While school performance suggests students with learning disabilities require intervention to demonstrate mathematics proficiency, little is known about how they approach problem solving in secondary geometry. Think aloud protocols highlight the higher order thinking skills underlying complex academic tasks. We conducted an exploratory descriptive…

Cognitive difficulty arises from two types of cognitive processes: treatments; within the same, conversions; between different types of representational registers. Conversions are difficult since they ask for understanding of two representations. Direction and the choice of first register could be a threshold for the student. Wasan geometry is…

As consultants who infuse the "Habits of Mind" into schools, the authors explain how spreading these habits through school can increase the whole school's well-being and feed teacher efficacy. They list seven factors that can create a "culture of efficacy" that draws on these 16 habits (thinking dispositions at the core of…

Informed by decades of research and standards-based policies, there has been a growing demand for high-quality teaching and learning in mathematics and science classrooms. Achieving these ambitious goals will not be easy; students' opportunities for learning as shaped by the tasks they are assigned will matter the most. The purpose of this article…

While past research has demonstrated a link between the subjective "Aha" experience of insight and verbal insight problem solution activation in the right hemisphere (RH), no one has yet linked insight to long term semantic priming. We propose that through a shared process of semantic integration both of these concepts are linked and…

Students need specific thinking--or Habits of Mind--to engage with problems and become self-directed learners, write Arthur L. Costa, Bena Kallick, Jay McTighe, and Allison Zmuda. A curricular approach based on enhancing students' understanding of conceptually significant, transferable ideas can help schools teach these dispositions.

Design education has moved towards a collaborative practice where designers work in teams and with other disciplines to solve unstructured problems. Along with the cognitive skills involved in the execution of the design process, designers also need skills to work in teams, share information, negotiate common ground and reach consensus.…

This study aims to explore all the types of students' mental models of number patterns. The study used a qualitative approach with an explorative type. The subjects used to characterize the student's mental models in this study were 46 eighth grade students in Indonesia. To reveal the subjects' mental model, they were asked to solve the number…

Background: To become qualified engineers, undergraduates must develop a contextualized epistemic cognition (EC) during the engineering design process (EDP), but little is known about their EC in the authentic EDP. This study aimed to gain an in-depth understanding of the EC and reported epistemic changes of undergraduate engineering students who…

Cross-cultural collaborative learning has been paid more and more attention in recent years. To promote productive cross-cultural collaborative learning, idea generation and improvement, and socially shared regulation is crucial. The study aimed to identify the differences in idea generation and improvement as well as socially shared regulation…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper…

To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

No matter what path students pursue in postsecondary education and in life, they need to be able to problem-solve and think critically. The study of mathematics teaches skills and habits of mind that are an essential part of the formula for students to succeed in further studies and in their careers. Requiring all students, regardless of the…

This study investigated the effects of pre-training types on the cognitive load, collaborative knowledge construction and level of learning in a computer-supported collaborative learning environment. Pre-training was provided to help learners optimise their cognitive load, build accurate shared-knowledge and achieve successful deep learning. The…