Following our previous paper (Chem. Educator, 2004, 9, 398405), we analyze further the results of a national examination from the perspective of conceptual learning versus algorithmic problem solving. Detailed achieve...
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algorithmic problem solving is a way of approaching and solvingproblems by using the advances that have been made in the principles of correct-by-construction algorithm design. The approach has been taught at first-y...
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ISBN:
(纸本)9783030549961;9783030549978
algorithmic problem solving is a way of approaching and solvingproblems by using the advances that have been made in the principles of correct-by-construction algorithm design. The approach has been taught at first-year undergraduate level since September 2003 and, since then, a substantial amount of learning materials have been developed. However, the existing materials are distributed in a conventional and static way (e.g. as a textbook and as several documents in PDF format available online), not leveraging the capabilities provided by modern collaborative and open-source platforms. In this paper, we propose the creation of an online, open-source repository of interactive learning materials on algorithmic problem solving. We show how the existing framework Mathigon can be used to support such a repository. By being open and hosted on a platform such as GitHub, the repository enables collaboration and anyone can create and submit new material. Furthermore, by making the material interactive, we hope to encourage engagement with and a better understanding of the materials.
The effectiveness of viewing, representing, and manipulating data via binary values is illustrated in the domain of algorithmic problem solving. A variety of illuminating binary aspects, regarded as binary perspective...
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The effectiveness of viewing, representing, and manipulating data via binary values is illustrated in the domain of algorithmic problem solving. A variety of illuminating binary aspects, regarded as binary perspectives, are displayed through four lively algorithmic challenges, some of which are two-player games. The illustrations demonstrate the benefits of invoking binary representation of numbers, binary complement, bit-by-bit processing, parity considerations, and the reduction of an integer task into a 0/1 task. The solutions to the challenges are presented gradually, encapsulating general algorithmic considerations and problem-solving methods, including invariant properties, stepwise refinement, processing by atomic components, auxiliary coloring, backward reasoning, and inductive generalization. Each of the illustrations is tied to a variety of referenced algorithmic schemes and applications, which employ the aspects demonstrated in this article. The variety of binary aspects, algorithmic considerations, and problem-solving methods make these illustrations appealing teaching resources for computer science educators, in particular in the domain of algorithms.
,Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory com...
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,Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in the course of solving an algorithmicproblem and highlights three distinct, although interrelated, facets of abstraction: pattern recognition, black-boxing, and structure identification. A study that examined the influence of the POI approach on students' abstraction skills is described;students who learned according to the POI approach were compared with students who learned in a traditional manner with regard to analogical reasoning and problem decomposition and solution, as well as verbal expression. The three facets of abstraction were used to analyze students' abstraction skills and their competency in algorithmic problem solving.
The torch problem (also known as the bridge problem or the flashlight problem) is about getting a number of people across a bridge as quickly as possible under certain constraints. Although a very simply stated proble...
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The torch problem (also known as the bridge problem or the flashlight problem) is about getting a number of people across a bridge as quickly as possible under certain constraints. Although a very simply stated problem, the solution is surprisingly non-trivial. The case in which there are just four people and the capacity of the bridge is two is a well-known puzzle, widely publicised on the Internet. We consider the general problem where the number of people, their individual crossing times and the capacity of the bridge are all input parameters. We present two methods to determine the shortest total crossing time: the first expresses the problem as an integer-programming problem that can be solved by a standard linear-programming package, and the second expresses the problem as a shortest-path problem in an acyclic directed graph, i.e. as a dynamic-programming problem. The complexity of the linear-programming solution is difficult to predict;its main purpose is to act as an independent test of the correctness of the results returned by the second solution method. The dynamic-programming solution has best- and worst-case time complexity proportional to the square of the number of people. An empirical comparison of the efficiency of both methods is also presented. (C) 2015 Elsevier B.V. All rights reserved.
This project aims to develop a pen-based software tool that will assist in the process of doing mathematics by providing structured manipulation of handwritten mathematical expressions. The tool will be used to suppor...
