Papers by CARMEN CEREZO DÍAZ
International Electronic Journal of Mathematics Education
In this paper we first describe the process of building a questionnaire directed to globally asse... more In this paper we first describe the process of building a questionnaire directed to globally assess formal understanding of conditional probability and the psychological biases related to this concept. We then present results from applying the questionnaire to a sample of 414 students, after they had been taught the topic. Finally, we use Factor Analysis to show that formal knowledge of conditional probability in these students was unrelated to the different biases in conditional probability reasoning. These biases also appeared unrelated in our sample. We conclude with some recommendations about how to improve the teaching of conditional probability.
International Electronic Journal of Mathematics Education
The research question in this study was assessing possible relationships between formal knowledge... more The research question in this study was assessing possible relationships between formal knowledge of conditional probability as well as biases related to conditional probability reasoning: fallacy of the transposed conditional; fallacy of the time axis; base rate fallacy; synchronic and diachronic situations; conjunction fallacy; and confusing independence and mutually exclusiveness. Two samples of university students majoring in psychology and following the same introductory statistics course were given the CPR test before (n = 177) and after (n = 206) formal teaching of conditional probability. Results indicate a systematic improvement in formal understanding of conditional probability and in problem solving capacity but little change in those items related to psychological biases.
STATISTICS EDUCATION RESEARCH JOURNAL, 2009
The focus of this research is the concept of median, which has received scarce interest in previo... more The focus of this research is the concept of median, which has received scarce interest in previous research. We analyse the open responses given by 518 Mexican students from Educación Secundaria (Junior) and Bachillerato (Senior) Secondary Education to a problem involving the computation of median. Using some ideas from the onto-semiotic approach, we classify the responses, taking into account the central tendency measure used, and describe the students’ semiotic conflicts. We use the chi-square test to study possible dependence between responses and students’ group. We observe better results in computation in Educación Secundaria students but better competence to select the best representative value in Bachillerato students. First published November 2009 at Statistics Education Research Journal: Archives
Understanding independence and conditional probability is essential for a correct application of ... more Understanding independence and conditional probability is essential for a correct application of many probabilistic and statistical concepts and methods. Although an intuitive definition of these two concepts is possible, psychological research shows that its application in some specific circumstances becomes difficult and produces biases and wrong decisions. This paper describes some of these findings with the aim of warning teachers to take them into account when planning the teaching and assessment of this topic. We finally suggest some possible teaching devices that can help students to better understand these two concepts.
La utilidad del razonamiento probabilistico condicional en psicologia y educacion se deriva de su... more La utilidad del razonamiento probabilistico condicional en psicologia y educacion se deriva de su aplicacion al diagnostico, evaluacion, toma de decisiones e inferencia. En este trabajo describimos la validacion de un cuestionario destinado a evaluar este razonamiento. A partir de las respuestas de una muestra de 591 sujetos se analizan la consistencia interna y estructura factorial, que sugiere un constructo subyacente, interpretado como conocimiento formal sobre probabilidad condicional y no relacionado con los sesgos de razonamiento descritos en la literatura. La fiabilidad test- restest es estimada en una segunda muestra de 102 participantes. El analisis discriminante de puntuaciones en dos grupos de alumnos con y sin instruccion (n=298 y n=177) indica la validez de criterio del cuestionario Conditional probabilistic reasoning is useful in psychology and education due to its applications to diagnose, assessment, decision making and inference. We describe the validation of a ques...
Resumen En este trabajo analizamos la forma en que los estudiantes universitarios establecen las ... more Resumen En este trabajo analizamos la forma en que los estudiantes universitarios establecen las hipotesis el analisis de varianza. Para ello realizamos un analisis semiotico de las respuestas dadas por un grupo de 224 estudiantes de Psicologia de la Universidad de Huelva, Espana, en un problema abierto, usando como marco teorico el enfoque ontosemiotico de la cognicion matematica. Este analisis nos permite identificar los objetos y procesos matematicos utilizado s , y los conflictos semioticos relacionados con los objetos que intervienen en el planteamiento de las hipotesis estadisticas. Abstract In this paper we analyse how undergraduate students establish the hypotheses in analysis of variance. We carry out a semiotic analysis of the answers given by 224 psychology students at the University of Huelva, Spain to an open problem, using as theoretical framework the ontosemiotic approach to mathematical cognition. This analysis allows us to identify the mathematical objects and proc...
