First Encounter with Variables by First and Third Grade Spanish Students

Molina, Marta; Ambrose, Rebecca; Río, A. del

doi:10.1007/978-3-319-68351-5_11

Cited by 12 publications

(11 citation statements)

References 13 publications

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“…In n-day case one student even explicitly contended indeterminacy of the independent variable to be inconceivable, whilst others assigned the letter a fixed numerical value and solved from that perspective. Similar results have been reported for younger students (e.g., Molina et al, 2018;Ureña et al, 2019). Such evidence reinforces the idea to foster generalisation with tasks involving familiarisation with indeterminacy and its representations as a preamble to formal algebra instruction.…”

Section: Representations Of Generalisationsupporting

confidence: 89%

Generalization strategies and representations used by final-year elementary school students

Ureña

Uclés

Cañadas

et al. 2022

International Journal of Mathematical Education in Science and

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Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, and also the strategies used by students and their connection with generalization. This paper jointly describes the strategies and representations of generalisation used by a group of 33 sixth-year elementary school students, with no former algebraic training, in two generalisation tasks involving a functional relationship. The strategies applied by the students differed depending on whether they were working on specific or general cases. To answer questions on near specific cases they resorted to counting or additive operational strategies. As higher values or indeterminate quantities were considered, the strategies diversified. The correspondence strategy was the most used and the common approach when students generalised.Students were able to generalise verbally as well as symbolically and varied their strategies flexibly when changing from specific to general cases, showing a clear preference for a functional approach in the latter.

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Section: Representations Of Generalisationsupporting

confidence: 89%

Generalization strategies and representations used by final-year elementary school students

Ureña

Uclés

Cañadas

et al. 2022

International Journal of Mathematical Education in Science and

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“…Certain word problem characteristics such as the use of additive functions (which are less complex than multiplicative functions) and the explicit mention of the functional relationship in the problem wording facilitated students' use of functional strategies (Merino et al 2016;Moss and Beatty 2006;Pinto et al 2016). With no prior instruction in the use of variable notation, the students in this study exhibited a lower level of symbolic representation of functional relationships than younger students analyzed by other authors (Author et al 2015;Molina et al 2018).…”

Section: Discussionmentioning

confidence: 50%

“…These findings underscore the importance of instruction or prior experience with symbolic notation for 9-to 10-year-olds (Carraher and Schliemann 2007;Radford 2018;Other et al 2019). When asked about indeterminate quantities, they spontaneously associated the letters used with positions in the alphabet, numbers beginning with the same letter, or with large numbers (Author and other 2019a;Author et al 2015;Molina et al 2018).…”

Section: Representations Of Generalizations In Functional Relationshipsmentioning

confidence: 99%

Word problems associated with the use of functional strategies among grade 4 students

2020

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This article discusses the characteristics of word problems that are associated with students' use of functional strategies and their ability to represent the generalization of functions. In the context of a broader research project designed to explore and foster functional thinking among elementary school students, twenty-five grade 4 (9-to 10-year-old) students were asked to identify functional relationships in five problems involving specific or indeterminate quantities. Their responses to a number of questions involving the generalization of the relationships in the problems were analyzed and associated to the characteristics of the problems. The type of representation of generalization used (verbal, generic, or symbolic) were also identified. Our findings indicate that grade 4 students showed potential for functional thinking prior to receiving instruction on variables and their notation. Such thinking was most effectively prompted when they worked with word problems that explicitly involved an additive function. When students generalized functional relationships, they represented them verbally or with generic examples. None of the students used symbolic representation. The originality of this study lies in the description of the specific characteristics of word problems that are associated with functional thinking; this information will prove useful to both teachers and curriculum designers. Identifying these characteristics could help build and propose tasks that encourage students to use more than one and more sophisticated strategies.

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“…The year before, these same students had participated in research designed to explore functional thinking (e.g., Molina, Ambrose, & Del Rio, 2018;Pinto, Cañadas, Moreno, & Castro, 2016). That was their first experience with functions and the use of symbolic-algebraic and tabular representations.…”

Section: Methodsmentioning

confidence: 99%

Representations of the generalization of a functional relationship and the relation with the interviewer’s mediation /Representaciones de la generalización de una relación funcional y el vínculo con la mediación del entrevistador

Ureña

Uclés

Molina

2019

Infancia y Aprendizaje

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First Encounter with Variables by First and Third Grade Spanish Students

Cited by 12 publications

References 13 publications

Generalization strategies and representations used by final-year elementary school students

Generalization strategies and representations used by final-year elementary school students

Word problems associated with the use of functional strategies among grade 4 students

Representations of the generalization of a functional relationship and the relation with the interviewer’s mediation /Representaciones de la generalización de una relación funcional y el vínculo con la mediación del entrevistador

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