Facilitating the Transition from Empirical Arguments to Proof.

By Gabriel J. Stylianides, Andreas J. Stylianides. 2009

215 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/52dbcfda692153c48f3024e16f448f3cc8fc4318

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Citations in the corpus

Proof constructions and evaluations (2009, background): “We describe five major aspects of this approach; detailed descriptions of the first four aspects can be found in Stylianides and Stylianides (2009a) and of the fifth in Stylianides and Stylianides (2009b).”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “Mathematics educators sometimes express concern that students believe things that are untrue based on empirical evidence (e.g., G. Stylianides & Stylianides, 2009).”
The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks (2014, background): “Indeed, instructional sequences and strategies have been developed (e.g., Buchbinder & Zaslavsky, 2011; Stylianides & Stylianides, 2009) to facilitate the intellectual transition from a sole reliance on empirical reasoning to the use and understanding of inductive and deductive reasoning together…”
Self-explanation training improves proof comprehension (2014, background): “Mejía-Ramos, Fuller, Weber, Rhoads, and Samkoff (2012) recently proposed a theoretical model of proof comprehension.”
The Knowledge-Learning-Instruction Framework: Bridging the Science-Practice Chasm to Enhance Robust Student Learning (2012, background): “…Reimann, & Glaser, 1989; Lewis, 1988; VanLehn, 1999), explicit hypothesizing and scientific discovery processes (Klahr & Dunbar, 1988; Levine, 1966), deductive proof (e.g., Stylianides & Stylianides, 2009), and explicit argumentation or collaborative discourse (e.g., Asterhan & Schwarz, 2009).”
Educating Critical Thinkers (2016, background): “Explicit instruction in the epistemic practices of mathematics has led to increases in students’ ability to engage in higher order mathematical activities, such as writing proofs (Weber, 2006) and using more than just empirical evidence to explore proofs (Stylianides & Stylianides, 2009).”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, background): “General arguments aim to cover appropriately the entire domain of a generalisation (which can have infi nite cardinality; cf. Stylianides and Stylianides 2009a ), whereas empirical arguments can be satisfi ed with the examination of only a subset of that domain.”
Research-based interventions in the area of proof: the past, the present, and the future (2017, background): “Indeed, a premise underlying our own research on classroom-based interventions (e.g., Stylianides & Stylianides, 2009, 2014) has been that, by engineering ways to address problems of classroom practice, one develops also a better theoretical understanding of the nature of these problems and their…”