Teachers’ Conceptions of Problem Solving

Grouws, Good and Dougherty interviewed junior high school teachers to determine their conceptions about problem solving and its instruction. They found four categories of conceptions of problem solving in which teachers could be grouped:

Problem Solving is
  1. Solving word problems, that is, the mode of presentation of the problems situation is the determining factor for these teachers. For these teachers a problem is a ‘word’ problem.
  2. Solving problems, that is anytime students found an answer to a mathematical problem, they are doing problem solving.
  3. Solving practical problems, that is, the content of the problem (what the teacher perceives as real-life) is the determining factors of whether or not learners are doing problem solving
  4. Solving thinking problems, that is, learners are engaged in problem solving when they incorporate their ideas and challenged to think to find a solution.

The first three focus on the nature of a problem and its computational process while the last one is primarily concerned with processes involved in finding a solution.

what is a problemA case study on teachers conception of problem solving and its teaching was also reported by Chapman. Her findings indicated that the teacher viewed problem solving as both cognitive and social endeavor. The teacher made no distinction between problem and problem solving, i.e., the problem solving is the problem, one does not have a problem until one starts to experience and deal with a barrier in a situation one is curious about or has interest in. She viewed teaching of problem solving of problem solving in terms of three stage process:

  1. Preparation
  2. Collaboration
  3. Presentation

References

Chapman, ). (2004). Facilitating peer instructions in learning mathematics: Teachers’ practical knowledge. In M. J, Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 191-198.

Grouws, D.A., Good, T. A., Dougherty, B.J. (1990). Teacher conceptions about problem solcing and problem solving instruction. I G. Booker, P. Cobb, & T.N. Mendecuti (Eds.) Proceedings of the 14th PME International Conference, 1, 135-142.

Vygotsky vs Durkheim’s Theories of Knowledge

Emile Durkheim is a French sociologist and is considered a ‘founding father’ of sociology as a separate field of study. Lev Vygotsky is a Russian psychologist who is the founder of a major school of developmental psychology.

Two major points common to both theorists

1. Knowledge is not in the ‘mind’ or located in the material world but in the historical development of human societies; it is the outcome of men and women acting on the world.

2. The acquisition and transmission of knowledge is central to education and to the possibilities of human societies; it is because human beings have the capacity to respond to pedagogy that they are able to create societies (and knowledge).

The above means that their theories of knowledge were also their theories of society and social change.

Vygotsky

More commonalities between Vygotsky and Durkheim
  1. Both had social theories of knowledge that were closely related to their ideas of education.
  2. Both shared a fundamentally social-evolutionary approach to knowledge and human development.
  3. Both recognized that knowledge is differentiated and not a seamless web; that theoretical and everyday or context-independent and context-bound forms of knowledge have different structures and different purposes.
  4. Both saw formal education as the source of and condition for our capacity for generalization and our development of the higher forms of thought.
  5. Both recognized that the acquisition of context-independent or theoretical knowledge was the main, if not the only goal of schooling and formal education generally.
  6. Both recognized that human beings are fundamentally social in ways that no animals are, and both interpreted man’s social relations as fundamentally pedagogic.

Although both were creatures of Enlightenment and believed in human and social progress, Durkheim tended to look backwards for the sources of knowledge and social stability whereas Vygotsky looked forward to men and women’s potential for creating a socialist society.

Reference: Young, M. (2007). Durkheim and Vygotsky’s theories of knowledge and their implications for a critical education theory. Critical Studies in Education. Vol. 48, No.1, pp. 43-6.

 

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