Connections Between Generalizing and Justifying: Students' Reasoning with Linear Relationships

By Amy B. Ellis. 2007

158 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8e9a32d51281b9c20d529806be0424b512d46c16

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Citations in the corpus

Teacher moves for supporting student reasoning (2018, unknown): “within the context of gear ratios (see Ellis 2007).”
“Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students (2008, background): “Ellis (2007) constructs a generalization taxonomy in which there are two main generalization levels: actions and reflection.”
An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation (2016, background): “This static view underlies the typical treatment of functions in school mathematics, but research on middle grades students’ emerging understanding of functional relationships suggests that beginning with a covariation approach can support a flexible, connected understanding of rate of change that s”
The fractional knowledge and algebraic reasoning of students with the first multiplicative concept (2013, result): “This finding is compatible with Ellis’s (2007c) generalization taxonomy, which comes from a position of actor-oriented generalizing.”
The Influence of Reasoning with Emergent Quantities on Students' Generalizations (2007, background): “Previous work has identified both instances in which focusing on quantitative relationships encouraged the development of meaningful concepts and generalizations (e.g., Curcio et al., 1997; Ellis, 2007b; Hall & Rubin, 1998; Lobato & Siebert, 2002), and instances in which placing students in quantita”
Students' overuse of proportionality on missing-value problems: how numbers may change solutions (2009, unknown): “often experience difficulties with affine situations (see, e.g., Cooper & Sakane, 1986; Ellis, 2007; Lee, 1996; Stacey, 1989).”
Relationships between Students' Fractional Knowledge and Equation Writing. (2015, background): “Some researchers study students’ generalizations and abstractions of numerical and quantitative relationships involving fractions (e.g., Ellis, 2007; Empson et al., 2011; Russell, Schifter, & Bastable, 2011a; Steffe, 2001).”
“Noticing” as an Alternative Transfer of Learning Process (2012, background): “…in classrooms that involve interconnected sets of events, engagement in social interactions with others, much longer instructional sequences, and the use of additional learning resources during transfer events (Bransford & Schwartz, 1999; Ellis, 2007a, 2007b; Engle, 2006; Sinha et al., 2010).”