This article describes teacher competencies for implementing collaborative learning in the
classroom. Research has shown that the effectiveness of collaborative learning largely …

Recently, there has been a growing interest in learning approaches that combine two
phases: an initial problem-solving phase followed by an instruction phase (PS-I). Two often …

Learning and performance are not always commensurable. Conditions that maximize
performance in the initial learning may not maximize learning in the longer term. I exploit this …

Theoretical Foundations of Learning Environments provides students, faculty, and
instructional designers with a clear, concise introduction to the major pedagogical and …

In this article, we describe the design principles undergirding productive failure (PF; M.). We
then report findings from an ongoing program of research on PF in mathematical problem …

In the traditional framework of cognitive load theory, it is assumed that the acquisition of
domain-specific knowledge structures (or schemas) is the only instructional goal, and …

Prior studies suggest that struggling to make sense of mathematics is a necessary
component of learning mathematics with understanding. Little research exists, however, on …

The paper reports a quasi-experimental study comparing the “traditional flipped classroom”
pedagogical design with the “productive failure”(Kapur, 2016) pedagogical design in the …

There are extensive concerns pertaining to the idea that students do not develop sufficient
mathematical competence. This problem is at least partially related to the teaching of …

To progress from intuitive ideas to deep conceptual understanding, students need to
become aware of gaps in their ideas. Attempting to solve problems prior to instruction may …