In this commentary, I reflect from a neurocognitive perspective on the four chapters on natural number development included in this section. These chapters show that the development of seemingly basic number processing is much more complex than is often portrayed in neurocognitive research. The chapters collectively illustrate that children's…

How people see the world, even how they research it, is influenced by beliefs. Some beliefs are conscious and the result of research, or at least amenable to research. Others are largely invisible. They may feel like "common knowledge" (though myth, not knowledge), unrecognized premises that are part of the surrounding culture. As we…

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

Domain-general cognitive knowledge has frequently been used to explain skill when domain-specific knowledge held in long-term memory may provide a better explanation. An emphasis on domain-general knowledge may be misplaced if domain-specific knowledge is the primary factor driving acquired intellectual skills. We trace the long history of…

The belief that studying mathematics improves reasoning skills, known as the Theory of Formal Discipline (TFD), has been held since the time of Plato. Research evidence supports this idea, at least in the context of students who had chosen to study post-compulsory mathematics. Here we examined the development of reasoning skills in 16- to…

Children's acquisition of tool use abilities is an important part of development but is not yet well understood. This study compares two modes of tool-use learning, observation and individual haptic experience. Two- and 3-year-olds had haptic experience with tools, observed tool use by others, had both haptic and observational experience, or no…

To design an effective computer science curriculum, educators require a systematic method of classifying the difficulty level of learning activities and assessment tasks. This is important for curriculum design and implementation and for communication between educators. Different educators must be able to use the method consistently, so that…

This chapter examines the various cognitive tools embedded in a multimedia-enriched PBL environment for middle school science known as "Alien Rescue" and shares the research findings of the use of these cognitive tools in assisting young learners' problem solving. The goal of this chapter is to illustrate strategies for designing…

According to cognitive complexity and control (CCC) theory complexity depends on number of levels of a hierarchy of rules. According to relational complexity (RC) theory complexity is a function of the number of related variables in the task, and the most difficult tasks are those in which there is a constraint on decomposition into simpler…

This study puts the Cognition Hypothesis (Robinson 2005) to the test with respect to its predictions of the effects of changes in task complexity ([plus or minus] few elements) and task condition ([plus or minus] monologic) on L2 performance. 44 learners of Dutch performed both a simple and a complex oral task in either a monologic or a dialogic…

Children (ages 5, 7, and 9 years) and young adults completed two visual attention tasks that required them to make a forced choice identification response to a target shape presented in the center of a computer screen. In the first task (high correlation condition) each target was flanked with the same distracters on 80% of the trials (valid…