Students often struggle in AP Physics 1 because they have not been previously trained to develop qualitative arguments. Extensive literature on multiple representations and qualitative reasoning provides strategies to address this challenge. Table I presents three examples, including SiQuENC, which I adapted from a strategy promoted by Etkina et…

A key property of relational representations is their "generativity": From partial descriptions of relations between entities, additional inferences can be drawn about other entities. A major theoretical challenge is to demonstrate how the capacity to make generative inferences could arise as a result of learning relations from…

As a programmer when solving a problem, a number of conscious and unconscious cognitive operations are being performed. Problem-solving is a gradual and cyclic activity; as the mind is adjusting the problem to its schemas formed by its previous experiences, the programmer gets closer and closer to understanding and defining the problem. The…

This commentary critiques Ambridge's radical exemplar model of language acquisition using research from the Longitudinal Study of Early Language, which has tracked the language development of 30+ children with Autism Spectrum Disorders (ASD) since 2002. This research has demonstrated that the children's capacity for abstraction at the grammatical…

Ambridge reviews and augments an impressive body of research demonstrating both the advantages and the necessity of an exemplar-based model of knowledge of one's language. He cites three computational models that have been applied successfully to issues of phonology and morphology. Focusing on Ambridge's discussion of sentence-level constructions,…

A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

The relations between the developing mind and developing brain are explored. We outline a theory of intellectual development postulating that the mind comprises four systems of processes (domain-specific, attention and working memory, reasoning, and cognizance) developing in four cycles (episodic, realistic, rule-based, and principle-based…

The spatial sense ability of elementary school students is still low. Concrete-Pictorial-Abstract (CPA) approach is considered able to improve students' spatial sense abilities. This research aims to find out the increase of spatial sense of elementary school students who learned with CPA approach and conventional learning in terms of overall…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

Scientific reasoning refers to the thinking skills involved in conceiving and conducting an investigation. This study examined how proficiency in performing these skills develops during the upper-elementary school years. A sample of 157 children (age 7-10) took a performance-based scientific reasoning test in three consecutive years. Four distinct…

Newton's third law is one of the most important concepts learned early in introductory mechanics courses; however, ample studies have documented a wide range of students' misconceptions and fragmented understandings of this concept that are difficult to change through traditional instruction. This research develops a conceptual framework model to…

With this article, we trace how specific pedagogical techniques can help pre-service teachers connect abstract topics related to international education policy to their own experiences and those of their future student populations. Currently, there is an increased focus in teacher education, at least discursively, on understanding issues related…

A study was conducted to explore the beliefs and practices of 49 New South Wales (NSW) primary school teachers regarding their beliefs and practices concerning the use of concrete materials in the learning and teaching of Number and Algebra. This paper reports on elements of the study regarding why and how teachers use concrete materials. Not only…

This paper investigates how an introductory philosophy course influences the moral and political development of undergraduate students in a Liberal Arts university in Central Asia. Within a context of rapid changes characteristic of transitional societies--reflected in the organization of higher education--philosophy provides students with the…