Abstract
Through the task of problem posing, we inquire into students’ conceptual knowledge of algebraic symbolism developed in compulsory secondary education. We focus on identifying the characteristics of equations and systems of equations that made the problem posing task difficult for the students and analyzing the meanings that they gave to the operations contained in the expressions. To collect the data we used two questionnaires in which students were asked to pose problems that could be solved by using given equations or system of equations. In the second questionnaire a specific meaning for the unknowns in the given expression was suggested. The results complement those of a previous study. Students evidence a good conceptual knowledge of algebraic symbolism when meanings for the unknowns are suggested. Decimal numbers and an equation including parenthesis and multiplication of unknowns are the main elements that made some weaknesses in students’ knowledge to surface. The results are more promising. They suggest the potential for compulsory algebra instruction to develop students’ conceptual knowledge, although greater attention should be paid to the semantic aspects of algebra if students are to access such knowledge unaided.
Highlights
For years research on students’ understanding of algebra has focused on their procedural knowledge, normally defined as the command of a sequence of steps or actions that may help solve problems (Crooks and Alibali, 2014; Ross and Willson, 2012)
The largest number of analysable problems were posed for equations 2 and 7 in both questionnaires, whereas the largest number of omitted problems were posed for equation 3 in questionnaire 1 and equations 1 and 3 in questionnaire 2 (Table 7)
This article, the continuation of an earlier study by Fernández-Millán and Molina (2016), compares the findings from both studies while further exploring the conceptual understanding of algebraic symbolism acquired by two groups of students in the last year of compulsory secondary school
Summary
For years research on students’ understanding of algebra has focused on their procedural knowledge, normally defined as the command of a sequence of steps or actions that may help solve problems (Crooks and Alibali, 2014; Ross and Willson, 2012). MOLİNA by students to solve problems, and their understanding of the concepts implicit in the solution Attendant upon this new approach has been a change in mathematics instruction in which curricular documents explicitly address the need for students to master both procedural and conceptual algebraic knowledge (Crooks and Alibali, 2014; Ross and Willson, 2012)
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