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…

Recent work has demonstrated that having students study worked examples and answer self-explanation prompts as part of their problem-solving practice improves learning on researcher-developed measures of mathematical proficiency. However, little work has been done to date to investigate whether these benefits translate to improvements on the types…

Intelligent tutoring systems (ITSs) have consistently been shown to improve the educational outcomes of students when used alone or combined with traditional instruction. However, building an ITS is a time-consuming process which requires specialized knowledge of existing tools. Extant authoring methods, including the Cognitive Tutor Authoring…

Analogies between old and new concepts are common during classroom instruction. Previous transfer studies focused on how features of initial learning guide later, spontaneous transfer to new problem solving. We argue for a shift in the focus of analogical-transfer research toward understanding how to best support analogical transfer from previous…

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…

Instruction in most STEM domains uses visuals to illustrate complex problems. During problem solving, students often manipulate and construct visuals. Traditionally, students draw visuals on paper and receive delayed feedback from an instructor. Educational technologies have the advantage that they can provide immediate feedback on students'…

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…

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…

Prior work has found benefits of interpersonal closeness, or rapport, on student learning, but has primarily investigated its impact on learning outcomes, not learning processes. Moreover, such work often analyzes the direct impact of dyadic features like rapport on learning, without considering the role played by individual factors, such as…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

Math and science textbook chapters invariably supply students with sets of problems to solve, but this widely used approach is not optimal for learning; instead, more effective learning can be achieved when many problems to solve are replaced with correct and incorrect worked examples for students to study and explain. In the present study, the…

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.…

Middle school algebra students (N = 125) randomly assigned within classroom to a Problem-solving control group, a Correct worked examples control group, or an Incorrect worked examples group, completed an experimental classroom study to assess the differential effects of incorrect examples versus the two control groups on students' algebra…