A further study of productive failure in mathematical problem solving: unpacking the design components

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b) productive failure (PF), where they solved complex problems in small groups without any instructional facilitation up until a teacher-led consolidation, or (c) facilitated complex problem solving (FCPS), which was the same as the PF condition except that students received instructional facilitation throughout their lessons. Despite seemingly failing in their collective and individual problem-solving efforts, PF students significantly outperformed their counterparts in the other two conditions on both the well-structured and higher-order application problems on the post-test, and demonstrated greater representation flexibility in working with graphical representations. The differences between the FCPS and LP conditions did not reach significance. Findings and implications of productive failure for theory, design of learning, and future research are discussed.     

Dynamic optimal control model for profit maximization of software product under the influence of promotional effort

In this paper, a decision model is presented for the sales of software product to determine the profit and marketing policy under the influence of promotional efforts. The paper focuses on dependence of the optimal profit on the promotional efforts when there is diffusion effect of demand on the sales function. An elaborate optimization policy considering the dynamic nature of production cost function is proposed and numerical example is illustrated. The paper also studies the behavior of the future profit and its impact on profit maximization model by considering the constant price during the entire planning horizon. The experimental results greatly help us to identify the contributions of each selected parameter and its weight. Some conclusions, limitations of this study and future direction are also discussed.     

Micro productive failure and the acquisition of algebraic procedural knowledge

Instructional Science - Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and...     

The factor structure of the longeot test: A measure of logical thinking

Using a random sample of 389 grade 11 science students, the factor structure of the Longeot test (a measure of logical thinking) is investigated and some psychometric properties of the test items are determined. Varimax rotation on six principal component factors resulted in a simple structure. An attempt is made to interpret the obtained orthogonal factors. Implications of the findings on the “unity hypothesis” of the Piagetian construct of logical thinking and, consequently, on grade 11 science education are discussed.     

Is having more prerequisite knowledge better for learning from productive failure?

A critical assumption made in Kapur’s (Instr Sci 40:651–672, 2012) productive failure design is that students have the necessary prerequisite knowledge resources to generate and explore solutions to problems before learning the targeted concept. Through two quasi-experimental studies, we interrogated this assumption in the context of learning a multilevel biological concept of monohybrid inheritance. In the first study, students were either provided or not provided with prerequisite micro-level knowledge prior to the generation phase. Findings suggested that students do not necessarily have adequate prior knowledge resources, especially those at the micro-level, to generate representations and solution methods for a multilevel concept such as monohybrid inheritance. The second study examined how this prerequisite knowledge provision influenced how much students learned from the subsequent instruction. Although the prerequisite knowledge provision helped students generate and explore the biological phenomenon at the micro- and macro-levels, the provision seemingly did not confer further learning advantage to these students. Instead, they had learning gains similar to those without the provision, and further reported lower lesson engagement and greater mental effort during the subsequent instruction.     

Accessing the elite figured world of science

This review explores Jackson and Seiler’s “I am smart enough to study postsecondary science: A critical discourse analysis of latecomers’ identity construction in an online forum” by considering the analytic framework for figured worlds guiding this study. We consider the specific affordances of cultural production theory for examining how sociohistorical and cultural discourses of science as elite impact individuals at every level of education. We then extend this discussion by exploring how an informal learning space at a prestigious science museum was designed to explicitly tackle cultural discourses of science as elite that act as barriers to identification with science.