We talk about our spatial thinking skills all the time, maybe without knowing that there is an entire domain of cognitive skills that connect these observations. Educators can also recognize these skills in our students. These include students who seem to have an intuitive understanding of computer-aided design and create complex and efficient 3-D…

Learning standards such as the "Common Core State Standards for Mathematics" [CCSSM] (NGA Center & CCSSO, 2010) advocate that we develop students' algebraic thinking "beginning in kindergarten." Such a tall order requires innovative approaches that re-imagine what teaching and learning mathematics means for the elementary…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Mechanical reasoning is crucial for many engineering fields, yet undergraduate engineering students struggle to understand discipline-specific formalisms from their courses that model mechanical concepts. The current investigation observed undergraduate engineering students' speech during mechanical reasoning and the benefits of attending to…

Reading and writing involve print-related and meaning-making processes, which draw on numerous skills and knowledge. The contributing skills and knowledge, and reading and writing have: a) hierarchical relations where lower order skills support higher order skills in a systematic and cascaded way; b) interactive relations where reading and writing…

This full paper concerns an exploratory study that investigates students' reasoning about torsion. Mechanical reasoning is critical to engineering applications and yet students still struggle to accurately predict, analyze, and model mechanical systems using formal symbolic notations (i.e., formalizations). To understand the nature of students'…

We examined the dimensionality of oral discourse skills (comprehension and retell of texts) and the relations of language and cognitive skills to the identified dimensions. Data were from 529 English-speaking second graders (M[subscript age] = 7.42; 46% female; 52.6% Whites, 33.8% African Americans, 4.9% Hispanics, 4.7% two or more races, 0.8%…

This full paper considers how collaborative discourse can reveal ways upper-class engineering students mechanically reason about engineering concepts. Argumentation and negotiation during collaborative, multimodal discourse using speech and gestures helps establish common ground between learners and fosters reflection on their conceptual…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons…

Visual media (pictures, photographs) are often used in adult literacy instruction, presumably because they are easy for adult literacy learners to process. However, relatively little research has been conducted on how adult literacy learners comprehend visual media, such as picture stories. Some have argued that picture stories could be used as a…

Performance measures, including standardized test scores or cognitive tasks, are commonly conceptualized as stable measures, yet are often unreliable indices of skill. We examine two contextual factors, performance pressure and feedback, that may influence the extent to which individuals demonstrate their cognitive capacity by manipulating…

Developing and supporting understanding of the meaning of multiplication and multiplicative relationships in students with mathematics learning disabilities requires carefully designed instruction that emphasizes strategic representation use. This article discusses three ways in which teachers can incorporate multiple representations within…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little evidence regarding the premise of a LT approach--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. This hypothesis was evaluated for an empirically-validated…

Purpose: This study tested whether the Sitting Together and Reaching to Play (START-Play) physical therapy intervention indirectly impacts cognition through changes in perceptual-motor skills in infants with motor delays. Methods: Participants were 50 infants with motor delays randomly assigned to START-Play plus Usual Care Early Intervention…

Research has shown that tape diagrams are beneficial for algebra learning. However, it is unclear whether certain visual features of tape diagrams have implications for learning. We investigated, with undergraduate students and math teachers, whether tape diagrams with different visual features (color, presence of outer lines, and position of the…