Developing Algebraic Aspects of Problem Solving within a Spreadsheet Environment

Is There Something to be Gained from Guessing? Middle School Students' Use of Systematic Guess and Check

“…These students also used their developed systems as function machines. Driscoll (1999), and Rojano (1996) argue that guess and check is much like generalization except that when systematically guessing and checking students use the generalized relationships to search for a specific case. Like the Carraher and colleagues (2006) intervention study with second‐through fourth‐grade students, these middle school students who had not had been taught algebraic techniques for solving these problems also seemed to be comfortable with the introduced use of letters to represent unknowns and were able to make inferences using the unknown quantities.…”

“…Similarly, Rojano (1996) argues that systematic guess and check can provide a foundation upon which the methods and strategies of algebraic thought are constructed. When students use systematic guess and check they can reason about algebraic situations without having to rely upon the traditional forms found in school algebra.…”

An “Instrumental Approach” to Study the Integration of a Computer Tool Into Mathematics Teaching: the Case of Spreadsheets

“…The use of spreadsheets in mathematics teaching has been studied for instance by Ainley (1999), Ainley et al (1999Ainley et al ( , 2003, Arzarello et al (1994Arzarello et al ( , 2001, Capponi ( , 2000, Dettori et al (1995), Rojano and Sutherland (1997), and Rojano (1996Rojano ( , 2001. All these studies relate to the learning of algebra at elementary stages and generally give spreadsheets a positive role in this learning.…”

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

“…Rojano (1996) points out that strategies such as trial and error or guess and check are sometimes seen as obstacles to learning algebraic methods, but argues that "trial and error, together with other strategies considered informal and found in students beginning the study of algebra, are indeed a real foundation upon which the methods or strategies of algebraic thought are constructed" (p. 137).…”

“…Research indicates that students with and without algebra backgrounds have informal strategies that allow them to effectively deal with algebraic word problems or problems that are start-unknown (Bednarz & Janvier, 1996;Hall, Kibler, Wenger, & Truxaw, 1989;Kieran, Boileau, & Garancon, 1996;Nathan & Koedinger, 2000;Rojano, 1996). Two of the most noted approaches are guess and check and the unwind strategy.…”