An analysis of mathematical concept representations and reflective practices in students’ math journals
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The purpose of this study was to identify the characteristics of “good mathematics journals” by analyzing how elementary students express and reflect on mathematical concepts through their journal writing. A total of 210 journals (141 manipulative-based and 69 curriculum-based) were collected and analyzed using a mixed-methods approach. The analysis revealed distinct representational and reflective features by journal type and grade level: manipulative-based journals primarily employed operational and visual representations, whereas curriculum-based journals showed more frequent verbal symbolic conversions and deeper, context-oriented reflection. In addition, upper-grade students demonstrated more advanced coordination among language, symbols, and visual representations than lower-grade students. These findings suggest that mathematics journaling provides a cognitive space in which students reconstruct their mathematical understanding through representational transformations and reflective reasoning. This study argues that a “good mathematics journal” is characterized by flexible use of multiple representations and multilayered reflection on mathematics, the models employed, and the contexts in which mathematical ideas operate.
Abstract
The purpose of this study was to identify the characteristics of “good mathematics journals” by analyzing how elementary students express and reflect on mathematical concepts through their journal writing. A total of 210 journals (141 manipulative-based and 69 curriculum-based) were collected and analyzed using a mixed-methods approach. The analysis revealed distinct representational and reflective features by journal type and grade level: manipulative-based journals primarily employed operational and visual representations, whereas curriculum-based journals showed more frequent verbal symbolic conversions and deeper, context-oriented reflection. In addition, upper-grade students demonstrated more advanced coordination among language, symbols, and visual representations than lower-grade students. These findings suggest that mathematics journaling provides a cognitive space in which students reconstruct their mathematical understanding through representational transformations and reflective reasoning. This study argues that a “good mathematics journal” is characterized by flexible use of multiple representations and multilayered reflection on mathematics, the models employed, and the contexts in which mathematical ideas operate.