Conjectures and Refutations in Grade 5 Mathematics.

By D. Reid. 2002

162 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ac3108d4352dc476ba258ce2e8f3dbf30ddba07e

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Citations in the corpus

Generalizing-Promoting Actions: how Classroom Collaborations Can Support Students Mathematical Generalizations (2011, background): “The results from this study contribute to a view of generalizing as a dynamic, evolving, and collective process, furthering the tradition of moving beyond viewing generalizing as an individual, cognitive construct (Davydov, 1990; Jurow, 2004; Reid, 2002; Tuomi-Gröhn & Engeström, 2003).”
Children's Mathematical Thinking in Different Classroom Cultures (2006, background): “construction of mathematical knowledge, that differentiate mathematical practices from other classroom practices (Reid, 2002; Russell, 1999).”
Using Novel Tasks in Teaching Mathematics: Three Tensions Affecting the Work of the Teacher (2003, background): “The task of ranking triangles according to area provided a context for a student to make a claim about what the relationship between two areas should be, basing that claim on mathematical rather than empirical reasoning (Reid, 2002).”
The Conjecturing Process: Perspectives in Theory and Implications in Practice (2007, background): “Reid (2001) describes Type 1 conjecturing in terms of several stages: • Observing a pattern, • Conjecturing (with doubt) that this pattern applies generally, • Testing of the conjecture (by predicting a further value and verifying), • Generalizing of the conjecture (that is, becoming certain of…”
The Effect of Authority on the Persuasiveness of Mathematical Arguments (2009, background): “Hanna (1983) and Reid (2002) both suggested that mathematicians use appeals to expert opinion to gain conviction in mathematical statements.”
Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks (2006, background): “By “reasoned conjecture” I mean a statement whose plausibility hinges on rational argument and is not contingent on perception or experience (see Reid, 2002).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “The process of constructing a proof can follow a “zigzag” path between attempts to generate valid arguments and criticisms of these attempts (e.g., through identification of counterexamples; Carpenter et al., 2003; Lakatos, 1976; Lampert, 1990, 1992; Reid, 2002; Schoenfeld, 1983).”
Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification (2017, background): “However, we must note that generalizations in the classroom may be unstated or incorrect (Becker and Rivera 2005; Reid 2002) and thus setting the need for elaboration and justification.”
PROSPECTIVE TEACHERS’ CHALLENGES IN TEACHING REASONING-AND-PROVING (2013, background): “, when they discover counterexamples to their conjectures (e.g. Mason, Burton & Stacey, 1982; Reid, 2002; Schoenfeld, 1983).”
Students' understandings of logical implication (2002, background): “…kinds of reasoning are entirely distinct and that, for example, broadly inductive reasoning may not contain deductive sequences, as the analysis by Reid (2002) clearly shows. ii In the past when students were taught Euclidean proofs, they would have come across conditional relationships when…”
Connections Between Generalizing and Justifying: Students' Reasoning with Linear Relationships (2007, background): “For instance, Reid (2002) suggested that generalization should be viewed as a collective construct, whereas others argue that generalization cannot be considered in absence of the social, historical, and mathematical context in which it occurs (Dreyfus, Hershkowitz, & Schwarz, 2001; Radford, 1996;…”