Focus on Autism and Other Developmental Disabilities
Students with autism spectrum disorder frequently face challenges when learning mathematical conc... more Students with autism spectrum disorder frequently face challenges when learning mathematical concepts. For example, they may have difficulties solving mathematical word problems, in particular Cartesian product problems. This research is a case study with a multiple probe design in which the participants were three students diagnosed with autism spectrum disorder. A conceptual model-based problem-solving approach adapted to the characteristics of the participants was used to teach them how to solve Cartesian product word problems introduced sequentially in the instruction (first multiplication, then division, and finally both operations). The results show a functional relationship between the intervention and the students’ performance. The three participants generalized their learning to two-operation Cartesian product problems (an addition and a multiplication). Moreover, two of them retained what they learned 6 weeks after completing the instruction. The implications for teaching ...
We study monomial ideals, always given by a unique monomial, like a reasonable first step to esti... more We study monomial ideals, always given by a unique monomial, like a reasonable first step to estimate in general the number of blow ups of the desingularization algorithm appearing in [EV]. To resolve a monomial ideal X a1
We study monomial ideals, always locally given by a monomial, like a reasonable first step to est... more We study monomial ideals, always locally given by a monomial, like a reasonable first step to estimate in general the number of monoidal transformations of Villamayor's algorithm of resolution of singularities. The resolution of a monomial ideal [Formula: see text] is interesting due to its identification with the particular toric problem [Formula: see text]. In the special case, when all the exponents ai are greater than or equal to the critical value c, we construct the largest branch of the resolution tree which provides an upper bound involving partial sums of Catalan numbers. This case will be called "minimal codimensional case". Partial sums of Catalan numbers (starting 1,2,5,…) are 1,3,8,22,…. These partial sums are well known in Combinatorics and count the number of paths starting from the root in all ordered trees with n + 1 edges. Catalan numbers appear in many combinatorial problems, counting the number of ways to insert n pairs of parenthesis in a word of n...
Edma 0-6: Educación Matemática en la Infancia, 2021
Presentamos una propuesta didáctica ideada para trabajar teoría de grafos, destinada a alumnos de... more Presentamos una propuesta didáctica ideada para trabajar teoría de grafos, destinada a alumnos de Educación Primaria con Altas Capacidades en Matemáticas. Queremos aportar a los alumnos contenidos matemáticos motivadores fuera del currículo escolar para favorecer el desarrollo de sus capacidades, además de proporcionarles una herramienta sencilla y potente de representación y resolución de problemas de la vida real. La propuesta se estructura en cuatro fases basadas en la metodología de Dienes, en las que seguimos el modelo de resolución de problemas de Pólya, con un número variable de sesiones en cada fase, según las necesidades del alumnado. Nuestro enfoque parte del coloreado de mapas como contexto en el que aparecen los grafos de forma natural, seguido del trazado de caminos y ciclos eulerianos. Aplicamos los grafos a la resolución de un problema de combinatoria mediante la inducción, y finalmente, descomponemos los grafos aparecidos en polígonos estrellados y estrellas. En una ...
Graph theory is a powerful representation and problem-solving tool, but it is not included in pre... more Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies.
Page 1. A New Desingularization Algorithm for Binomial Varieties in Arbitrary Characteristic Rocı... more Page 1. A New Desingularization Algorithm for Binomial Varieties in Arbitrary Characteristic Rocıo Blanco ⋆ Universidad de Castilla-La Mancha. Departamento de Matemáticas, EU de Magisterio, Edificio Fray Luis de León, Avda ...
Focus on Autism and Other Developmental Disabilities
Students with autism spectrum disorder frequently face challenges when learning mathematical conc... more Students with autism spectrum disorder frequently face challenges when learning mathematical concepts. For example, they may have difficulties solving mathematical word problems, in particular Cartesian product problems. This research is a case study with a multiple probe design in which the participants were three students diagnosed with autism spectrum disorder. A conceptual model-based problem-solving approach adapted to the characteristics of the participants was used to teach them how to solve Cartesian product word problems introduced sequentially in the instruction (first multiplication, then division, and finally both operations). The results show a functional relationship between the intervention and the students’ performance. The three participants generalized their learning to two-operation Cartesian product problems (an addition and a multiplication). Moreover, two of them retained what they learned 6 weeks after completing the instruction. The implications for teaching ...
We study monomial ideals, always given by a unique monomial, like a reasonable first step to esti... more We study monomial ideals, always given by a unique monomial, like a reasonable first step to estimate in general the number of blow ups of the desingularization algorithm appearing in [EV]. To resolve a monomial ideal X a1
We study monomial ideals, always locally given by a monomial, like a reasonable first step to est... more We study monomial ideals, always locally given by a monomial, like a reasonable first step to estimate in general the number of monoidal transformations of Villamayor's algorithm of resolution of singularities. The resolution of a monomial ideal [Formula: see text] is interesting due to its identification with the particular toric problem [Formula: see text]. In the special case, when all the exponents ai are greater than or equal to the critical value c, we construct the largest branch of the resolution tree which provides an upper bound involving partial sums of Catalan numbers. This case will be called "minimal codimensional case". Partial sums of Catalan numbers (starting 1,2,5,…) are 1,3,8,22,…. These partial sums are well known in Combinatorics and count the number of paths starting from the root in all ordered trees with n + 1 edges. Catalan numbers appear in many combinatorial problems, counting the number of ways to insert n pairs of parenthesis in a word of n...
Edma 0-6: Educación Matemática en la Infancia, 2021
Presentamos una propuesta didáctica ideada para trabajar teoría de grafos, destinada a alumnos de... more Presentamos una propuesta didáctica ideada para trabajar teoría de grafos, destinada a alumnos de Educación Primaria con Altas Capacidades en Matemáticas. Queremos aportar a los alumnos contenidos matemáticos motivadores fuera del currículo escolar para favorecer el desarrollo de sus capacidades, además de proporcionarles una herramienta sencilla y potente de representación y resolución de problemas de la vida real. La propuesta se estructura en cuatro fases basadas en la metodología de Dienes, en las que seguimos el modelo de resolución de problemas de Pólya, con un número variable de sesiones en cada fase, según las necesidades del alumnado. Nuestro enfoque parte del coloreado de mapas como contexto en el que aparecen los grafos de forma natural, seguido del trazado de caminos y ciclos eulerianos. Aplicamos los grafos a la resolución de un problema de combinatoria mediante la inducción, y finalmente, descomponemos los grafos aparecidos en polígonos estrellados y estrellas. En una ...
Graph theory is a powerful representation and problem-solving tool, but it is not included in pre... more Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies.
Page 1. A New Desingularization Algorithm for Binomial Varieties in Arbitrary Characteristic Rocı... more Page 1. A New Desingularization Algorithm for Binomial Varieties in Arbitrary Characteristic Rocıo Blanco ⋆ Universidad de Castilla-La Mancha. Departamento de Matemáticas, EU de Magisterio, Edificio Fray Luis de León, Avda ...
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