Browsing by Author "Orozco Hormaza, Mariela"

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    A mathematical model to describe the learning process to write Arabic numerals
    (2014-04) Quimbay Herrera, Carlos José; Hurtado, Rafael Germán; Orozco Hormaza, Mariela; Guerrero López, Diego Fernando
    We use results from cognitive psychology and statistical mechanics to describe the ordering process of children when learning to write numerical. Children of the same elementary school grade were asked to write in Arabic format dictated numerals in three sessions and the production of all children in each session was classified. The classification contains one class for the correct production and four classes for syntactic errors. Each class is characterized by the value of a quantity that is assumed to be discrete and valued from the order of appearance of syntactic errors in children's production. We call this quantity distance. The class containing the correct production has the minimum value for distance and the other classes have larger values. To model the system from a statistical mechanics perspective, we consider each class as a subsystem of a theoretical ensemble and define the spectrum of distance from three models, two of them with degenerate states and one using the quantum harmonic oscillator. We calculate the entropy and the temperature of the system and use them to describe the ordering process for children in the first three elementary school grades. We found that both temperature and entropy values reduce with time and that they can be used to describe the learning process of Arabic numerals.
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    Construcción de la operación multiplicativa y del sistema notacional en base 10: una relación posible: I y II etapa
    (Universidad del Valle, 2002-02) Orozco Hormaza, Mariela
    La investigación contempla dos etapas. En la primera etapa se adelanta un estudio descriptivo, con diseño cuasi-experimental y transversal, que indaga sobre la relación entre la construcción de la operación multiplicativa y la comprensión del sistema de notación en base diez; la presencia de diferencias en estilos cognitivos - independiente analítico y sensible (independiente)-holístico (Witkin, 1977; Riding, 1993)- y capacidad mental de los sujetos, en la construcción de la multiplicación y su interacción con la comprensión del sistema de notación. Para el estudio se seleccionan 123 niños y niñas - que asisten a los 7 primeros grados de educación básica primaria (18 por grado), en un colegio de Cali, Colombia - en función de: edad, correspondiente a cada grado; capacidad mental, superior o más baja que la preescrita por la teoría para la edad; y estilo cognitivo.
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    Diagnóstico de la comprensión de escolares en relación con el manejo y comprensión del sistema de notación en base diez
    (Universidad del Valle, 2001-08-08) Orozco Hormaza, Mariela
    Desde la puesta en marcha del Sistema Nacional de Evaluación (SABER) se han vuelto evidentes las dificultad de los alumnos para lograr una adecuada apropiación del conocimiento matemático en primaria. Estos resultados, compatibles con la Prueba Internacional de la lEA (TIMSS) y con otras pruebas a nivel local, llevan a suponer que las dificultades que presentan en la comprensión del número natural y su escritura y el manejo de los algoritmos de las operaciones básicas resulta más generalizado de que lo previsto. La lógica operatoria del sistema de notación en base diez (SNBD), fundamenta la escritura de los números naturales y por lo tanto, los algoritmos de las operaciones. Su carácter básico, permite suponer que muchos de los errores que los alumnos presentan al escribir numerales y en el manejo de los algoritmos se producen porque no la manejan.
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    Exponential distributions in the syntactic structure of written numerals: A linguistic model
    (2014-04) Hurtado, Rafael Germán; Quimbay Herrera, Carlos José; Santos, Alex; Orozco Hormaza, Mariela; Guerrero López, Diego Fernando; Otálora Sevilla, Yenny
    The linguistic structure of numbers supports the grammar that children have to learn to write Arabic numerals The main linguistic components for the base-10 number of primitive number concepts and sum and product relations. Any com numerical expression can be reduced to primitive concepts by applying in successive times both relations. The grammar contains the set of rules that children have to master to produce well-formed numerical expressions. These rules or procedures are the operations that the subject has to perform and their acquisition corresponds to a learning process. Children production when learning numerals contain both well-formed and ill-formed numerical expressions with syntactic structures coming from the sequence of rules that used to write each numeral We analyze the data from two experiments with children from 6 to 8 years old transcoding oral verbal numerals to the Arabic format under dictation. The first experiment makes measurements in short period of time between successive tests, one week, and the second uses periods of two months. The analysis relates to the syntactic structure of written Arabic numerals with the linguistic structure of the dictated number and measures of their frequency distributions in children's production. The results indicate that these distributions fit exponential functions and we calculate the scale parameter associated to temperature in the description of some economic and social systems. Temperature and Shannon's entropy decrease as children learn describing an ordering process. Finally we find that heterogeneous groups of children produce neat distributions with exponential behavior.
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    Interaction between lexical and syntactic structures in transcoding from verbal to Arabic numerals
    (2011) Guerrero López, Diego Fernando; Orozco Hormaza, Mariela; Hurtado, Rafael Germán
    We explore the relationship between the lexical structure and the syntactical structure of numerical expressions in number transcoding from the oral verbal format to the Arabic digital format. The experimental setup included asking six to eight-year old Spanish-speaking children attending elementary school to write in Arabic format a set of dictated numerals. The method of analysis includes the construction of a relational representation of children's production and the use of clustering techniques to identify patterns. The model relates to children and dictated numerals by children's accomplishment and general to subsidiary similitude relation between dictated numerals with patterns that show differentiated structures. We find that presence or absence of a verbal expression for the Hundred position digit in the dictated numeral marks one of the structures. The second structure comes from the role of two digit numbers (e.g. 20 or 34): homogeneous in the Decade position and heterogeneous in the Thousand position. We interpret the results as consistent with the semantic-lexical internal number representation model by R.J.D. Power and MF. Dal Martello, The dictation of Italian numerals, Language and Cognitive Processes, 5, 237-254; 1990
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    Orden y aprendizaje de los numerales Arábigos
    (2010-04) Hurtado, Rafael Germán; Quimbay Herrera, Carlos José; Orozco Hormaza, Mariela; Guerrero López, Diego Fernando; Santos, Alex
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    Prueba piloto a escala real para la evaluación del aprendizaje de la escritura de los numerales en comunidades escolares
    (2011-04) Otálora Sevilla, Yenny; Orozco Hormaza, Mariela; Hurtado, Rafael Germán; Quimbay Herrera, Carlos José; Gutiérrez, Rafael María
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    The role of verbal forms in number transcoding to Arabic numerals: children six to eight-years-old
    (2011-04) Hurtado, Rafael Germán; Orozco Hormaza, Mariela; Guerrero López, Diego Fernando
    We explore patterns of structure in children's production of written numerals in number transcoding. The model of analysis defines a relational representation of children's production and applies results from graph theory to find the dominant structures. This work focuses on the role of verbal expressions in the Hundred position of dictate numerals and on differentiated structures for verbal numerals that embed Decade (D) and Decade-Unit (DU) forms. We analyzed the data from Power and Dal Martello (1990) and data obtained from six to eight-years-old Spanish-speaking children attending elementary school and were asked to write down in Arabic format sets or dictated numerals. Results show the dominant role in four and five digit numbers of verbal expressions in the Hundred position of the dictated numeral, and evidence the existence of differences between processing D and DU forms. We compare our results with previous analyses for three and four digit numbers and present new data and digit numbers. Finally, we give new evidence on the acquisition order of transcoding rules.