Theme: Positive relationships and peer collaboration Component #259: Students work together in self-selected investigations and other aspects of learning to be with others Sociocultural approach in mathematics education is different from traditional approach in that it views mathematics teaching learning as social activities that require the formation of a classroom community of practice (Lave & Wenger, 1991). With the sociocultural approach, teacher is no longer an “unquestioned authority,” (Goos, 2004, p. 259) and students are expected to discuss and defend mathematical ideas and to respond thoughtfully to the mathematical arguments of their peers (communities of mathematical inquiry) (Goos, 2004). In her qualitative research study in Australia, Goos (2004) examined how community of practice could be formed in high school mathematics classrooms. In her observations, the participating teacher scaffolded students’ thinking by modeling and providing a structure for inquiry. As time passed by, students were able to engage in more independent mathematical discussions without much teacher support. Students were also willing to form informal groups to work on math problems together and to monitor their progress, seek feedback on ideas, and explain ideas to one another. Project-based learning is a specific example where we can find students working together in self-selected investigations and other aspects of learning to be with others. Features of projectbased learning include the following (Ayas & Zeniuk, 2001): 1) there is “sense of purpose” for short- and long-term goals; 2) there is “psychological safety” in the project environment; 3) there is a “learning infratrastructure;” 4) there are “communities of practice;” 4) there are “leaders that set the tone” for learning and modeling; and 5) there is “systemic and collective reflection.” Project-based learning allows students to move away from mere memorization and put more emphasis on deeper thinking through authentic problem solving (Meyer, Turner, & Spencer, 1997). It is also hypothesized that project-based learning helps students to develop self-directed learning skills and effective collaboration skills (Hmelo-Silver, 2004). There has been some research supporting that project-based learning helps students become self-directed learner. For instance, Evensen (2000) found that students who were involved in project-based learning eventually developed strategies for coping with challenges, reflected on their own learning strategies and information-seeking strategies. However, evidence that supports the hypothesis that project-based learning helps students become better collaborators are somewhat weak. Hmelo-Silver (2002) found that students do work together when put in groups, but not all groups were collaborating at the ideal level. In their meta-analysis, Doch, Segers, Van den Bossche, and Gijbels (2003) examined the effects of problem-based learning on students’ knowledge and skills. In their analysis of 43 empirical studies, they found that students in the problem-based learning condition were better in applying their knowledge (skills). However, they found negative effects of problem-based learning on the knowledge base of the students (compared to those in the conventional learning environment); there were 14 studies that yielded significantly negative effects and seven studies with significantly positive effects. Despite negative effects on students’ knowledge shown in this meta-analysis, it has also been found that peer support could also help students to delve deeper into scientific issues (Scardamalia & Bereiter, 1994) and provide more scientific justifications for their designs (Puntambekar, Nagel, Hübscher, Guzdial, & Kolodner, 1997). When students of varying levels get together to collaborate, less knowledgeable students bring up questions and ask for clarifications whereas more knowledgeable ones contribute to the discussion by providing clarifications and pointing to available resources (Puntambekar & Hübscher, 2005).

This process could eventually deepen students’ understanding about any given problem, however, it could be difficult to prove this with traditional assessments that we often use for preand posttests. References Ayas, K., & Zeniuk, N. (2001). Project-based learning: Building communities of reflective practitioners. Management Learning, 32(1), 61-76. Dochy, F., Segers, M., Van den Bossche, P., & Gijbels, D. (2003). Effects of problem-based learning: A meta-analysis. Learning and Instruction, 13(5), 533-568. Evensen, D. (2000). Observing self-directed learners in a problem-based learning context: Two case studies. In Evensen, D., and Hmelo, C. E. (eds.), Problem-Based Learning: A Research Perspective on Learning Interactions, Erlbaum, Mahwah, NJ, pp. 263–298. Hmelo-Silver, C. E. (2002). Collaborative ways of knowing: Issues in facilitation. In Stahl, G.(ed.), Proceedings of CSCL 2002, Erlbaum, Hillsdale, NJ, pp. 199–208. Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266. Meyer, D. K., Turner, J. C., & Spencer, C. A. (1997). Challenge in a mathematics classroom: Students' motivation and strategies in project-based learning. The Elementary School Journal, 501-521. Puntambekar, S., Nagel, K., Hübscher, R., Guzdial, M., & Kolodner, J. L.(1997). Intragroup and intergroup: An exploration of learning with complementary. collaboration tools. In R. Hall, N. Miyake, & N. Enyedy (Eds.), Proceedings of the 2nd International Conference on Computer Support for Collaborative Learning (pp. 207– 215). Mahwah: NJ: Lawrence Erlbaum Associates, Inc. Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge building communities. The Journal of the Learning Sciences, 3, 265–283.

Good Literature Review (Adequate Research) Number of sources q ≤2

3 Different types of sources (i.e. journal, publication, peer-reviewed)

q ≤2

3 Word Count

q ≤ 499 words

500+ words

Adequate level of evidence indicating effectiveness of component (Relevancy) Feasibility of Implementation q No evidence

q Minimal evidence

Strong evidence

q Overwhelming evidence

Applied to a Variety of Subject Areas q No specific subject areas q No evidence

q 1 subject area

q 2 subject areas

3+ subject areas

Increases student achievement q Minimal evidence Moderate q Strong evidence

q Overwhelming evidence

Helps teacher to understand students’ needs q No evidence

Minimal evidence

q Strong evidence

q Overwhelming evidence