• Journal of Computing Science and Engineering
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• v.10 no.3
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• pp.85-94
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• 2016

We propose a model-based method for information alignment using educational standards as a case study. Discrepancies and inconsistencies in educational standards across different states/cities hinder the retrieval and sharing of educational resources. Unlike existing educational standards alignment systems that only give binary judgments (either "aligned" or "not-aligned"), our proposed system classifies each pair of educational standard statements in one of seven levels of alignments: Strongly Fully-aligned, Weakly Fully-aligned, Partially-$aligned^{***}$, Partially-$aligned^{**}$, Partially-$aligned^*$, Poorly-aligned, and Not-aligned. Such a 7-level categorization extends the notion of binary alignment and provides a finer-grained system for comparing educational standards that can broaden categories of resource discovery and retrieval. This study continues our previous use of mathematics education as a domain, because of its generally unambiguous concepts. We adopt a materialization pattern (MP) model developed in our earlier work to represent each standard statement as a verb-phrase graph and a noun-phrase graph; we align a pair of statements using graph matching based on Bloom's Taxonomy, WordNet, and taxonomy of mathematics concepts. Our experiments on data sets of mathematics educational standards show that our proposed system can provide alignment results with a high degree of agreement with domain expert's judgments.

• Research in Mathematical Education
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• v.22 no.3
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• pp.153-174
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• 2019

Measuring alignment of various educational components is an important issue in educational research because with aligned educational system, we can have clear expectations about what to teach and assess. In this study, we examined the alignment between mathematics curriculum standards and college entrance examinations from Korea and China. The results indicate that curriculum standards and high stakes assessments from both countries are not well aligned to each other. Their Surveys of Enacted Curriculum (SEC) indices were lower than what previous studies have found and the critical values (Fulmer, 2011; Liu & Fulmer, 2008; Liu et al., 2009). There are several topics that are not assessed in both countries' national assessments. Also, discrepancies between the most frequently covered topics in the curriculum standards and the most frequently assessed mathematical topics in the national assessments caused topic level misalignment. We also found misalignment in cognitive level. Both national assessments included more perform procedures and demonstrate understanding items than their respective curriculum standards. Thus, previous findings about the inclusion of more items with higher cognitive demand in assessments is only partially true for either country. With these results, it is difficult to say that whether mathematical topics in the curriculum standards appropriately represent and support students to do well on the CSAT and the NCEE or that the mathematical items in the CSAT and the NCEE validly assess students' level of mathematical understanding.