Including causal links in concept maps enables learners to meaningfully relate concepts to a larger context or problem in terms of how and where concepts apply within the chains of causal events that lead to a given goal or outcome. Given that higher quality maps are produced when students link and sequence events to flow temporally and…

Understanding the intricate quantifier relations in the formal definitions of both convergence and continuity is highly relevant for students to use these definitions for mathematical reasoning. However, there has been limited research about how students relearn previous school mathematics for understanding multiply quantified statements. This…

This paper takes issue with the view of conceptual structures as autonomous syntactic structures generated by syntactic formation rules. Instead, it adopts the position developed by Croft and Cruse (2004), in showing that linguistic knowledge -- knowledge of meaning and form -- is basically conceptual structure. In fact the, fundamental problem…

This study compares the relative influence of syntax, semantics, and pragmatics in university students' interpretation of multiply quantified statements in mathematics, both before and after instruction. Like previous studies, results show that semantics plays a heavy role in student interpretation, especially before instruction. Unlike previous…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

This dissertation focuses on when and how children learn about the meanings of the propositional attitude" verbs know" and "think". "Know" and "think" both express belief. But they differ in their veridicality: "think" is non-veridical and can report a false belief; but "know" can only…

Entropy is a central concept in thermodynamics, but has been found to be challenging to students due to its abstract nature and the fact that it is not part of students' everyday language. Interviews with three pairs of engineering students (N = 6) were conducted and video recorded regarding their interpretation and use of the entropy concept, one…

The article shows how mind-mapping software can be used to help premedical students learn, apply and relate terminology sharing Greek and Latin roots. Mind-mapping software use a center, branches, and sub-branches to show connections between Greek and Latin roots generated on the mind map. Instruction with the mind-mapping software goes through…

Logic has been intertwined with the study of language and meaning since antiquity, and such connections persist in present day research in linguistic theory (formal semantics) and cognitive psychology (e.g., studies of human reasoning). However, few studies in cognitive neuroscience have addressed logical dimensions of sentence-level language…

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students'…

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

In a recent study of conceptual combination, Estes (2003) presented evidence for the priming of relational information in the absence of shared constituents between the prime and target (e.g., "pancake spatula" was interpreted more quickly following "bacon tongs" than following "city riots"). He argued that these data support the view that…

Previous cognitive science research demonstrates how the Agent-action-Objective (AaO) paradigm controls the cognitive processes of differentiation and integration. The present discussion advances the process to the fourth of five phases. Of the four dependent variables emerging at this stage, two are discussed: zero processing and variations in…

The nature of the task of defining words by means of other words and the development of language responses (from children aged four to seven) are discussed in terms of a linguistic analysis of the definitional form and its semantic relations. (Author/RM)