Students' problem-solving success depends on more than their knowledge and abilities. One factor that may play a role is the teacher's expectations of students. The current study focused on how a teacher's explicitly-stated expectations influence students' ability to learn from corrective feedback during problem solving. On the one hand, setting…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

Metacognition is central to children's cognitive development. However, there is conflicting evidence about children's ability to accurately monitor their performance and subsequently control their behavior. This is of particular interest for mathematics topics on which children exhibit persistent misconceptions--that is, when children's knowledge…

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

Making connections during math instruction is a recommended practice, but may increase the difficulty of the lesson. We used an avatar video instructor to qualitatively examine the role of linking multiple representations for 24 middle school students learning algebra. Students were taught how to solve polynomial multiplication problems, such as…

Recent research highlights the potential benefits of practice without feedback on learner's strategy knowledge. However, most prior work has been conducted in one-on-one settings with short retention intervals. We compared the effects of mathematics practice with and without correct-answer feedback on immediate and 1-week delayed performance in a…

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…

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.…

Feedback is a ubiquitous learning tool that is theorized to help learners detect and correct their errors. The goal of this study was to examine the effects of feedback in a classroom context for children solving math equivalence problems (problems with operations on both sides of the equal sign). The authors worked with children in 7 second-grade…

Math homework is transforming at a rapid rate with the 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. In the current study, middle school students (N = 143) solved a set of challenging…

The goal of the current research was to better understand when and why feedback has positive effects on learning and to identify features of feedback that may improve its efficacy. In a randomized experiment, second-grade children (N = 75) received instruction on a correct problem-solving strategy and then solved a set of relevant problems.…

Background: The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear.…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…

An emerging consensus suggests that guided discovery, which combines discovery and instruction, is a more effective educational approach than either one in isolation. The goal of this study was to examine two specific forms of guided discovery, testing whether conceptual instruction should precede or follow exploratory problem solving. In both…