Cognitive Models Underlying Students' Formulation of Simple Linear Equations

Following the standard form: Effects of equation format on algebraic modeling

“…We then examined whether participants came up with different modeling interpretations of the MF and DF equations. Specifically, building on the distinction made by Kieran (1990) and Sfard (1991), and the linguistic analysis discussed by MacGregor and Stacey (1993), we developed a categorization scheme that distinguished between Equivalence (E) interpretations that view algebraic equations as representing equivalence relations between variable quantities, and Computation (C) interpretations that view such equations as representing problem-solving solutions. We then examined whether standard-form equations (MF) evoke more equivalence interpretations (and fewer computation interpretations) than do DF equations.…”

“…The dominant explanation for the fact that college students commit reversal errors is their poor understanding of algebra, although people who commit such errors may hold distinct algebraic misconceptions (e.g., Clement, Lochhead, & Monk, 1981;Cohen & Kanim, 2005;Herscovics, 1989;Kieran, 1990Kieran, , 1992Lochhead & Mestre, 1988;MacGregor & Stacey, 1993;Rosnick & Clement, 1980). For example, Clement et al (1981) found that some college students did not understand that the letters S and P stand for variables (i.e., that S denotes the number of students and P denotes the number of professors).…”

The Analysis of the Problems Posed by the Pre-Service Teachers About Equations

“…In the syntactic translations, the equations are formed by writing the mathematical symbols from left to the right in order in place of the words in the verbal expressions. MacGregor and Stacey (1993) researched the cognitive models of the students in the 8-10 age group in forming the equations corresponding to the verbal expressions. In their study, they posed a problem as "s and t are numbers.…”

Assessment of Activity-Based Instruction in Overcoming 7th Grade Middle School Students’ Misconceptions in Algebra

“…Öğrencilerin yaptıkları hataların ve bu hatalara sebep olan kavram yanılgılarının tespit edilmesi etkili bir öğretimin sağlanabilmesi için yapılması gerekenlerden ilkidir (Gilbert, 1982;Ryan & Williams, 2007). Cebir kavramlarında da öğrencilerin yaptıkları hatalara ve kavram yanılgılarına rastlanmaktadır (Baki, 1998;Dede ve Argün, 2003;Ersoy ve Erbas, 1998;Kaput, 1999;Kieran, 1992;MacGregor & Stacey, 1993).…”

“…(Gilbert, 1982;Ryan & Williams, 2007). It is also encountered with some mistakes and misconceptions in Algebraic concepts (Baki, 1998;Dede & Argün, 2003;Ersoy & Erbas, 1998;Kaput, 1999;Kieran, 1992;MacGregor & Stacey, 1993).…”