Structures and representations used by 6th graders when working with quadratic functions

Uclés, Rafael Ramírez; Cañadas, María C.; Damián, Alba

doi:10.1007/s11858-022-01423-w

Cited by 9 publications

(1 citation statement)

References 32 publications

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“…3 / 14 quadratic function, emphasizing the idea of vertex and its critical points, using different representations. Following this line, Ramírez et al (2022) observe the different representations of a quadratic function and conclude that it is usual-for students with higher capabilities-to promote the use of various representations and algebraic symbols; at the same time, they indicate that it is expected that students who work with quadratic functions opt for the handling of verbal and symbolic representations, this mainly due to the ease that such registers provide to explain some idea. Finally, Ledezma et al (2022) focus on the knowledge about mathematical modelling that can be inferred from the reflection of a prospective teacher on a didactic unit with the linear function for secondary education students in the Spanish context.…”

Section: Contribution To the Literaturementioning

confidence: 98%

University teachers’ didactic-mathematical knowledge for teaching the effect of coefficient b on the quadratic function

Ledezma,

Vargas,

Hidalgo-Moncada

et al. 2023

EURASIA J Math Sci Tech Ed

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Literature shows a tendency to relegate the role of coefficient b to second place in the teaching of the quadratic function. We report an experience with Chilean university teachers, who designed a teaching and learning sequence with this function for construction engineering students. Our focus was on the didactic-mathematical knowledge about the effects of varying coefficient b on the graphical representation of this function that the participating teachers made evident. We constituted a focus group with 10 teachers and then qualitatively analyzed their dialogues using the mathematics teacher’s didactic-mathematical knowledge and competencies model. We highlight the following results: (a) the importance of mathematical knowledge and that of the epistemic facet to interpret the effect of coefficient b on the graphical representation of the quadratic function and (b) the proposal of an interpretation for the graphical behavior of coefficient b that contributes to the teaching of the quadratic function.

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Section: Contribution To the Literaturementioning

confidence: 98%

University teachers’ didactic-mathematical knowledge for teaching the effect of coefficient b on the quadratic function

Ledezma,

Vargas,

Hidalgo-Moncada

et al. 2023

EURASIA J Math Sci Tech Ed

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Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

Pittalis,

Sproesser,

Demosthenous

et al. 2024

Educ Inf Technol

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The aim of this study was to develop, implement, and evaluate an intervention program focusing on developing Grade 5 and 6 students’ functional thinking. The innovative aspect lies in addressing simultaneously various aspects of function—input–output, covariation, correspondence, and object— in terms of manipulating tasks that involve functional relationships. The program adopts promising design principles, including an inquiry-based approach, engaging students in embodied dynamic mathematics learning environments, and making connections to real-world situations. A sample of 104 students took part in the program. The results showed a significant improvement in students’ performance related to functional thinking between the pre- and post-tests. Grade 5 students’ mean value improved from 0.29 to 0.58 and Grade 6 students from 0.37 to 0.60, respectively. Analysis indicated that students with varying performance potential in developing functional thinking are likely to be significantly affected by the program. Regression analysis showed that students’ gender as well as mathematics- and functions-related self-concept and interest did not serve as predictive factors of students’ gain score magnitude. Students' progression goes along with a significant shift in strategies used. While the dominant strategies in the pre-test relied on recursive and single variation, in the post-test, students moved to covariational and correspondence approaches. The findings indicate that upper primary school students are capable of grappling abstract facets of functions. This underscores the potential effectiveness of targeted interventions that adopt innovative design principles, particularly in light of the limitations of conventional curricula in adequately preparing students to explore functional relationships across diverse contexts.

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The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions

Kieran

2022

ZDM Mathematics Education

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Structures and representations used by 6th graders when working with quadratic functions

Cited by 9 publications

References 32 publications

University teachers’ didactic-mathematical knowledge for teaching the effect of coefficient <i>b</i> on the quadratic function

University teachers’ didactic-mathematical knowledge for teaching the effect of coefficient <i>b</i> on the quadratic function

Enhancing functional thinking in grade 5–6 students through a dynamic mathematics intervention program

The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions

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