STATISTICS EDUCATION RESEARCH JOURNAL, 2016
In this paper we describe the development of a questionnaire designed to assess the probability c... more In this paper we describe the development of a questionnaire designed to assess the probability content knowledge of prospective primary school teachers. Three components of mathematical knowledge for teaching and three different meanings of probability (classical, frequentist and subjective) are considered. The questionnaire content is based on curricular guidelines and primary school textbooks in Spain. The items were selected and adapted, after expert judgment, from previous research. The responses of 157 prospective primary school teachers were used to analyze the psychometric properties of the questionnaire and to provide information about various aspects of participants’ probability content knowledge. First published November 2016 at Statistics Education Research Journal Archives
Revista Latinoamericana de Investigación en Matemática Educativa, 2018
El objetivo de esta investigación fue identificar el conocimiento del contenido: correlación y re... more El objetivo de esta investigación fue identificar el conocimiento del contenido: correlación y regresión (común, avanzado y especializado) en una muestra de 65 futuros profesores de Educación Secundaria Obligatoria y Bachillerato. Para ello se analizaron sus respuestas escritas en diferentes tareas relacionadas con un proyecto estadístico basado en datos de las Naciones Unidas. Los resultados indican buena estimación de la correlación e identificación de la función ajuste (conocimiento común), corrección en la ordenación de las variables explicativas según su poder predictivo y mayor dificultad para explicar la correlación por relaciones diferentes a la causalidad (conocimiento avanzado) y un análisis razonable de la idoneidad didáctica del proyecto (conocimiento especializado). Se informa también de algunos sesgos y del efecto de las variables de tarea sobre las respuestas.
Revista Diálogo Educacional, 2016
In this paper we present a study directed to assess the students’ difficulties in understanding e... more In this paper we present a study directed to assess the students’ difficulties in understanding elementary variance analysis. Responses from 224 undergraduate psychology students who had previously studied this topic to a questionnaire are analysed. Contents of the questionnaire include the selection of a variance analysis model, understanding of assumptions and the associated linear model in this procedure, the computations involved in variance analysis and the interpretation of results. While the understanding of computations, the selection of the model, and the understanding of the decomposition of the variance in the linear model were easy, the students had difficulties in understanding the assumptions of variance analysis and in interpreting the results in the problem context. These results provide information in an area where little prior research is available.
Revista Digital: Matemática, Educación e Internet, 2014
En este trabajo analizamos algunos de los sesgos frecuentes en la comprensión de la probabilidad ... more En este trabajo analizamos algunos de los sesgos frecuentes en la comprensión de la probabilidad condicional.También presentamos algunos resultados obtenidos en dos estudios de evaluación realizados con estudiantes dePsicología y futuros profesores de matemáticas en España. Finalizamos con algunas reflexiones sobre la enseñanzade la probabilidad.
Revemat: revista eletrônica de educação matemática, 2013
La finalidad del estudio es evaluar la competencia de futuros profesores españoles de Enseñanza S... more La finalidad del estudio es evaluar la competencia de futuros profesores españoles de Enseñanza Secundaria y Bachillerato para definir de forma adecuada la probabilidad simple y condicional. Las definiciones proporcionadas por una muestra de 196 futuros profesores se analizan, clasificándolas en función de su corrección y precisión. Se comparan los resultados en dos grupos de profesores, de acuerdo a su formación inicial y con los obtenidos en estudiantes de psicología. Palabra claves: Futuros profesores. Probabilidade simples e condicional, definição. Resumo A finalidade deste estudo é avaliar a competência de futuros professores espanhóis do ensino secundário e do bacharelato para definir, de forma adequada, a probabilidade simples e condicional. As definições obtidas em uma amostra de 196 professores são analisadas classificando-as em função da sua correção e precisão. Os resultados são comparados entre dois grupos de professores de acordo com a formação e também com dados obtidos com estudantes de psicologia.
