Proportional reasoning is the cornerstone of many higher-level mathematics topics. We evaluated the sustainability effects of schema-based instruction (SBI) on proportional reasoning and the impact of professional development (PD) on the instructional practices of two cohorts of seventh-grade teachers (i.e., SBI-experienced-teacher implementers, who taught SBI in a previous study; SBI-novice-teacher implementers, who taught SBI for the first time with PD) and mathematics outcomes of students with mathematics learning difficulties. SBI was implemented for 6 weeks by 49 teachers in two distal states. Despite the cessation of PD provided to SBI experienced-teacher implementers, teachers in both cohorts demonstrated similar levels of fidelity. Results indicated no SBI experience effect on the immediate and 11-week retention tests of proportional problem solving, on a general measure of problem solving, and on an end-of-year mathematics achievement test, suggesting that the effectiveness of SBI generalizes over time to different cohorts of teachers and students.

比例推理是许多高级数学主题的基石。我们评估了基于模式的教学 (SBI) 对比例推理的可持续性影响以及专业发展 (PD) 对两组七年级教师的教学实践的影响（即 SBI 经验丰富的教师实施者，他们教授 SBI在之前的一项研究中；SBI 新手教师实施者，他们第一次用 PD 教授 SBI）和有数学学习困难的学生的数学成绩。SBI 由两个远端州的 49 名教师实施了 6 周。尽管停止向 SBI 经验丰富的教师实施者提供 PD，但两个队列中的教师表现出相似的忠诚度。