The area of mathematical psychology concerning knowledge spaces is complemented by the theoretical notion of a “curriculum space,” which is developed as a mathematical model for curriculum design in order to illuminate the interplay between learners and the curricula in which they enroll. The analysis is carried out in terms of concepts from graph theory and order theory, yielding a precise language in which to communicate aspects of curricular influences on student-achievement. Emphasis is placed on the structure of tasks that are addressed in a curriculum, the structure of prerequisite-course assignments within the curriculum, and the compatibility between these structures. Among the main results, conditions are given under which the tasks in a curriculum induce a partially ordered set, curricula that admit “compatible” prerequisite-structures are completely characterized, and a greedy algorithm is presented for categorizing courses into “curriculum maps” that respect the compatibility condition.

与知识空间有关的数学心理学领域被“课程空间”的理论概念所补充，“课程空间”被开发为课程设计的数学模型，目的是阐明学习者与他们所报读的课程之间的相互作用。分析是根据图论和顺序论的概念进行的，产生了一种精确的语言，可以用来传达对学生成就产生的课程影响方面。重点放在课程中要解决的任务的结构，课程中前提课程分配的结构以及这些结构之间的兼容性上。在主要结果中，给出了课程中的任务诱发部分有序集合的条件，