ARTÍCULOS

 

Construcción de un test de matemática para adolescentes y adultos

 

Construction of a mathematic test for adolescents and adults

 

 

Nuria Cortada de Kohan^*; Guillermo Macbeth^**

^* MA en Psicología. Profesora Honoraria de la Universidad de Buenos Aires (UBA). Miembro de la Comisión de Doctorado de la Facultad de Psicología y Psicopedagogía de la Universidad del Salvador (USAL). Asesora metodológica de la Universidad Argentina John F. Kennedy. E-Mail: ncortada@psi.uba.ar
^** Doctor en Psicología. Becario postdoctoral del Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).

 

 

---

RESUMEN

El propósito de este trabajo es presentar un test de matemática construido con una muestra de 564 sujetos, para evaluar los conocimientos matemáticos de jóvenes con estudios secundarios completos o que están cursando el primer año de carreras universitarias. La muestra tiene una edad promedio de 24 años (DE = 8.7 años) y está constituida por un 40% de varones y un 60% de mujeres. El instrumento consta de 50 ítem que evalúan cálculos aritméticos simples, cálculos con decimales, proporciones, regla de tres simple, algunos problemas algebraicos de pasaje de términos y algunos problemas de tipo geométrico. Todos los ítem son de opción múltiple con cuatro alternativas, de las cuales sólo una es la correcta. La media de los puntajes totales es 25.36 (DE = 8.06). Se realizó un análisis de ítem calculando el porcentaje de respuestas correctas para cada uno de ellos, se analizaron los errores y se calculó para cada ítem su correlación con el puntaje total. El resultado del alpha de Cronbach para la confiabilidad total es .936. Para obtener la validez de constructo del test se ha realizado un análisis factorial, en el que sobresale un factor muy claro que satura a una gran cantidad de ítem, en su mayoría de tipo cálculo aritmético, y otros tres factores cuya interpretación es más difícil, que saturan a los ítem en forma mínima. El test mide fundamentalmente, cálculo aritmético, pero un análisis detenido indica que los ítem implican otros procesos inferenciales.

Palabras clave: Matemática - Procesos inferenciales - Análisis de ítem - Confiabilidad.

---

ABSTRACT

There are three different stages that generally take place while learning mathematics: the first concrete stage is when children learn to add, usually incorporating fingers as the most common object of support; a second pictorial stage or of icons, in which children assimilate a pictorial representation of the concrete object and, finally, an abstract or symbolic stage, in which children handle symbols that represent mathematical quantities. The main goal of this paper is to discuss the construction of a mathematics test for university students administered to a sample of 564 participants. The aim of this study is to evaluate achievements in mathematic abilities of young people that have finished high school and are ready to start university studies. The sample’s mean age was 24 years old with a standard deviation of 8.7 years and was 40% male and 60% female. The test has 50 items that measure simple algorithms for arithmetic problems: some items require the use of decimal numbers, some stress the use of proportions or percentages, and a few others are algebraic and geometric questions. All of the items are multiple choice tasks with four options and only one correct answer. There is no time limit to take the test, but its duration is usually not longer than one hour. The mean of the total scores is 25.36 with a standard deviation of 8.06. The exploratory item analysis shows the percentages of correct answers for each item, as well as the values of item-total correlations. Cronbach’s alpha reliability index is .936. To study the construct validity we factor analyzed the results and came up with one factor that saturates many items of arithmetic calculation type and three other factors which are not very significant. The test measures, fundamentally, arithmetic calculation, but a lengthy analysis indicates that the items imply other inferential processes. The application of this test indicates that it is very difficult to differentiate mathematical abilities from the aptitude to solve new problems, and that, we are actually evaluating an individual’s problem-solving abilities. Such an aptitude improves only with a mathematical instruction centered on the understanding processes, so that if the students are taught to understand the structure and the logic of mathematics, they will have more flexibility and will be more capable of remembering, adapting and organizing data. One of the difficulties observed in the test was that some participants thought that, when multiplying, the values always increase and, when dividing, they always diminish. That is the reason why they struggled so much with decimal exercises. The 50% of the examined participants had difficulties in solving problems with decimals, many had difficulties in finding percentage or interpreting a simple graph of columns. Currently, manual computers are used, but students have difficulties in the interpretation of its results, e.g. when it is presented in mathematical notation. It is very difficult, in this type of test, to differentiate mathematical abilities from mathematical knowledge because it is also important to consider a very strong inferential cognitive aspect.

Keywords: Mathematics - Inferential reasoning - Item analysis - Reliability.

---

 

 

Texto completo

 

Referencias bibliográficas

1 Ashlock, R.B. (1986). Error patterns in computation. Ohio: Charles E. Merrill.        [ Links ]

2 Bruner, J.S. (1963). Toward a theory of instruction. Cambridge, MA: Harvard University Press.        [ Links ]

3 Carroll, J.B. (1993). Human cognitive habilities. A survey of factor analytic studies. NY: Cambridge University Press.        [ Links ]

4 Cortada de Kohan, N. (1998). La Teoría de la Respuesta al Item y su aplicación al “Test Verbal Buenos Aires” [Item Response Theory and its application to the “Verbal Test Buenos Aires”]. Interdisciplinaria, 15 (1-2), 101-129.

5 Cortada de Kohan, N. (2004). BAIRES. Test de aptitud verbal “Buenos Aires”. Madrid: TEA.

6 Cox, L.S. (1975). Using research in teaching. Arithmetic Teacher, 22(2), 151-157.        [ Links ]

7 Crown, W.D. (1993). Assessment of Mathematics ability. En C.K. Reynolds & R. Kamthaus (Eds.), Handbook of psychological & educational assessment of children (pp. 504-523). NY: The Guilford Press.        [ Links ]

8 Horn, J.L. & Cattell, R.B. (1966). Refinement and test of the theory of fluid and crystallized intelligence. Journal of Educational Psychology, 57, 253-270.        [ Links ]

9 Jacobini, O.R. & Wodewotzki, M.L.L. (2006). Mathematical modelling: A path to political reflection in the mathematics class. Teaching Mathematics and its Applications, 25(1), 33-42.        [ Links ]

10 La Nación (2006, Enero, 25). En Astronomía ningún estudiante aprobó el ingreso. Sección Cultura. Extraído de la World Wide Web el 25 de enero de 2006: http://www.lanacion.com.ar/774977        [ Links ]

11 Snow, R.E. & Lohrman, D.F. (1993). Cognitive Psychology. New test design and new test theory. En N. Frederiksen, R.J. Mislevy & N. Bejar (Eds.), Test theory for a new generation of tests (pp. 1-18). Hillsdale, NJ: Lawrence Erlbaum & Associates.        [ Links ]

12 Wang, W.C., Cheng, Y.Y. & Wilson, M. (2005). Local item dependence for items across tests connected by common stimuli. Educational and Psychological Measurement, 65(1), 5-27.        [ Links ]

 

 

Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
Instituto de Investigaciones Psicológicas de la Universidad del Salvador (IIPUS). Marcelo T. de Alvear 1312 - (C1058AAV) Ciudad Autónoma de Buenos Aires - República Argentina.

Fecha de recepción: 6 de marzo de 2006
Fecha de aceptación: 18 de julio de 2006