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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. 

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. 

AI-based educational technologies may be most welcome in classrooms when they align with teachers' goals, preferences, and instructional practices. Teachers, however, have scarce time to make such customizations themselves. How might the crowd be leveraged to help time-strapped teachers? Crowdsourcing pipelines have traditionally focused on content generation. It is an open question how a pipeline might be designed so the crowd can succeed in a revision/customization task. In this paper, we explore an initial version of a teacher-guided crowdsourcing pipeline designed to improve the adaptive math hints of an AI-based tutoring system so they fit teachers' preferences, while requiring minimal expert guidance. In two experiments involving 144 math teachers and 481 crowdworkers, we found that such an expert-guided revision pipeline could save experts' time and produce better crowd-revised hints (in terms of teacher satisfaction) than two comparison conditions. The revised hints however, did not improve on the existing hints in the AI tutor, which were carefully-written but still have room for improvement and customization. Further analysis revealed that the main challenge for crowdworkers may lie in understanding teachers' brief written comments and implementing them in the form of effective edits, without introducing new problems. We also found that teachers preferred their own revisions over other sources of hints, and exhibited varying preferences for hints. Overall, the results confirm that there is a clear need for customizing hints to individual teachers' preferences. They also highlight the need for more elaborate scaffolds so the crowd can have specific knowledge of the requirements that teachers have for hints. The study represents a first exploration in the literature of how to support crowds with minimal expert guidance in revising and customizing instructional materials. 

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. 

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. 

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.