The main purpose of this study is to investigate eighth-grade students¡¦ understanding of the equal sign and analyzed error types of quadratic equation in one variable. To achieve this purpose, the investigator did a survey and development instruments. Participants were 215 eighth-grade students who formed a convenient sample. There are three results. First, participants with a relational definition of the equal sign added to about 80% of the sample. Second, the performance of students with relational definitions is higher than the performance of students with operational definitions. Third, students¡¦ understanding of the equal sign was related to their respective problem-solving performance on quadratic equation in one variable. In this study, participants with an operational definition of the equal sign tended to guess randomly or leave a blank. Problem-solving performance of participants with a relational definition of the equal sign involved multiple strategies. The researcher suggested that teachers should strengthen students¡¦ understanding of equal sign and related students¡¦ prior algebraic knowledge.

Abstract The fundamental purpose of this research is to discuss the solution strategies and error types when seventh-grade students in middle school solved simple equations with one unknown and application problems; we hope results can provide reference for teachers in remedial teaching and in improving instructional. The items in the examination paper used in this research were taken from 12 past papers of basic competency test in Taiwan (2001 to 2006, twice a year). The subjects were students from Kaohsiung City Y Middle School (City region), Kaohsiung County T Middle School (Ordinary town) and Pingtung County Z Middle School (Near seacoast) forming a convenience sample. The investigators selected 2 classes from each school by random, with a total of 188 students. The main results of this research are as follows: 1. There are ten questions and the average proportion of correct answers is 49.10%; it shows that, at least 51% students have difficulties in solving symbolic operation and linear equations with one unknown. 2. The solution strategy student used most frequently is Removal of Term. Equal Axiom and Enumeration Evaluation Method were used occasionally. No student used Substitution method, Reduction method and Hidden method. 3. The main error types are: missing knowledge of using symbol; do not understand meanings of symbols; combine dissimilar terms freely; do not understand the meaning of bracket; cannot do calculation involving bracket; and, cannot simplify equation etc. 4. The main reasons for failures are: do not understand the meaning of equation; do not understand combination rules of like terms, position of symbol, unknown variables; whether containing fractions in reducing equation will also cause an error. Keywords: linear equations with one unknown, solution strategies, error types.

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The present study investigates three teacher trainees and three teachers’ views on error correction during oral communication, and the similarities and differences between them. These six people were interviewed separately and they were asked six questions; the first five questions were asked to all six people but the last question differed between the teacher trainees and the teachers. My result shows that the teacher trainees are insecure when it comes to error correction and that the teachers´ sees it as a part of their job, and that is the biggest difference between them. The teacher trainees and the teachers focus on the same types of errors and those are the errors that can cause problems in communication, and that can be pronunciation errors, grammatical errors or vocabulary errors.

The present study aimed to investigate whether students¡¦ error types in word recognition would be contingent upon teaching strategies. Based on the perspectives of feature-matching theory in pattern recognition, it was predicted that, the phonetic compound strategy would reduce the error rate in the recognition of the picto-phonetic character, whereas the radical recognition strategy would lower the error rate in the recognition of the radical character. A quasi-experiment was conducted in which ninety-nine 4th-grade elementary students were assigned to three groups receiving phonetic compound strategy, radical recognition strategy, and distributed recognition strategy respectively. The dependent measures consisted of shape error rate and pronunciation error rate. The results showed that those students who received the phonetic compound strategy exhibited lower shape and pronunciation error rates of the picto-phonetic character than the students who received the distributed recognition strategy. On the other hand, those students who received the radical recognition strategy exhibited lower shape error rate of the radical character than the students who received the distributed recognition strategy. Regarding the interaction of character types and error types within a specific teaching strategy, for those students who received the phonetic compound strategy, the shape error rate of the picto-phonetic character was lower than the pronunciation error rate of the radical character. For those students who received the radical recognition strategy, both the shape and pronunciation error rates of the radical character were lower than those of the picto-phonetic character. The contingent relationships between teaching strategies and error types in word recognition were partially supported by empirical data. Possible reason would be that the pronunciation might produce a more prominent facilitation effect than that of the shape in Chinese word recognition. Finally, implications for teaching strategies in word recognition and directions for future research are also discussed.

