Using Concept Maps in Teacher Education: Building Connections Among Multiple Mathematical Knowledge Bases and Assessing Mathematical Understanding

2018 ◽  
pp. 287-307
Author(s):  
Lynette DeAun Guzmán
Keyword(s):  
Teacher Education ◽  
Mathematical Knowledge ◽  
Concept Maps ◽  
Knowledge Bases ◽  
Mathematical Understanding

Decision Making Modeled as a Theorem Proving Process

2012 ◽  
Vol 4 (3) ◽  
pp. 1-11
Author(s):  
Jacques Calmet ◽  
Marvin Oliver Schneider
Keyword(s):  
Artificial Intelligence ◽  
Decision Making ◽  
Information Technology ◽  
Multiagent Systems ◽  
Theorem Proving ◽  
Mathematical Knowledge ◽  
Knowledge Bases ◽  
Advanced Mathematics ◽  
Knowledge Communities ◽  
Computational Systems

The authors introduce a theoretical framework enabling to process decisions making along some of the lines and methodologies used to mechanize mathematics and more specifically to mechanize the proofs of theorems. An underlying goal of Decision Support Systems is to trust the decision that is designed. This is also the main goal of their framework. Indeed, the proof of a theorem is always trustworthy. By analogy, this implies that a decision validated through theorem proving methodologies brings trust. To reach such a goal the authors have to rely on a series of abstractions enabling to process all of the knowledge involved in decision making. They deal with an Agent Oriented Abstraction for Multiagent Systems, Object Mechanized Computational Systems, Abstraction Based Information Technology, Virtual Knowledge Communities, topological specification of knowledge bases using Logical Fibering. This approach considers some underlying hypothesis such that knowledge is at the heart of any decision making and that trust transcends the concept of belief. This introduces methodologies from Artificial Intelligence. Another overall goal is to build tools using advanced mathematics for users without specific mathematical knowledge.

Knowledge bases for diversity in teacher education

1999 ◽  
Vol 1 (1) ◽  
pp. 49-58
Author(s):  
G. Pritchy Smith ◽  
Deborah A. Batiste
Keyword(s):  
Teacher Education ◽  
Knowledge Bases

The Cost of Knowledge Recovery: A Challenge for the Application of Concept Mapping

2007 ◽  
Vol 51 (4) ◽  
pp. 328-331
Author(s):  
Robert R. Hoffman ◽  
Paul J. Feltovich ◽  
David W. Eccles
Keyword(s):  
Concept Maps ◽  
Expert Knowledge ◽  
Knowledge Bases ◽  
Knowledge Elicitation ◽  
Terrain Analysis ◽  
Aerial Photos ◽  
Knowledge Based ◽  
Knowledge Models ◽  
Rock Types ◽  
The Cost

Whereas knowledge management relies on processes of knowledge elicitation, there is also a process in which knowledge is “recovered,” typically from archived documents. We conducted a knowledge recovery (KR) effort, going from documents to a structured set of propositions concerning expert knowledge about terrain analysis, discussing landforms, soils, rock types, etc. Assertions and feature associations were recast as over 3,000 propositions. When contrasted with results from previous evaluations of methods of knowledge elicitation, KR was costly in terms of time and effort, suggesting that knowledge-based organizations should make knowledge capture an on-going aspect of work, rather than finding themselves in the “catch-up mode” to recover lost expertise. For both knowledge elicitation and recovery, the knowledge has to be represented in a form that is usable and useful (e.g., instantiation in knowledge bases). We created from the propositions a navigable knowledge model based on over 150 Concept Maps, which were hyperlinked together and to dozens of resources (aerial photos, maps, diagrams, etc.). Such knowledge models are intended to make the “expertise of the past” more useful and usable in training and in performance support.

scholarly journals Ethnomathematics and indigenous teacher education: Waka migrations

Revemop ◽  
2020 ◽  
Vol 2 ◽  
pp. e202008
Author(s):  
Tony Trinick ◽  
Tamsin Tamsin Meaney
Keyword(s):  
Teacher Education ◽  
Preservice Teacher ◽  
Indigenous Peoples ◽  
Mathematical Knowledge ◽  
Preservice Teacher Education ◽  
Traditional Methods ◽  
Mathematical Practices ◽  
Language And Culture ◽  
Primary Identification

In order to assist Indigenous peoples to revive their language and culture, teachers need strategies to enhance both cultural and mathematical knowledge for students. This paper presents findings from a project in which pre-service teachers investigated ethnomathematical practices using the context of ancestral ocean voyages by canoes. This context was chosen because a primary identification marker for Māori are their ancestral canoes. The results indicated that these pre-service teachers did not generally associate these ancestral voyages with mathematical practices, indicating that more work is needed to increase their understandings of ethnomathematics. Their understandings about the knowledge and practices connected to traditional methods of navigation were disrupted by myths perpetuated by European colonists. Despite this, a renaissance in canoe building and interest in traditional navigation practices provided the pre-service teachers with valuable information.Keywords: Traditional navigation. Ethnomathematics. Preservice teacher education. Cultural symmetry.Etnomatemáticas y formación de professores indígenas: migraciones de canoas WakaPara ayudar a los pueblos indígenas a revivir su idioma y su cultura, los maestros necesitan estrategias para mejorar el conocimiento cultural y matemático de los estudiantes. Este artículo presenta los hallazgos de un proyecto en el cual los maestros de pre-servicio investigaron las prácticas etnomatemáticas utilizando el contexto de viajes oceánicos ancestrales en canoas. Este contexto fue elegido porque un marcador de identificación principal para los Māori son sus canoas ancestrales. Los resultados indicaron que estos maestros de pre-servicio generalmente no asociaron estos viajes ancestrales con las prácticas matemáticas, lo que indica que se necesita más trabajo para aumentar su comprensión de las etnomatemáticas. Su comprensión sobre el conocimiento y las prácticas relacionadas con los métodos tradicionales de navegación fueron interrumpidos por los mitos perpetuados por los colonos europeos. A pesar de esto, un renacimiento en la construcción de canoas y el interés en las prácticas tradicionales de navegación proporcionaron a los maestros de pre-servicio informaciones valiosas.Palabras clave: Navegaciones tradicionales. Etnomatemáticas. Formación de profesores. Simetría cultural.Etnomatemática e formação de professores indígenas: migrações de canoas WakaBuscando auxiliar os povos indígenas a reavivar a sua língua e cultura, os professores precisam utilizar estratégias para aprimorar os conhecimentos culturais e matemáticos dos alunos. Esse trabalho apresenta os resultados de um projeto em que os professores em formação docente investigaram as práticas etnomatemáticas utilizando o contexto de viagens oceânicas ancestrais por canoas. Essa conjuntura foi escolhida porque uma das principais marcas identitárias dos Māori são as suas canoas ancestrais. Os resultados indicaram que, geralmente, esses professores não associaram essas jornadas ancestrais com as práticas matemáticas, sinalizando ser necessário um maior treinamento para aumentar o seu entendimento da etnomatemática. A compreensão sobre os conhecimentos e as práticas ligadas aos métodos tradicionais de navegação foram prejudicados por mitos perpetuados pelos colonizadores europeus. Contudo, um ressurgimento da construção de canoas e do interesse pelas práticas tradicionais de navegação propiciou valiosas informações para os professores em formação docente.Palavras-chave: Navegações tradicionais. Etnomatemática. Formação de professores. Simetria cultural.

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