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…

Information and Communication Technology (ICT) education has been actively implemented around the world recently. ICT curriculum in schools is intended to improve students' programming-oriented thinking rather than to train them as programmers. The core of ICT education is 'computational thinking'. Computational thinking is taking an approach to…

This study used integrative data analysis (Curran & Hussong, 2009), which allows combining data from different studies, to examine the generalizability of a research-based mathematics program, schema-based instruction (SBI), with a focus on proportional reasoning. Data were pooled from existing SBI studies spanning three U.S. states in which…

Purpose: This paper aims to compare two types of prompts, encouraging participants to think about real-world examples or engineering principles to show how these two approaches can result in vastly different design practices. Design/methodology/approach: Two studies (N = 20, N = 40) examine the impact of two different prompts. Non-expert students,…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

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…

In this paper, we contend that what to teach about scientific reasoning has been bedeviled by a lack of clarity about the construct. Drawing on the insights emerging from a cognitive history of science, we argue for a conception of scientific reasoning based on six "styles of scientific reasoning." Each "style" requires its own…

This article describes how to play two abstract strategy board games: (1) "Blokus" which uses polyominoes--plane geometric figures formed by joining one or more equal squares edge to edge; and (2) "Gemblo" which uses translucent, colored pieces, each of which is made up of one to five hexagons.

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…

Complex thinking is a desired competency in 21st-century university students, so technology-based teaching and learning strategies must be carefully considered when training them in complex reasoning skills. This systematic review aims to map research on the use of teaching and learning strategies supported by technology to enhance complex…

To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the…

The main aim of the present investigation was to examine conditional reasoning skills in college students whose educational past had emphasized verbatim learning. A successive independent-samples design was utilized to explore the effects of instruction that explicitly targeted critical thinking principles in either freshman students or…

One of the challenges that commencing university students in computing degree programs face is the difficulty in engaging with the abstract and complicated theories in the computing discipline. In particular, it is hard for beginner computer architecture students to visualise the link between the theory of digital logic and the behaviour of the…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

In 'Against Stored Abstractions,' Ambridge uses neural and computational evidence to make his case against abstract representations. He argues that storing only exemplars is more parsimonious -- why bother with abstraction when exemplar models with on-the-fly calculation can do everything abstracting models can and more -- and implies that his…