What is design-based research methodology?

Design-based research as described by Wang and Hannafin is “a systematic but flexible research methodology aiming at improving practice through iterative processes of analysis, design and revision in real-world settings”. In this approach, the refinement of practical products works hand-in hand with the refinement of theory.

My interest in this research methodology is its similarity with the Lesson Study process which although considered more as as model of professional development for teachers but is also a rich context for investigating learning objects, students learning and teacher learning.

Design research is conducted iteratively as a collaboration between researchers and practitioners in a real-world setting. Each iteration or cycle contributes to sharpening the aims and bringing the interventions closer to the desired design outcomes and research outputs. These outputs are of course the design principles and empirically underpinned innovative interventions.

Van den Akker emphasizes the following six features of design and development research:

  1. Interventionist: the research aims at designing an intervention in a real-world setting.
  2. Iterative: the research incorporates cycles of analysis, design and development, evaluation and revision.
  3. Involvement of practitioners: active participation of practitioners in the various stages and activities of the research.
  4. Process oriented: the focus is on understanding and improving interventions (a black box model of input – output measurement is avoided).
  5. Utility oriented: the merit of a design is measured, in part on its practicality for users in real contexts.
  6. Theory oriented: the design is (at least partly) based on a conceptual framework and upon theoretical propositions, whilst the systematic evaluation of consecutive prototypes of the intervention contributes to theory building (Van den Akker et al., 2006, p. 5).

Reference
Van den Akker, J., Gravemeijer, K., McKenney, S. and Nieveen, N. (Eds) (2006), Educational Design Research, Routledge, London.

Wang, F. and Hannafin, M. (2005), “Design-based research and technology-enhanced learning environments”, ETR&D, Vol. 53 No. 4, pp. 5-23.

You may want to read:

The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom

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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