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  1. de Vries, E. ; Ahn, J. ; Hod, Y. (Ed.)
    Despite the prevalence of conducting classroom studies using educational technology, it is underexplored what practical benefits classroom studies with educational technology offer to teachers and students, and what concerns or challenges they perceive. Our interviews found that teachers view study participation as a meaningful learning opportunity but also shared challenges and concerns, some of which are related to remote learning during the COVID-19 pandemic. We offer strategies that researchers can employ when conducting classroom studies.
  2. 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.
  3. 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.
  4. 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.
  5. Fitch, T. ; Lamm, C. ; Leder, H. ; Teßmar-Raible, K. (Ed.)
    Although visual representations are generally beneficial for learners, past research also suggests that often only a subset of learners benefits from visual representations. In this work, we designed and evaluated anticipatory diagrammatic self-explanation, a novel form of instructional scaffolding in which visual representations are used to guide learners’ inference generation as they solve algebra problems in an Intelligent Tutoring System. We conducted a classroom experiment with 84 students in grades 5-8 in the US to investigate the effectiveness of anticipatory diagrammatic self-explanation on algebra performance and learning. The results show that anticipatory diagrammatic self-explanation benefits learners on problem-solving performance and the acquisition of formal problem-solving strategies. These effects mostly did not depend on students’ prior knowledge. We analyze and discuss how performance with the visual representation may have influenced the enhanced problem-solving performance.
  6. de Vries, E. ; Ahn, J. ; Y. Hod, Y. (Ed.)
    Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design self-explanation support that simultaneously facilitates performance and learning outcomes. Towards this goal, we designed anticipatory diagrammatic self-explanation, a novel form of self-explanation embedded in an Intelligent Tutoring System (ITS). In our ITS, anticipatory diagrammatic self-explanation scaffolds learners by providing visual representations to help learners predict an upcoming strategic step in algebra problem solving. A classroom experiment with 108 middle-school students found that anticipatory diagrammatic self-explanation helped students learn formal algebraic strategies and significantly improve their problem-solving performance. This study contributes to understanding of how self-explanation can be scaffolded to support learning and performance.
  7. de Vries, E. ; Ahn, J. ; Hod, Y. (Ed.)
    Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design self-explanation support that simultaneously facilitates performance and learning outcomes. Towards this goal, we designed anticipatory diagrammatic self-explanation, a novel form of self-explanation embedded in an Intelligent Tutoring System (ITS). In our ITS, anticipatory diagrammatic self-explanation scaffolds learners by providing visual representations to help learners predict an upcoming strategic step in algebra problem solving. A classroom experiment with 108 middle-school students found that anticipatory diagrammatic self-explanation helped students learn formal algebraic strategies and significantly improve their problem-solving performance. This study contributes to understanding of how self-explanation can be scaffolded to support learning and performance.
  8. When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed Pedagogical Affordance Analysis (PAA). PAA involves analyzing teachers’ Pedagogical Content Knowledge and/or Technological Pedagogical Content Knowledge to elicit pedagogical affordances and constraints that are specific to a given instructional goal. Information obtained through PAA can help in designing, refining, and/or evaluating instructional tools. We present a case study in which we used PAA to successfully design a visual representation for middle-school algebra. To the best of our knowledge, PAA is the only available systematic method that leverages teachers’ pedagogical knowledge in identifying pedagogical affordances and constraints. PAA can be used across a wide range of existing tools and prototypes of to-be-designed tools.
  9. 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.
  10. Gresalfi, M. ; Horn, I. S. (Ed.)
    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.