A Study of Proof Conceptions in Algebra

By Lulu Healy, Celia Hoyles. 2000

511 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/e6452abec3c2427f8dc26c95a9ae42794ffd0c4c

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Citations in the corpus

Mathematicians’ perspectives on their pedagogical practice with respect to proof (2012, background): “In general, empirical studies suggest that students and high school mathematics teachers [22,23] fail to recognize these various roles of proof, with many believing that the only function of proof is to provide conviction.”
Actions speak louder with words: The roles of action and pedagogical language for grounding mathematical proof (2014, background): “Mathematical proof is an area of generalized, propositional reasoning that is notoriously difficult for students (Healy & Hoyles, 2000).”
Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving (2008, background): “Second, given the well-documented difficulties of students in tasks that involve infinitely many cases (e.g., Chazan, 1993; Healy & Hoyles, 2000 ), we thought important to consider these tasks for our framework; this led us, naturally, to also consider the other category of proving tasks that invol”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “, Hofer & Pintrich, 1997; King & Kitchener, 1994; Muis & Franco, 2009; Perry, 1970; Schommer, 1990). In her summary of this research, Hofer (2000) claimed that “at lower levels of most models, knowledge originates outside the self and resides in external authority, from whom it may be transmitted.”
Teachers' Conceptions of Proof in the Context of Secondary School Mathematics (2002, background): “The challenge of meeting these demands is particularly daunting given that many school mathematics students have found the study of proof difficult (e.g., Balacheff, 1991; Bell, 1976; Chazan, 1993; Coe & Ruthven, 1994; Healy & Hoyles, 2000; Porteous, 1990; Senk, 1985).”
The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks (2014, background): “Third, students who still entertain the possibility of finding a counterexample after seeing a correct deductive argument (Chazan, 1993; Fischbein, 1982; Healy & Hoyles, 2000) may be failing to grasp the intellectual link between deduction and general claims.”
MATHEMATICS TEACHERS’ CONCEPTIONS OF PROOF: IMPLICATIONS FOR EDUCATIONAL RESEARCH (2010, background): “Balacheff, 1991; Chazan, 1993; Healy & Hoyles, 2000 ; K nuth et al.,2002; Lin, Yang & Chen, 2004 ;S enk,1985; Thompson, 1996), perhaps due to their mathematics teachers’ inappropriate instruction or task selection (Herbst, 2002).”
Proof constructions and evaluations (2009, background): “Let us consider the misconception that empirical evidence is proof, which was found to be widespread both among elementary teachers (Goetting, 1995; Martin & Harel, 1989) and among secondary students (e.g., Coe & Ruthven, 1994; Healy & Hoyles, 2000; Sowder & Harel, 1998).”
How can the relationship between argumentation and proof be analysed? (2007, background): “Epistemological research in mathematics education underlines the importance of justifying activities connected to the construction of proof (Hanna 1991, 1995; Healy and Hoyles 2000).”
The Need for Proof and Proving: Mathematical and Pedagogical Perspectives (2011, background): “In fact, many school students, including advanced or high-attaining secondary students, (e.g., Coe and Ruthven 1994 ; Healy and Hoyles 2000 ; Knuth et al. 2002 ) and university students, including mathematics majors (e.g., Goetting 1995 ; Sowder and Harel 2003 ; Stylianides and Stylianides 2009a, b…”
Misconceptions In Geometry And Suggested Solutions For Seventh Grade Students (2012, background): “…learners: incomplete comprehension of the problem and mathematical symbols, producing proofs based on direct visual elements (e.g., Chazan, 1993; Healy & Hoyles, 2000), lacking strategic knowledge in producing proofs, etc. Addressing the difficulties in learning geometry, Duval (1998) and Healy…”
Why and how mathematicians read proofs: an exploratory study (2011, background): “First, students at all levels often find empirical arguments to be personally convincing and representative of the ways that they would justify mathematical statements (e.g., Martin & Harel, 1989; Healy & Hoyles, 2000 ).”