The new curriculum material

I’ve been delving into research on virtual manipulatives this semester, and recently I’ve asked myself this question: Are virtual manipulatives curriculum materials?

From what I know of print curriculum-materials research (e.g., Choppin, 2011; Drake & Sherin, 2009; Remillard & Bryans, 2004), physical manipulatives haven’t generally been considered as curriculum materials in their own right. On the other hand, in the last few months I’ve read at least two studies (Hansen, Mavrikis, & Geraniou, 2016; Trgalová, & Rousson, 2017) that treat a digital manipulative as a curriculum material, studying their use quite similarly to the way that use of curriculum guides have been studied.

Why the contrast? I think there are at least two reasons.

First, virtual manipulatives have a lot more elements that can be intentionally designed. Actions on virtual manipulatives can be constrained (Manches, O’Malley, & Benford, 2010; Moyer-Packenham & Westenskow, 2013), sound and visual effects can be chosen (Moyer-Packenham et al., 2016; Paek, Hoffman, & Black, 2016), representations can be dynamically linked to each other (Moyer-Packenham & Westenskow, 2013; Sarama & Clements, 2009), and so on. Any sort of deliberate choice — of which there are many — by a designer is likely influenced by a particular imagined use.

Second, it’s common for virtual manipulatives to be embedded in apps or websites that either directly provide or are highly suggestive of specific tasks (e.g., Watts et al., 2016). This is in contrast to most physical manipulatives, which are generally sold and stored independently of any particular scheme of use. Activities (within curriculum materials or elsewhere) often assume their use, but the manipulatives themselves don’t assume a task the way that tasks sometimes assume use of physical manipulatives.

In all, virtual manipulatives seem much harder than physical manipulatives to separate from the tasks they’re used to accomplish. And tasks are at the heart of curriculum. While physical manipulatives have not generally been considered as curriculum materials, I think virtual manipulatives should be.

Why does it matter?

One of my biggest worries related to technology trends in classrooms is the overuse of adaptive-tutor-like programs that (claim to) use sophisticated algorithms to diagnose students’ exact position along learning paths and walk them forward. I think the desires for automated assessment and personalized learning are, to a point, understandable, but I worry that overuse of such programs removes the teacher from having a role in making instructional decisions. It speaks to a trend of deprofessionalization of teaching, which I think is a mistake. My hope would be that if we treat virtual manipulatives as curriculum materials — if we take seriously the teacher’s role in their use (Remillard, 2005) — it might prevent the potential of virtual manipulatives as teaching tools from morphing into attempts to turn virtual manipulatives into replacements for teachers.


Choppin, J. (2011). Learned adaptations: Teachers’ understanding and use of curriculum resources. Journal of Mathematics Teacher Education, 14(5), 331–353.

Drake, C., & Sherin, M. G. (2009). Developing curriculum vision and trust: Changes in teachers’ curriculum strategies. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction (pp. 322–337). New York: Routledge.

Hansen, A., Mavrikis, M., & Geraniou, E. (2016). Supporting teachers’ technological pedagogical content knowledge of fractions through co-designing a virtual manipulative. Journal of Mathematics Teacher Education, 19(2–3), 205–226.

Manches, A., O’Malley, C., & Benford, S. (2010). The role of physical representations in solving number problems: A comparison of young children’s use of physical and virtual materials. Computers and Education, 54(3), 622–640.

Moyer-Packenham, P. S., Bullock, E. K., Shumway, J. F., Tucker, S. I., Watts, C. M., Westenskow, A., … Jordan, K. (2016). The role of affordances in children’s learning performance and efficiency when using virtual manipulative mathematics touch-screen apps. Mathematics Education Research Journal, 28(1), 79–105.

Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of Virtual Manipulatives on Student Achievement and Mathematics Learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35–50.

Paek, S., Hoffman, D. L., & Black, J. B. (2016). Perceptual factors and learning in digital environments. Educational Technology Research and Development, 64(3), 435–457.

Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.

Remillard, J. T., & Bryans, B. (2004). Teachers ’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388.

Sarama, J., & Clements, D. H. (2009). “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), 145–150.

Trgalová, J., & Rousson, L. (2017). Model of appropriation of a curricular resource: a case of a digital game for the teaching of enumeration skills in kindergarten. ZDM – Mathematics Education, 49(5), 769–784.

Watts, C. M., Moyer-Packenham, P. S., Tucker, S. I., Bullock, E. P., Shumway, J. F., Westenskow, A., … Jordan, K. (2016). An examination of children’s learning progression shifts while using touch screen virtual manipulative mathematics apps. Computers in Human Behavior, 64, 814–828.


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