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Although students’ self-regulated learning has been studied extensively, past research has not investigated students’ fine-grained, self regulated choice-making processes during learning with visual representations and strategies to support such processes. We conducted design and experimental studies with 148 students to develop and evaluate an intervention package for supporting students’ self-regulated choice-making in using diagrammatic scaffolding in algebra tutoring software. A classroom experiment showed that students with the intervention learned greater conceptual and procedural knowledge in algebra than students in the control condition whose choices were not supported. Also, students with the intervention chose to use diagrams less frequently overall but showed distinctive use patterns that changed over time, indicating a form of self-regulated diagram use. This study demonstrates the importance of understanding and supporting choice behaviors that change over time during learning, going beyond simply measuring the frequency of choice behaviors and encouraging students to engage in these behaviors more frequently. 

Although students’ self-regulated learning has been studied extensively, past research has not investigated students’ fine-grained, self-regulated choice-making processes during learning with visual representations and strategies to support such processes. We conducted design and experimental studies with 148 students to develop and evaluate an intervention package for supporting students’ self-regulated choice-making in using diagrammatic scaffolding in algebra tutoring software. A classroom experiment showed that students with the intervention learned greater conceptual and procedural knowledge in algebra than students in the control condition whose choices were not supported. Also, students with the intervention chose to use diagrams less frequently overall but showed distinctive use patterns that changed over time, indicating a form of self-regulated diagram use. This study demonstrates the importance of understanding and supporting choice behaviors that change over time during learning, going beyond simply measuring the frequency of choice behaviors and encouraging students to engage in these behaviors more frequently. 

In designing learning technology, it is critical that the technology supports both learning and engagement of students. However, achieving both aspects in a single technology design is challenging. We report on the design and evaluation of Gwynnette, intelligent tutoring software for early algebra. Gwynnette was deliberately designed to enhance students’ algebra learning and engagement, integrating several playful interaction and gamification features such as drag-and-drop interactions, an alien character, and sound effects. A virtual classroom experiment with 60 students showed that the system significantly enhanced both engagement and conceptual learning in early algebra, compared to the older version of the same software. Log data analyses gave insights into how the design might have affected the out-comes. This study demonstrates that a deliberate design of learning technology can help students learn and engage well in an unpopular subject such as algebra, a challenging dual goal in designing learning technologies. 

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. 

In designing learning technology, it is critical that the technology supports both learning and engagement of students. However, achieving both aspects in a single technology design is challenging. We report on the design and evaluation of Gwynnette, intelligent tutoring software for early algebra. Gwynnette was deliberately designed to enhance students’ algebra learning and engagement, integrating several playful interaction and gamification features such as dragand- drop interactions, an alien character, and sound effects. A virtual classroom experiment with 60 students showed that the system significantly enhanced both engagement and conceptual learning in early algebra, compared to the older version of the same software. Log data analyses gave insights into how the design might have affected the outcomes. This study demonstrates that a deliberate design of learning technology can help students learn and engage well in an unpopular subject such as algebra, a challenging dual goal in designing learning technologies. 

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.