Over the first year of life, infants gain conceptual skills which allow them to construe semantically related items as similar, even when they have few if any directly-perceived attributes in common. Moreover, this skill first encompasses only broad semantic categories, and only later extends to more subtle distinctions, when conceptual and perceptual similarity relations do not coincide. In this paper we suggest that a new mechanism must be added to the mix of possible bases for this observed developmental change. In agreement with many others, we suggest that infants’ earliest conceptual representations are organised with respect to certain especially useful or salient properties, regardless of whether such properties can be directly observed. However we suggest that in many cases this salience may itself be acquired, through domain-general learning mechanisms that are sensitive to the high-order coherent covariation of directly-observed stimulus properties across a breadth of experience. To support this argument we will describe simulations with a simple PDP model of semantic memory. When trained with backpropagation to complete queries about the properties of different objects, the model’s internal representations differentiate in a coarse-to-fine manner. As a consequence, different sets of properties come to be especially “salient” to the

There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design methods to fill this gap in a way that is not only consistent with psychological and content theories but prompts and guides us beyond what those theories can do. Toward this goal, I reflect on lessons from past and current Cognitive Tutor mathematics projects. From this experience, I have abstracted four instructional bridging principles, Situation-Abstraction, Action-Generalization, Visual-Verbal, and Conceptual-Procedural, and associated methods for applying them. I illustrate these in the context of the design of the successful Cognitive Tutor Algebra course (now in more than 800 schools) and the on-going research and development of a Cognitive Tutor course for 6 th grade mathematics.

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participatory simulation (Wilensky & Stroup, 1999a). In participatory simulations, a classroom of students collectively simulates a complex phenomenon that they are studying, with each student playing the role of a single agent or a set of agents in this phenomenon. For example, students each may “be ” an atom in a molecule, a bird in a flock, or a distributed population sample-mean. Technology-based participatory simulations are built in the NetLogo cross-platform agent-based modeling-and-simulation environment (Wilensky, 1999) and operate through the HubNet architecture (Wilensky & Stroup, 1999b). Each student operates a NetLogo “client, ” e.g., a computer or a calculator, that is connected through wireless hubs to the NetLogo “server. ” This server “scoops up ” student input, processes and displays this collective input, and sends information back to the students–clients. The activity moderator, e.g., the teacher or student leader, controls the simulation parameters. So students embody agents in the virtual simulation they see projected onto a classroom screen. Also on this screen, monitors and plots display mathematizations of the simulation, so the class can explore relations between the model’s initial conditions, student–agent rules of behavior, and collective outcomes. One example of a HubNet participatory simulation is “Disease, ” in which students “become infected ” and then infect others

Evolutionary developmental psychology involves the expression of evolved, epigenetic programs, as described by the developmental systems approach, over the course of ontogeny. There have been different selection pressures on organisms at different times in ontogeny, and some characteristics of infants and children were selected in evolution to serve an adaptive function at that time in their life history rather than to prepare individuals for later adulthood. Examples of such adaptive functions of immaturity are provided from infancy, play, and cognitive development. Most evolved psychological mechanisms are proposed to be domain specific in nature and have been identified for various aspects of children’s cognitive and social development, most notably for the acquisition of language and for theory of mind. Differences in the quality and quantity of parental investment affect children’s development and influence their subsequent reproductive and childcare strategies. Some sex differences observed in childhood, particularly as expressed during play, are seen as antecedents and preparations for adult sex differences. Because evolved mechanisms were adaptive to ancestral environments, they are not always adaptive for contemporary people, and this mismatch of evolved mechanisms with modern environments is seen in children’s maladjustment to some aspects of formal schooling. We argue that an evolutionary perspective can be valuable for developing a better understanding of human ontogeny in contemporary society and that a developmental perspective is important for a better understanding of evolutionary psychology.

Young children often exhibit flexible behaviors relying on different kinds of information in different situations. This flexibility has been traditionally attributed to conceptual knowledge. Reported research demonstrates that flexibility can be acquired implicitly and it does not require conceptual knowledge. In Experiment 1, 4- to 5-yearolds successfully learned different context-predictor contingencies and subsequently flexibly relied on different predictors in different contexts. Experiments 2A and 2B indicated that flexible generalization stems from implicit attentional learning rather than from rule discovery, and Experiment 3 pointed to very limited strategic control over generalization behaviors in 4- to 5-year-olds. These findings indicate that mundane mechanisms grounded in associative and attentional learning may give rise to smart flexible behaviors. Even early in development, people’s generalization is remarkably flexible—depending on a situation, people may rely on different kinds of information. This flexibility has been found in a variety of generalization tasks, including lexical extension, categorization, and property induction. For example, in a lexical extension task (Jones, Smith, & Landau, 1991), 2- to 3-year-olds were presented with a target, which was named (i.e., ‘‘this is a dax’’), and asked to find another dax among test items. Children extended the label by shape alone when the target and test objects were presented without eyes. However, they extended the label by shape and texture when the objects were presented with eyes. Children exhibit similar flexibility in categorization and induction tasks. For example, in a categorization task, 3- to 4-year-olds were more likely to group items on the basis of color if the items were introduced as food, but on the basis of shape if the items were introduced as toys (Macario, 1991). In another task, 4- to 5-year-olds were presented with a target and two test items, such that one test item shared the label with the target and the other looked similar to the target. Participants were then told that the target had a particular property and asked which

Interest in the nature of conceptual knowledge extends back at least to the ancient Greek philosophers. In recent years, there has been a wide range of different approaches to understanding the nature of conceptual knowledge, its development, and its neural basis. In most other work, however, these issues are not all treated together. Instead, workers in philosophy, adult experimental psychology, child development, and cognitive neuroscience have pursued related questions in relative ignorance of each other's efforts. Even within cognitive neuroscience, there has been until recently a relative separation between approaches taken by neuropsychologists, who study the effects of brain disease on cognition in patients, and researchers who study the neural basis of conceptual knowledge in neurologically intact populations, using functional imaging and related methods.

Abrahamson, D. (2010). A tempest in a teapot is but a drop in the ocean: action-objects in analogical mathematical

How do you know that Socrates is mortal? More generally, how do you know what properties to attribute to an object? How is the relevant knowledge acquired? How is the knowledge organized in the brain, and how is it affected by brain damage? My colleagues and I have been seeking to answer such questions by developing computational models of semantic cognition and its development. Parallel-Distributed Processing Our overall framework relies on an approach to semantic cognition first suggested by Hinton (1981). Hinton’s proposal was that our knowledge of the properties of objects as expressed in propositions about them, such as ‘A canary can fly’, is not stored directly in propositional form but in the strengths of connections between simple processing units that allow propositions to be formed mentally by

Abstract Design-based research studies are conducted as iterative implementationanalysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains underconceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students ’ observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants ’ compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.