Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

Blended learning (BL) is regarded as an effective strategy for combining traditional face-to-face classroom activities with various types of online learning tools (e.g., e-books). An effective feature of e-books is the ability to use digital notes. When e-books are used in BL, the strategic adoption of note-taking provides benefits that influence…

Understanding scientific phenomena requires learners to construct mental models of causal systems. Simulation-based discovery learning offers learners the opportunity to construct mental models and test them against the behavior of a simulation. The purpose of this study was to investigate sequential patterns of learner actions and utterances…

The present study investigates primary school students' self-regulated learning (SRL) process by exploring the sequence in which SRL activities are conducted during learning. The aims of this study are twofold: investigating the presence of the theoretically hypothesized cyclical nature in students' SRL process, as well as potential differences…

The current study used microanalytic interviews and behavioral traces to examine sequential phase relations among forethought, performance, and self-reflection processes, and to investigate the predictive influence of these processes on mathematics performance of 96 eighth grade students. Consistent with expectations, students' microanlaytic goals…

Review of the history of trigonometry content and pedagogy indicates the necessity and importance of trigonometry in the school curriculum (e.g., van Brummelen, 2009; van Sickel, 2011). For example, understanding trigonometric functions is a requirement for understanding some other areas of science, such as Newtonian physics, architecture,…

Educational software data promises unique insights into students' study behaviors and drivers of success. While much work has been dedicated to performance prediction in massive open online courses, it is unclear if the same methods can be applied to blended courses and a deeper understanding of student strategies is often missing. We use pattern…

Spaced repetition is among the most studied learning strategies in the cognitive science literature. It consists in temporally distributing exposure to an information so as to improve long-term memorization. Providing students with an adaptive and personalized distributed practice schedule would benefit more than just a generic scheduler. However,…

This study investigates students' ways of attending to linear sequential data in two tasks, and conjectures possible relationships between those ways and elements of the task design. Drawing on the substantial literature about such situations, we focus for this paper on linear rate of change, and on covariation and correspondence approaches to…

In nonmonotonic decision problems, the magnitude of outcomes can both increase and decrease over time depending on the state of the decision problem. These increases and decreases may occur repeatedly and result in a variety of possible outcome distributions. In many previously investigated sequential decision problems, in contrast, outcomes (or…

This article describes a visual approach to integrating observational data into self-evaluation and peer review of teaching, practices that can lead to adoption of evidence-based active-learning strategies in STEM. This approach was designed to be implemented for undergraduate courses across disciplines. The presentation of observational data in a…

Learning by repetition engages distinct cognitive strategies whose contributions are adjusted with experience. Early in learning, performance relies upon flexible, attentive strategies. With extended practice, inflexible, automatic strategies emerge. This transition is thought fundamental to habit formation and applies to human and animal…

The objective of this paper is to discuss how blind students learn basic concepts of probability using the tactile model proposed by Vita (2012). Among the activities were part of the teaching sequence "Jefferson's Random Walk", in which students built a tree diagram (using plastic trays, foam cards, and toys), and pictograms in 3D…

Online collaborative learning allows discussion to occur at greater depth where knowledge can be constructed remotely. However students were found to construct knowledge at low-level where they discussed by sharing and comparing opinions; those are inadequate for new knowledge creation. As such, this research attempted to investigate the students'…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…