Researched literature
Sorted alphabetically.
Each bibliographic element includes short in-text notation, full bibliographic description (following APA standard) and some notes.
This is legacy literature, from the Programming paradigms project.
TODO: Review all again.
(Donnarumma et al., 2016)
Donnarumma F, Maisto D, Pezzulo G, (2016). Problem Solving as Probabilistic Inference with Sub-goaling: Explaining Human Successes and Pitfalls in the Tower of Hanoi. PLOS Comput Biol 12(4): e1004864. doi:10.1371/journal.pcbi.1004864
The usual view of problem-solving as a separate "brain module" is discarded and instead problem-solving is viewed through probabilistic inference framework (planning-as-inference (PAI)).
They tested their model using Tower of Hanoi (TOH) task to study executive function and deficits in planning.
Their research focuses heavily on the concept of subgoals, which divide the task at hand into several parts, which (1) provide smaller and more manageable (sub)problems and (2) provide way-points / milestones in the probabilistic problem solving.
Studied: a probabilistic inference scheme enhanced with subgoals.
(Fenton and Melton, 1990)
Fenton N.E., Melton A. (1990). ‘Deriving Structurally Based Software Measures’, J System Software, 12, pp 177-187
Identification and definition of internal metrics of code / documents produced, in order to provide a common way to compare those.
Comparing low coupling, high cohesion, reuse in designs and code, and control structures and data-abstraction in code to provide desirable external attributes, like reliability and maintainability.
Relevance: This article provides a good evaluation on metrics used to compare programming paradigms.
(Fenton and Bieman, 2014)
Fenton N., Bieman J. (2014). Software Metrics: A Rigorous and Practical Approach, Third Edition. Chapman & Hall/CRC Innovations in Software Engineering and Software Development Series, CRC Press
(Not fully read - the book is too long. Read at opportunity.)
Reflecting the immense progress in the development and use of software metrics in the past decades, Software Metrics: A Rigorous and Practical Approach, Third Edition provides an up-to-date, accessible, and comprehensive introduction to software metrics. Like its popular predecessors, this third edition discusses important issues, explains essential concepts, and offers new approaches for tackling long-standing problems.
Relevance: This article provides a good evaluation on metrics used to compare programming paradigms.
Connections: Builds upon (Fenton, 1990).
(Harrison et al., 2012)
Harrison R., Samaraweera L. G., Dobie M. R., Lewis P. H. (2012). Comparing Programming Paradigms: an Evaluation of Functional and Object-Oriented Programs. Dept. of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK, April 24.
This is a sample test article.
Researchers compared programs written in Functional paradigm (language: SML) and Object-Oriented paradigm (language: C++) with various metrics in order to figure out the quality of each code. Programs were made for image analysis domain. Through the code quality they wish to determine the usefulness of product code. Many metrics were applied: (1) known errors, suggested modifications, time to fix the code and (2) internal attributes of the code, such as length, the number of functions called, the number of functions declared, etc. A lot of language-specific significant differences were found.
Language SML exhibited more (+60%) functions and (+300%) library-functions used (due to list processing functions) than C++, however it also exhibited more (+50%) code re-usability. No significant differences were found in the number of known errors, modification requests, fixing times, a subjective measure of complexity, and the total development time.
Relevance: This article provides a good evaluation on metrics used to compare programming paradigms.
Connections: Builds upon (Fenton, 1990).
(Kotovsky and Fallside, 1988)
Kotovsky K., Fallside D. (1988). Representation and Transfer in Problem Solving. Community college of Algeheny county, Behavioral Sciences Department. To appear in Klahr, D. & Kotovsky, K., Complex Information Processing: The Impact of Herbert A. Simon, Eribaum, Hillsdale, New Jersey, September 1988 (TODO: Check bibliography!)
Herbert A. Simon had made tremendous discoveries in field of problem solving. In this article, authors focus on his work on transfer in problem solving.