Bolema: Boletim de Educação Matemática, 2013
Las tablas de contingencia son un recurso frecuente para presentar información estadística en pre... more Las tablas de contingencia son un recurso frecuente para presentar información estadística en prensa e Internet, así como en documentos técnicos usados en el trabajo profesional, aunque la enseñanza actual no presta mucha importancia a este tema, suponiendo que su interpretación es sencilla. En este trabajo analizamos la percepción de la asociación y estimación de su intensidad en tablas de contingencia en una muestra de 414 estudiantes de psicología de tres universidades españolas. Se observan respuesta similares en las tres universidades, alta consistencia entre percepción subjetiva de la asociación y precisión de la estimación y mejores resultados que los obtenidos en un estudio previo de Estepa (1994) con estudiantes de Bachillerato. Sin embargo, las estrategias al realizar el juicio de asociación son mayoritariamente incorrectas y sólo influyen en la precisión del juicio en el caso de independencia en los datos. Estos problemas podrían presentarse en otros estudiantes, por lo q...
Studies in Computational Intelligence, 2008
In this research implicative analysis served to study some previous hypotheses about the interrel... more In this research implicative analysis served to study some previous hypotheses about the interrelationships in students' understanding of different concepts and procedures after 12 hours of teaching elementary Bayesian inference. A questionnaire made up of 20 multiple choice items was used to assess learning of 78 psychology students. Results suggest four groups of interrelated concepts: conditional probability, logic of statistical inference, probability models and random variables.
Bolema: Boletim de Educação Matemática, 2012
En este trabajo presentamos un estudio dirigido a evaluar los sesgos presentes en el razonamiento... more En este trabajo presentamos un estudio dirigido a evaluar los sesgos presentes en el razonamiento probabilístico condicional en futuros profesores de educación secundaria y bachillerato. Se analizan las respuestas a 7 ítems tomados del cuestionario RPC (razonamiento sobre probabilidad condicional) de 196 alumnos de matemáticas de último curso y alumnos del Máster de Secundaria en España, encontrando una alta incidencia en ambos grupos de la falacia del eje temporal, la condicional transpuesta, confusión entre probabilidad condicional y conjunta, falacia de las tasas base y concepciones incorrectas sobre la independencia. Se concluye la necesidad de una mejor formación de los futuros profesores, que evite que estos sesgos puedan transmitirse a sus estudiantes.
In this paper, we present results from a study aimed to assess potential relationships between bi... more In this paper, we present results from a study aimed to assess potential relationships between biases in conditional probability reasoning (fallacy of the transposed conditional, fallacy of the time axis, conjunction fallacy, base rate fallacy and confusing independence and mutually exclusiveness) and formal knowledge of the concepts. Factor analysis of the responses by 414 psychology students to a questionnaire suggest that the psychological biases investigated are unrelated to conditional probability problem solving performance in these students. Comparison of responses of two groups before and after instruction shows systematic improvement in problem solving capacity but little change in part of the items related to psychological biases.
This paper describes a study of the competence to carry out the Chi-squared test, which is freque... more This paper describes a study of the competence to carry out the Chi-squared test, which is frequently used in psychology and education, in a sample of psychology students after studying the subject. Using an open-ended problem that is solved with the help of an Excel program, we analyse the setting of hypotheses, identification of the statistics and p-value, decision taken and interpretation of results. Some implications for teaching are also included.
Proyecto académico sin fines de lucro, desarrollado bajo la iniciativa de acceso abierto conflict... more Proyecto académico sin fines de lucro, desarrollado bajo la iniciativa de acceso abierto conflictos semióticos de estudiantes mexicanos
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Papers by CARMEN CEREZO DÍAZ