Making Believe: The Collective Construction of Public Mathematical Knowledge in the Elementary Classroom

By Deborah Loewenberg Ball, H. Bass. 2000

128 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/098b15ab789a33a570b232a4faac27fb52911a7b

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Citations in the corpus

Engaging Students in Proving: A Double Bind on the Teacher (2002, background): “Yet, that reduced efficiency may be a fair price for teachers to pay in order to reserve for themselves a legitimate role in the work of engaging students in proving propositions that expand the base of public knowledge in the classroom (Ball & Bass, 2000).”
Content Knowledge for Teaching (2008, unknown): “We have been studying not only specific episodes but also instruction over time, considering the work of developing both mathematics and students across the school year (Ball & Bass, 2000, 2003a).”
Studying the Practical Rationality of Mathematics Teaching: What Goes Into “Installing” a Theorem in Geometry? (2011, unknown): “In particular, what dispositions frame the work of making a geometric statement part of the public knowledge (Ball & Bass, 2000) that can be used later in justifying other claims?”
The Teaching of Proof (2003, background): “We need (1) a more refined perception of the role and function of proof in mathematics, including studies of the practices of proving in which active mathematicians engage (epistemological analysis), (2) a deeper understanding of the gradual processes and complexities involved in learning to prove (”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “(See a student from Ball & Bass, 2000, who produced a similar solution.)”
The Cultural Myths and Realities of Classroom Teaching and Learning: A Personal Journey. (2005, background): “It is now more widely understood that students learn by constructing their own knowledge (Ball & Bass, 2000; Hogan, Nastasi, & Pressley, 2000).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “An important ability required for successful performance in this process is to understand the role of assumptions (e.g., definitions, axioms) that underlie a mathematical argument or a proof (Ball & Bass, 2000; Mariotti & Fischbein, 1997; Stylianides, 2007a; Vinner, 1991; Zaslavsky & Shir, 2005).”
Mathematical Reasoning: Adults' Ability to Make the Inductive-Deductive Distinction (2002, background): “Although this research provides no information about the sources of these different belief structures, there is indirect evidence that (given opportunities to develop the notion of proof) children may show the same three types of beliefs (see Ball & Bass, 2000).”
Establishing a custom of proving in american school geometry: evolution of the two-column proof in the early twentieth century (2002, background): “Under this two-column proving custom, proving activities for students have often been closer to exercising logic to validate obvious and inconsequential statements (Kline, 1965), than to building compelling arguments for the reasonableness of important mathematical ideas (Ball and Bass, 2000; Schoen”
Teachers' Conceptions of Proof in the Context of Secondary School Mathematics (2002, background): “There are examples in the literature of elementary school students engaged in such proving practices (e.g., Ball & Bass, 2000; Maher & Martino, 1996), yet such examples are more the exception rather than the rule, and are rare at the secondary level.”