The current study investigated how prior knowledge moderated the effects of three educational technologies ("From Here to There," "DragonBox 12+," and problem sets in "ASSISTments") on seventh-grade students' later algebraic knowledge. Pretest scores only moderated effects of "From Here to There," with…

Effective personalization of education requires knowing how each student will perform under certain conditions, given their specific characteristics. Thus, the demand for interpretable and precise estimation of heterogeneous treatment effects is ever-present. This paper outlines a new approach to this problem based on the Leave-One-Out Potential…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

An intelligent tutoring system (ITS, henceforth) is currently defined as a computer system that delivers personalized instruction to students by using computational techniques to evaluate the learner in a variety of ways, including (but not limited to) their prior knowledge, competency/skill levels, motivation, and affective states. ITSs are…

Prior research has shown negative relations between math anxiety and math performance. We posit that one potential pathway through which math anxiety influences performance of math equivalencies is through help seeking behavior during learning. Here, we examine whether middle school students' behavior, specifically the frequency of hint requests,…

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…

We investigated the effects of proximal grouping of numbers, problem-solving goals to make 100, and prior knowledge on students' solution strategies in an online mathematics game. Logistic regression on 857 problem-level data points from 227 middle-school students showed that students were more likely to use productive solution strategies on…

We report on a randomized controlled trial of an intervention that leverages the availability of laptops for all public-school students in the state of Maine. The intervention, called "ASSISTments," provides feedback to students as they solve mathematics homework problems and automatically prepares reports for teachers about student…

Past research has suggested that there may be benefits in learning from expository science text when students study with the expectation that they will need to teach another student. The present experiments were designed to extend prior work by testing if an effect would be seen on both immediate tests (similar to those used in most prior studies)…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

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…

Fraction and decimal arithmetic are crucial for later mathematics achievement and for ability to succeed in many professions. Unfortunately, these capabilities pose large difficulties for many children and adults, and students' proficiency in them has shown little sign of improvement over the past three decades. To summarize what is known about…

Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students' limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on…

Homework is transforming at a rapid rate with continuous advances in educational technology. Computer-based homework, in particular, is gaining popularity across a range of schools, with little empirical evidence on how to optimize student learning. The current aim was to test the effects of different types of feedback on computer-based homework.…

Current educational policies in the United States attempt to boost student achievement and promote equality by intensifying the curriculum and exposing students to more advanced coursework. This paper investigates the relationship between one such effort -- California's push to enroll all 8th grade students in Algebra -- and the distribution of…