Progressive structural analysis for dynamic recognition of on-line handwritten mathematical expressions

Structural analysis in handwritten mathematical expressions focuses on interpreting the recognized symbols using geometrical information such as relative sizes and positions of the symbols. Most existing approaches rely on hand-crafted grammar rules to identify semantic relationships among the recognized mathematical symbols. They could easily fail when writing errors occurred. Moreover, they assume the availability of the whole mathematical expression before being able to analyze the semantic information of the expression. To tackle these problems, we propose a progressive structural analysis (PSA) approach for dynamic recognition of handwritten mathematical expressions. The proposed PSA approach is able to provide analysis result immediately after each written input symbol. This has an advantage that users are able to detect any recognition errors immediately and correct only the mis-recognized symbols rather than the whole expression. Experiments conducted on 57 most commonly used mathematical expressions have shown that the PSA approach is able to achieve very good performance results.

Integrating grammar in adult TESOL classrooms

This paper examines the beliefs and practices about the integration of grammar and skills teaching reported by 176 English language teachers from 18 countries. Teachers completed a questionnaire which elicited beliefs about grammar teaching generally as well as specific beliefs and reported practices about the integration of grammar and skills teaching. Teachers expressed strong beliefs in the need to avoid teaching grammar in isolation and reported high levels of integration of grammar in their practices. This study also examines how teachers conceptualize integration and the sources of evidence they draw on in assessing the effectiveness of their instructional practices in teaching grammar. The major findings for this paper stem from an analysis of these two issues. A range of ways in which teachers understood integration are identified and classified into two broad orientations which we label temporal and contextual. An analysis of the evidence which teachers cited in making judgements about the effectiveness of their grammar teaching practices showed that it was overwhelmingly practical and experiential and did not refer in any explicit way to second language acquisition theory. Given the volume of available theory about L2 grammar teaching generally and integration specifically, the lack of direct reference to such evidence in teachers’ accounts is noteworthy.