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ISBN:
(纸本)9781424419692
This project aims to develop a pen-based software tool that will assist in the process of doing mathematics by providing structured manipulation of handwritten mathematical expressions. The tool will be used to support the teaching of the dynamics of problemsolving in a way that combines the advantages of the traditional blackboard style of teaching with the flexibility and accuracy of computer software. It will provide not only a simpler way to input mathematics - by allowing the recognition of handwritten mathematics but also enhance students' understanding of the calculational techniques and facilitate the process of doing mathematics - by providing structure editing. Some of the most important features of this tool are the accurate selection and copy of expressions, the automatic application of algebraic rules and the use of gestures to apply them, and also the combined writing of mathematics and text. These features will have a major impact on writing, doing, and presenting mathematics. This project includes the required technical developments and also the application and testing of the tool in concrete situations, namely in mathematics and computing science courses.
Informally, a first-past-the-post game is a (probabilistic) game where the winner is the person who predicts the event that occurs first among a set of events. Examples of first-past-the-post games include so-called b...
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Informally, a first-past-the-post game is a (probabilistic) game where the winner is the person who predicts the event that occurs first among a set of events. Examples of first-past-the-post games include so-called block and hidden patterns and the Penney-Ante game invented by Walter Penney. We formalise the abstract notion of a first-past-the-post game, and the process of extending a probability distribution on symbols of an alphabet to the plays of a game. We establish a number of properties of such games, for example, the property that an incomplete first-past-the-post game is also a first-past-the-post game. Penney-Ante games are multi-player games characterised by a collection of regular, prefix-free languages. Analysis of such games is facilitated by a collection of simultaneous (nonlinear) equations in languages. Essentially, the equations are due to Guibas and Odlyzko. However, they did not formulate them as equations in languages but as equations in generating functions detailing lengths of words. For such games, we show how to use the equations in languages to calculate the probability of winning and how to calculate the expected length of a game for a given outcome. We also exploit the properties of first-past-the-post games to show how to calculate the probability of winning in the course of a play of the game. In this way, we avoid the construction of a deterministic finite-state machine or the use of generating functions, the two methods traditionally used for the task. We observe that Aho and Corasick's generalisation of the Knuth-Morris-Pratt pattern-matching algorithm can be used to construct the deterministic finite-state machine that recognises the language underlying a Penney-Ante game. The two methods of calculating the probabilities and expected values, one based on the finite-state machine and the other based on the non-linear equations in languages, have been implemented and verified to yield the same results. (C) 2013 Elsevier B.V. All righ
solvingalgorithmicproblems and implementing them in code is a major theme in introductory computer science courses. problems related to string manipulation are common and of great importance in various domains. In t...
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ISBN:
(纸本)9781424462599
solvingalgorithmicproblems and implementing them in code is a major theme in introductory computer science courses. problems related to string manipulation are common and of great importance in various domains. In the context of computer science education, solvingalgorithmicproblems of this type may be very challenging for novices, even for the more competent students. Analysis of novice students' solutions to a specific class of problems dealing with string manipulation revealed that a widespread intuitive and non-linear approach was used to solve these problems, which led to cumbersome and erroneous solutions. On the other hand, a straightforward linear approach that leads to shorter and more elegant solutions is uncommon. Uncovering students' common and unsatisfactory approaches in problemsolving have significant implications on instruction.
This paper presents the organization of the Polish Olympiad in Informatics, together with tasks preparation process and evaluation. It is a result of over 14 years of experience in organization of programming contests...
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This paper presents the organization of the Polish Olympiad in Informatics, together with tasks preparation process and evaluation. It is a result of over 14 years of experience in organization of programming contests for high-school pupils. We believe, that although described procedures are rather widely know, their rigorous implementation is the key to organization of a successful programming contest.
Instructional design has a significant influence on the construction of knowledge, especially for novices. Specifically, the way the instruction of algorithmic problem solving is designed has a significant effect on t...
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ISBN:
(纸本)9783540699231
Instructional design has a significant influence on the construction of knowledge, especially for novices. Specifically, the way the instruction of algorithmic problem solving is designed has a significant effect on the development of the student's capabilities to analyze and solve problems. We present a pedagogical approach regarding teaching algorithmic problem solving, which is based on the assimilation of a new concept by demonstrating its different facets through a variety of relevant examples. The approach aims to support multi-facet problem comprehension, as well as to enhance the student's ability to utilize algorithmic ideas in different contexts. The approach was introduced to computer science teachers through a workshop activity aimed at discussing the topic of evaluating the complexity level of problems and their challenging characteristics. We think that an activity of this kind is beneficial for raising teachers' awareness of the way they select problems in order to develop students' problem-solving skills.
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