Systems and system models are recognized as a crosscutting concept in the newly released framework for K-12 science education (NRC [National Research Council], 2012). In previous work, I developed a learning progression for systemic reasoning in ecology at the elementary level. The learning progression captured five levels of students' reasoning…

The paper focuses on student-teachers' geometric diagrams to mediate the emergence of different proofs for a geometric proposition. For Peirce, a diagram is an icon that explicitly and implicitly represents the deep structural relations among the parts of the object that it stands for. Geometric diagrams can be seen as epistemological tools to…

This study examines differences in English language comprehension, reading fluency, and executive functions among Spanish-English bilinguals with reading difficulties. Reading difficulties examined included general reading difficulties, defined by low word reading and reading comprehension, and specific-reading comprehension difficulties, defined…

This study examines differences in English language comprehension, reading fluency, and executive functions among Spanish-English bilinguals with reading difficulties. Reading difficulties examined included general reading difficulties, defined by low word reading and reading comprehension, and specific-reading comprehension difficulties, defined…

We investigated "scalar implicature" in adolescents and children with autism spectrum disorder (ASD) to test whether theory of mind deficits associated with autism affect pragmatic inferences in language. We tested scalar implicature computation in adolescents with ASD (12-18 years) and asked whether they reason about mental states when…

Detecting a pattern within a sequence of ordered units, defined as patterning, is a cognitive ability that is important in learning mathematics and influential in learning to read. The present study was designed to examine relations between first-grade children's executive functions, patterning, and reading abilities, and to examine whether these…

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of…

This article considers a set of well-researched default assumptions that people make in reasoning about complex causality and argues that, in part, they result from the forms of causal induction that we engage in and the type of information available in complex environments. It considers how information often falls outside our attentional frame…

Inequalities are everywhere, yet little is known about how children respond to people affected by inequalities. This article explores two responses--minimizing inequalities and favoring those who are advantaged by them. In Studies 1a (N = 37) and 1b (N = 38), 4- and 5-year-olds allocated a resource to a disadvantaged recipient, but judged…

Complex Problem Solving (CPS) can be defined as those psychological processes that enable a person to achieve goals under complex conditions, which are characterized by their complexity, connectivity, dynamics, lack of transparency, and polytely. Although many hypothesized influences have previously been tested concerning their relevance for the…

With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students'…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

The present study addressed the effectiveness of an educational math game for improving proportional reasoning in prevocational education, and examined the added value of support in the form of reflection. The study compared four conditions: the game with reflection prompts, the game with reflection prompts plus procedural information, the game…