Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

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…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

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…

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…

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.…

This study examined the interaction effects of self-explanation and game-reward strategies on sixth graders' algebra variable learning achievement, learning attitude, and meta-cognitive awareness. A learning system was developed to support the learning activity, and a 2×2 quasi-experiment was conducted. Ninety-seven students were invited to…

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…

This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they…

With the aim to promote students' mathematics learning, we extended the Cognitive Tutor Algebra (CTA), a computer-based tutoring system for high school mathematics, to a collaborative setting. Furthermore we developed a collaboration script to support students' interactions. In an experimental classroom study, we compared three conditions:…

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing…