When time is an implicit variable: An investigation of students’ ways of understanding graphing tasks

Patterson, Cody L.; McGraw, Rebecca

doi:10.1080/10986065.2018.1509421

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…The first feature is the presence of time in the data as an explicit or implicit variable serving as a strong precedent identifier for its use as the independent variable in the current task situation, even though the problem formulation asks for something different. This strong influence of precedent events echoes findings by Patterson and McGraw (2018) as well as Bowen et al (1999). School and university mathematics pedagogy may need to facilitate students' building of a more diverse PSS, with exposure to mathematical problems in which engaging with a greater range of variables is necessary.…”

Section: Students' Graphing Activity As Running To Keep Up With Varyi...mentioning

confidence: 69%

“…Already in the 1990s, Leinhardt, Zaslavsky and Stein (1990) pointed out that "variables that are not time dependent are rare" (p. 23), that "students deal much more competently with graphs of functions in which one of the variables is time or time-dependent" (p. 28) and that students seem to have difficulty "grasping concepts that arise from variables not actually shown on the graph" (p. 42). A number of studies (e.g., Paoletti & Moore, 2017;Patterson & McGraw, 2018) have investigated students' parametric reasoning and the implicit role of time in covariational tasks, largely with a focus on graphing. Patterson and McGraw (2018), for instance, exemplify how students' inclination to use time as the independent variable leads to difficulty with tasks where they are asked to graph other types of time-dependent relationships such as relative positions.…”

Section: Graphing In University Students' Mathematical Activitymentioning

confidence: 99%

“…A number of studies (e.g., Paoletti & Moore, 2017;Patterson & McGraw, 2018) have investigated students' parametric reasoning and the implicit role of time in covariational tasks, largely with a focus on graphing. Patterson and McGraw (2018), for instance, exemplify how students' inclination to use time as the independent variable leads to difficulty with tasks where they are asked to graph other types of time-dependent relationships such as relative positions.…”

Section: Graphing In University Students' Mathematical Activitymentioning

confidence: 99%

See 2 more Smart Citations

Running to keep up with the lecturer or gradual de-ritualization? Biology students’ engagement with construction and data interpretation graphing routines in mathematical modelling tasks

Viirman

Nardi

2021

The Journal of Mathematical Behavior

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Section: Students' Graphing Activity As Running To Keep Up With Varyi...mentioning

confidence: 69%

Section: Graphing In University Students' Mathematical Activitymentioning

confidence: 99%

Section: Graphing In University Students' Mathematical Activitymentioning

confidence: 99%

See 1 more Smart Citation

Running to keep up with the lecturer or gradual de-ritualization? Biology students’ engagement with construction and data interpretation graphing routines in mathematical modelling tasks

Viirman

Nardi

2021

The Journal of Mathematical Behavior

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“…Nevertheless, there is still an important number of Portuguese PTs who do not provide an answer and a majority from both countries who reveal difficulties in connecting the information about the variables provided by the graph with the real context. This finding suggests that using graphs to model concrete situations may not only entail great complexity for students (Patterson & McGraw, 2018), but also for many elementary PTs, and it may prevent them from promoting the exploration of such representations in their future teaching practice.…”

Section: Figure 10 Example Of Correspondence In the Graph -S38mentioning

confidence: 99%

Exploring Prospective Elementary Mathematics Teachers’ Knowledge: A Focus on Functional Thinking

2021

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The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge, which need to be diagnosed aiming to assist them in developing the required knowledge to teach according to that perspective. This study aims to understand what aspects of functional thinking Spanish and Portuguese elementary PTs exhibit at the beginning of their teacher education program. The findings show that although PTs from both countries use different strategies to generalize functional relationships, the occurrence of successful strategies is low. Also, most participants provide local approaches in their interpretation of relationships between variables and reveal difficulties in understanding and connecting different representations of functions. These difficulties show that PTs lack important knowledge about functional thinking. By providing a framework concerning the functional thinking required for PTs to teach within an early algebra perspective, we shed light on a necessary step for teacher education programs to diagnose PTs’ functional thinking and to assist them in developing the needed mathematical knowledge to teach accordingly.

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“…Even if time is not represented explicitly on a graph axis, it can be an implicit variable. Patterson and McGraw (2018) presented paper and pencil graphing tasks to individual secondary students enrolled in a selective summer mathematics program; they found that an implicit variable of time could influence students' meanings for graphs. In our tasks, time is also an implicit variable.…”

Section: Promoting Student Conception Of Graphs As Representing Relatmentioning

confidence: 99%

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Johnson

McClintock

Gardner

2020

Digit Exp Math Educ

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We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative reasoning, we designed digital task sequences, in which students were to create different graphs linked to the same video animations. We report results of a qualitative study of thirteen secondary students (aged 15-17), who participated in digital, taskbased, individual interviews. We investigated two questions: (1) How do students conceive of what graphs represent when engaging with digital task sequences? (2) How do student conceptions of graphs shift when working within and across digital task sequences? Two conceptions were particularly stablerelationships between quantities and literal motion of an object. When students demonstrated conceptions of graphs as representing change in a single quantity, they shifted to conceptions of relationships between quantities. We explain how a critical aspect: What graphs should represent, intertwined with students' graph-sketching. Finally, we discuss implications for digital task design to promote students' conceptions of mathematical representations, such as graphs. Keywords Digital task design. Variation theory. Quantitative reasoning. Graphs By means of digital technology, students have opportunities to sketch and interpret dynamic graphs linked to video animations (Kaput 1994; Kaput and Roschelle 1999; Schorr and Goldin 2008). Yet, such opportunities are only a starting point. Instead of promoting reasoning, student interactions with digital technology may focus on skills and recall (Kitchen and Berk 2016). We developed digital task sequences that center on Digital Experiences in Mathematics Education

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When time is an implicit variable: An investigation of students’ ways of understanding graphing tasks

Cited by 6 publications

References 25 publications

Running to keep up with the lecturer or gradual de-ritualization? Biology students’ engagement with construction and data interpretation graphing routines in mathematical modelling tasks

Running to keep up with the lecturer or gradual de-ritualization? Biology students’ engagement with construction and data interpretation graphing routines in mathematical modelling tasks

Exploring Prospective Elementary Mathematics Teachers’ Knowledge: A Focus on Functional Thinking

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

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