This study explores, from both constructivist and cognitive perspectives, teacher guidance in student-centered classrooms when addressing a common learning difficulty with equivalent fractions—lines or pieces—based on number line models. Findings from three contrasting cases reveal differences in teachers’ facilitating and direct guidance in terms of anticipating and responding to student difficulties, which leads to differences in students’ exploration opportunity and quality. These findings demonstrate the plausibility and benefit of integrating facilitating and direct guidance in student-centered classrooms. Findings also suggest two key components of effective teacher guidance including (a) using pretraining through worked examples and (b) focusing on the relevant information and explanations of concepts. Implementations are discussed.
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We wish to thank Kelley Marshall for helpful assistance. Special thanks to Dr. Xiaobao Li at Widener University for serving as the second coder in this study.
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Ding, M., Li, X. Facilitating and direct guidance in student-centered classrooms: addressing “lines or pieces” difficulty. Math Ed Res J 26, 353–376 (2014). https://doi.org/10.1007/s13394-013-0095-2