• School Mathematics
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• v.12 no.4
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• pp.605-617
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• 2010

This study explores the characteristics and roles of non-textual elements in secondary mathematics textbooks in the United States and South Korea, using a conceptual framework that I have developed: variety, contextuality, and connectivity. Analyzing five U.S. standards-based textbooks and 13 Korean textbooks, this study shows that although non-textual elements in mathematics textbooks are free of literal language, they exhibit different emphases and reflect assumptions about what is important in learning mathematics and how it can be taught and learned in a particular societal context (Mishra, 1999; Zazkis & Gadowsky, 2001). While there are similar patterns in the use of different types of non-textual elements in textbooks from both countries, different opportunities are provided for students to learn mathematics between the two countries.

• Research in Mathematical Education
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• v.23 no.4
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• pp.181-217
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• 2020

This study explores how pre-service teachers (PSTs) view, interpret, and utilize non-textual elements (NTEs) in mathematics curriculum. Fifty-two PSTs, who enrolled in a mathematics methods course at a Midwestern university in the U.S., engaged in a three-part task that consisted of evaluations and modifications of NTEs in the sample mathematics curriculum materials. We ascertain what PSTs consider to be the strengths and weaknesses of NTEs, how they define the primary goals of NTEs, and how they would work to modify or adapt existing NTEs with effective teaching in mind. By using the Curricular Noticing Framework, we can better understand how PSTs recognize opportunities within mathematics curriculum and gain a deeper understanding regarding how PSTs' prior experiences may affect their curricular-attending habits, which has consequences for their future teaching. Findings indicate that PSTs understand NTEs to be simply a support for traditional mathematics curriculum, rather than tools on their own. Also, they tend to prefer NTEs that are familiar to them. From our findings, we draw implications for teacher educators who support PSTs' interpretation and utilization of NTEs.

• Korean Journal of English Language and Linguistics
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• v.4 no.2
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• pp.117-149
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• 2004

The paper is to argue against the asymmetric CP-V2 analysis of Old English, according to which finite verbs invariably undergo movement into a clause-final T within subordinate clauses and reach the functional head C within main clauses. The asymmetric CP-V2 analysis, first of all, faces difficulty in explaining a wide range of post-verbal elements within subordinate clauses. To resolve the problem, the analysis has to abandon the obligatoriness of V-to-T movement or introduce various types of extraposition whose status is dubious as a legitimate syntactic operation. Obligatory V-to-T movement in Old English lacks conceptual justification as well. Crosslinguistic evidence reveals that morphological richness in verbal inflection cannot entail overt verb movement. Moreover, the operation is always string-vacuous under the asymmetric CP- V2 analysis and has no effect at the interfaces, in violation of the principle of economy. The distribution of Old English finite verbs in main clauses also undermines the asymmetric CP-V2 analysis. Conceptually speaking, a proper syntactic trigger cannot be confirmed to motivate obligatory verb movement to C. The operation not only gets little support from nominative Case marking, the distribution of expletives, or complementizer agreement but also requires the unconvincing stipulation that expletives as well as sentence-initial subjects result from string-vacuous topicalization. Finally, textual evidence testifies that Old English sometimes permits non-V2 ordering patterns, many of which remain unexplained under the asymmetric CP-V2 analysis.

• Journal of English Language & Literature
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• v.56 no.6
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• pp.1047-1065
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• 2010

English inversion constructions are not only hard for non-native speakers to learn but also difficult to teach mainly because of their intriguing grammatical and discourse properties. This paper addresses grammatical issues in learning or teaching the so-called 'predicate inversion (PI)' construction (e.g., Equally important in terms of forest depletion is the continuous logging of the forests). In particular, we chart the grammatical (distributional, syntactic, semantic, pragmatic) properties of the PI construction, and argue for adata-driven teaching for English grammar. To depart from the arm-chaired style of grammar teaching (relying on author-made simple sentences), our teaching method introduces a datadriven teaching. With total 25 university students in a grammar-related class, students together have analyzed the British Component of the International Corpus of English (ICE-GB), containing about one million words distributed across a variety of textual categories. We have identified total 290 PI sentences (206 from spoken and 87 from written texts). The preposed syntactic categories of the PI involve five main types: AdvP, PP, VP(ed/ing), NP, AP, and so, all of which function as the complement of the copula. In terms of discourse, we have observed, supporting Birner and Ward's (1998) observation that these preposed phrases represent more familiar information than the postposed subject. The corpus examples gave us the three possible types: The preposed element is discourse-old whereas the postposed one is discourse-new as in Putting wire mesh over a few bricks is a good idea. Both preposed and postposed elements can also be discourse new as in But a fly in the ointment is inflation. These two elements can also be discourse old as in Racing with him on the near-side is Rinus. The dominant occurrence of the PI in the spoken texts also supports the view that the balance (or scene-setting) in information structure is the main trigger for the use of the PI construction. After being exposed to the real data and in-depth syntactic as well as informationstructure analysis of the PI construction, it is proved that the class students have had a farmore clear understanding of the construction in question and have realized that grammar does not mean to live on by itself but tightly interacts with other important grammatical components such as information structure. The study directs us toward both a datadriven and interactive grammar teaching.