A study in higher education calculus and students' learning styles

This research is devoted to focussing on the influence of different learning style on the performance of undergraduate students in various parts of calculus. In carrying out the study, calculus materials were classified into four main categories (Z4,Z5,Z6,Cals) and, for the Iranian students, the results of their mathematical performance in the university entrance examination is labelled (En) to identify their grounding in high school mathematics at the beginning of the calculus course in higher education. Also, in the present study, students' performance (weakness) in the manipulation of mathematical notation and logical discussion is called (Z1) category and (Cal) indicates students' total achievement in calculus examination which is, in fact, the students' performance on the combination of the categories (Z4,Z5,Z6). These calculus categories are described in Chapter 5. However in short term, multi-conceptual and procedural tasks are classified as (Z4). The (Z5) category is defined as the translation processes between mathematical abstraction (analytic/symbolic) and (pictorial/visual) forms of calculus materials. Moreover, multi-skilled, transferable and procedural skills are labelled as (Z6) category. It should be noted that these categories are interrelated in a scheme to exhibit activities in calculus. 572 students participated in the experimental part of this study and were selected from two Iranian universities (Sabzvar University and Mashhad University) and Glasgow University in Scotland, U.K. During the period of the study, the samples of students were subjected to some psychological tests in order to assign their Field-dependent/Field-independent and Convergent/Divergent learning styles. It was found throughout the study that the most effective combination of learning styles which emerged from the interacting picture of all the psychological factors used in the research, were field-independent/convergent (F1+Con) in Iran, and field-independent/divergent (FI+Div) in Scotland in performing on the calculus. On the other hand, the combination of field-dependent and convergent styles (FD+Con) could lessen achievement in calculus by mathematics/physics students, and field-dependent and divergent styles (FD+Div) would lessen attainment in calculus by engineering students. In addition, when the mean scores in calculus categories were calculated for various groups of students with different learning styles, the convergent thinkers (Con) were found to be best in (Z6), while divergent thinkers (Div) exhibited higher performance in (Z5). These findings demonstrate that the Con/Div way of thinking is the most effective in influencing performance in different areas of calculus, the FI/FD factor takes the second position. All these findings have been combined to form a model which emerges at the end of this thesis. Moreover, in Chapters 3 and 4, a comparison is made between calculus in secondary (high school) and higher education in Iran and Scotland, focussing on content, teaching order, learning objectives and teaching methods

Análisis de desafíos y desempeños de los estudiantes para resolver problemas integrales

Integral is the base of pure and applied mathematics for all students of science, especially engineering, which some of their lessons are dependent to it directly or indirectly. In fact, Integral is an indisputable concept for solve practical and executive problems of students, so it is important to pay attention to it. On the other hand, experiences of teaching Integral have indicated that most students have weakness in solve Integral problems. Through case study, an exam has been conducted in the form of six problems on six good experienced students in order to study the students' behaviors in coping with the integral problems and also to reach a proposed method for teaching the integral concept, in which each question has in turn two parts. The analysis of their responses and discussion with them have led some light on more details about the integral, how to teach it and also the problems as a result of the teaching method and the problems to which they would encounter, so that by their citation, an appropriate teaching method could be presented in order to maximally conceptualize the integral in students. On the other hand, these studies reveal that in order to solve the integral-related problems, most students first refer to the initial function approach and try to solve the problem by the direct method rather than spending their time learning conceptually and meaningfully. But those students who have used Riemann concept and infinite collection in solve Integral problems were successful in compare to others.Integral es la base de las matemáticas puras y aplicadas para todos los estudiantes de ciencias, especialmente de ingeniería, de las cuales algunas de sus lecciones dependen directa o indirectamente. De hecho, Integral es un concepto indiscutible para resolver problemas prácticos y ejecutivos de los estudiantes, por lo que es importante prestarle atención. Por otro lado, las experiencias de enseñanza de Integral han indicado que la mayoría de los estudiantes tienen debilidad para resolver problemas de Integral. A través del estudio de caso, se realizó un examen en forma de seis problemas en seis estudiantes con buena experiencia para estudiar las conductas de los estudiantes para enfrentar los problemas integrales y también para alcanzar un método propuesto para enseñar el concepto integral, en el que cada uno La pregunta tiene a su vez dos partes. El análisis de sus respuestas y la discusión con ellos han dado luz sobre más detalles sobre la integral, cómo enseñarla y también sobre los problemas como resultado del método de enseñanza y los problemas con los que se encontrarían, por lo que, según su cita, Se podría presentar un método de enseñanza apropiado para conceptualizar al máximo la integral en los estudiantes. Por otro lado, estos estudios revelan que para resolver los problemas relacionados con la integralidad, la mayoría de los estudiantes primero se refieren al enfoque de la función inicial y tratan de resolver el problema por el método directo, en lugar de pasar el tiempo aprendiendo de manera conceptual y significativa. Pero aquellos estudiantes que han utilizado el concepto de Riemann y la colección infinita para resolver problemas integrales tuvieron éxito en comparación con otros

A study on the relationship between students’ cognitive style and Mathematical word and procedural problem solving while controlling for students’ intelligent quotient and math anxiety

