This paper offers an explanation of how collaboration leads to abstract and flexible problem solving. We asked the individual and paired subjects to indicate 3/4 of 2/3 of the area of a square sheet of paper and found that (1) they primarily folded or partitioned the paper rather than algorithmically calculating the answer, (2) they strongly tendened to backtrack and confirm their proto-plans on externalized traces such as creases on the paper, and (3) only the paired subjects shifted to the mathematical strategy in their second trials. Based on these results, we propose that two factors, individuals' activeness in choosing and confirming the initial strategies and the frequent role exchange between task-doing and monitoring in collaborative situations, interact in collaboration to generate various solutions differing in the degree of abstraction, which are then reflected upon by the participants to lead them to abstraction.

Recently, the practice of active learning has spread, increasingly recognized as an essential component of academic studies. Classes incorporating small group discussion (SGD) are conducted at many universities. At present, assessments of the eŠectiveness of SGD have mostly involved evaluation by questionnaires conducted by teachers, by peer assessment, and by self-evaluation of students. However, qualitative data, such as open-ended descriptions by students, have not been widely evaluated. As a result, we have been unable to analyze the processes and methods involved in how students acquire knowledge in SGD. In recent years, due to advances in information and communication technology (ICT), text mining has enabled the analysis of qualitative data. We therefore investigated whether the introduction of a learning system comprising the jigsaw method and problem-based learning (PBL) would improve student attitudes toward learning; we did this by text mining analysis of the content of student reports. We found that by applying the jigsaw method before PBL, we were able to improve student attitudes toward learning and increase the depth of their understanding of the area of study as a result of working with others. The use of text mining to analyze qualitative data also allowed us to understand the processes and methods by which students acquired knowledge in SGD and also changes in students' understanding and performance based on improvements to the class. Thisˆnding suggests that the use of text mining to analyze qualitative data could enable teachers to evaluate the eŠectiveness of various methods employed to improve learning.

The Learning Sciences constitute a rapidly expanding discipline that focuses on the learning potential of humans. In this paper, I will discuss the particular learning mechanism involved in the concomitant advancement of domain knowledge and 21st century skills, as well as the Constructive Jigsaw Method of knowledge construction through collaboration-that is, collaborative problem solving. An especially important focus on knowledge construction separates routine experts from adaptive experts. While routine experts develop a core set of skills that they apply throughout their lives with increasing e‹ciency, adaptive experts are much more likely to change their core skills and continually expand the depth of their expertise. This restructuring of core ideas and skills may reduce their e‹ciency in the short run but make them more ‰exible in the long run. The Constructive Jigsaw Method employs a learning mechanism that encourages the development of adaptive experts. Under this method, studentsˆrst study a piece of material in an expert group. One member from each of several expert groups then joins a new study group, a jigsaw group. The members of this new group then combine what they have learned, creating new knowledge and a deeper understanding of the concept through collaboration, communication, and innovation.

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