The main focus is on the Tower of Hanoi task and two new isomorphic tasks: (a) Monster Change Problem and (b) Monster Move Problem. All three tasks are fully isomorphic, and the only difference is in their real world interpretations - problem descriptions.
(1) The first conclusion of a study, in which subjects were asked to solve each problem, shows great differences in time used to solve each one. The time used increases greatly alongside the amount of representations the subject has to hold in the memory, which provide difficulty to identify possible moves. This holds until the subject is trained enough in this specific task to easily identify possible moves in each problem state.
(2) The second conclusion: The amount of transfer obtained was shown to be related to the degree of representational overlap that existed between a pair of problems. The more similar and/or more rehearsed the problems are, the more likely it is for transfer to occur between them.
Studied: Human problem solving with isomorphic tasks.
Relevance: This article provides a good insight on human problem solving and the importance of representation in knowledge transfer.
(Kotovsky and Simon, 1988)
Kotovsky K., Simon H. A. (1988). What Makes Some Problems Really Hard: Explorations in the Problem Space of Difficulty. Community College of Allegheny County, Behavioral Sciences Department, September 1988. (TODO: Check bibliography!)
Authors checked human problem-solving abilities on the Chinese Ring Puzzle, which proved to be of high degree of difficulty. Participants were unable to solve the task at hand and even after they were shown how to distinguish the possible set of moves (which is linear - ergo, the puzzle is simple) only half of them succeeded. The difficulty resides largely in the move operator: isomorphs with difficult-to-discover analog move operators are inordinately difficult, while those with moves that are discrete and easily defined are much easier. Subjects focus mainly on move identification to the point that they are unable to do the planning.
Even when presented with an isomorph (the Tower of Hanoi), subject transferred little to no knowledge between problems with moves of little similarity. The transfer results parallel the findings about problem difficulty: the determining factor is the nature of the move operator rather than the problem search space.
Studied: Human problem solving with isomorphic tasks.
Relevance: This article provides a good insight on human problem solving and the difficulty of move discovery.
Maybe useful
(Stein and Schwan, 2011)
Stein M. K., Schwan Smith M. (2011). Mathematical Tasks as a Framework for Reflection: From Research to Practice. Designing and Enacting Rich Instructional Experiences, Activities for Junior High School and Middle School Mathematics. (TODO: Check bibliography!)
This article talks about students' process of learning in QUASAR Project. 4 mathematical tasks were distinguished in terms of the underlying task-idea and level of their demands. Low-level-demand tasks contained the idea of basic memorization and procedures without connections - the student had to memorize result or the simple process to achieve the result. High-level-demand tasks required students to combine different mathematical perspectives of the same value and to understand their connections. Two teachers applied this test and their observations were logged.
Relevance: This article provides an overview of 4 mathematical tasks and the core ideas behind them. In addition it also provides a simple peak into students' learning of a problem-solving process.
(Marek and Truszczyński)
Marek V. W., Truszczyński M. Stable Models and an Alternative Logic Programming Paradigm. Part of the series Artificial Intelligence pp 375-398. Accessed: http://link.springer.com/chapter/10.1007/978-3-642-60085-2_17#page-1
This article talks about variation to standard logic paradigm, called the Stable logic programming (SLP). Here, the recursive processes have been limited and symbolic representations omitted in pursuit to better retain the true essence of logic paradigm SLD resolution.
(Pfenning)
Frank Pfenning F. Types in Logic Programming. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA. Accessed: https://www.cs.cmu.edu/~fp/papers/iclp90.pdf
This article talks about "types" in logic paradigms / programming languages. These types are mostly used for first-hand error checking.
(Schoenfeld, 1992).
Schoenfeld A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Handbook for Research on Mathematics, Teaching and Learning; New York, Macmillan.
Chapter in a book discusses problems in American school system about low mathenatic performance in students.
It provides a neat example how to approach basic equations in a simple way ->
(6.25 72) = ((5/8 10) 72) = (5/8 (10 72)) = (5/8 720) = (5 * 90) = 450