The main purpose of the study is to investigate whether field dependency could predict students‟ mathematical problem solving in word and procedural mathematical problems and to explore whether this association remains significant when students‟ Mathematics anxiety and intelligent quotient (IQ) is controlled. So, we used data of 100 samples of guidance school girls and inferential statistical analysis (ANOVA and ANCOVA) for investigating the hypothesis of the study. Obtained results indicated that there were significant differences in students‟ mathematical performance in word and procedural problems by the groups of field dependency. Moreover, this difference is still significant when IQ and Mathematics anxiety as covariate variables were considered. However, the amount of omega square for ANCOVA analysis decreased when covariate variables inserted to the model. Findings of this study are suitable for researchers in field of psychology of learning Mathematics and who interested in how cognitive style affect students‟ performance in particular Mathematics.El principal objetivo de este estudio es investigar si la dependencia en el área puede predecir la forma en que los estudiantes resuelven los problemas matemáticos en escritos o procedimientos matemáticos y explorar si esta asociación se mantiene cuando la ansiedad matemática o coeficiente intelectual (IQ) es controlado. Por consiguiente, se usó una muestra de 100 niñas de escuela y análisis estadístico inferencial (ANOVA y ANCOVA) para investigar la hipótesis del estudio. Los resultados obtenidos indicaron que hubo sustanciales diferencias en los estudiantes y el desempeño matemático obtenido en palabras y procedimiento en la ejecución de los problemas por los grupos o área de dependencia. Sin embargo, esta diferencia es aún más significativa cuando el coeficiente intelectual (IQ) y la ansiedad matemática como covariable y variables fueron considerados. Sin embargo la cantidad de Omega Cuadrada para el análisis ANCOVA decreció cuando las covariables fueron insertadas en el modelo. Los hallazgos de este estudio son adecuados para los investigadores en el campo de la psicología del aprendizaje de las matemáticas y, en particular, cómo el estilo cognitivo afecta al desempeño de los estudiantes en Matemáticas

The role of Metacognition on effect of Working Memory Capacity on students' mathematical problem solving

The main objective of this study was to investigate the effects of Working Memory Capacity (WMC) on students' mathematical problem solving while considering different psychological factors. A sample of 256 high school girls students from Tehran (17-18 years old) were tested on (a) Metacognitive Awareness Inventory (MAI), (b) Mathematics Attention Test (MAT), (c) Mathematics Anxiety Rating Scale (MARS), (d) Digit Span Backward Test (DBT), and (e) a Mathematics Exam. Data of the present study were analyzed by descriptive and inferential statistics by T-test and Spearman correlation with the Statistical Package for the Social Sciences (SPSS). Results obtained indicate that metacognition had distinctive and challenging variable than other factors in use of WMC in mathematical problem solving. In other words, the correlation superiority between WMC and mathematical performance was found in group of high metacognition. Moreover, in each group of low/high metacognition, low/high math attention, and low/high math anxiety, the students with high WMC showed better mathematical performance than low WMC ones. The findings of the study are suitable for researchers who interested how different factors influence students’ mathematical problems solving.El principal objetivo de este estudio era investigar los efectos de la capacidad de memoria en el Trabajo (CMT) en los estudiantes, y la forma de resolver los ejercicios matemáticos planteados, mientras se consideraban diferentes factores psicológicos. En una muestra de 256 estudiantes mujeres entre los desde Teherán 17 y 18 años fueron evaluadas en a) Inventario conciencia meta cognitiva (ICM), (b) Prueba de atención Matemáticas (PAM), (c) Escala de ansiedad ante mas matemáticas (EAAM), (d) Prueba “Digit Span Backward”, y (e) un examen de Matemáticas. Los datos del presente estudio se analizaron mediante estadística descriptiva e inferencial de T-test y correlación de Spearman con el Paquete Estadístico para las Ciencias Sociales (SPSS). Los resultados indicaron que la meta cognición tiene distintivos y distintas variables desafiantes que otros factores usados en el WMC en la resolución de problemas matemáticos. En otras palabras, la superioridad correlación entre WMC y el rendimiento matemático se encontró en el grupo de alta metacognición. Además, en cada grupo de baja/ alta metacognición, atención alta/ baja de matemáticas, y bajo altos niveles de ansiedad/ matemáticas, los estudiantes con alta WMC mostraron mejor rendimiento matemático de los bajos de WMC. Los resultados del estudio son adecuados para los investigadores que estén interesados en los diferentes factores que influyen en los problemas matemáticos que los estudiantes resuelven

Comparison of the Effectiveness of Game-Based Therapy and Game-Based Therapy Integrated with Cognitive Rehabilitation on the Math Performance and Attitude towards Mathematics in Students with Learning Disabilities

The aim of this study was to compare the effectiveness of game-based therapy and game-based therapy integrated with cognitive rehabilitation techniques on the math performance and attitude of students with mathematical learning disabilities (MLD). A pre-test post-test quasi-experimental design was utilized to investigate the impact of independent variables on the dependent variable, with the use of a control group. The statistical population of the study consisted of male students with MLD in third to sixth grades from a school in Khomeynishahr, Iran, in 2020. A purposive sampling method was used to select 36 students with MLD, who were randomly assigned to three groups, including an experimental group receiving game-based therapy, an experimental group receiving game-based therapy integrated with cognitive rehabilitation techniques, and a control group receiving no intervention. Shalev arithmetic disorder scale and Aiken's mathematics attitude scale were used to collect data. MANCOVA was used to test the hypotheses. The findings revealed that game-based therapy and game-based therapy integrated with cognitive rehabilitation techniques significantly improved the math performance and attitude of the students (p < 0.05). Additionally, game-based therapy integrated with cognitive rehabilitation techniques was found to be more effective in improving math performance compared to game-based therapy alone (p < 0.05), while no significant difference was observed between the two interventions in improving attitude (p = 0.792). Therefore, it can be concluded that integrating game-based therapy with cognitive rehabilitation techniques can be more effective than other interventions in improving the math performance of students with MLD