He teaches mathematics and mathematics education courses to undergraduate and graduate students. ... more He teaches mathematics and mathematics education courses to undergraduate and graduate students. He likes to use technology to help develop understanding of mathematical concepts. Emily Gustafson is an undergraduate student of mathematics education at the University of Delaware. She likes to work with children and help them improve their mathematical skills. She is very excited about becoming a teacher. activity addresses the Data Analysis and Probability Standard for grades 9-12 of the National Council of Teachers of Mathematics (NCTM 2000), by helping students learn to select and use appropriate statistical methods to analyze data. Students work with bivariate data, display a scatterplot, describe its shape, and determine lines of best fit using technological tools.
El cálculo es una herramienta poderosa para resolver problemas relacionados con el cambio, variac... more El cálculo es una herramienta poderosa para resolver problemas relacionados con el cambio, variación y acumulación. Los estudiantes exitosos adquieren un dominio de una serie de técnicas para derivar e integrar, y desarrollan habilidad para resolver problemas. Desafortunadamente este dominio de los procedimientos muchas veces no va acompañado de una sólida comprensión conceptual. Incluso los alumnos exitosos tienen con frecuencia problemas para explicar qué significan los conceptos de límite, derivada e integral y cómo se relacionan entre sí. Por ejemplo, estudios recientes muestran que los alumnos de cálculo tienen muchas concepciones erróneas acerca del concepto de derivada en un punto y función derivada (Park, 2011, 2013). Es deseable que los futuros maestros desarrollen una comprensión relacional y no meramente instrumental (Skemp, 1987) de los temas que van a enseñar. Sin embargo, los alumnos en Delaware, como en otros lugares en Estados Unidos, no tienen muchas oportunidades de desarrollar una compresión conceptual profunda en sus cursos de cálculo en el nivel medio superior, ni en los cursos de cálculo en la universidad. En el nivel medio superior, la enseñanza del cálculo está dominada por el curso Advanced Placement Calculus, un curso que da crédito a nivel universitario. El contenido del curso está determinado por el examen a nivel nacional. El examen enfatiza dominio de procedimientos y solución de problemas aplicados, no una comprensión conceptual. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Funes Alfinio Flores Peñafiel Enfoque conceptual del cálculo en la formación de docentes: Ejemplos con uso de tecnología interactiva
<jats:p>Teaching concepts relating to rational numbers is a challenging task for most teach... more <jats:p>Teaching concepts relating to rational numbers is a challenging task for most teachers. National assessments show that many students in the United States have a poor understanding of rational numbers. For example, on the 1996 National Assessment of Education Progress only 50 percent of fourth graders could answer correctly how many fourths make a whole, only 45 percent could identify a diagram illustrating the equivalence of two fractions, only 21 percent could compare fractions, and only 10 percent could show how three figures can be partitioned (Arbaugh et al. 2004, Wearne and Kouba 2000).</jats:p>
<jats:p>During their first mathematics methods course, many prospective elementary teachers... more <jats:p>During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.</jats:p>
International Journal of Mathematical Education in Science and Technology, 2017
Students use GeoGebra to explore the mathematical relations among different radii of circles in a... more Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with preservice teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.
Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first appr... more Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.
He teaches mathematics and mathematics education courses to undergraduate and graduate students. ... more He teaches mathematics and mathematics education courses to undergraduate and graduate students. He likes to use technology to help develop understanding of mathematical concepts. Emily Gustafson is an undergraduate student of mathematics education at the University of Delaware. She likes to work with children and help them improve their mathematical skills. She is very excited about becoming a teacher. activity addresses the Data Analysis and Probability Standard for grades 9-12 of the National Council of Teachers of Mathematics (NCTM 2000), by helping students learn to select and use appropriate statistical methods to analyze data. Students work with bivariate data, display a scatterplot, describe its shape, and determine lines of best fit using technological tools.
El cálculo es una herramienta poderosa para resolver problemas relacionados con el cambio, variac... more El cálculo es una herramienta poderosa para resolver problemas relacionados con el cambio, variación y acumulación. Los estudiantes exitosos adquieren un dominio de una serie de técnicas para derivar e integrar, y desarrollan habilidad para resolver problemas. Desafortunadamente este dominio de los procedimientos muchas veces no va acompañado de una sólida comprensión conceptual. Incluso los alumnos exitosos tienen con frecuencia problemas para explicar qué significan los conceptos de límite, derivada e integral y cómo se relacionan entre sí. Por ejemplo, estudios recientes muestran que los alumnos de cálculo tienen muchas concepciones erróneas acerca del concepto de derivada en un punto y función derivada (Park, 2011, 2013). Es deseable que los futuros maestros desarrollen una comprensión relacional y no meramente instrumental (Skemp, 1987) de los temas que van a enseñar. Sin embargo, los alumnos en Delaware, como en otros lugares en Estados Unidos, no tienen muchas oportunidades de desarrollar una compresión conceptual profunda en sus cursos de cálculo en el nivel medio superior, ni en los cursos de cálculo en la universidad. En el nivel medio superior, la enseñanza del cálculo está dominada por el curso Advanced Placement Calculus, un curso que da crédito a nivel universitario. El contenido del curso está determinado por el examen a nivel nacional. El examen enfatiza dominio de procedimientos y solución de problemas aplicados, no una comprensión conceptual. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Funes Alfinio Flores Peñafiel Enfoque conceptual del cálculo en la formación de docentes: Ejemplos con uso de tecnología interactiva
<jats:p>Teaching concepts relating to rational numbers is a challenging task for most teach... more <jats:p>Teaching concepts relating to rational numbers is a challenging task for most teachers. National assessments show that many students in the United States have a poor understanding of rational numbers. For example, on the 1996 National Assessment of Education Progress only 50 percent of fourth graders could answer correctly how many fourths make a whole, only 45 percent could identify a diagram illustrating the equivalence of two fractions, only 21 percent could compare fractions, and only 10 percent could show how three figures can be partitioned (Arbaugh et al. 2004, Wearne and Kouba 2000).</jats:p>
<jats:p>During their first mathematics methods course, many prospective elementary teachers... more <jats:p>During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.</jats:p>
International Journal of Mathematical Education in Science and Technology, 2017
Students use GeoGebra to explore the mathematical relations among different radii of circles in a... more Students use GeoGebra to explore the mathematical relations among different radii of circles in a triangle (circumcircle, incircle, excircles) and the sides and other segments in the triangle. The more formal mathematical development of the relations that follows the explorations is based on known geometrical properties, different formulas relating the radii to the sides and the inequalities between the different averages. The activities described were conducted with preservice teachers of mathematics, with empirical investigation of the relations using dynamical geometry software, and formal presentation of proofs.
Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first appr... more Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.
Uploads
Papers by Alfinio Flores