Learning to notice students’ mathematical thinking through on-line discussions

Fernández, Ceneida; González, Julia Valls

doi:10.1007/s11858-012-0425-y

Cited by 81 publications

(52 citation statements)

References 16 publications

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“…The results of this study indicate that prospective teachers have similar interpretative characteristics. Interpreting of students' mathematical thinking are key teaching tasks in which teachers must generate hypotheses about how students' mathematical thinking could be developed (Fernández, Llinares, & Valls, 2012;Norton, McCloskey, & Hudson, 2011).…”

Section: The Use Of Representation In Interpreting Students' Mathematmentioning

confidence: 99%

Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking

et al. 2019

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Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students' mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students' work with their knowledge or thought.

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Section: The Use Of Representation In Interpreting Students' Mathematmentioning

confidence: 99%

Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking

et al. 2019

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“…La importancia del conocimiento de matemáticas especializado que permite a los profesores implicarse en tareas profesionales como proporcionar explicaciones para las reglas y procedimientos y examinar y comprender los métodos de soluciones no usuales también ha sido puesta de manifiesto recientemente VALLS, 2012;ZAZKIS, 2011). En particular, aprender a mirar de una manera profesional los métodos de resolución de problemas realizados por los estudiantes, entendido como una manera de usar el ISSN 1980ISSN -4415 http://dx.doi.org/10.1590ISSN /1980 conocimiento de matemáticas especializado en la resolución de tareas profesionales, se apoya en que los estudiantes para maestro sean capaces de identificar los aspectos matemáticamente significativos de las situaciones de proporcionalidad.…”

Section: El Razonamiento Proporcional De Los Futuros Maestros De Educunclassified

Conocimiento de matemáticas especializado de los estudiantes para maestro de primaria en relación al razonamiento proporcional

Buforn

Fernández

2014

Bolema

Self Cite

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ResumenUn dominio particular del conocimiento matemático para la enseñanza es el conocimiento de matemáticas especializado. Este estudio se centra en examinar el conocimiento de matemáticas especializado en el ámbito del razonamiento proporcional de un grupo de estudiantes para maestro de Educación Primaria. Los resultados muestran que los estudiantes para maestro tienen un conocimiento especializado sobre el razonamiento proporcional limitado puesto de manifiesto por la dificultad en identificar situaciones no proporcionales, en desarrollar formas de razonar en relación a la construcción de la unidad y en manejar el significado multiplicativo de la idea de operador.Palabras-Clave: Razonamiento proporcional. Estudiantes para maestro de primaria. Conocimiento de matemáticas para la enseñanza. Conocimiento de matemáticas especializado. AbstractA particular domain of mathematical knowledge for teaching is the specialized content knowledge. This study focuses on examining pre-service primary school teachers' mathematical content knowledge related to proportional reasoning. Results show that pre-service teachers' mathematical content knowledge is limited. These results are supported by pre-service teachers' difficulties in identifying non-proportional situations, in the development of ways of thinking related to the construction of the unit and in the use of the meaning of operator Recientemente se ha empezado a reconocer que la enseñanza de la idea de razón y proporción que subyacen en el desarrollo del razonamiento proporcional no es una tarea fácil para los maestros. En este sentido, las investigaciones han empezado a mostrar algunas características del conocimiento de matemáticas necesarias para la enseñanza de la idea de razón y proporción (LAMON, 2005;LIVY;VALE, 2011;PITTA-PANTAZI: CHRISTOU, 2011 El razonamiento proporcional de los futuros maestros de Educación PrimariaLas investigaciones han revelado las dificultades que tienen algunos maestros de primaria y secundaria con la idea de proporcionalidad, identificando, además, una falta de comprensión de la forma en la que el razonamiento proporcional se desarrolla. Este hecho hace que algunos profesores enfaticen procedimientos rutinarios como la regla de tres para enseñar a resolver las situaciones proporcionales (HAREL; BEHR, 1995).Las investigaciones centradas en el conocimiento de matemáticas para enseñar (MKT) ponen de manifiesto esta falta de comprensión relacionándola, además, con el desarrollo de las competencias docentes que debe poseer un maestro. Livy y Vale (2011) indican que solo 5% de los estudiantes para maestro de su estudio fueron capaces de resolver correctamente dos tareas relacionadas con el concepto de razón, donde se realizaba una comparación todotodo en un contexto de escalas.Por otra parte, Valverde y Castro (2009) señalan el predominio de un razonamiento pre-proporcional en las actuaciones de un grupo de estudiantes para maestro en tareas de proporcionalidad de valor perdido. Los estudiantes para maestro de este estudio aplicaban estrat...

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“…This is a shared purpose by other approaches oriented to the professional knowledge, the aim of which is to recognize the actions that allow the mathematics teacher to successfully develop their profession. Mason (2002), for example, highlights the importance of the competence referred to as "looking with sense" the mathematical thinking of the students (Fernández, Llinares & Valls, 2012;Mason, 2002). Such competence, allows the mathematics teacher to see contexts of teaching and learning mathematics in a professional way that can be differentiated from the way in which a non-mathematics teacher would look at the situation.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice

Breda

Pino-Fan

Moll

2017

EURASIA J MATH SCI T

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The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this aim, the results of a multiple case study are presented which prove that when teachers are faced with the task of evaluating processes of instruction, they employ-either implicitly or explicitly-the OSA criteria of didactical suitability (epistemic, cognitive, affective, mediational, interactional and ecological). Therefore, the explicit application of said criteria in teachers' education cycles contributes to the development of the didactic analysis competence that is necessary for teachers to be able to reflect on their own practices.

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Learning to notice students’ mathematical thinking through on-line discussions

Cited by 81 publications

References 16 publications

Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking

Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking

Conocimiento de matemáticas especializado de los estudiantes para maestro de primaria en relación al razonamiento proporcional

Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice

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