The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion…

Data-driven decision making has become an essential component of educational practice across all levels, from chief state school officers to classroom teachers, and has received unprecedented attention in terms of policy and financial support. It was included as one of the four pillars in the American Recovery and Reinvestment Act (2009),…

The unfolding of individual interests is reconstructed as part of a person's everyday experience in dealing with multiple goals. This is exemplified by referring to how adolescents cope with developmental tasks while striving for their ideal selves. Exploratory interaction with objects of potential interest is regarded as a central element that…

Asked to review the four articles that appear in this special issue of "Educational Psychologist," these authors discuss the articles in alphabetical order, describe their major arguments, analyze strengths and weaknesses from their perspective, and provide some considerations. The analysis section about each article brings their perspective to…

In this response, we acknowledge the central concerns of the commentators to our article on learning's topography. We respond to those concerns on the basis of the multiplicity of views about learning that reside within the learning terrain we outlined in Alexander, Schallert, and Reynolds (2009/this issue).

Over the past decades research on learning has become more diverse and complex. The concern expressed by Alexander, Schallert, and Reynolds (2009/this issue) is that this diversity of theoretical perspectives has resulted in a fragmentation that is destructive to the field. Although it is important to engage in explicit discussions of how learning…

Alexander, Schallert, and Reynolds's (2009/this issue) "what," "where," "who," and "when" framework situates different perspectives on learning in different places in this multidimensional space and by doing so helps us to better understand seemingly disparate approaches to learning. The framework is in need of a fifth, "why" dimension. The "why"…

This article presents a commentary on Stellan Ohlsson's (2009) theory of conceptual change by resubsumption and competitive evaluation of cognitive utility. We note two features of Ohlsson's theory that we think are particularly strong. We then argue that Ohlsson's theory explains one route to conceptual change but that there are many other routes…

Ohlsson's proposal of resubsumption as the dominant process in conceptual, or nonmonotonic, change presents a worthy challenge to more established theories, such as Chi's theory of ontological shift. The two approaches differ primarily in that Ohlsson's theory emphasizes a process of learning in which narrower, more specific concepts are subsumed…

Successful learning sometimes requires that the learner abandons or rejects one or more prior concepts, beliefs, or intuitive theories. Such "nonmonotonic changes" are widely believed to have a low probability of occurring spontaneously and to be difficult to promote with instruction. A theory of nonmonotonic cognitive change should explain both…

Why is conceptual change difficult yet possible? Ohlsson (2009/this issue) proposes that the answer can be found in the dynamics of resubsumption, or the process by which a domain of experience is resubsumed under an intuitive theory originally constructed to explain some other domain of experience. Here, it is argued that conceptual change is…

Alexander, Schallert, and Reynolds (2009/this issue) proposed a definition and landscape of learning that included 9 principles and 4 dimensions ("what," "who," "where," "when"). This commentary reflects on the utility of this definition and 4-dimensional landscape from the standpoint of educational psychologists who have a cognitive science…

In response to a stimulating article by David C. Geary on the value of understanding the evolutionary basis of learning as a guide to instruction, I raise several objections. When evolutionary theory is used to explain everything from sex differences in math and reading to why children are bored in school, it loses its explanatory power. There is…

Kirschner, Sweller, and Clark (2006) make a general case for the effectiveness of a teaching method--direct instruction--without reference to any context of what it is that is being taught by whom and to whom. In so doing, they bypass what is arguably the most pressing concern facing educators--not how to teach students but what to teach them. An…

Kirschner, Sweller, and Clark (2006) suggest that unguided or minimally guided instructional approaches are less effective and efficient for novices than guided instructional approaches because they ignore the structures that constitute human cognitive architecture. While we concur with the authors on this point, we do not agree to their equation…