Encyclopedia of Mathematics Education

2014 Edition
| Editors: Stephen Lerman

Critical Thinking in Mathematics Education

Reference work entry
DOI: https://doi.org/10.1007/978-94-007-4978-8_35
  • 645 Downloads

Characteristics

Educational psychologists frame critical thinking (CT) as a set of generic thinking and reasoning skills, including a disposition for using them, as well as a commitment to using the outcomes of CT as a basis for decision-making and problem solving. In such descriptions, CT is established as a general standard for making judgments and decisions. Some descriptions of CT activities and skills include a sense for fairness and the assessment of practical consequences of decisions as characteristics of CT (e.g., Paul and Elder 2001). This assumes autonomous subjects who share a common frame of reference for representation of facts and ideas, for their communication, as well as for appropriate (morally “good”) action. Important is also the difference as to what extent a critical examination of the criteria for CT is included in the definition: If education for CT is conceptualized as instilling a belief in a more or less fixed and shared system of skills and criteria for...

Keywords

Logical thinking Argumentation Deductive reasoning Mathematical problem solving Critique Mathematical literacy Critical judgment Goals of mathematics education 
This is a preview of subscription content, log in to check access.

References

  1. Appelbaum P, Davila E (2009) Math education and social justice: gatekeepers, politics and teacher agency. In: Ernest P, Greer B, Sriraman B (eds) Critical issues in mathematics education. Information Age, Charlotte, pp 375–394Google Scholar
  2. Applebaum M, Leikin R (2007) Looking back at the beginning: critical thinking in solving unrealistic problems. Mont Math Enthus 4(2):258–265Google Scholar
  3. Bacon F (1605) Of the proficience and advancement of learning, divine and human. Second Book (transcribed from the 1893 Cassell & Company edition by David Price. Available at: http://www.gutenberg.org/dirs/etext04/adlr10h.htm
  4. Common Core State Standards Initiative (2010) Mathematics standards. http://www.corestandards.org/Math. Accessed 20 July 2013
  5. Ernest P (2010) The scope and limits of critical mathematics education. In: Alrø H, Ravn O, Valero P (eds) Critical mathematics education: past, present and future. Sense Publishers, Rotterdam, pp 65–87Google Scholar
  6. Fawcett HP (1938) The nature of proof. Bureau of Publications, Columbia, New York City. University (Re-printed by the National Council of Teachers of Mathematics in 1995)Google Scholar
  7. Fenner P (1994) Spiritual inquiry in Buddhism. ReVision 17(2):13–24Google Scholar
  8. Fish M, Persaud A (2012) (Re)presenting critical mathematical thinking through sociopolitical narratives as mathematics texts. In: Hickman H, Porfilio BJ (eds) The new politics of the textbook. Sense Publishers, Rotterdam, pp 89–110Google Scholar
  9. Garfield JL (1990) Epoche and śūnyatā: skepticism east and west. Philos East West 40(3):285–307Google Scholar
  10. Jablonka E (1997) What makes a model effective and useful (or not)? In: Blum W, Huntley I, Houston SK, Neill N (eds) Teaching and learning mathematical modelling: innovation, investigation and applications. Albion Publishing, Chichester, pp 39–50Google Scholar
  11. Keitel C, Kotzmann E, Skovsmose O (1993) Beyond the tunnel vision: analyzing the relationship between mathematics, society and technology. In: Keitel C, Ruthven K (eds) Learning from computers: mathematics education and technology. Springer, New York, pp 243–279Google Scholar
  12. Legrand M (2001) Scientific debate in mathematics courses. In: Holton D (ed) The teaching and learning of mathematics at university level: an ICMI study. Kluwer, Dordrect, pp 127–137Google Scholar
  13. National Council of Teachers of Mathematics (NCTM) (1989) Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics (NCTM), RestonGoogle Scholar
  14. O’Daffer PG, Thomquist B (1993) Critical thinking, mathematical reasoning, and proof. In: Wilson PS (ed) Research ideas for the classroom: high school mathematics. MacMillan/National Council of Teachers of Mathematics, New York, pp 31–40Google Scholar
  15. Paul R, Elder L (2001) The miniature guide to critical thinking concepts and tools. Foundation for Critical Thinking Press, Dillon BeachGoogle Scholar
  16. Pimm D (1990) Mathematical versus political awareness: some political dangers inherent in the teaching of mathematics. In: Noss R, Brown A, Dowling P, Drake P, Harris M, Hoyles C et al (eds) Political dimensions of mathematics education: action and critique. Institute of Education, University of London, LondonGoogle Scholar
  17. Skovsmose O (1989) Models and reflective knowledge. Zentralblatt für Didaktik der Mathematik 89(1):3–8Google Scholar
  18. Stallman J (2003) John Dewey’s new humanism and liberal education for the 21st century. Educ Cult 20(2):18–22Google Scholar
  19. Steiner H-G (1988) Theory of mathematics education and implications for scholarship. In: Steiner H-G, Vermandel A (eds) Foundations and methodology of the discipline mathematics education, didactics of mathematics. In: Proceedings of the second tme conference, Bielefeld-Antwerpen, pp 5–20Google Scholar
  20. Walkerdine V (1988) The mastery of reason: cognitive development and the production of rationality. Routledge, LondonGoogle Scholar
  21. Walshaw M (2003) Democratic education under scrutiny: connections between mathematics education and feminist political discourses. Philos Math Educ J 17. http://people.exeter.ac.uk/PErnest/pome17/contents.htm

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Education and Professional StudiesKing’s College LondonLondonUK