Mixed media modelling of technological concepts in electricity, methods for supporting learning styles

The overarching objective of this research is to recognize the learning styles of engineering and technology students and to propose pedagogical methods for the comprehension of technological concepts in electricity. The topic of electrical resistor-capacitor (RC) circuits has been chosen because it is fundamental to engineering and technology courses. There is substantial evidence to suggest that students find such a concept difficult to grasp. The focus of the research lies in explicating undergraduate students cognitive structures about RC circuits, and proposing a method related to students learning styles of how these cognitive structures may be enhanced. The main thesis argument claims that the transfer of knowledge from familiar RC circuit configurations to unfamiliar RC circuit configurations does not occur easily even if the problem-space is kept identical. The methodology used in this research is a mixed-method approach employing qualitative and quantitative data-gathering and analysis processes. This research concludes that the reasons for lack of transfer of knowledge stem from conceptual and perceptual constraints. Constraints involve: (a) which analogical models are employed in relation to the RC circuit, (b) how the circuit schematic diagram is drawn, and (c) relations between analogy, circuit schematic diagram, voltage-time graphs and verbal jargon used to describe circuit behaviour. The research presents a variety of novel, custom-designed learning aids which are employed within the research methodology to rectify the lack of transfer of knowledge for the RC circuits considered in the study. The design of these learning aids is based on the concept of embodied cognition and mainly makes use of visual and kinaesthetic means to appeal to students who may have different learning styles. The use of such learning aids is proposed as a complementary teaching strategy. The approach taken in this research and its outcomes are significant because they continue to inform the research and educational communities about how human development may be fostered through engineering and technology education (Barak and Hacker, 2011)

Prospective Teachers’ Interactive Visualization and Affect in Mathematical Problem-Solving

Research on technology-assisted teaching and learning has identified several families of factors that contribute to the effective integration of such tools. Focusing on one such family, affective factors, this article reports on a qualitative study of 30 prospective secondary school mathematics teachers designed to acquire insight into the affect associated with the visualization of geometric loci using GeoGebra. Affect as a representational system was the approach adopted to gain insight into how the use of dynamic geometry applications impacted students’ affective pathways. The data suggests that affect is related to motivation through goals and self-concept. Basic instrumental knowledge and the application of modeling to generate interactive images, along with the use of analogical visualization, played a role in local affect and prospective teachers’ use of visualization

Cognitive Conditions of Diagrammatic Reasoning

Forthcoming in Semiotica (ISSN: 0037-1998), published by Walter de Gruyter & Co.In the first part of this paper, I delineate Peirce's general concept of diagrammatic reasoning from other usages of the term that focus either on diagrammatic systems as developed in logic and AI or on reasoning with mental models. The main function of Peirce's form of diagrammatic reasoning is to facilitate individual or social thinking processes in situations that are too complex to be coped with exclusively by internal cognitive means. I provide a diagrammatic definition of diagrammatic reasoning that emphasizes the construction of, and experimentation with, external representations based on the rules and conventions of a chosen representation system. The second part starts with a summary of empirical research regarding cognitive effects of working with diagrams and a critique of approaches that use 'mental models' to explain those effects. The main focus of this section is, however, to elaborate the idea that diagrammatic reasoning should be conceptualized as a case of 'distributed cognition.' Using the mathematics lesson described by Plato in his Meno, I analyze those cognitive conditions of diagrammatic reasoning that are relevant in this case

CHEMISTRY LEARNING WITH APPLICATION OF THE ZONE OF PROXIMAL DEVELOPMENT AND USE OF CONCEPTUAL MAPS IN THE CHEMISTRY LAB

Indexación: Scopus; Scielo.The present study focuses on the deficient learning of health science students in the General Chemistry course in the first level higher education, specifically regarding the topic of aqueous dissolutions in terms of the meaning of pH and how to determine it. The causes of this problem are: i) the difficulty relating the theory to the practice, ii) the lack of strategies that help and motivate learning, iii) the inability to underst and and resolve problems or exercises, and iv) a deficiencyon basic mathematical aptitudes for application in resolving problems and exercises, among others. The research considered the academic results obtained bystudents of various careers in the area of health sciences students in the past, to subsequently determine the research group, resulting it the career of nursingstudents. To achieve this type of learning, the Zone of Proximal Development (ZPD) was applied, together with the metacognitive strategy of Conceptual Maps (CM) and feedback & self-correction in practical laboratory activities. This study was carried out at a university and involved nursing students because they havemany difficulties learning experimental sciences, especially chemistry, because the students of other careers do not have many weaknesses in this science, beingevidenced in the results at end of the semester-The sample experimental group consisted of 336 nursing students and the control group 420 students of nutrition and dietetics and dentistry taking the unit "General Chemistry", who provided all the information for this study.http://www.scielo.cl/pdf/jcchems/v61n1/art02.pd

Inducing visibility and visual deduction

Scientists use diagrams not just to visualize objects and relations in their fields, both empirical and theoretical, but to reason with them as tools of their science. While the two dimensional space of diagrams might seem restrictive, scientific diagrams can depict many more than two elements, can be used to visualise the same materials in myriad different ways, and can be constructed in a considerable variety of forms. This paper takes up two generic puzzles about 2D visualizations. First: How do scientists in different communities use 2D spaces to depict materials which are not fundamentally spatial? This prompts the distinction between diagrams that operate in different kinds of spaces: ‘real’, ‘ideal’, and ‘artificial’. And second: How do diagrams, in these different usages of 2D space, support various kinds of visual reasoning that cross over between inductive and deductive? The argument links the representational form and content of a diagram (its vocabulary and grammar) with the kinds of inferential and manipulative reasoning that are afforded, and constrained, by scientists’ different usages of 2D space

Imagination in mathematics

This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras

Hybrid Reasoning and the Future of Iconic Representations

We give a brief overview of the main characteristics of diagrammatic reasoning, analyze a case of human reasoning in a mastermind game, and explain why hybrid representation systems (HRS) are particularly attractive and promising for Artificial General Intelligence and Computer Science in general.Comment: pp. 299-31

Arithmetic, Set Theory, Reduction and Explanation

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences

Theories in and of Mathematics Education

Mathematics Education; Learning; Teachin

Diagrammatic Reasoning Skills of Pre-Service Mathematics Teachers

This study attempted to explore a possible relationship between diagrammatic reasoning and geometric knowledge of pre-service mathematics teachers. Diagrammatic reasoning skills, as a sequence of steps from visualization, to interpretation, to formalisms, are at the core of teachers' content knowledge for teaching. However, there is no course in the mathematics curriculum that systematically develops diagrammatic reasoning skills, except Geometry. In the course of this study, a group of volunteers in the last semester of their teacher preparation program were presented with "visual proofs" of certain theorems from high school mathematics curriculum and asked to prove/explain these theorems by reasoning from the diagrams. The results of the interviews were analyzed with respect to the participants' attained van Hiele levels. The study found that participants who attained higher van Hiele levels were more skilled at recognizing visual theorems and "proving" them. Moreover, the study found a correspondence between participants' diagrammatic reasoning skills and certain behaviors attributed to van Hiele levels. However, the van Hiele levels attained by the participants were consistently higher than their diagrammatic reasoning skills would indicate