Abstraction and Common Classroom Activities

In popularizing computational thinking, Wing notes that ‘abstraction is described as underlying computational thinking and computational thinking is described as fundamental to computing.’ Emerging curricular now require educators to incorporate computational thinking and abstraction into their teaching. Many refer to Piaget’s work as evidence of an age-related ceiling preventing younger pupils from being able to abstract. However, more recent evidence suggests that pupils use elements of abstraction in their general process of learning, and that the skill of abstraction can be explicitly taught. We draw on personal classroom experience to illustrate the points made in the literature. Common classroom activities such as using labelled diagrams, concept maps and storyboards are aligned to features of abstraction. We argue that abstraction can and should be taught to young pupils

Automation and schema acquisition in learning elementary computer programming: Implications for the design of practice

Two complementary processes may be distinguished in learning a complex cognitive skill such as computer programming. First, automation offers task-specific procedures that may directly control programming behavior, second, schema acquisition offers cognitive structures that provide analogies in new problem situations. The goal of this paper is to explore what the nature of these processes can teach us for a more effective design of practice. The authors argue that conventional training strategies in elementary programming provide little guidance to the learner and offer little opportunities for mindful abstraction, which results in suboptimal automation and schema acquisition. Practice is considered to be most beneficial to learning outcomes and transfer under strict conditions, in particular, a heavy emphasis on the use of worked examples during practice and the assignment of programming tasks that demand mindful abstraction from these examples

The abstraction transition taxonomy: developing desired learning outcomes through the lens of situated cognition

We report on a post-hoc analysis of introductory programming lecture materials. The purpose of this analysis is to identify what knowledge and skills we are asking students to acquire, as situated in the activity, tools, and culture of what programmers do and how they think. The specific materials analyzed are the 133 Peer Instruction questions used in lecture to support cognitive apprenticeship -- honoring the situated nature of knowledge. We propose an Abstraction Transition Taxonomy for classifying the kinds of knowing and practices we engage students in as we seek to apprentice them into the programming world. We find students are asked to answer questions expressed using three levels of abstraction: English, CS Speak, and Code. Moreover, many questions involve asking students to transition between levels of abstraction within the context of a computational problem. Finally, by applying our taxonomy in classifying a range of introductory programming exams, we find that summative assessments (including our own) tend to emphasize a small range of the skills fostered in students during the formative/apprenticeship phase

Value’s of Mathematics Education and Citizenship Education

Currently, the Indonesian plane of life is miserable, inparticular on behavior. It is shown by the mushrooming acts of corruption, bribery, anarchy, public deceiving, traffic incompliance, etc. This mean any problem in nation character. The nation character building is the duty of citizenship education. The mission of citizenship education in Indonesian is develop or build the nation character as the instructional effects and nurturant effects. Whereas, another courses include mathematics course have to develop the nation characters through the nurturent effect of the instructional. This paper discussed about the relationship between values of mathematics education and characters contained in Citizenship Education. Key word: value, character, mathematics, citizenshi

The mathematical components of engineering expertise: the relationship between doing and understanding mathematics

this paper are extracts from our interviews with engineers.) Where, then, is the complex mathematics that certainly exists in modern engineering? Throughout all aspects of engineering design, computer software has an overwhelming presence. Also, in the particular firm that we visited, there a small number of analytical specialists (a few per cent of the professional engineers employed) who act as consultants for the mathematical/analytical problems which the general design engineers cannot readily solve. (In general in structural engineering, such specialist work is often carried out by external consultants, eg. academic researchers

Teaching programming with computational and informational thinking

Computers are the dominant technology of the early 21st century: pretty well all aspects of economic, social and personal life are now unthinkable without them. In turn, computer hardware is controlled by software, that is, codes written in programming languages. Programming, the construction of software, is thus a fundamental activity, in which millions of people are engaged worldwide, and the teaching of programming is long established in international secondary and higher education. Yet, going on 70 years after the first computers were built, there is no well-established pedagogy for teaching programming. There has certainly been no shortage of approaches. However, these have often been driven by fashion, an enthusiastic amateurism or a wish to follow best industrial practice, which, while appropriate for mature professionals, is poorly suited to novice programmers. Much of the difficulty lies in the very close relationship between problem solving and programming. Once a problem is well characterised it is relatively straightforward to realise a solution in software. However, teaching problem solving is, if anything, less well understood than teaching programming. Problem solving seems to be a creative, holistic, dialectical, multi-dimensional, iterative process. While there are well established techniques for analysing problems, arbitrary problems cannot be solved by rote, by mechanically applying techniques in some prescribed linear order. Furthermore, historically, approaches to teaching programming have failed to account for this complexity in problem solving, focusing strongly on programming itself and, if at all, only partially and superficially exploring problem solving. Recently, an integrated approach to problem solving and programming called Computational Thinking (CT) (Wing, 2006) has gained considerable currency. CT has the enormous advantage over prior approaches of strongly emphasising problem solving and of making explicit core techniques. Nonetheless, there is still a tendency to view CT as prescriptive rather than creative, engendering scholastic arguments about the nature and status of CT techniques. Programming at heart is concerned with processing information but many accounts of CT emphasise processing over information rather than seeing then as intimately related. In this paper, while acknowledging and building on the strengths of CT, I argue that understanding the form and structure of information should be primary in any pedagogy of programming

Junior High School Students’ Abstraction In Learning Geometry

Abstraction is a fundamental process in learning mathematics. Although it is a fundamental process but it is still an unfamiliar issue in mathematics education. On the other side, geometry, one of the fields in mathematics, consists of abstracts ideas having big portion in Junior High School. It is known that in this stage most students’ still thinks in concrete orientation. That is why it is necessary to know how the abstraction process in learning geometry. The aims of this research are capturing the students’ abstraction process during geometry instruction process and capturing students’ abstraction process during solving geometry problems. It is a qualitative research study. This research was conducted at Public Junior High School I Cimahi in RSBI classes, which subjects are students in grade VII. The data were collected by observation, test, and interview. Further the data were analyzed using analytical induction and constant comparative techniques. The results of this research are (1) the type of students’ abstraction process when learning geometry is a theoretical abstraction process and (2) the students’ abstraction process in solving geometry problems in that class is a type of abstraction, namely empirical abstraction process. However, the student’s abstraction has emphasis in terms of aspects of abstraction. The aspect of identifying objects’ characteristics through field experiences is more dominant than others. Key Words: Abstraction, Geometry, Empirical abstraction, Theoretical Abstraction