Activity Theory as a Foundation of Real-World Problem Solving in School Mathematics

Author(s):  
Murad Jurdak
1995 ◽  
Vol 88 (9) ◽  
pp. 731-733
Author(s):  
Vincent P. Schielack

Situations arise in many everyday endeavors that can be analyzed using various mathematical techniques. These situations give mathematics educators many opportunities to connect real-world problem-solving situations with appropriate mathematical models, as recommended in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The mathematics topic here involves applying elementary concepts of probability to a hotly debated question arising in football. h will be assumed throughout that a team values a win significantly more than a tie and also values a tie considerably more than a loss.


Author(s):  
Marc J. Stern

This chapter covers systems theories relevant to understanding and working to enhance the resilience of social-ecological systems. Social-ecological systems contain natural resources, users of those resources, and the interactions between each. The theories in the chapter share lessons about how to build effective governance structures for common pool resources, how to facilitate the spread of worthwhile ideas across social networks, and how to promote collaboration for greater collective impacts than any one organization alone could achieve. Each theory is summarized succinctly and followed by guidance on how to apply it to real world problem solving.


2020 ◽  
Author(s):  
David Kelso ◽  
John D. Enderle ◽  
Kristina Ropella

Author(s):  
Caitlin Dippo ◽  
Barry Kudrowitz

Previous studies have found that the first few ideas we think of for a given prompt are likely to be less original than the later ideas. In this study, 460 participants were given the Alternative Uses Test (AUT) where they were asked to list alternative uses for a paperclip, creating a database of 235 unique answers, each having a relative occurrence rate in that pool. It was found that later responses were significantly more novel than early responses and on average the originality of responses exponentially increased with quantity. A closer look at this data reveals that a person is likely to have a lower overall originality score if he or she has more elaborate responses. 89 of these participants were also given the Abbreviated Torrance Test For Adults (ATTA) and the data from both tests was used to study relationships between elaboration, fluency, and originality. The data from the AUT reveals a strong negative correlation between an individual’s average number of words per response and his or her average originality score. It is hypothesized that people who spend more time writing multiple-word responses have less time to generate many different ideas thus hindering their ability to reach the novel ideas. Similarly, the ATTA reveals that after two extraneous details, elaboration on a drawing will negatively impact fluency and originality scores. This is not to say that elaborate ideas cannot be original, but rather that in time-limited situations, elaboration may hinder the production of original ideas. In applying this to real world problem solving and idea generation, it is suggested that people may prevent themselves from finding creative solutions if too much time is spent on discussing the first few suggested ideas from a brainstorming session. It is suggested that a more effective brainstorming session will delay discussion until a significant number of ideas are generated.


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