Tag: knowledge

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.

 

What is mathematical knowledge for teaching?

It was Shulman in 1986 who first thought and recognized that the nature of knowledge for teaching a subject matter is different from knowledge of the subject matter itself (content knowledge or CK) and from general knowledge of pedagogy. He introduced the phrase pedagogical content knowledge (PCK) to describe the blending of content and pedagogy. He describes PCK as follows:

Within the category of pedagogical content knowledge, I include, for the most regularly taught topics in one subject area, the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations – in a word, the ways of representing and formulating the subject that makes it comprehensible to others. (1986, p.9)

Shulman’s description of knowledge needed by a teacher have been developed further. In mathematics, Ball and Bass (2003) introduced the notion of mathematical knowledge for teaching (MKT) which is similar to PCK and they include the idea of ‘unpacking’. Ball and Bass argued that in advance mathematical work, knowledge is ‘compressed’ and that the teachers work is to ‘decompress’ or ‘unpack’ this knowledge for their students.

Bernardz and Proulx (2009) also characterized mathematics for teaching knowledge as  knowledge-in-action or knowing-to-act (as opposed to factual knowledge) and that it is situated  since it develops in a specific context linked to a practice in mathematics teaching and is not independent of students’ learning, of the classroom, etc. They describe the work of a teachers as:

The teacher must constantly reflect on possibilities, offer and invent new avenues and representations in reaction to students’ action, think of additional explanations to clarify or re situate the tasks offered, choose to emphasize some aspects and not others, know that this or that explanation or representation is related to what the student offered as a solution and may eventually benefit this students’s understanding, etc.

Here’s a picture that will illustrate this: (I’m still looking for the powerpoint in slideshare where I got this picture)

Reference

Knowing and Using Mathematics in Teaching: Conceptual and Epistemological ClarificationsAuthor(s): Nadine Bednarz and Jérôme ProulxReviewed work(s):Source: For the Learning of Mathematics, Vol. 29, No. 3.

 

 

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