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1. Reasoning about Equations with Tape Diagrams: Insights from Math Teachers and College Students

   https://doi.org/https://doi.dx.org/10.22318/icls2021.685  

   Bartel, A. N.; Silla, E. M.; Vest, N. A.; Nagashima, T.; Aleven, V.; Alibali, M. W. (January 2021, Proceedings of the 15th International Conference of the Learning Sciences - ICLS 2021)

   de Vries, E.; Hod, Y.; Ahn, J. (Ed.)

   Research has shown that tape diagrams are beneficial for algebra learning. However, it is unclear whether certain visual features of tape diagrams have implications for learning. We investigated, with undergraduate students and math teachers, whether tape diagrams with different visual features (color, presence of outer lines, and position of the constant) differentially support reasoning about equations and whether people have preferences for certain visual features. Variations in visual features did not affect students’ or teachers’ reasoning accuracy; but each group displayed systematic preferences for most visual features considered. Future research should examine the effects of these visual features on performance while solving equations. 

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2. Reasoning about equations with tape diagrams: Insights from math teachers and college students

   Bartel, A. N.; Silla, E. M.; Vest, N. A.; Nagashima, T.; Aleven, V.; Alibali, M. W. (January 2021, Proceedings of the 15th International Conference of the Learning Sciences - ICLS 2021)

   de Vries, E.; Hod, Y.; Ahn, J. (Ed.)

   Research has shown that tape diagrams are beneficial for algebra learning. However, it is unclear whether certain visual features of tape diagrams have implications for learning. We investigated, with undergraduate students and math teachers, whether tape diagrams with different visual features (color, presence of outer lines, and position of the constant) differentially support reasoning about equations and whether people have preferences for certain visual features. Variations in visual features did not affect students’ or teachers’ reasoning accuracy; but each group displayed systematic preferences for most visual features considered. Future research should examine the effects of these visual features on performance while solving equations. 

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3. Students’ Self-Regulated Use of Diagrams in a Choice-based Intelligent Tutoring System

   Nagashima, T.; Tseng, S.; Ling, E.; Bartel, A. N.; Vest, N. A.; Silla, E. M.; Alibali, M. W.; Aleven, V. (January 2022, Proceedings of the 16th International Conference of the Learning Sciences - ICLS 2022)

   Chinn, C.; Tan, E.; Chao, C.; Kali, Y. (Ed.)

   Learners’ choices as to whether and how to use visual representations during learning are an important yet understudied aspect of self-regulated learning. To gain insight, we developed a choice-based intelligent tutor in which students can choose whether and when to use diagrams to aid their problem solving in algebra. In an exploratory classroom study with 26 students, we investigated how learners choose diagrams and how their choice behaviors relate to learning outcomes. Students who proactively chose to use diagrams achieved higher learning outcomes than those who reactively used diagrams when they made incorrect attempts. This study contributes to understanding of self-regulated use of visual representations during problem solving. 

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4. Students’ self-regulated use of diagrams in a choice-based intelligent tutoring system

   Nagashima, T.; Tseng, S.; Ling, E.; Bartel, A. N.; Vest, N. A.; Silla, E. M.; Alibali, M. W.; Aleven, V. (June 2022, Proceedings of the 16th International Conference of the Learning Sciences , ICLS 2022)

   Chinn, C.; Tan, E.; Chan, C.; Kali, Y. (Ed.)

   Learners’ choices as to whether and how to use visual representations during learning are an important yet understudied aspect of self-regulated learning. To gain insight, we developed a choice-based intelligent tutor in which students can choose whether and when to use diagrams to aid their problem solving in algebra. In an exploratory classroom study with 26 students, we investigated how learners choose diagrams and how their choice behaviors relate to learning outcomes. Students who proactively chose to use diagrams achieved higher learning outcomes than those who reactively used diagrams when they made incorrect attempts. This study contributes to understanding of self-regulated use of visual representations during problem solving. 

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5. Enhancing conceptual knowledge in early algebra through scaffolding diagrammatic self-explanation

   Nagashima, T. (January 2020, 14th International Conference of the Learning Sciences (ICLS) 2020)

   Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students explain their problem-solving steps in the form of diagrams. We used contrasting cases to support students’ sense-making between algebraic equations and diagrams in the self-explanation activity. We conducted a classroom experiment with 41 students in grades 5 and 6 to test the effectiveness of this strategy when embedded in an Intelligent Tutoring System for algebra. We found that scaffolded diagrammatic self-explanation enhanced conceptual knowledge for students who did not have prior knowledge of formal equation-solving strategies. The study is the first experimental study showing that visual representations can enhance conceptual knowledge in early algebra. 

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