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From the static to the dynamic: teachers’ varying use of digital technology to support conceptual learning in a curricular activity system

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Abstract

Dynamic representational technologies (DRTs), influenced by the seminal work of James Kaput and colleagues, have been in use in mathematics classrooms for decades. In this paper, we analyze 24 classrooms in the United States where teachers support students’ conceptual learning with technologies that support explorations of dynamic connections both within and across mathematical representations. These DRTs, built in alignment with Kaput’s principles, form part of a curricular activity system that embeds a central pedagogical routine. Yet despite the use of common DRTs, lessons, and professional development, classroom teaching practices varied widely. We characterize and analyze levels of technology use, which vary from using the technology as a static resource to taking advantage of dynamism to support students’ emerging explanations of mathematical concepts. There are important implications for further research into classroom use of DRTs and, more broadly, for curriculum developers and teacher educators.

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Acknowledgements

This chapter is based on the project funded by a grant from the Department of Education (U411B130019) and partly based on the evaluation study conducted by authors from Consortium for Policy Research in Education Report for the efficacy of the project. Any opinions and recommendations made in this chapter do not necessarily represent the views of the Department of Education or CPRE authors. We acknowledge the contributions of our colleagues Teresa Lara-Meloy and Ken Rafanan in conceiving the SunBay DRTs and the curriculum units that structured their use.

Author information

Authors and Affiliations

  1. SRI International, Menlo Park, CA, USA

    Philip Vahey & Nicholas Jackiw

  2. TERC, Cambridge, MA, USA

    Hee-Joon Kim & Jennifer Knudsen

  3. Independent Consultant, Boca Raton, FL, USA

    Hagit Sela

Authors
  1. Philip Vahey
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  2. Hee-Joon Kim
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  3. Nicholas Jackiw
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  4. Hagit Sela
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  5. Jennifer Knudsen
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Correspondence to Philip Vahey.

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Appendices

Appendix A

Teacher Survey of Comfort and Confidence in using technology for instructional items (Sirinides & Gray, 2018):

  • I have the knowledge and skills I need to use technology effectively for math instruction. (TCK)

  • I often use computers for instructional purposes. (TPK)

  • I am often frustrated when I use technology. (TK)

  • Students’ use of technology is more effective when they are working individually rather than in pairs or groups. (TPK)

  • Using technology enhances my mathematics instruction and delivery of content. (TPACK)

  • I learn technologies easily. (TK)

  • I feel comfortable having my students use a tablet/laptop during instruction. (TPK)

  • Using technology enhances students’ learning of mathematical concepts in my classroom.(TCK)

  • Using technology increases student engagement and interest in learning mathematics. (TCK, TPACK)

  • I frequently explore new technology for instruction. (TPK)

Examples items from the Teacher Allowance for Student Struggle with Problems (TASSP) measure (Clark et al., 2014):

  • Students learn mathematics best by working to solve accessible problems that entail a solution process that has not been demonstrated to them.

  • During mathematics class, I do not necessarily answer students’ questions immediately but rather let them struggle and puzzle things out for themselves.

  • During mathematics class, discussion should focus on students’ ideas and approaches, no matter whether their answers are correct or incorrect.

  • During mathematics class, students should be asked to solve problems and complete activities by relying on their own thinking without teachers modeling an approach.

  • Students can figure out how to solve many mathematics problems without being told what to do.

Appendix B: Selected themes and codes

Theme

Code

Description

Norms for prediction as conjecture

Prediction as conjecture

Teacher states that prediction is a quick conjecture

Non-judgmental for correctness

Teacher states that it’s okay for a prediction to be falsified

Absence of prediction norms

Missing norms for prediction

There is no evidence of discussion of prediction norms

Representation as static

No interaction with representation

Teacher does not indicate that DRTs are interactive

Representation as dynamic

Interaction with representation

Teacher demonstrates interaction with DRT such as dragging or testing predictions

Eliciting changing aspect of representation

Teacher orients student attention to how DRT changes through interaction

Procedure-based explanation

Elicit procedure

Teacher elicits procedures unrelated to DRT in student explanation

Recall facts

Teacher prompts students to recall facts/prior knowledge

DRT-based explanation - correctness

Elicit representation

Teacher elicits and scaffolds student explanation by orienting them to DRT

Correctness

Teacher shows how DRT reveals correctness of prediction without linking to math concept

DRT-based explanation - reasoning

Elicit representation

Teacher elicits and scaffolds student explanation by orienting them to DRT in technology

Structure/mathematical properties

Teacher focuses on DRT to reveal mathematical meanings or structure

Connecting representations

Eliciting more than one representation

Teacher elicits and scaffolds student explanation by orienting them to refer to multiple representations in technology

Attending to connections between representations

Teacher orients student attention to connections between representations

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Vahey, P., Kim, HJ., Jackiw, N. et al. From the static to the dynamic: teachers’ varying use of digital technology to support conceptual learning in a curricular activity system. ZDM Mathematics Education 52, 1275–1290 (2020). https://doi.org/10.1007/s11858-020-01182-6

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