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Systems thinking and abstract thinking are important skills for engineers in general and hardware and software engineers in particular. Systems thinking emphasises the interdependence of system components and their synergy. Abstract thinking permits one to focus on the significant details of the current perspective, while temporarily neglecting the less relevant details of the stage in question. So far, systems thinking and abstract thinking have each been characterised separately, but a possible relation between them has not yet been examined. The study described in the paper explored the interrelations between systems thinking and abstract thinking among high-school students executing their final project. In the study, which used quantitative and qualitative tools, participated 239 Israeli twelve graders majoring in electronics. The findings indicate a significant moderate positive correlation between systems thinking and abstract thinking. The systems thinker and the abstract thinker share common cognitive characteristics, but differ in features related to knowledge and background, and interpersonal skills. [ABSTRACT FROM AUTHOR]

This paper discusses the role of reduction in computer science and describes a study on undergraduate students' perception of the concept of reduction. Specifically, based on an analysis of students' answers to questions addressing different computer science topics, we present several findings regarding the ways in which undergraduate students conceive of and apply reduction. These findings can be interpreted within the framework of the tension that exists between the following two factors: The need to think in terms of high levels of abstraction, on one hand, and the fact that reduction introduces a new approach to be used in problem-solving situations, on the other. In addition the paper suggests several teaching applications. [ABSTRACT FROM AUTHOR]

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. “Reducing abstraction” is a theoretical framework that examines learners’ behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate concepts presented in a given problem; therefore, they unconsciously reduce the level of abstraction of the concepts involved to make these concepts mentally accessible. This framework has been used for explaining students’ conception in different areas of undergraduate mathematics and computer science. This article extends the applicability scope of this framework from undergraduate mathematics to school mathematics. We draw on recently published research articles and exemplify how students’ behavior can be described in terms of various interpretations of reducing abstraction level. [ABSTRACT FROM AUTHOR]

This article focuses on abstraction and ways in which students cope with abstraction. The article has two goals: first, it illustrates how the theme of reducing abstraction (Hazzan, 1999) is useful for analyzing students' thinking about abstract concepts in mathematics and in computer science; science; second, it demonstrates how theories based on mathematics education research can be applied to analyzing students' understanding of computer science concepts. The main section of the article analyzes the understanding of concepts from four fields - abstract algebra, computability, data structures and difffeerntial equations - through the lens of reducing abstraction. The analysis shows that a wide range of cognitive phenomena can be explained by one throetical framework. [ABSTRACT FROM AUTHOR]

Computational thinking is accepted today as a collection of cognitive and social skills required for functioning in the 21st century. The paper presents a conceptual view at computational thinking that encompass concepts, problem-solving skills, application skills, and social skills. To impart those perceptions and skills the paper proposes the Four Pedagogies for Developing Computational Thinking (4P4CT) framework, which relies on active learning, project-based learning, product-based learning, and context-based learning, and advocates implementing computational thinking across all the education system in all subject matters at all ages by all teachers. The framework is presented and its implementation in an academic course for preservice K-12 teachers, taught so far in 16 classes attended by 409 preservice K-12 teachers, is described in detail. To support the effective development of the expected competences among preservice teachers, two types of empirical qualitative evidence, related to student outcomes, are presented: (a) simulations of computational processes, and (b) reflections that indicate a change in preservice teachers' perceptions and the application of computational thinking in their future teaching work.Graphical abstract: Computational thinking is accepted today as a collection of cognitive and social skills required for functioning in the 21st century. The paper presents a conceptual view at computational thinking that encompass concepts, problem-solving skills, application skills, and social skills. To impart those perceptions and skills the paper proposes the Four Pedagogies for Developing Computational Thinking (4P4CT) framework, which relies on active learning, project-based learning, product-based learning, and context-based learning, and advocates implementing computational thinking across all the education system in all subject matters at all ages by all teachers. The framework is presented and its implementation in an academic course for preservice K-12 teachers, taught so far in 16 classes attended by 409 preservice K-12 teachers, is described in detail. To support the effective development of the expected competences among preservice teachers, two types of empirical qualitative evidence, related to student outcomes, are presented: (a) simulations of computational processes, and (b) reflections that indicate a change in preservice teachers' perceptions and the application of computational thinking in their future teaching work. [ABSTRACT FROM AUTHOR]

How do undergraduate students cope with abstract algebra concepts? How should we go about researching this question? Based on interviews with undergraduate students and on written questionnaires, a theoretical framework evolved which could coherently account for most of the data. According to this theoretical framework, students‘ responses can be interpreted as a result of reducing the level of abstraction. In this paper, the theme of reducing abstraction is examined, based on three interpretations for levels of abstraction discussed in mathematics education research literature. From these three perspectives on abstraction, ways in which students reduce abstraction level are analyzed and exemplified. [ABSTRACT FROM AUTHOR]

The article presents a paper from the Research Conference in Collegiate Mathematics Education (RCCME) held at Central Michigan University in September 1996. It attempted to define abstraction but it resulted to a dialogue which gathered different perspectives and written statements. Cited are the conversations of two mathematics instructors at a conference, Allie and Bert, discussing topics such as locating abstraction in mathematics, and relationships between the person and the object about which she or he thinks.