In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

Developing fluency and flexibility in mathematics is a key goal of upper primary schooling, however, while fluency can be developed with practice, designing activities that support the development of flexibility is more difficult. Drawing on concepts of adaptive expertise, we developed a task for a multi-touch classroom, NumberNet, that aimed to…

Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this…

Although feedback is a popular topic in educational research, the question of how and on what conditions feedback in mathematics affects learning seldom has been addressed. In this study, we investigated: (1) whether process-oriented feedback in mathematics leads to greater interest and higher achievement development compared to social-comparative…

Theories of psychology and mathematics education recommend two instructional approaches to develop students' mental representations of number: The "exact" approach focuses on the development of exact representations of organized dot patterns; the "approximate" approach focuses on the approximate representation of analogue magnitudes. This study…

Reducing problem complexity by isolating elements has been shown to be an effective instructional strategy. Novices, in particular, benefit from learning from worked examples that contain partially interacting elements rather than worked examples that provide full interacting elements. This study investigated whether the isolating-elements…

We tested whether the provision of metacognitive knowledge on how to cope with the complexity of a learning environment improved learning. In an experimental setting, high-school students (N = 60) worked through a computer-based geometry lesson either with or without metacognitive support in the form of a cue card. This cue card encouraged…

In a three-group, gender-matched, preexisting knowledge-controlled, randomized experiment, we evaluated the effect of learner control over study pace on healthcare executives' performance in an online statistics course. Overall, frequent deadlines enhanced distribution of practice and improved learning. Students with less control over pace (in…

Self-regulated learning (SRL) actions of 30 Canadian and 30 Chinese university students were studied in a face-to-face problem-based learning environment. Participants were randomly assigned to work in dyads consisting of Chinese, Canadian, or mixed Chinese-Canadian pairs to learn Analysis of Variance collaboratively using a computer coach. Dialog…

Research shows that multiple representations can enhance student learning. Many curricula use multiple representations across multiple task types. The temporal sequence of representations and task types is likely to impact student learning. Research on contextual interference shows that interleaving learning tasks leads to better learning results…

Comparing common mathematical errors to correct examples may facilitate learning, even for students with limited prior domain knowledge. We examined whether studying incorrect and correct examples was more effective than studying two correct examples across prior knowledge levels. Fourth- and fifth-grade students (N = 74) learned about decimal…

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are "faded" into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three…

Support for children with special educational needs in inclusive classrooms is increasingly provided by teaching assistants (TAs). They often have a direct pedagogical role, taking responsibility for instruction in mathematics. The quality of TAs' oral skills is crucial for learning but has rarely been researched. Using conversation analysis, this…

It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number…

This study investigated students' activating positive affective experiences in mathematics lessons, their antecedents, their cognitive and motivational consequences, as well as their effect on achievement. The participants were 682 Grade 8 and 9 students from 37 classes from Germany and Switzerland who participated in a video study of lessons on…