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Integrating visual representations in an interactive learning activity effectively scaffolds performance and learning. However, it is unclear whether and how sustaining or interleaving visual scaffolding helps learners solve problems efficiently and learn from problem solving. We conducted a classroom study with 63 middle-school students in which we tested whether sustaining or interleaving a particular form of visual scaffolding, called anticipatory diagrammatic self-explanation in an Intelligent Tutoring System, helps students’ learning and performance in the domain of early algebra. Sustaining visual scaffolding during problem solving helped students solve problems efficiently with no negative effects on learning. However, in-depth log data analyses suggest that interleaving visual scaffolding allowed students to practice important skills that may help them in later phases of algebra learning. This paper extends scientific understanding that sustaining visual scaffold does not over-scaffold student learning in the early phase of skill acquisition in algebra. 

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. 

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We developed an approach to eliciting self-explanations in which the ITS guided students to select explanations that were conceptually rich in nature. Students who used the ITS with self-explanations scored higher on a posttest that included items tapping both conceptual and procedural knowledge than did students who used a version of the ITS that included only traditional problem-solving practice. This study replicates previous findings that self-explanation and worked examples in an ITS can foster algebra learning (Booth et al., 2013). Further, this study extends prior work to show that guiding students towards conceptual explanations is beneficial. 

Integrating visual representations in an interactive learning activity effectively scaffolds performance and learning. However, it is unclear whether and how sustaining or interleaving visual scaffolding helps learners solve problems efficiently and learn from problem solving. We conducted a classroom study with 63 middle-school students in which we tested whether sustaining or interleaving a particular form of visual scaffolding, called anticipatory diagrammatic self-explanation in an Intelligent Tutoring System, helps students’ learning and performance in the domain of early algebra. Sustaining visual scaffolding during problem solving helped students solve problems efficiently with no negative effects on learning. However, in-depth log data analyses suggest that interleaving visual scaffolding allowed students to practice important skills that may help them in later phases of algebra learning. This paper extends scientific understanding that sustaining visual scaffold does not over-scaffold student learning in the early phase of skill acquisition in algebra. 

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. 

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. 

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. 

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. 

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. 

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.