utilizes a combination of them has not been well studied at the empirical level (cf. Davis & Autin, 2020). Most existing studies have empirically examined only two of these dimensions at most [e.g., Charalambous et al. (2023) examined cognitive activation and differentiation]. Additionally, researchers have not investigated the impact of such teaching on learning outcomes, despite all the theoretical claims of its potential significant benefits (Fauth et al., 2024; Keuning et al., 2022). Nor have they focused on the challenges experienced by the teachers in trying to design and implement teaching that utilizes a combination of these dimensions, despite claims that such teaching is particularly ambitious (Charalambous et al., 2023; Keuning et al., 2022).

Taking these research gaps into consideration, the present study aimed to design, implement, and empirically evaluate teaching that brings together cognitive activation, differentiation, and formative assessment. In particular, the study sought to address the following questions:

• What challenges do teachers face in trying to design and implement teaching that utilizes a combination of differentiation and formative assessment in teaching cognitive demanding tasks in mathematics? 
• To what extent and in what ways can a teaching intervention on cognitively challenging teaching that builds on differentiation and formative assessment support students’ cognitive, meta-cognitive, and affective learning?

Design: The present study employed a mixed-methods approach utilizing a convergent design, with quantitative and qualitative data concurrently being used to provide insights into the research questions (Creswell & Plano Clark, 2017). Additionally, it employed the approach of studying one’s own teaching, as modeled by scholars such as Lampert (2001). Participants and Context: Eleven 6th grade students (age 12) of an urban, underprivileged primary school with a high percentage of students from immigrant backgrounds participated in the study. Despite its small size, its composition made this class a critical case (Patton, 2015), as it rendered cognitively challenging teaching quite demanding, thus serving as an appropriate site for exploring the implementation of the focal teaching intervention. Content-wise, the intervention focused on pre-algebra, covering two units with topics such as variables, properties of equalities, and equations. Data Collection: The teacher-researcher (first author) kept a detailed reflective journal, in which she detailed the challenges she faced during the intervention, her decision making, and her observations on students’ progress. The lesson plans utilized in the intervention—based on the principles of cognitive activation, differentiation, and formative assessment—were co-designed and revised in collaboration with a researcher with expertise in teaching quality (second author). Ten 80-minute algebra lessons were conducted and videotaped. A validated mathematics pre-algebra test (Sergiou et al., 2019) was administered before and after the intervention, as well as three months after the intervention to check for retention effects; students were also asked to predict their performance before answering the test tasks to measure their meta-cognitive skills. Two surveys were also administered: one to investigate students’ attitudes towards mathematics (drawn from IEA, 2022), and another to investigate students’ metacognitive skills (validated in Kyriakides et al., 2020). Pre- and post-intervention interviews were also conducted with each student-participant to investigate their attitudes and feelings towards the mathematics lessons. At the end of the intervention, the students also completed a questionnaire to explore their views regarding the usefulness and appeal of the differentiation and formative assessment techniques utilized in the lessons. Data Analysis: The quantitative data of the tests and surveys were analyzed using Wilcoxon’s Singed Rank test to discover any potential improvements in students’ cognitive, meta-cognitive, and affective learning. The data collected from students’ interviews and the teacher’s reflective journal were analyzed using the constant comparative method (Patton, 2015).

