The extension of the natural-number domain to the integers in the transition from arithmetic to algebra

By Aurora Gallardo. 2002

104 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/78e1ab1937d14215add957c5a94168a23d5a89f8

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Citations in the corpus

Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition (2012, background): “They offer descriptions and analyses of the erroneous use of integers due to the students’ experiences with natural numbers (Gallardo, 2002; Glaeser, 1981; Hefendehl-Hebeker, 1989; Thompson and Dreyfus, 1988; Vergnaud, 1989).”
Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics (2014, methodology): “…of the historical development of integers, we found that some authors focused squarely on the historical evolution of integers (Glaeser, 1981; Hefendehl-Hebeker, 1991; Henley, 1999) and others on the intersection between integers and algebra (Gallardo, 1995, 2002; Thomaidis & Tzanakis, 2007).”
Algebraic Equations: Can Middle-School Students Meaningfully Translate from Words to Mathematical Symbols? (2006, background): “Lodholz (1990) observed that writing equations from word problems is often a skill taught in contrived situations or in isolation.”
The Role of Mathematical Symbols in the Development of Number Conceptualization: The Case of the Minus Sign (2008, background): “Few authors have taken a specific interest in the issue of negative numbers in learning (Gallardo, 2002; Gallardo & Rojano; 1994; Glaeser, 1981; Hefendhel-Hebeker, 1991).”
A Proposed Instructional Theory for Integer Addition and Subtraction (2012, background): “Many researchers have interviewed, surveyed, and conducted teaching experiments (Steffe & Thompson, 2000) as a way to document students’ conceptions of integers from very early ages (Bofferding, 2010) to early adolescence (Gallardo, 2002; Vlassis, 2004, 2008).”
What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra (2012, background): “” Some other researchers have also noted a similar phenomenon (Chiarugi, Fracassina, & Furinghetti, 1990; Crowley et al., 1994; Gallardo, 2002; Vlassis, 2004).”
Handbook of research on the psychology of mathematics education: past, present and future (2006, background): “However, according to Vlassis, if students have not already extended their numerical range to encompass the negative integers, cancellation errors will be inevitable (for further research on negative numbers, see Gallardo, 2002).”