Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study.

By M. Carlson, Sally Jacobs, Edward Coe, Sean Larsen, Eric Hsu. 2002

649 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e65300b65ba4705d004e65daf346e6856343b9c9

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Citations in the corpus

Decentering: A construct to analyze and explain teacher actions as they relate to student thinking (2016, methodology): “The Pathways curriculum is informed by theory on learning the concept of function (Carlson 1995, 1998), the processes of covariational reasoning (Carlson et al. 2002), and literature about mathematical discourse (Carlson et al.”
THE CONCEPT OF ACCUMULATION IN CALCULUS (2008, background): “To understand an accumulation function, students also need a covariational understanding of the relationship between x and f ( Carlson, Jacobs, Coe, Larsen, & Hsu, 2002; Saldanha & Thompson, 1998; P. W. Thompson, 1994b, 1994c).”
Why don't well-educated adults understand accumulation? A challenge to researchers, educators, and citizens (2009, background): “Poor ability to interpret and construct graphs among both students and adults is well documented in the mathematics education literature and related fields (e.g., Berry & Nyman, 2003; Carlson, Jacobs, Coe, Larsen, & Hsu, 2002; Gattis, 2002, 2004; Gattis & Holyoak, 1996; Paulos, 1988; Tufte 1983, 1”
Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning (2011, background): “Students’ difficulties in acquiring the function concept is well documented (e.g., Carlson 1998; Carlson et al. 2002; Cooney and Wilson 1996; Monk and Nemirovsky 1994), which highlights the need to better support students’ emerging function concepts in ways that are mathematically productive, settin”
Documenting the emergence of “speaking with meaning” as a sociomathematical norm in professional learning community discourse (2008, positive): “In partnership with school leaders, university faculty developed four mathematics/science graduate courses, all of which had a focus on modeling and a connecting theme of covariation, i.e., models emerged from attending to the variation of two quantities as they changed in tandem (Carlson, 1998; Ca”
Quantifying exponential growth: Three conceptual shifts in coordinating multiplicative and additive growth (2015, methodology): “In order to develop an initial task sequence to support the five ideas, we drew loosely on Carlson et al.’s covariation framework (2002). The framework addresses the reasoning involved in the representation and interpretation of graphical models in calculus, but served useful to guide our thinking a”
The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings (2010, methodology): “A student might be able to engage in mental action 5 without being able to coordinate how the change in one quantity affects the change in another (Carlson et al., 2002).”
Contrasting Cases of Calculus Students' Understanding of Derivative Graphs (2010, background): “Similarly, Carlson, Jacobs, Coe, Larsen, and Hsu (2002 ) investigated high-achieving calculus students' ability to reason about covarying quantities in dynamic situations and concluded that students could construct images, but had difficulty forming images of continuously changing rates.”
Together yet separate: Students’ associating amounts of change in quantities involved in rate of change (2015, background): “Researchers (Carlson et al., 2002; Saldanha & Thompson, 1998) have identified that students can associate quantities to make sense of situations involving quantities that change together.”