Information Processing Taxonomy (IPT): An Alternative Technique for Assessing Mathematical Problem-Solving

This paper describes the development of the Information Processing Taxonomy (IPT) Model which models children's thinking at different hierarchical levels. The main features of the Model consist of retrieving information from external memory and primary and secondary productions of Type A and B information. These features constitute the components of different levels of thinking which could be used to confirm and describe the children's cognitive processes. Examples are shown to illustrate how the Model could be used to construct test items at different levels on the basis of these features. The Guttman procedure was applied to test the consistency of the hierarchical nature of the Model. Results show that the items constructed using the Model were scalable.     

The effects of teacher discourse on students’ discourse,problem-solving and reasoning during cooperative learning

The study sought to determine if teachers who are taught specific communication skills designed to challenge students’ cognitive and metacognitive thinking during cooperative learning use more challenging and scaffolding behaviours to mediate students’ learning than teachers who implement cooperative learning or small-group work who have not been taught these skills. The study involved 51 teachers in three conditions (cooperative + communication conditions; cooperative condition, group-work condition) and two groups of students from each of the above teachers’ classes. The results show that the teachers in the cooperative + communication condition used significantly more challenging and scaffolding behaviours than teachers in the group-work condition but not more than the teachers in the cooperative condition. The study also showed that the children in the cooperative + communication condition provided significantly more elaborative and help-giving behaviours to group members than peers in the other two conditions and they obtained higher scores on the follow-up reasoning and problem-solving activities than their peers in the group-work condition.     

用于小学算术应用题自动解答系统的解题策略的分解和表示

解题策略能表明应用题中的数量关系,策略分解和表示是小学算术应用题自动解题系统中十分关键的一步。共提炼197条解题策略,将其分为三个层次,且提出策略生长图表明其层次关系,选择框架知识表示方法表示策略,以构建解题策略知识库,供自动解题程序调用。     

A framework to foster problem-solving in STEM and computing education

ABSTRACT

Background: Recent developments in STEM and computer science education put a strong emphasis on twenty-first-century skills, such as solving authentic problems. These skills typically transcend single disciplines. Thus, problem-solving must be seen as a multidisciplinary challenge, and the corresponding practices and processes need to be described using an integrated framework.

Purpose: We present a fine-grained, integrated, and interdisciplinary framework of problem-solving for education in STEM and computer science by cumulatively including ways of problem-solving from all of these domains. Thus, the framework serves as a tool box with a variety of options that are described by steps and processes for students to choose from. The framework can be used to develop competences in problem-solving.

Sources of evidence: The framework was developed on the basis of a literature review. We included all prominent ways of domain-specific problem-solving in STEM and computer science, consisting mainly of empirically orientated approaches, such as inquiry in science, and solely theory-orientated approaches, such as proofs in mathematics.

Main argument: Since there is an increasing demand for integrated STEM and computer science education when working on natural phenomena and authentic problems, a problem-solving framework exclusively covering the natural sciences or other single domains falls short.

Conclusions: Our framework can support both practice and research by providing a common background that relates the ways, steps, processes, and activities of problem-solving in the different domains to one single common reference. In doing so, it can support teachers in explaining the multiple ways in which science problems can be solved and in constructing problems that reflect these numerous ways. STEM and computer science educational research can use the framework to develop competences of problem-solving at a fine-grained level, to construct corresponding assessment tools, and to investigate under what conditions learning progressions can be achieved.     

It's Mathematical, After All—the Nature of Learning Computer Programming

It is argued that some mathematical skills may be directly linked to learning programming language constructs. It is also argued that problem-solving through programming demands solid foundation in algorithms, and thus should be taught as if it were a process of learning mathematics. An analysis is given showing how mathematical maturity may impact learning programming language constructs. Conclusions are made based on the analysis.     

Classroom discussion and individual problem-solving in the teaching of history: Do different instructional approaches affect interest in different ways?

In this study, 100 Italian eighth graders were divided into two groups to compare the effects of two instructional interventions – the first based on problem-solving through discussion, the second on individual problem-solving – on students' learning of two historical topics (World War I and the economic boom), interest and self-perception of competence in history. The intervention based on discussion produced greater situational interest and understanding of the historical inquiry. The topic of World War I turned out to be an effective source of situational interest. Structural equation models showed that situational interest elicited by the use of discussion and by World War I impacted both on students' individual interest and on self-perception of competence in history.     

小学数学解决问题方法多样化的策略分析

引导小学生独立解决数学问题是目前我国小学数学教学的目标,而数学因其本身的属性及特点,因此要求学生能够充分发挥逻辑思维能力去寻找更多的解题方法,这就对教师的教学提出了更高的要求。教师在教学过程中要不断创新教学模式,通过现代化教学理念来锻炼学生的自主学习能力,拓宽学生的思维路径,从而使其可以衍生出更加多样化的解题方法。     

Teacher learning on problem-solving teams

Problem-solving teams address student difficulties. Teams comprised of teachers, specialists, and administrators identify the student problem, develop individualized interventions, and assess student change. Teacher experiences of teams are understudied. In a prospective, mixed-method study conducted in the United States, 34 teachers were followed through the team process. Interview coding showed that 60% of teachers reported they gained new intervention skills. Yet, 40% of teachers reported no professional benefits. Logistic regression showed that differences in teacher learning were partially explained by teachers' negative or positive expectations at the outset of the team. The expectancy effects have implications for teacher professional development.     

Disciplinary Foundations for Solving Interdisciplinary Scientific Problems

Problem-solving has been one of the major strands in science education research. But much of the problem-solving research has been conducted on discipline-based contexts; little research has been done on how students, especially individuals, solve interdisciplinary problems. To understand how individuals reason about interdisciplinary problems, we conducted an interview study with 16 graduate students coming from a variety of disciplinary backgrounds. During the interviews, we asked participants to solve two interdisciplinary science problems on the topic of osmosis. We investigated participants’ problem reasoning processes and probed in their attitudes toward general interdisciplinary approach and specific interdisciplinary problems. Through a careful inductive content analysis of their responses, we studied how disciplinary, cognitive, and affective factors influenced their interdisciplinary problems-solving. We found that participants’ prior discipline-based science learning experiences had both positive and negative influences on their interdisciplinary problem-solving. These influences were embodied in their conceptualization of the interdisciplinary problems, the strategies they used to integrate different disciplinary knowledge, and the attitudes they had toward interdisciplinary approach in general and specific interdisciplinary problems. This study sheds light on interdisciplinary science education by revealing the complex relationship between disciplinary learning and interdisciplinary problem-solving.