Citation: Shirouzu, H., Miyake, N., & Masukawa, H. (2002). Cognitively active externalization for situated reflection. Cognitive Science, 26, 469-501. [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W48-45WGK5F-1&_user=4429&_coverDate=08%2F31%2F2002&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1715786909&_rerunOrigin=scholar.google&_acct=C000059602&_version=1&_urlVersion=0&_userid=4429&md5=554262656e79bb35e90db258f03252dc&searchtype=a]

Kim’s 2011 presentation

(Annotated by Kim, 2011)

What is learned and how?

Participants in this study were asked to find either:

• ⅔ of ¾ and then  ¾ of ⅔   OR
• ¾ of ⅔ and then ⅔ of ¾

The study was conducted in solos and pairs of college students.  An depth exploration of the many ways of representations was conducted, in particular, how pairs and solos solved this fractional problem using a 15 cm by 15 cm piece of origami paper in which they shaded the corresponding area as their final solution.

The authors looked at how participants actively used external strategies (non-procedural, which they defined as non-mathematical) to find solutions and how these strategies produced a proto-plan that was resilient to mathematical (procedural - algorithmic) strategies in their second trial.  Additionally, these external strategies left physical traces (written notations and folding) which allowed the researchers to follow and identify problem-solving schemata.

The researchers found that reflecting on strategies occurred primarily in collaboration (in pairs) which means that participants were able to generalize and abstract their strategies when they vocalized their steps.  Whereas in the solo condition, individual subjects did not look objectively at their results from their first trials and only followed their traces reproducing their proto-plan strategies.

What is distributed?

In the solo condition, for most cases (37 out of 40) the problem solving steps of 2/3 of 3/4 and 3/4 of 2/3 were distributed through the steps of folding paper and shading areas, indicating external strategies - a non-mathematical procedure. In less cases (3 out of 40), the problems were solved using internal strategies - the mathematical procedure of multiplying two fractions and then shading the corresponding area.

The external strategies left traces which indicated the different pathways in which the problem-solving was distributed.

In the pair condition, the roles of problem solving were distributed between the task-doer and the monitor.  As a result of collaboration, the pairs were more reflective and thus shifted in strategies significantly more (p < 0.01) than participants in the solo condition.

How are the distributions mediated?

For both the solo and pair condition, the distributions were mediated over tools – origami, acrylic board, and cardboard.

In the pair condition the distributions were also mediated through talk.

Other important points?

This was a mixed-methods study which analyzed quantitative and qualitative data.  The methodological strategies were laboriously described and well documented - there was a total of two independent studies with four analytical levels.  The studies were controlled for gender, culture, and content knowledge.  The researchers transcribed video for both dialogue and gestures to show indication of thinking.  They also analyzed external traces of folding and shading to determine how thinking was ordered.