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<p>Given preservice teachers’ (PSTs’) persistent challenges in developing the deep fraction knowledge they need to deliver high-quality mathematics instruction, understanding how they internalize fraction concepts is essential. This exploratory investigation explicates how a theoretically informed dynamic digital tool we developed, FracTopia, can mediate PSTs’ internalization of fraction concepts and operations by enabling learners to visualize, manipulate, and make sense of fractional relationships in ways that static representations cannot. After qualitatively analyzing 44 PSTs’ responses to eight problems using the tool for insight into their learning processes, we identified overall trends and selected representative examples of the most common strategies used to solve each problem. The findings suggest that FracTopia, and by extension similar digital tools as active semiotic mediators, can facilitate the transformation of external representations into internal cognitive tools that support PSTs’ development of robust understanding of fractions. This study highlights the potential of integrating semiotic mediation into digital tool design to enhance mathematics education in the digital age.</p>

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Exploring preservice teachers’ problem-solving with fractopia: A dynamic digital tool developed to support semiotic mediation in fraction learning

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Mi Yeon Lee,
  • Sheunghyun Yeo

摘要

Given preservice teachers’ (PSTs’) persistent challenges in developing the deep fraction knowledge they need to deliver high-quality mathematics instruction, understanding how they internalize fraction concepts is essential. This exploratory investigation explicates how a theoretically informed dynamic digital tool we developed, FracTopia, can mediate PSTs’ internalization of fraction concepts and operations by enabling learners to visualize, manipulate, and make sense of fractional relationships in ways that static representations cannot. After qualitatively analyzing 44 PSTs’ responses to eight problems using the tool for insight into their learning processes, we identified overall trends and selected representative examples of the most common strategies used to solve each problem. The findings suggest that FracTopia, and by extension similar digital tools as active semiotic mediators, can facilitate the transformation of external representations into internal cognitive tools that support PSTs’ development of robust understanding of fractions. This study highlights the potential of integrating semiotic mediation into digital tool design to enhance mathematics education in the digital age.