Assessing Proceptual Understanding In the Context of Connected Classroom

  • Ernawati Ernawati University of Bristol


Some mathematics teachers in Indonesia still find it challenging to conduct a formative assessment in a class with many students. A problem emerges in how to facilitate an environment that uses the type of engaging discussion needed for formative assessment to be successful. Meanwhile, in mathematics learning, proceptual (process and conceptual) understanding is considered prominent for success in learning mathematics. This understanding could be enhanced by using an appropriate strategy of discussion, which could be managed along with conducting a formative assessment. Overcoming this challenge, promoting a connected classroom might be beneficial to facilitating formative evaluation in a large class. Therefore, this paper aims to develop a method for formatively assessing students’ mathematics understanding that mathematics teachers could use with a focus on proceptual understanding. Reviewing some literature on the topics of mathematics understanding, formative assessment, and connected classroom has established a framework to help teachers develop guidance for conducting formative assessment in proceptual understanding using a connected classroom. The framework based might be used to help mathematics teachers prepare formative assessments in a class with many students. An example of how to develop a guide to assess students' proceptual understanding of algebra is also provided in this paper.

Keywords: proceptual understanding, formative assessment, connected classroom 


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Barnett, C. (1991). Building a case-based curriculum to enhance the pedagogical content knowledge of mathematics teachers. Journal of Teacher Education, 42(4), 263-272.

Beatty, I. D., & Gerace, W. J. (2009). Technology-enhanced formative assessment: A research-based pedagogy for teaching science with classroom response technology. Journal of Science Education and Technology, 18(2), 146-162.

Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2004). Working inside the black box: Assessment for learning in the classroom. Phi delta kappan, 86(1), 8-21.

Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: principles, policy & practice, 5(1), 7-74.

Cross, B. E. (2003). Learning or unlearning racism: Transferring teacher education curriculum to classroom practices. Theory into practice, 42(3), 203-20.

Cusi, A., Morselli, F., & Sabena, C. (2017). Promoting formative assessment in a connected classroom environment: Design and implementation of digital resources. ZDM, 49(5), 755-767.

Drijvers, P. H. M. (2003). Learning algebra in a computer algebra environment: Design research on the understanding of the concept of parameter (Doctoral dissertation).

Ferry, B., Hedberg, J., & Harper, B. (1998). How do preservice teachers use concept maps to organize their curriculum content knowledge?. Journal of Interactive Learning Research, 9, 83-104.

Gray, E., & Tall, D. (1993). Success and failure in mathematics: the flexible meaning of symbols as process and concept. Mathematics teaching, 142, 6-10.

Hodgen, J., & Wiliam, D. (2006). Mathematics inside the black box. London: GL Assessment.

Hunter, M., & Monaghan, J. (1996). Some issues in assessing proceptual understanding. In L. Puig & A. Gutiérrez (Ed.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, 3, 97-104.

Irving, K. E. (2006). The Impact of Educational Technology on Student Achievement: Assessment. Science Educator, 15(1), 13-20.

Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26, 683-710.

Mason, J. (2002). Minding Your Qs and Rs: effective questioning and responding in the mathematics classroom. in L. Haggerty (Ed.) Aspects of Teaching Secondary Mathematics: perspectives on practice, RoutledgeFalmer, London, 248-258.

Quyen, N. T. D., & Khairani, A. Z. (2017). Reviewing the challenges of implementing formative assessment in Asia: The need for a professional development program. Journal of Social Science Studies, 4(1), 160-177.

Roschelle, J., Penuel, W. R., & Abrahamson, L. (2004). The networked classroom. Educational Leadership, 61(5), 50-54.

Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36.

Shirley, M. L., & Irving, K. E. (2015). Connected classroom technology facilitates multiple components of formative assessment practice. Journal of Science Education and Technology, 24(1), 56-68.

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics teaching, 77(1), 20-26.

Smith, M. K. (2000) 'Curriculum theory and practice' the encyclopaedia of informal education. Retrieved May, 14, 2020 from

Wiliam, D. (2001). An overview of the relationship between assessment and the curriculum. Curriculum and assessment, 1, 165-181.

Wiliam, D., & Thompson, M. (2008) Integrating Assessment with Learning: What Will It Take to Make It Work? In: Dwyer, CA, (Ed.) The Future of Assessment: Shaping Teaching and Learning, 53-82.
How to Cite
ERNAWATI, Ernawati. Assessing Proceptual Understanding In the Context of Connected Classroom. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 6, n. 2, p. 133-146, july 2022. ISSN 2549-5070. Available at: <>. Date accessed: 04 dec. 2023. doi: