This article offers an overview of the nature and role of relational thinking and relational reasoning in human learning and performance, both of which pertain to the discernment of meaningful patterns within any informational stream. Distinctions between thinking and reasoning relationally are summarized, along with specific forms of patterning…

The Inclusive Assessment of Computational Thinking (CT) designed for accessibility and learner variability was studied in over 50 classes in US schools (grades 3-8). The validation studies of IACT sampled thousands of students to establish IACT's construct and concurrent validity as well as test-retest reliability. IACT items for each CT practice…

Computational thinking can provide a basis for problem solving, for making evidence-based decisions, and for learning to code or create programs. Therefore, it is critical that all students across the K-12 continuum--including students in the early grades--have opportunities to begin developing problem solving and computational thinking skills.…

Giftedness in numeracy skills in young children is a phenomenon that is not always visible and easily identifiable. However, these numeracy skills should be recognised in the early years of pre-school education for adequate enrichment on curriculum and pedagogy in teaching young children. Numeracy skills in young children at pre-schools involves…

A number of efforts have focused on preparing teachers to integrate CT within secondary disciplinary subject areas; however, there is little research on how CT ideas could be embedded within elementary subjects. We designed a professional development activity for elementary teachers to embed CT within science and examined how their understanding…

Similar to mammalian brains, Artificial Neural Networks (ANN) are universal approximators, capable of yielding near-optimal solutions to a wide assortment of problems. ANNs are used in many fields including medicine, internet security, engineering, retail, robotics, warfare, intelligence control, and finance. "ANNs have a tendency to get…

The purpose of this study was to demonstrate that transfer ability (positive and negative) varies depending on the nature of the problems, using the knowledge transfer matrix, as well as being dependent on the individual differences of the learner. A total of 178 participants from the United States and New Zealand completed measures of prior…

This study aims to determine the explanatory and discriminative powers of non-routine problem solving strategies used by fourth graders. Six problems were asked to 240 pupils. After scoring answers between 0 and 10, bottom and top segments of 27% were determined based on total scores. Lastly, all scripts of students in these segments were…

The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…

We use a concept of framing to explain 3 cases in which participants initially lacked mutual understanding but then achieved significant mutual understanding. The cases were all consistent with a pattern of "positional framing" that includes a human participant who is inquiring, which we call a "listener", and a "source", which may be another…

Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel…

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

Road map problems ask students to integrate their knowledge of organic reactions with pattern recognition skills to "fill in the blanks" in the synthesis of an organic compound. Students are asked to identify familiar organic reactions in unfamiliar contexts. A practical context, such as a medicinally useful target compound, helps…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…