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…

Internationally, coding is increasingly introduced into primary and junior high schools (children generally aged between 5 and 15) on a compulsory basis, though not all stakeholders support this 'initiative'. In response to the public reception, discussion highlights popular argument around compulsory coding in school education. This is an…

Educational systems worldwide underscore the importance of developing higher-order thinking skills (HOTS) to prepare students for the new challenges of the XXI century. Some pressing issues faced by educators include the ambiguity of the construct; the implementation of HOTS in classroom practices; and the implications for teaching students from…

Most studies suggest that students develop computational thinking (CT) through learning programming. However, when the target of CT is decoupled from programming, emerging evidence challenges the assertion of CT transferability from programming. In this study, CT was operationalized in everyday problem-solving contexts in a learning experiment (n…

Learning progressions (LPs) are novel models for the development of assessments in science education, that often use a scale to categorize students' levels of reasoning. Pictorial representations are important in chemistry teaching and learning, and also in LPs, but the differences between pictorial and verbal items in chemistry LPs is unclear. In…

The paper explains the role of oral language and dialogic interactions in the development of individual thinking and reasoning processes. Collaborative reasoning and its contribution is explained while examples are shared to illustrate ways to scaffold students' questioning, meaning making, and writing in the context of read alouds during…

Research indicates that understanding levels of abstraction (LOA) and being able to move between the levels is essential to programming success. For K-5 contexts LOA levels have been named: problem, design, code and running the code. In a qualitative exploratory study, five K-5 teachers were interviewed on their uses of LOA, particularly the…

Abstraction is a core principle of Distributional Semantic Models (DSMs) that learn semantic representations for words by applying dimensional reduction to statistical redundancies in language. Although the posited learning mechanisms vary widely, virtually all DSMs are prototype models in that they create a single abstract representation of a…

After describing Wittgenstein's notion of "certainty", in this article I provide four arguments to demonstrate that no certainty can be acquired at will. Specifically, I argue that, in order to assimilate a certainty, it is irrelevant whether the individual concerned (1) has found a ground that seemingly justifies that certainty; (2) has…

This article assesses how people reason with categories whose features are related in causal cycles. Whereas models based on causal graphical models (CGMs) have enjoyed success modeling category-based judgments as well as a number of other cognitive phenomena, CGMs are only able to represent causal structures that are acyclic. A number of new…