Engaging Students in Proving: A Double Bind on the Teacher

By Patricio G. Herbst. 2002

122 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/095c1958e8214b788acef2d1f0288bb213864e9a

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Citations in the corpus

Using Novel Tasks in Teaching Mathematics: Three Tensions Affecting the Work of the Teacher (2003, methodology): “The first step of the analysis consisted of examining the ranking triangles task a priori (i.e., in terms of what it might have elicited; see Comiti, Grenier, & Margolinas, 1995; Herbst, 2002; Stein et al., 1996).”
Approaching Proof in a Community of Mathematical Practice (2008, unknown): “Studies on proof have recently been carried out employing socio-cultural approaches (e.g. Herbst, 2002a; Herbst, 2002b).”
When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers (2008, background): “Beyond those temporal considerations, the execution of the proof of a theorem is also subject to temporal norms that regulate, for example, the time it takes to produce each of the statements or reasons that compose the proof and by the structures that are used to punctuate the timeline in which tho”
Interactions with Diagrams and the Making of Reasoned Conjectures in Geometry (2004, background): “Elsewhere (Herbst 2002b) I have described this as the logical ordering of a list of descriptive assertions about a figure, noting in particular how some geometric assertions—those involving incidence and separation—are often invisible; and hence very rarely will students be held accountable for…”
Mathematicians’ perspectives on their pedagogical practice with respect to proof (2012, background): “Herbst [40] illustrates how high school teachers, when teaching proofs in geometry, sometimes engage in practices that they know will not enhance students’ understanding out of respect for the customs associated with the two-column geometry proof format.”
Teachers’ perspectives on “authentic mathematics” and the two-column proof form (2009, background): “For this reason, dispositions important for the working mathematician, such as working backwards, mapping a strategy, or structuring a proof, are poorly accommodated in the way geometry classes tend to use the two-column format (see Anderson 1982; Greeno 1980; Herbst 2002b; Leron 1983; Thurston 19”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, background): “It is surprising that so little attention has been paid to mathematics teachers’ instruction of proof (although Herbst, 2002 and Martin, McCrone, Bower & Dindyal, 2005 are exceptions).”
Proof in School Mathematics: Insights from Psychological Research into Students' Ability for Deductive Reasoning (2008, background): “…play a role in facilitating students’ use of deductive reasoning in the context of proof (e.g., Balacheff, 1991; Ball & Bass, 2003; Boero et al., 1996; Herbst, 2002a; Jones, 2000; Lampert, 1992; Mariotti, Bussi, Boero, Ferri, & Garutti, 1997; Stylianides, 2007b, 2007c; Weber, 2001; Yackel & Cobb,…”
Proving and Doing Proofs in High School Geometry Classes: What Is It That Is Going On for Students? (2006, background): “” Thus, the situation of doing proofs places high accountability demands on the teacher, and not just from the perspective of an observer looking at the teacher’s management of students’ proving work (Herbst, 2002a).”
Studying the Practical Rationality of Mathematics Teaching: What Goes Into “Installing” a Theorem in Geometry? (2011, unknown): “…operate like a contract particularly defining role relationships between teacher and students vis-à-vis the subject of studies (Brousseau, 1997; Herbst, 2002, 2003): In general, for highschool geometry, the contract says that the geometry teacher must teach geometry to his or her students and…”
Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks (2006, methodology): “The first consisted of an analysis a priori (Comiti, Grenier, & Margolinas, 1995; Herbst, 2002a, 2003) of the task that could develop around the problem chosen.”
Enacting proof-related tasks in middle school mathematics: Challenges and opportunities (2010, background): “This role requires teachers to strike a precarious balance between illustrating norms of proving as characteristic of the discipline and leaving room for students to discover and learn the necessity and utility of those norms (Herbst, 2002a).”