Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

We review and extend existing frameworks on modeling to develop a new framework that describes model-based reasoning in introductory and upper-division physics laboratories. Constructing and using models are core scientific practices that have gained significant attention within K-12 and higher education. Although modeling is a broadly applicable…

Interacting with and translating across multiple representations is an essential characteristic of expertise and representational fluency. In this study, we explored the effect of interacting with and translating between representations in a computer simulation or in a paper-based assignment on scientific accuracy of undergraduate science…

Several studies have demonstrated that affective states influence the number of associations formed between remotely related concepts. Someone in a neutral or negative affective state might draw the association between "cold" and "hot", whereas someone in a positive affective state might spontaneously form the more distant association between…

The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that…

Background: Education Standards highlight the importance of conceptual knowledge. Instructional tasks play a key role in biology instruction and offer learning opportunities for students. Tasks contain of a content and a demands part. Therefore, complexity and cognitive level are adequate variables to describe tasks and are assumed effective for…

This study sought to identify specific types of discussion-based strategies that two successful high school physics teachers using a model-based approach utilized in attempting to foster students' construction of explanatory models for scientific concepts. We found evidence that, in addition to previously documented dialogical strategies that…

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…

Religious poetry is, a heightened and impregnated form of expression. There is a marriage of form and sense. Linguistically speaking, religious poetry has a conceptual interface between syntax and semantics; a strong relationship between language and thought; universality and cultural specificity; the discourse context and the psychological…

This paper presents a model of how children generate concrete concepts from perception through processes of differentiation and integration. The model informs the design of a novel methodology ("evolutionary maps" or "emaps"), whose implementation on certain domains unfolds the web of itineraries that children may follow in the…

Peer Instruction (PI) is an evidence based pedagogy commonly used in undergraduate physics instruction. When asked questions designed to test conceptual understanding, it has been observed that the proportion of students choosing the correct answer increases following peer discussion; however, relatively little is known about what takes place…

Individuals with autism spectrum disorder (ASD) have difficulty comprehending metaphors. However, no study to date has examined whether or not they understand conceptual metaphors (i.e. mappings between conceptual structures), which could be the building blocks of metaphoric thinking and understanding. We investigated whether 13 participants with…

There is a growing amount of evidence suggesting that individuals with autism have difficulty with categorization. One basic cognitive ability that may underlie this difficulty is the ability to abstract a prototype. The current study examined prototype and category formation with dot patterns in high-functioning adults with autism and matched…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

Earlier research has found that it is useful to distinguish situations in which students construct external representations on their own from situations in which they are expected to interpret already provided external representations. One type of representations that is particularly important for teaching mechanics is the free-body diagram. In…