How Exploratory Problem Solving Versus Problem Posing Helps Learning From Instruction

• In Event: Discovery-Based STEM Learning 2.0: Are We There Yet?

Abstract

Objective
There is now a growing body of evidence that preparatory activities such as generating solutions to novel problems prior to instruction can help students learn better from the instruction (Authos, 2012a). Evidence comes not only from quasi-experimental studies conducted in the real ecologies of classrooms (e.g., Author, 2012a, 2013; Schwartz & Bransford, 1998; Schwartz & Martin, 2004), but also from controlled experimental studies (e.g., DeCaro & Rittle-Johnson, 2012; Author, 2014b; Loibl & Rummel, 2013, 2014; Authors, 2011; Schmidt & Bjork, 1992; Schwartz, Chase, Oppezzo, & Chin, 2011).

The preparatory activities in above studies present students with contexts where the problem is given. However, an equally, if not more, important mathematical skill is to generate problems in the first place (Jay & Perkins, 1997; Silver, 1994). The proposition being: students need to be provided opportunities for both problem-solving and problem-posing.

In two randomized-controlled studies, I compared the preparatory effects of problem-solving versus problem-posing on learning from subsequent instruction.

Methods
In Study 1, students engaged in either problem-solving (where they generated solutions to a novel problem; see Fig 3) or problem-posing (where they generated problems, and where possible, the associated solutions; see Fig. 4) prior to learning the math concept of Standard Deviation. Study 1 found that problem-posing prior to instruction resulted in significantly better transfer to novel problems than problem-solving, without any significant difference in procedural knowledge and conceptual understanding.

Study 2 was designed to further examine the trade-off between problem and solution generation on conceptual understanding and transfer. Students engaged in either problem-solving (as in Fig 3) or problem-posing (where they generated only problems without solutions; see Fig. 5) prior to learning the novel math concept.

Results
Findings showed that problem-solving prior to instruction resulted in better conceptual understanding than problem-posing without solutions. However, the transfer effect remained in favor of problem-posing, albeit weaker than in Study 1.

Significance
Taken together, Study 1 suggested a trade-off between the benefits of wider activation afforded by problem-posing and that of a more relevant activation afforded by problem-solving. Study 2 further demonstrated that absent the opportunity to generate solutions, conceptual understanding suffered, and that the wider activation afforded by problem generation was not sufficient to compensate for the relevant activation due to solution generation.

The transfer findings are intriguing. In both studies, the problem-posing afforded wider knowledge activation, even though not all relevant to the targeted concept. Furthermore, the number of problems generated was the most strongly correlated with transfer performance. Even though this correlation was relatively weaker in Study 2 (problem posing with only problem generation) than in Study 1 (problem posing with problem and solution generation), it was still stronger than the same for solution generation. These findings suggest that whereas solution generation and its attendant preparatory mechanisms play an important role for transfer (given the correlation between solution generation and transfer), problem generation, even if part of it is not directly relevant, plays a more critical role.

Author

• Manu Kapur, The Hong Kong Institute of Education