Creative Discovery

2020 ◽  
Vol 24 (2) ◽  
pp. 299-321
Author(s):  
John V. Garner ◽  
Keyword(s):  
Scientific Inquiry ◽  
Mathematical Thinking ◽  
Self Engagement

In his commentary on Euclid, Proclus develops what he takes to be an important Platonic critique of the epistemology of abstraction. As I argue, his argument closely reflects terminology and concepts from Plato’s Philebus. Both emphasize the priority—in reality and in our awareness—of the precise over the imprecise. Specifically, Proclus’s famous notion of the psychical “projection” of intermediate mathematical entities, while having no technically exact precedent in Plato, finds a conceptual neighbor in the Philebus’s suggestion that philosophical arithmeticians “posit” pure units for counting. Likewise, for both our self-engagement in mathematical thinking (which has importance even for non-mathematical inquiries) serves to clarify the independence of the precise sciences—both in their content and in their practice—from perception. Thus, as I argue, Plato and Proclus, with their different terms and nuances, develop a shared conception scientific inquiry in which an activity of “creative discovery” plays a central role.

Review of Mathematical Thinking and Problem Solving.

1996 ◽  
Vol 41 (1) ◽  
pp. 80-80
Author(s):  
Daniel Stalder ◽  
Shubhangi Stalder
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking

Thinking About Mathematical Thinking

PsycCRITIQUES ◽  
2010 ◽  
Vol 55 (23) ◽  
Author(s):  
Gordon Pitz
Keyword(s):  
Mathematical Thinking

APA Summit on National Assessment of Psychology: Executive Summary: Goal 2: Scientific Inquiry and Critical Thinking

2016 ◽  
Author(s):  
Jon Mueller ◽  
Keisa Kelly ◽  
Helen Taylor ◽  
Karen Brakke ◽  
Gary Levine ◽  
...  
Keyword(s):  
Critical Thinking ◽  
Scientific Inquiry ◽  
National Assessment ◽  
Executive Summary

Death in the City

2017 ◽  
Author(s):  
Kathryn A. Sloan
Keyword(s):  
Scientific Inquiry ◽  
The United States ◽  
Violent Death ◽  
Special Relationship ◽  
Intimate Friend ◽  
Counter Narrative ◽  
Wide Range ◽  
European Heritage ◽  
The City ◽  
The Temple

Popular culture has long conflated Mexico with the macabre. Some persuasive intellectuals argue that Mexicans have a special relationship with death, formed in the crucible of their hybrid Aztec-European heritage. Death is their intimate friend; death is mocked and accepted with irony and fatalistic abandon. The commonplace nature of death desensitizes Mexicans to suffering. Death, simply put, defines Mexico. There must have been historical actors who looked away from human misery, but to essentialize a diverse group of people as possessing a unique death cult delights those who want to see the exotic in Mexico or distinguish that society from its peers. Examining tragic and untimely death—namely self-annihilation—reveals a counter narrative. What could be more chilling than suicide, especially the violent death of the young? What desperation or madness pushed the victim to raise the gun to the temple or slip the noose around the neck? A close examination of a wide range of twentieth-century historical documents proves that Mexicans did not accept death with a cavalier chuckle nor develop a unique death cult, for that matter. Quite the reverse, Mexicans behaved just as their contemporaries did in Austria, France, England, and the United States. They devoted scientific inquiry to the malady and mourned the loss of each life to suicide.

Divine Machines

2011 ◽  
Author(s):  
Justin E. H. Smith
Keyword(s):  
Seventeenth Century ◽  
Early Modern ◽  
Scientific Inquiry ◽  
Life Sciences ◽  
Theoretical Interest ◽  
Living World ◽  
Mechanical Philosophy ◽  
Organic Life ◽  
The World ◽  
Generation Theory

Though it did not yet exist as a discrete field of scientific inquiry, biology was at the heart of many of the most important debates in seventeenth-century philosophy. Nowhere is this more apparent than in the work of G. W. Leibniz. This book offers the first in-depth examination of Leibniz's deep and complex engagement with the empirical life sciences of his day, in areas as diverse as medicine, physiology, taxonomy, generation theory, and paleontology. The book shows how these wide-ranging pursuits were not only central to Leibniz's philosophical interests, but often provided the insights that led to some of his best-known philosophical doctrines. Presenting the clearest picture yet of the scope of Leibniz's theoretical interest in the life sciences, the book takes seriously the philosopher's own repeated claims that the world must be understood in fundamentally biological terms. Here it reveals a thinker who was immersed in the sciences of life, and looked to the living world for answers to vexing metaphysical problems. The book casts Leibniz's philosophy in an entirely new light, demonstrating how it radically departed from the prevailing models of mechanical philosophy and had an enduring influence on the history and development of the life sciences. Along the way, the book provides a fascinating glimpse into early modern debates about the nature and origins of organic life, and into how philosophers such as Leibniz engaged with the scientific dilemmas of their era.

Exploring the Implementation of Early Math Assessments in Kindergarten Classrooms: A Research-Practice Collaboration

2020 ◽  
Author(s):  
Jennifer McDonald ◽  
Rebecca Merkley ◽  
Jacqueline Mickle ◽  
Lisa Collimore ◽  
Daniel Ansari
Keyword(s):  
Mathematical Thinking ◽  
Math Education ◽  
Kindergarten Students ◽  
First Year ◽  
Research Practice ◽  
Early Numeracy ◽  
Future Directions ◽  
Collaborative Project ◽  
Practice Gap ◽  
Second Year

Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative project between cognitive scientists and school board researchers/educators implementing numeracy screeners with kindergarten students over the course of three school years. The Give-A-Number task (Wynn, 1990) was used with first-year kindergarten students and the Numeracy Screener [BLINDED] with second-year kindergarten students. Results indicated that educators (N = 59) found the tools feasible to implement and helpful for exploring their students’ thinking and targeting instruction. The Educators’ feedback also helped inform improvements to the implementation of the tools and future directions for both the schools and the researchers. This work emphasizes the importance of transdisciplinary collaboration to address the research-practice gap.

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