Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary ... more Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences.
Students in elementary grades encounter the equal sign but many misunderstand its meaning , Follo... more Students in elementary grades encounter the equal sign but many misunderstand its meaning , Following early algebra researchers' recommendations of smoothing the transition from arithmetic to algebra, we focus on the understanding of the equal sign as one of the keys in the development of mathematical and particularly algebraic thinking. This understanding enables to employ relational thinking where students look across the equal sign at relationships between numbers to solve equations, as in 8 + 4 = _ + 5.
This paper focuses on eight-year old students' ways of approaching true/false number sentenc... more This paper focuses on eight-year old students' ways of approaching true/false number sentences. The data presented here belongs to a teach-ing experiment in which the use of relational thinking when solving number sentences was explicitly promoted. The study of the way of ...
Canadian Journal of Science, Mathematics and Technology Education, 2009
Student responses to arithmetical questions that can be solved by using arithmetical structure ca... more Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-ondemand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), mediumterm (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed.
Presentamos una experiencia docente en un aula de 2 ESO en la que trabajamos los fractales median... more Presentamos una experiencia docente en un aula de 2 ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.
En este documento presentamos algunos de los resultados de un estudio que aporta evidencias de la... more En este documento presentamos algunos de los resultados de un estudio que aporta evidencias de la capacidad, de los alumnos de tercero de educación primaria, para desarrollar pensamiento relacional y comprensión del significado del signo igual "equivalencia numérica", trabajando en un contexto de igualdades numéricas.
Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary ... more Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences.
Students in elementary grades encounter the equal sign but many misunderstand its meaning , Follo... more Students in elementary grades encounter the equal sign but many misunderstand its meaning , Following early algebra researchers' recommendations of smoothing the transition from arithmetic to algebra, we focus on the understanding of the equal sign as one of the keys in the development of mathematical and particularly algebraic thinking. This understanding enables to employ relational thinking where students look across the equal sign at relationships between numbers to solve equations, as in 8 + 4 = _ + 5.
This paper focuses on eight-year old students' ways of approaching true/false number sentenc... more This paper focuses on eight-year old students' ways of approaching true/false number sentences. The data presented here belongs to a teach-ing experiment in which the use of relational thinking when solving number sentences was explicitly promoted. The study of the way of ...
Canadian Journal of Science, Mathematics and Technology Education, 2009
Student responses to arithmetical questions that can be solved by using arithmetical structure ca... more Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-ondemand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), mediumterm (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed.
Presentamos una experiencia docente en un aula de 2 ESO en la que trabajamos los fractales median... more Presentamos una experiencia docente en un aula de 2 ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.
En este documento presentamos algunos de los resultados de un estudio que aporta evidencias de la... more En este documento presentamos algunos de los resultados de un estudio que aporta evidencias de la capacidad, de los alumnos de tercero de educación primaria, para desarrollar pensamiento relacional y comprensión del significado del signo igual "equivalencia numérica", trabajando en un contexto de igualdades numéricas.
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