Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies

By D. Johanning. 2004

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What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra (2012, background): “For instance, “guess and check” with specific numbers has often proven to be an effective strategy for dealing with mathematical problems (see Cerulli & Mariotti, 2001 ; Johanning, 2004 ) despite the fact that it rarely provides mathematically accepted solutions.”
Supporting Algebraic Reasoning through Personalized Story Scenarios: How Situational Understanding Mediates Performance (2013, background): “First, research has revealed the ways in which students use informal methods, such as systematic guess and check, when confronted with algebraic tasks (Carraher et al., 2006; Hall, Kibler, Wenger, & Truxaw, 1989; Johanning, 2004; Kieran, 1988; Koedinger & Nathan, 2004; Nathan & Koedinger, 2000a, 200”
Relationships between Students' Fractional Knowledge and Equation Writing. (2015, background): “First, it may help account for why students do not write and solve equations when they can use strategies like guessing and checking values or unwinding arithmetical operations (Bednarz & Janvier, 1996; Johanning, 2004; Nathan & Koedinger, 2000; Swafford & Langrall, 2000).”