Developing both conceptual and procedural knowledge is important for students’ mathematics competence. This study examined whether Grade 9 general education mathematics teachers’ self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders’ algebra achievement after 2.5 years, depending on students’ mathematics difficulty (MD) status. Data for this study were drawn from the High School Longitudinal Study for the years 2009–2010 and 2011–2012 ( N = 19,104). Multiple regression analyses indicated that students with MD who participated in Grade 9 mathematics classrooms where teachers self-reported the use of less CFI and more PFI were more positively associated with having higher algebra achievement after 2.5 years. Conversely, students without MD in classrooms where mathematics teachers self-reported the use of more CFI and less PFI were positively associated with having higher algebra achievement after 2.5 years. However, this study’s findings do not suggest that teachers should disregard CFI and provide only PFI when teaching students with MD. Because the data set did not include any variable to discover whether teachers provided sufficient support (i.e., evidence-based practices) for students with MD, who have more constraints in their cognitive skills compared to students without MD, to benefit from CFI, the findings of this study should be interpreted cautiously. Directions for future research and practical implications are discussed.

中文翻译：

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对有数学困难和没有数学困难的九年级学生代数表现的以概念为中心和以程序为中心的教学


发展概念性和程序性知识对于学生的数学能力非常重要。本研究调查了 9 年级普通教育数学教师自我报告的以概念为中心的教学 (CFI) 和以过程为中心的教学 (PFI) 的使用是否与 2.5 年后九年级学生的代数成绩存在不同的相关性，具体取决于学生的数学难度（MD）状态。本研究的数据取自 2009-2010 年和 2011-2012 年的高中纵向研究（N = 19,104）。多元回归分析表明，参加 9 年级数学课堂的 MD 学生（教师自我报告使用较少的 CFI 和较多的 PFI）与 2.5 年后更高的代数成绩呈正相关。相反，在数学教师自我报告使用更多 CFI 和更少 PFI 的课堂上，没有 MD 的学生在 2.5 年后与更高的代数成绩呈正相关。然而，本研究的结果并不表明教师在教授 MD 学生时应忽视 CFI 而仅提供 PFI。由于数据集不包含任何变量来发现教师是否为患有 MD 的学生提供了足够的支持（即基于证据的实践），与没有 MD 的学生相比，他们的认知技能受到更多限制，从而从 CFI 中受益，研究结果应谨慎解释本研究的内容。讨论了未来研究的方向和实际意义。