scholarly journals The Role of Multiple Representations and Representational Fluency in Cryptography Education

Author(s):  
Ziyang Tang ◽  
Xiang Liu ◽  
Yingjie Chen ◽  
Baijian Yang
2011 ◽  
pp. 204-224 ◽  
Author(s):  
Fernand Gobet ◽  
Peter C.R. Logan

This chapter provides an introduction to the CHREST architecture of cognition and shows how this architecture can help develop a full theory of mind. After describing the main components and mechanisms of the architecture, we discuss several domains where it has already been successfully applied, such as in the psychology of expert behaviour, the acquisition of language by children, and the learning of multiple representations in physics. We highlight the characteristics of CHREST that enable it to account for empirical data, including self-organisation, an emphasis on cognitive limitations, the presence of a perception-learning cycle, and the use of naturalistic data as input for learning. We argue that some of these characteristics can help shed light on the hard questions facing theorists developing a full theory of mind, such as intuition, the acquisition and use of concepts, the link between cognition and emotions, and the role of embodiment.


2007 ◽  
Vol 100 (7) ◽  
pp. 494-500
Author(s):  
Robin Rider

Algebraic reasoning skills can be enhanced by building connections among symbolic, tabular, and graphical representations. But how do classroom teachers change traditional teaching practices to foster the use of different representational forms? This article explores how I learned to incorporate representational fluency in teaching and assessment. It builds on ideas from classroom practice and advocates making small changes in teaching practices to foster connections between representations.


2011 ◽  
Vol 12 (3) ◽  
pp. 283-293 ◽  
Author(s):  
Seán P. Madden ◽  
Loretta L. Jones ◽  
Jrène Rahm

Author(s):  
Wendy Nielsen ◽  
Annette Turney ◽  
Helen Georgiou ◽  
Pauline Jones

AbstractThe construction of dynamic multimedia products requires the selection and integration of a range of semiotic resources. As an assessment task for preservice teachers, this construction process is complex but has significant potential for learning. To investigate how weaving together multiple representations in such tasks enables learners to develop conceptual understanding, the paper presents an indicative case study of a 2nd-year preservice primary (K-6) teacher who created a digital explanation on the topic of ‘transparency’ for stage 3 children (ages 11–12). We focus on data gathered during the 3-h construction process including artefacts such as images, online searches, websites accessed and paper records used for planning; the digital explanation as product; audio and video capture of the construction process and pre- and post-construction interviews. Using multimodal analysis, we examine these data to understand how meanings are negotiated as the maker moves iteratively among multiple representations and through semiotic choices within these representations to explain the science concept. The analyses illustrate the complexity of the construction process while providing insight into the creator’s decision-making and to her developing semiotic and conceptual understandings. These findings allow us to build on the concept of cumulative semiotic progression (Hoban & Nielsen, Research in Science Education, 35, 1101-1119, 2013) by explicating the role of iterative reasoning in the production of pedagogic multimedia.


2008 ◽  
Vol 14 (1) ◽  
pp. 44-50
Author(s):  
Jennifer M. Suh ◽  
Chris Johnston ◽  
Spencer Jamieson ◽  
Michelle Mills

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical concepts. This article shares a collaborative lesson study experience in planning and teaching a unit on decimals. Participants included fifth- and sixth-grade teachers and lesson study facilitators, including a university mathematics educator, a doctoral student, and a school mathematics specialist. The lesson was taught in a fifth-grade class with a high population of English language learners (ELL) and special needs students. The overarching goal of the lesson study was to develop students' representational fluency and mathematical proficiency with decimals. While working with teachers, the lesson study facilitators shared related research on representations and the importance of selecting and evaluating effective mathematical models to give the diverse population access to decimal concepts. The lesson study facilitators' goal was to heighten teachers' awareness of the importance of multiple representations and introduce a planning process that allows teachers to select models in a thoughtful and critical way that would facilitate the teaching and learning of a mathematics concept.


2014 ◽  
Vol 91 (6) ◽  
pp. 784-792 ◽  
Author(s):  
Abdi-Rizak M. Warfa ◽  
Gillian H. Roehrig ◽  
Jamie L. Schneider ◽  
James Nyachwaya

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