Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development

By Guershon Harel, Larry Sowder. 2005

126 citations recorded by the source corpus.

Subfields: Computer Science Applications, Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c987e01be89badd5325ab6a8e2787f1b55e9fc66

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In Computer Science Applications

In Education

In Statistics and Probability

Citations in the corpus

From arithmetical thought to algebraic thought: The role of the “variable” (2009, result): “These results coincide with those found in Harel and Sowder (2005).”
The Effect of Authority on the Persuasiveness of Mathematical Arguments (2009, background): “Others have argued that mathematicians may be influenced by such appeals when engaged in this latter activity (Weber, 2008); and some have implied that experts do not take into account authority figures when gaining conviction in statements (Harel & Sowder, 2005; Stylianides, 2007).”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “For instance, Harel and Sowder (2005) described the authoritarian proof scheme, that is, seeking conviction from authority, as “an undesirable, yet common way of thinking” and instruction must attempt “to suppress the authoritarian proof scheme” (p. 42); Selden and Selden (2003) claimed that…”
Demystifying computational thinking (2017, background): “Harel and Sowder (2005) defined mathematical thinking as global across many problems and “… governs one's ways of understanding” (p. 31).”
Advanced Mathematical Knowledge in Teaching Practice: Perceptions of Secondary Mathematics Teachers (2010, background): “Harel and Sowder (2005 ) highlighted this tension by relocating the hyphen, posing “advanced-mathematical thinking” (ie, thinking in advanced mathematics) versus “advanced mathematical-thinking” (ie, mathematical thinking of an advanced nature).”
Cognitive Development of Proof (2011, background): “Harel and Sowder (1998, 2005) describe cognitive growth of proof in terms of the learner’s development of proof schemes – relatively stable cognitive/affective configurations responsible for what constitutes ascertaining and persuading an individual of the truth of a statement at a particular stage…”