ALGEBRAIC THINKING AND THE GENERALIZATION OF PATTERNS: A SEMIOTIC PERSPECTIVE

By Luis Radford. 2006

196 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/827271ea10f5794998611dc01e2e47f4cb8aaf8e

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Citations in the corpus

“Rising to the challenge”: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students (2008, background): “…been found to be efficient in providing students with experiences that promote and reveal the development of algebraic thinking among students and preservice teachers alike (Amit and Neria 2007; Becker and Rivera 2004; English and Warren 1998; Radford 2006; Stacy 1989; Zazkis and Lijendak 2002).”
Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning (2011, background): “Before this teaching, generalisation from visual or iconic contexts was less robust than for symbolic ( Radford 2006 ).”
Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns (2008, background): “Radford (2006) notes that while some students may display knowledge of using algebraic language to express a constructive generalization, the variables used in such contexts have to reach their objective state of being subjectified and disembodied placeholders.”
Algebraic thinking from a cultural semiotic perspective (2010, background): “Conversely, Chinese and Babylonian mathematicians thought algebraically without using letters (Radford 2006).”
Grade 2 Students’ Non-Symbolic Algebraic Thinking (2011, methodology): “However, as I have argued in previous articles, the use of notations (i.e., alphanumeric symbolism) is neither a necessary nor a sufficient condition for thinking algebraically ( Radford 2006a, 2009a ).”
Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas (2015, background): “While prior research has found that students in the early elementary grades can use verbalizations to express generalizations (e.g., Radford, 2006, 2011), and while we agree with Radford (e.g., 2011) that “the use of notations (i.e., alphanumeric symbolism) is neither a necessary nor a sufficient…”
From arithmetical thought to algebraic thought: The role of the “variable” (2009, background): “ Radford (2006) claims that algebra not only uses letters, it rather uses letters or other signs (spoken words, gestures etc.) to think in a certain way.”
The effect of different representations on Years 3 to 5 students’ ability to generalise (2008, background): “Students were asked to find a step sufficiently large enough (e.g., the 22nd step) that directed attention towards commonality but not so large that it prevented any commonalities being noticed ( Radford, 2006 ).”