“How I Want to Teach the Lesson”: Framing Children’s Multiple Mathematical Knowledge Bases in the Analysis and Adaptation of Existing Curriculum Materials

2018 ◽  
pp. 241-262
Author(s):  
Frances K. Harper ◽  
Corey Drake ◽  
Tonya Gau Bartell ◽  
Eduardo Najarro
Keyword(s):  
Mathematical Knowledge ◽  
Knowledge Bases ◽  
Curriculum Materials

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.

Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases

2013 ◽  
Vol 17 (3) ◽  
pp. 245-270 ◽  
Author(s):  
Amy Roth McDuffie ◽  
Mary Q. Foote ◽  
Catherine Bolson ◽  
Erin E. Turner ◽  
Julia M. Aguirre ◽  
...  
Keyword(s):  
Video Analysis ◽  
Mathematical Knowledge ◽  
Knowledge Bases

Three Strategies for Opening Curriculum Spaces

2015 ◽  
Vol 21 (6) ◽  
pp. 346-353 ◽  
Author(s):  
Corey Drake ◽  
Tonia J. Land ◽  
Tonya Gau Bartell ◽  
Julia M. Aguirre ◽  
Mary Q. Foote ◽  
...  
Keyword(s):  
Mathematical Knowledge ◽  
Knowledge Bases

Make these small adjustments to your syllabus and watch spaces open to connect to children's multiple mathematical knowledge bases.

scholarly journals Mathematics Teacher and Curriculum Quality, 2005 and 2016

AERA Open ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 233285841988052
Author(s):  
Heather C. Hill ◽  
Virginia Lovison ◽  
Thomas Kelley-Kemple
Keyword(s):  
Middle School Teachers ◽  
Great Recession ◽  
Mathematics Teacher ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Demographic Characteristics ◽  
Curriculum Materials ◽  
School Teachers ◽  
The Great Recession ◽  
Knowledge For Teaching

Efforts to improve teachers’ knowledge and to change the nature of curriculum materials have dominated mathematics reforms since the late 1990s. In this article, we compared middle school teachers’ mathematical knowledge for teaching (MKT) and curriculum use between 2005 and 2016 to assess progress toward these key goals. We found teachers’ MKT increased an amount equal to the average teacher in the 2005 sample improving five percentile points. However, No Child Left Behind’s attempts to encourage mathematics degrees in this population do not explain this increase, as teachers were less likely in 2016 than in 2005 to possess such a degree. Instead, our data are consistent with schools hiring more knowledgeable individuals during the Great Recession. Between surveys, the strength of the association between teacher MKT and student demographic characteristics decreased, although equity gaps still persist. Finally, our data suggest a modest movement toward standards-based curriculum materials over this period.

Curriculum spaces for connecting to children’s multiple mathematical knowledge bases

2018 ◽  
Vol 51 (4) ◽  
pp. 471-493 ◽  
Author(s):  
Tonia J. Land ◽  
Tonya G. Bartell ◽  
Corey Drake ◽  
Mary Q. Foote ◽  
Amy Roth McDuffie ◽  
...  
Keyword(s):  
Mathematical Knowledge ◽  
Knowledge Bases
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