We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

Classroom methods that facilitate student learning from iteration have received little attention from scholars. Iterative learning requires students to repeat a problem-solving task in new contexts each time applying lessons from previous applications. Iterative learning formats improve students' learning outcomes and help instructors ensure that…

Project-based learning (PjBL) has been widely promoted in educational practice, for example, computer programming education. While PiBL may help learners to connect abstract knowledge with authentic practice, the complexity of completing an authentic project may overwhelm learners, making them unable to achieve the desired learning outcomes. This…

Chunking, namely the grouping of sequence elements in clusters, is ubiquitous during sequence processing, but its impact on performance remains debated. Here, we found that participants who adopted a consistent chunking strategy during symbolic sequence learning showed a greater improvement of their performance and a larger decrease in cognitive…

Graph complexity as measured by topological entropy has been previously shown to affect performance on artificial grammar learning tasks among typically developing children. The aim of this study was to examine the effect of graph complexity on implicit sequential learning among children with developmental dyslexia. Our goal was to determine…

The procedural deficit hypothesis claims that impaired procedural learning is a causal risk factor for developmental dyslexia and developmental language disorder. We investigated the relationships between measures of basic cognitive processes (declarative learning, procedural learning and attention) and measures of attainment (reading, grammar and…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Executing actions in a specific order is a critical component of many action sequences that children must acquire, the majority of which are learned through observation and imitation of others. Although a wealth of evidence indicates that children can process and represent temporal order in memory, relatively little is known about the development…

With the increasing strategic importance of Massive Online Open Courses (MOOCs) in higher education, this paper offers an innovative approach to advancing discussions and practice around MOOC learning design, in the context of staff development. The study provides a deeper understanding of staff (academic and learning technologists') experience…

Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to…

Integration of learning (IOL) has been defined as an essential learning outcome in higher education. The IOL model describes the process of learning through three types of integration: connection, application, and synthesis. This manuscript applies the IOL model to counselor education in order to examine how counselor education programs implement…

The goal of this study was to investigate non-adjacent consonant sequence patterns in target words during the first-word period in infants learning American English. In the spontaneous speech of eighteen participants, target words with a Consonant-Vowel-Consonant (C[subscript 1]VC[subscript 2]) shape were analyzed. Target words were grouped into…

In 1979, Gavin Bolton posed a question that is still fundamental to the development of process drama: "Is it possible to steer a course that does not come down in support of any particular point of view but causes children to examine and re-examine their own views and values?" Inspired by Bakhtinian theory, Brian Edmiston developed a…

Time and space represent two key aspects of episodic memories, forming the spatiotemporal context of events in a sequence. Little is known, however, about how temporal information, such as the duration and the order of particular events, are encoded into memory, and if it matters whether the memory representation is based on recollection or…

This case study of one small urban California high school enrolling predominantly low-socioeconomic status (SES) Latinx youth and many emergent bilinguals found that a college-for-all school culture, guided by leadership and school vision, was enacted in classrooms as caring, safe, productive spaces promoting college-going comportment. However,…