An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

Haspékian, Mariam

doi:10.1007/s10758-005-0395-z

Cited by 66 publications

(38 citation statements)

References 11 publications

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“…Using the spreadsheet in the context of problem solving emphasizes the need to identify the relevant variables involved and fosters the search for variables that depend on other variables, resulting in composed relations. The definition of intermediate relations, by means of spreadsheet formulas in intermediate columns, meaning the decomposition of more complex relations in chained simpler ones, is a special feature inherent to the use of the spreadsheet that amounts to important results in solving algebraic contextual problems (Carreira, 1992;Haspekian, 2005). Moreover, as noted by Haspekian (2005) a spreadsheet also allows an algebraic organization of apparently arithmetical solutions and this kind of hybridism, where arithmetic and algebra naturally cohabit, becomes an educational option that may help students in moving from arithmetic to algebra (Kieran, 1996).…”

Section: Problem Solving With the Spreadsheet And The Development Of mentioning

confidence: 99%

“…The definition of intermediate relations, by means of spreadsheet formulas in intermediate columns, meaning the decomposition of more complex relations in chained simpler ones, is a special feature inherent to the use of the spreadsheet that amounts to important results in solving algebraic contextual problems (Carreira, 1992;Haspekian, 2005). Moreover, as noted by Haspekian (2005) a spreadsheet also allows an algebraic organization of apparently arithmetical solutions and this kind of hybridism, where arithmetic and algebra naturally cohabit, becomes an educational option that may help students in moving from arithmetic to algebra (Kieran, 1996). Spreadsheets can act as a bridge between arithmetic and algebra by helping students generalize patterns, develop an understanding of variable, facilitate transformation of algebraic expressions, and provide a space to explore equations (Tabach et al, 2008).…”

Section: Problem Solving With the Spreadsheet And The Development Of mentioning

confidence: 99%

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Solving a contextual problem with the spreadsheet as an environment for algebraic thinking development

Nobre

Amado

Carreira

2012

Teaching Mathematics and its Applications

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In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13^14 -year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in the process of translating relations between variables and combining them in chained models, while working with fractions, multiples and expressions. We intend to highlight the role of the spreadsheet in students' processes of variable identification and translation of the problem conditions, their numerical approaches to algebraic models and their experimental forms of finding solutions to equations.

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Section: Problem Solving With the Spreadsheet And The Development Of mentioning

confidence: 99%

Section: Problem Solving With the Spreadsheet And The Development Of mentioning

confidence: 99%

Solving a contextual problem with the spreadsheet as an environment for algebraic thinking development

Nobre

Amado

Carreira

2012

Teaching Mathematics and its Applications

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“…Mostraremos casos en los que los estudiantes consideraron necesario construir nombres para las cantidades con la intención de dotar de sentido a la historia del problema en el espacio semiótico de la hoja de cálculo. También ofreceremos ejemplos que pondrán de manifiesto cómo lo que Haspekian (2005) llama carácter híbrido del lenguaje de la hoja de cálculo (un lenguaje a medio camino entre el de la aritmética y el del álgebra) permite la aparición de estrategias de resolución aritméticas en las que no se procede de manera exclusiva de lo conocido hacia lo desconocido.…”

Section: Objetivosunclassified

Influencia de la representación de las cantidades en la resolución de problemas verbales en el entorno de la hoja de cálculo

Vera

2012

EDMETIC

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Resumen:Hemos llevado a cabo una experimentación en la que pretendíamos observar las consecuencias de enseñar a resolver problemas de manera algebraica en el entorno de la hoja de cálculo a un grupo de estudiantes de primer curso de secundaria que no habían sido introducidos previamente en el mundo del álgebra. En este artículo ofreceremos ejemplos de fenómenos de anclaje en las formas de resolver propias de la aritmética por parte de algunos alumnos cuando resolvían en la hoja de cálculo. Mostraremos cómo estas resoluciones aritméticas se veían influidas por la enseñanza y el entorno dando lugar a: (1) la imposibilidad de introducir una fórmula en una celda que no hubiera sido etiquetada previamente con un nombre propio del espacio semiótico en que se ofrecía el problema; y (2) la aparición de resoluciones con características aritméticas en las que se operaba con lo desconocido. Palabras clave: resolución de problemas; aritmética; álgebra; hoja de cálculo. Abstract:We have carried out an experiment in which we intended to observe the consequences of teaching the algebraic way of solving problems in the spreadsheet environment to a group of secondary school freshmen that had not been previously entered into the realm of algebra. In this paper, we will offer examples of anchoring phenomena in arithmetical methods by some students when solving problems in the spreadsheet. We will show how these arithmetic resolutions were influenced by the teaching sequence and the environment resulting in: (1) the inability to enter a formula in a cell that had not previously been labelled with a name proper to the semiotic space in which the problem has been offered; (2) the emergence of resolutions with arithmetical characteristics in which students operated with the unknown.

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“…Jackiw and Sinclair (2006), when discussing the learning of grades 3 to 5 children as they engaged in activities involving dragging, described how the exploration with movement enabled students to gain some understanding of continuity and abstract relations. Instrumentalisation has also been applied to the relationship between the learner and the integration of computer algebra systems (CAS) in mathematics programmes (e.g., Artigue, 2002;Lagrange, 2005) and with spreadsheets (Haspekian, 2005). This aspect gestures towards contemporary hermeneutics from the perspective that the affordances of the digital technology might influence the learners' approach, their dialogue and hence mathematical understanding.…”

Section: Current Perspectivesmentioning

confidence: 99%

The layering of mathematical interpretations through digital media

Calder

2011

Educ Stud Math

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How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children's mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital technologies in mathematics education is predominantly positioned within two theoretical perspectives, semiotic mediation and the instrumental approach. Meanwhile, within a contemporary hermeneutic position, mathematical learning comprises a process of interpretation, where understanding is seen as a formative process as the learner views events from fresh, ever-evolving perspectives. Concepts are then seen in ongoing formation. This paper examines learning through a contemporary hermeneutic frame and the contention is that this opens opportunity for learning to be perceived in alternative ways. PreambleThis paper is concerned with the ways learning evolves as the learner engages mathematical tasks through digital pedagogical media. The learner's preconceptions of the pedagogical media, in conjunction with the opportunities and constraints offered by the media themselves, promote distinct pathways in the learning process. That is, mathematical activity is inseparable from the pedagogical device, as it were, derived as it is from a particular understanding of social organisation. Hence, the device will inevitably influence the mathematical ideas developed. This pedagogical device is more than an environment. It is Educ Stud Math (2012) 80:269-285

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An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

Cited by 66 publications

References 11 publications

Solving a contextual problem with the spreadsheet as an environment for algebraic thinking development

Solving a contextual problem with the spreadsheet as an environment for algebraic thinking development

Influencia de la representación de las cantidades en la resolución de problemas verbales en el entorno de la hoja de cálculo

The layering of mathematical interpretations through digital media

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