In this study I explore the construction of algebraic structure sense through engaging students in task sequences designed to elicit the development of competencies related to this understanding. The primary task-design principle employed in this study is strategic variation, in which certain components of items within task sequences vary while…

This article explores the potential use metacognitive skills learned in computer games to teach mathematics. This study explored the similarities and differences in the learning of metacognitive skills between computer games and mathematics education. A mixed-methods approach was employed in which a quantitative survey (students, n=174) and a…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of a LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of an LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

When projects are the spine of a course, they are systematically sequenced one after the other, and they do the heavy lifting of the course. They teach its core content and skills. The author has been testing this model of course design for several years, aiming for experiential learning that is tied to deep rather than superficial learning of…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

Reconstructing memory for sequences is a complex process, likely involving multiple sources of information. In 3 experiments, we examined the source(s) of information that might underlie the ability to accurately place an event within a temporal context. The task was to estimate, after studying each list, the temporal position of a single test…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

The research purpose was to investigate the differences between learning preferences (i.e., Active-Reflective, Sensing-Intuitive, Visual-Verbal, and Sequential-Global) determined by the Index of Learning Style and gender (i.e., Male and Female) in regards to standardized achievement multiple-choice test performance determined by the Illinois Nurse…

Sleep is considered to support the formation of skill memory. In juvenile but not adult song birds learning a tutor's song, a stronger initial deterioration of song performance over night-sleep predicts better song performance in the long run. This and similar observations have stimulated the view of sleep supporting skill formation during…

This study aimed at investigating the ability to learn regularities across the life span and examine whether this learning process can be supported or hampered by verbalizations. For this purpose, children (aged 8-10 years) and younger (aged 19-30 years) and older (aged 70-80 years) adults took part in a sequence learning experiment. We found that…

Natural language is highly complex and can be challenging for some learners, yet the contribution of complexity to individual differences in language learning remains poorly understood. This poor understanding appears due to both a lack of consensus among researchers regarding what complexity is, and to on-line language research often employing…

Learners make a number of decisions when attempting to study efficiently: they must choose which information to study, for how long to study it, and whether to restudy it later. The current experiments examine whether documented impairments to self-regulated learning when studying information sequentially, as opposed to simultaneously, extend to…