Resolución de problemas, Matemáticas y Computación

Profesor Emérito de la Universidad del Zulia. Adscrito al Programa de Promoción al Investigador (PPI)
Enl@ce: revista Venezolana de Información, Tecnología y Conocimiento, ISSN 1690-7515, null 2, Nº. 2, 2005, pags. 37-45
Source: OAI


The objective of the work of this paper is to make a reflection on the importance of problem solving in the process of teaching and learning science, particularly in the cases of mathematics and computer science. The work shows the form in which problems are solved from the method proposed by George Pólya are due to solve (1887-1985). From there, it were considered the experiences and results obtained in the Mathematical Olympic Games that are celebrated in Venezuela, doing an analogy of the resolution of problems in the world of the computation. Also, it analyzes the reaches of the different events that support the education of science, in special with mathematical Olympic competition and computer programming competition, and how they stimulate to prepare them for the resolution of problems. El objetivo del trabajo es presentar una reflexión sobre la importancia de la resolución de problemas en el proceso de enseñanza y aprendizaje de la ciencia, en particular en los casos de la matemática y la ciencia de la computación. El trabajo muestra la forma en que se deben resolver problemas a partir del método propuesto por George Pólya (1887-1985). A partir de allí, se consideraron las experiencias y resultados obtenidos en las Olimpiadas Matemáticas que se celebran en Venezuela, haciendo una analogía de la resolución de problemas en el mundo de la computación. Igualmente, se plantean los alcances de los diferentes eventos que apoyan la enseñanza de la ciencia, en especial con las olimpíadas matemática y los maratones de programación en computación, y cómo ellos incentivan y estimulan a preparase para la resolución de problemas.

127 Reads
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Our investigation focused on historical, pedagogical, and social-political aspects of Hungarian mathematical life. We did not attempt to survey Hungarian mathematical research of the present. Even so, our time proved too short for our ambitions. The important Hungarian mathematicians whom we missed are certainly more numerous than those we interviewed. We spoke in depth to a dozen people, and carried out formal interviews with eight: in Hungary, Belaszokefalvi-Nagy, Pal Erdos, Tibor Gallai (recently deceased), Istvan Vincze, and Lajos Posa; in the United States, Agnes Berger, John Horvath, and Peter Lax. (While we were in Budapest, two of the leading newspapers carried major articles honoring Szokefalvi - Nagy's 75th birthday.) We asked all our interviewees the question "What is so special about Hungarian mathematics? What made possible the production of so many famous mathematicians in such a small, poor country, in the period between the two Wars?" In our interviews, and also in our reading, we got two quite distinct kinds of answers. Type 1 was internal. It related to institutions and practices within the world of mathematics. The other kind, type 2, was external. It related to trends and conditions in Hungarian history and social life at large. Perhaps one contribution of this article is to point out the importance of both types of answer. One could conjecture that favorable conditions of both types---within mathematical life and within socio-politico-economic life at large--- are necessary to produce a brilliant result such as the Hungarian mathematics of the 1920s and 1930s. In the terminology used by Mihaly Csikszentmihalyi and Rick Robinson (5) in their study of creativity, perhaps conditions have to be right both in the "domain"---the area of creative work and in the "field"---the ambient culture.
    The Mathematical Intelligencer 05/1993; 15(2):13-26. DOI:10.1007/BF03024187 · 0.30 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A student is engaged in (non-routine) problem solving when there is no clear pathway to the solution. In contrast to routine problems, non-routine ones cannot be solved through the direct application of a standard procedure. Consider the following problem: In a quiz you get two points for each correct answer. If a question is not answered or the answer is wrong, one point is subtracted from your score. The quiz contains 10 questions. Tina received 8 points in total. How many questions did Tina answer correctly? The complexity of this problem lies neither in the size of the numbers nor in the execution of the appropriate calculations. What makes this problem perplexing for primary school students is that it requires keeping track of several interrelated values. Introducing such problems in primary school serves a two-fold role: firstly, to offer students opportunities to develop problem solving skills and reasoning, and secondly, to provide entry points to the development of algebraic thinking; therefore, we call these problems early algebra problems. In this thesis we investigated the ability of Dutch upper primary school students to solve early algebra problems and ways to support this ability. The results of the first study with 152 high achievers from grade 4 revealed that their performance in problem solving lagged behind their general mathematical performance and that they often lacked essential problem solving skills. To shed light on the students’ low performance we investigated the cognitive demand of the tasks in the mathematics textbook series for grade 4. This analysis showed that challenging non-routine tasks are rare and are mostly found outside the main book of the textbook series. Subsequently, we aimed to address the difficulties students encounter when solving non-routine problems by providing an environment for experiencing the interdependency of values. A dynamic interactive computer game called Hit the target was developed for this purpose. In this environment the students can observe how the score varies as they manipulate the values of the hits, the misses, or the game rule. After piloting the game with 24 high achievers from grade 4, we conducted a large-scale study with 785 students from grades 4, 5, and 6. The students of the experimental group were asked to solve a series of problems at home using an online version of the game. The analysis of the data for grade 6 showed that the intervention had a significant effect on students’ problem solving performance. Furthermore, although girls put more effort in the online activity than boys, their achievement gains were the same as for boys. A closer analysis of student activity in the online environment showed that they applied various strategies, ranging from trial-and-error to strategies implying exploring relations between variables. In conclusion, the interactive dynamic character of the computer environment and the variation in the series of problems had a significant role in supporting students’ reasoning when dealing with early algebra problems. The above-mentioned findings lead to suggestions for educational practice.


127 Reads
Available from