A semi-automatic alignment method for math educational standards using the MP (materialization pattern) model

Educational standards alignment, which matches similar or equivalent concepts of educational standards, is a necessary task for educational resource discovery and retrieval. Automated or semi-automated alignment systems for educational standards have been recently available. However, existing systems frequently result in inconsistency in interpreting a correct alignment or give only a “yes” or no” Boolean decision for alignment. In this research, we present a novel semi-automatic alignment method for math educational standards that goes beyond simple Boolean decision making. Our approach gives seven different degrees of alignments: Strongly Fully-aligned (SFA), Weakly Fully-aligned (WFA), Partially-aligned*** (PA***), Partially-aligned** (PA**), Partially-aligned* (PA*), Poorly-aligned (PR), and Not-aligned (NA). We aim to clarify and extend the notion of alignment for math educational standards, and to broaden categories of resource discovery and retrieval. First, we propose the MP (Materialization Pattern) model for representing the semantics of math educational standards for the purpose of aligning these standards. The MP model captures the semantics of English sentences used in math educational standards based on the Reed-Kellogg sentence diagram. We develop a semi-automatic tool, MPViz, for creating the MP model using the UML notation. The MPViz also converts an MP diagram to two graphs—a verb-phrase graph and a noun-phrase graph—which facilitate the process of automatic alignments. We align math educational standard statements using graph matching with the Bloomtaxonomy, the WordNet, and taxonomies of math concepts. We also develop a semiautomatic tool, MPComp, for aligning math educational standards. This dissertation describes a novel semi-automatic alignment method that utilizes the MP modeling and graph matching. Our experiments show that our alignment method provides the result that is comparable to human judgment. The contributions of our alignment method are as follows: 1) We propose the MP model that can explicitly model the semantics of English sentence structures used in math educational standards; 2) Using the MP model we develop a semi-automatic alignment method that produces seven different degrees of alignments, instead of simple Boolean decisions in existing alignment systems; 3) The multiple degrees of alignments empower education professionals by broadening categories of search or retrieval for educational resources.Ph.D., Information Science and Technology -- Drexel University, 201