浅谈小学数学课堂教学中问题意识的培养

数学既是小学阶段就开始接触的学科,也是对小学生数学思维运用和解题能力要求较高的学科,没有问题可“问”的小学数学课堂无疑是枯燥和无趣的,难以真正实现对小学生思维能力的培养,因此,本文结合目前小学数学课堂出现的问题,探究怎样在小学数学教学中将学生问题意识培养起来。     

Fostering analogical transfer: The multiple components approach to algebra word problem solving in a chemistry context

Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated multiple components (symbolic equations, symbols, categorization, hint) in the source, or target, or both, to address the four analogical tasks. Different combinations of the components were tested in a series of four experiments. Symbolic equations (main component) fostered a mental construction of the problem in its solution mode. Categorization enabled an identification of the problem category. A hint in the target directed the learners to the source problem. The interaction between these components facilitated the mapping of the symbolic equations in the source onto the target, resulting in the superiority of the MC approach in fostering analogical transfer. Neither the main component alone nor the main component plus one sub-component was sufficient for analogical transfer. Hence for analogical transfer to occur, at least the main component (symbolic equations) and two sub-components (categorization and hint) are required. However, symbols may not have additional effects for transfer to occur.     

Epistemic profiles and self-regulated learning: Examining relations in the context of mathematics problem solving

Relations were examined between epistemic profiles, regulation of cognition, and mathematics problem solving. Two hundred sixty-eight students were sampled from undergraduate mathematics and statistics courses. Students completed inventories reflecting their epistemic profiles and learning strategies, and were profiled as rational, empirical, or both. Based on their profiles, 24 students participated in two problem-solving sessions. Episodes were coded for planning, monitoring, control, use of empirical and rational argumentation, and justification for solutions. For both self-reported metacognitive self-regulation and regulation of cognition during problem solving, students profiled as rational had the highest self-reported mean and actual frequency of regulation of cognition compared to students profiled as predominantly empirical. Moreover, students profiled as predominantly rational correctly solved more problems than the other two groups. Finally, students’ approaches to problem solving were consistent with their epistemic profiles. Relations are discussed in the context of various theoretical frameworks.     

Designing and implementing a case-based learning environment for enhancing ill-structured problem solving: classroom management problems for prospective teachers

This design-based research study is aimed at two goals: (1) developing a feasible case-based instructional model that could enhance college students’ ill-structured problem solving abilities, while (2) implementing the model to improve teacher education students’ real-world problem solving abilities to deal with dilemmas faced by practicing teachers in elementary classrooms. To achieve these goals, an online case-based learning environment for classroom management problem solving (CBL-CMPS) was developed based on Jonassen’s (in: Reigeluth (ed.) Instructional-Design Theories and Models: A New Paradigm of Instructional Theory, 1999) constructivist learning environment model and the general process of ill-structured problem solving (1997). Two successive studies, in which the effectiveness of the CBL-CMPS was tested while the CBL-CMPS was revised, showed that the individual components of the CBL-CMPS promoted ill-structured problem solving abilities respectively, and that the CBL-CMPS as a whole learning environment was effective to a degree for the transfer of learning in ill-structured problem solving. The potential, challenge, and implications of the CBL-CMPS are discussed.