A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated risk for severe MD at kindergarten entry and examined whether these students improved from a category of high MD risk (i.e., <10th percentile) to a lower risk of MD (i.e., norm-referenced performance at or above the 10th, 20th, 30th, and 40th percentiles) between the fall and spring of kindergarten. Differential response to the program based on the classroom-level proportion of students with severe MD was also explored. A total of 795 kindergarteners with severe MD from 122 classrooms were included in the analyses. Results suggested students with severe MD in treatment classrooms improved from fall to spring at a greater rate than their control peers. Treatment students also demonstrated higher rates of improvement from below the 10th percentile to a performance at or above the 20th, 30th, and 40th percentiles across the school year. No evidence of differential efficacy of the program by the classroom-level proportion of students with severe MD was found. Implications for using explicit mathematics programs to thwart the onset of severe MD among academically vulnerable students are discussed.

中文翻译：

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面临严重数学困难风险的幼儿园儿童：调查核心数学教学的临界点

相当数量的学生进入幼儿园时面临着难以处理的数学困难 (MD)。本研究调查了明确的核心幼儿园数学课程对幼儿园入学时表现出严重 MD 风险的幼儿园儿童数学成绩的影响，并检查这些学生是否从高 MD 风险类别（即 <10%）改善到幼儿园秋季和春季之间发生 MD 的风险较低（即，常模参考表现处于或高于第 10、20、30 和 40 个百分位数）。还探讨了基于课堂水平的严重 MD 学生比例对该计划的不同反应。来自 122 个教室的 795 名患有严重 MD 的幼儿园儿童被纳入分析。结果表明，治疗教室中患有严重 MD 的学生从秋季到春季的改善速度高于对照组。在整个学年中，接受治疗的学生从低于 10% 到达到或高于 20%、30% 和 40% 的表现也表现出更高的改善率。没有证据表明该计划在课堂级比例的严重 MD 学生中存在差异。讨论了使用明确的数学程序来阻止学业弱势学生发生严重 MD 的意义。没有证据表明该计划在课堂级比例的严重 MD 学生中存在差异。讨论了使用明确的数学程序来阻止学业弱势学生发生严重 MD 的意义。没有证据表明该计划在课堂级比例的严重 MD 学生中存在差异。讨论了使用明确的数学程序来阻止学业弱势学生发生严重 MD 的意义。