Students’ understanding of the general notion of a function of two variables

Martínez-Planell, Rafael; Gaismán, María Trigueros

doi:10.1007/s10649-012-9408-8

Cited by 44 publications

(16 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Subsequently, Martinez-Planell and Trigueros (2012) proposed a genetic decomposition to postulate about constructions the students might make as they think about two variable functions and their graphs. The genetic decomposition consisted of the following:…”

Section: Introductionmentioning

confidence: 99%

Students’ images of two-variable functions and their graphs

Weber

Thompson

2014

Educ Stud Math

View full text Add to dashboard Cite

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory for how students might generalize their understanding of graphs of one variable functions to graphs of two variable functions. To evaluate the viability of this learning trajectory, we use data from two teaching experiments based on tasks intended to support development of the schemes in the HLT. We focus on the schemes that two students developed in these teaching experiments and discuss their relationship to the original HLT. We close by considering the role of covariational reasoning in generalization, consider other ways in which students might come to conceptualize graphs of two-variable functions, and discuss implications for instruction.

show abstract

Section: Introductionmentioning

confidence: 99%

Students’ images of two-variable functions and their graphs

Weber

Thompson

2014

Educ Stud Math

View full text Add to dashboard Cite

show abstract

“…of domain and range function. The studies reported that a large majority of students have difficulty in determining the domain of multivariable functions (Martínez-Planell & Gaisman, 2012), the domain of a composite function (Neger & Frame, 2005;Özkan & Ünal, 2009), and the domain of square root function (Drlik, 2015). Also, even though students are taught the way how to determine the domain and range of a function, they encounter difficulty when dealing with various types of problems.…”

mentioning

confidence: 99%

External Representation Flexibility of Domain and Range of Function

Aziz

Kurniasih

2019

J. Math. Educ.

View full text Add to dashboard Cite

This study attempts to analyze pre-service secondary mathematics teachers’ flexibility of external representations of domain and range of functions. To reach the purpose, a task consisted of thirty question items were designed. Participants of the study were thirty-eight Indonesian pre-service secondary mathematics teachers attending mathematics education department at one private university in Jakarta, Indonesia. Based on the analysis participants written responses, this paper revealed participants’ difficulties in providing a proper and consistent definition of the concept of domain and range of functions. We also disclosed the participants’ lack of flexibility in doing translation among representations under the concept of domain and range of function. In general, participants written responses to the task did not provide evidence of a solid understanding of domain and range. There are several implications of these findings offered for secondary mathematics teacher education’s program.

show abstract

“…Their learning has received more attention lately from the Mathematics Education community. Starting with the analysis of students' understanding about two-variable functions (for example: Trigueros and Martínez-Planell, 2010;Martínez-Planell and Trigueros, 2012) researchers have documented students' difficulties and have shown that the transition from one-variable Calculus to multivariable Calculus is far from being smooth. There are few studies in the literature that deal with students' difficulties and understanding of the integral multivariable Calculus (Jones and Dorko, 2015;Martínez-Planell and Trigueros, 2017).…”

mentioning

confidence: 99%