Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

The main goal of this study was to investigate how readers' visual attention distribution during reading of conflicting science information is related to their scientific reasoning behavior. A total of 25 university students voluntarily participated in the study. They were given conflicting science information about earthquake predictions to read…

Video games offer an exciting opportunity for learners to engage in computational thinking in informal contexts. This paper describes a genre of learning environments called constructionist video games that are especially well suited for developing learners' computational thinking skills. These games blend features of conventional video games with…

Thinking Maps is a language of eight visual patterns, each based on a fundamental thought process, designed by Dr. David N. Hyerle. The visual patterns are based on cognitive skills and applied in all content areas. Not only are they used in different combinations for depth and complexity, but are also used by all members in the school community.…

Little to no information exists explaining the nature of conceptual gaps in understanding fractions for students with learning disabilities (LD); such information is vital to practitioners seeking to develop instruction or interventions. Many researchers argue such knowledge can be revealed through student's problem-solving strategies. Despite…

We identify and document 3 cognitive obstacles, 3 cognitive affordances, and 1 type of integer understanding that can function as either an obstacle or affordance for learners while they extend their numeric domains from whole numbers to include negative integers. In particular, we highlight 2 key subsets of integer reasoning: understanding or…

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…

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…

The capacity to imagine oneself experiencing future events has important implications for effective daily living but investigation of this ability in autism spectrum disorder (ASD) is limited. This study investigated future thinking in 30 children with high functioning ASD (IQ > 85) and 30 typically developing children. They completed the…

Relational reasoning is the foundational cognitive ability to discern meaningful patterns within an informational stream, but its reliable and valid measurement remains problematic. In this investigation, the measurement of relational reasoning unfolded in three stages. Stage 1 entailed the establishment of a research-based conceptualization of…

One of the facets of geographic literacy is the ability to think in a structured way about geographic relationships. Geospatial technologies offer many opportunities to stimulate students' geographic relational thinking. The question is: How can these opportunities be effectuated? This paper discusses the results of a process-oriented experiment…

The goals of this dissertation were to examine how novice calculus teachers used questions in their classrooms, how those questions and their use might change after video case-based course coordination, and what evidence of influence on student learning might be seen in undergraduate student achievement. This research focused on one way to elicit…

To investigate relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems…

The purpose of this study was primarily to explore high school students' cognitive structures and to identify their learning difficulties on ethanoic acid through the flow map method. The subjects of this study were 30 grade 1 students from Dong Yuan Road Senior High School in Xi'an, China. The interviews were conducted a week after the students…

Critical thinking, problem solving, the use of tools, and the ability to consume and analyze information are important skills for the 21st century workforce. This article presents a qualitative case study that follows five undergraduate biology majors in a computer science course (CS0). This CS0 course teaches programming within a data-driven…