The study highlighted several challenges experienced by the teacher in trying to design and implement teaching that combines the above dimensions. Specifically, (a) the process proved to be time-consuming, particularly in planning and implementation; (b) the wide variation in students’ learning profiles made it more difficult to adequately meet students’ learning needs; and (c) the frequent absenteeism of students and their unsupportive family environment with respect to learning further aggravated the complexity. Despite these challenges, the study showed significant improvement in students’ learning. In the cognitive domain, students’ performance between the pre-intervention and either the post-intervention test (W(10) =0, z=2.94, p<.05) or the retention test (W(10) =0, z=2.93, p<.05) was significantly improved. In the affective domain, students’ positive attitude towards mathematics was improved (W(10) =0, z=2.52, p<.05), but no significant decrease was observed in their negative attitudes toward mathematics (W(10) =14.50, z=0.49, p>.05). Finally, there was an improvement in students’ meta-cognitive performance, but it was marginally significant regarding planning (W(10) =6, z=1.73, p<.10) and not significant in the other three domains examined [performance predicting: W(10) =28, z=0.45, p>.05; controlling: W(10)=30.50, z=.0.23, p>.05; and evaluating: W(10) =27.50, z=0.49, p>.05]. The student interview data showcased students’ positive appraisal of the intervention tools as a key element for supporting their learning (e.g., “The enablers helped me understand the problems and think more clearly how to solve them”, “I was able to solve difficult problems in this unit and this made me feel better”). In conclusion, the study provides empirical support that despite being challenging, teaching that combines cognitive activation, differentiation, and formative assessment has significant potential for supporting student learning. Therefore, such findings respond to international calls to support quality and equity in education (Kyriakides et al., 2021), by showing that it is possible to productively engage all students in cognitively activating teaching.

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139-148. Charalambous C.Y., Agathangelou S.A., Kasapi, E. & Christofidou, E. (2023). Learning to teach ambitiously: a multiple case study of practicing teachers’ experimentation with enablers and extenders. Journal of Mathematics Teacher Education, 26, 363–394. Clarke, D.M., Cheeseman, J., Roche, A., & van der Schans, S. (2014). Teaching strategies for building student persistence on challenging tasks: insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development, 16(2), 46-70. Creswell, J.W., & Plano Clark, V. L. (2017). Designing and conducting mixed methods research. Sage. Davis, T. C., & Autin, N. P. (2020). The cognitive trio: Backward design, formative assessment, and differentiated instruction. Research Issues in Contemporary Education, 5(2), 55-70. Eysink, T. H. S. & Schildkamp, K. (2021). A conceptual framework for assessment-informed differentiation in the classroom. Educational Research, 63(3), 261-278. doi: 10.1080/00131881.2021.1942118 Fauth, B., Decristan, J., & Dumont, H. (2024). Kognitive Aktivierung und adaptiver Unterricht. In A.-K. Praetorius, W. Wemmer-Rogh, P. Schreyer & M. Brinkmann (Eds.). Kognitive Aktivierung unter der Lupe (pp. 248-260). Waxmann. International Evaluation Association (IEA) (2022). TIMSS 2023: Student questionnaire. IEA. Kyriakides, L. Anthimou, M., & Panayiotou, A. (2020). Searching for the impact of teacher behavior on promoting students’ cognitive and metacognitive skills. Studies in Educational Evaluation, 64, 100810. Kyriakides, L., Creemers, B. P., Panayiotou, A., & Charalambous, E. (2021). Quality and equity in education: Revisiting theory and research on educational effectiveness and improvement. Routledge. Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press. Moon, T. R. (2005). The role of assessment in differentiation. Theory into Practice, 44(3), 226-233. Patton, M. Q. (2015). Qualitative evaluation and research methods. Sage. Russo, J., Livy, S., Bobis, J., McCormick, M., Downton, A., Sullivan, P. & Hughes, S. (2019). Teaching with challenging tasks in the first years of school: What are the obstacles and how can teachers overcome them. Australian Primary Mathematics Classroom, 24(1), 11-18. Sergiou, S., & Charalambous, C. Y. (2019). A pilot study validating a tool measuring student learning in algebra. In C. Christou (Ed.), Proceedings of the 8th Panhellenic Conference of ENEDIM (pp. 113–123). ENEDIM. Tekkumru-Kisa, M., Stein, M. K., & Doyle, W. (2020). Theory and research on tasks revisited: Task as a context for students' thinking in the era of ambitious reforms in mathematics and science. Educational Researcher, 49(8), 606-617.