本研究的主要目的是探討國一學生在一元一次不等式的錯誤類型，並分析錯誤原因。 本研究的設計採用調查研究法，共分成兩個階段進行，第一階段為準備階段，主要工作為文獻探討、分析國中數學教材、自編「一元一次不等式錯誤類型分析研究」試卷，進行試卷的施測，預試樣本共56名國三學生，抽樣方式非隨機取樣，採方便取樣進行，再由預試結果經修改編製正式施測之試卷。第二階段為正式施測與分析階段，正式施測樣本共30名國一學生，男生12名、女生18名，根據施測結果，依成績分成高分組、中分組、低分組三組，再隨機抽取男女生各2名進行半結構的晤談，以瞭解學生答題的想法，分析學生錯誤的原因。 本研究的主要結果如下： 一、不等式答題表現在文字問題的錯誤比率、空白比率最高。 二、在一元一次不等式的錯誤類型為： （一）同義詞的轉換：1.不等號的同義詞概念；2.不等號的符號認知。 （二）範圍解與圖示：1.數的運算；2.無法判斷範圍解；3.數線的認知；4.不等號的圖示認知；5.不等號的方向。 （三）解不等式：1.不等號改變方向；2.去括號；3.數的運算；4.遺漏或增加符號；5.移項的錯誤；6.等量公理的誤用；7.未化簡；8.不等號概念的錯誤9.多項錯誤；10.抄錯題目或答案；11.胡亂猜測答案。 （四）文字問題：1.無法理解題意；2.列式錯誤；3.三角形面積公式錯誤；4.忽略題目的已知條件；5.答案遺漏或錯誤；6.不等號的概念；7.數的運算；8.多項錯誤9.不等號的同義詞概念。 三、一元一次不等式的錯誤原因：1.先備知識的不足；2.資料使用錯誤；3.新舊學習經驗的互相干擾；4.錯誤的使用運算規則；5.由題目所給數字直接產生答案；6.不清楚題目設計或文字敘述而產生錯誤；7.忽略題目所給條件或答案不夠完備而產生錯誤；8.沒有從離散量概念延伸至連續量概念。 / The main purpose of this study is to investigate “seventh grade students' misconceptions and error types of linear inequalities in one unknown”and analyze the causes of the errors. This study adopts survey research and includes two phases. The first stage is the preparation phase, including literature review, analysis of mathematics textbooks, self-compiled test papers on “misconceptions and error types of linear inequalities in one unknown,” and the pretest. The pretest adopts convenience sampling- totally 56 students from ninth grade. The results were later revised to compile the formal test papers. The second stage is the official survey and analysis phase. The 30 samples are seventh grade students, 12 boys and 18 girls. According to the results of the test, these sample students are divided into three groups-high, medium and low performances. Out of each group, two boys and two girls are randomly sampled and conduct semi-structured interviews to analyze the causes of the errors. The findings of this study are as follows: 1.Most of the errors are due to text problems. 2.Error types of linear inequalities in one unknown are: (1)The conversion of synonyms: a. the concept of synonyms; b. symbolic cognitive. (2)The range of solution: a. calculation; b. to determine the range of solution; c. number line; d. notation of inequality sign; e. direction of inequality sign. (3)Problem-solving in inequality: a. to reverse symbol; b. to remove bracket; c. calculation; d. to omit or add symbols; e. transposition errors; f. isometric axiom errors; g. lack of simplification; h. the misconception of inequality sign; i. multinomial errors; j. to copy wrong questions or answers; k. to speculate answers. (4)Text problem: a. not to understand the questions; b. mistakes in formulating expressions; c. triangle area formula errors; d. to ignore provided conditions; e. omission or wrong answers; f. notation of inequality sign; g. calculation; h. multinomial errors; I. the concept of synonyms. 3.Cause of errors: (1) lack of prior knowledge; (2) to use wrong data; (3) the mutual interference of old and new learning experiences; (4) to use wrong calculating rules; (5) to generate answers from given numbers of the questions; (6) not to understand description of the questions; (7) to ignore the provided conditions or the answers are not complete; (8) not extend to continuous volume.

The hP’ags-pa script was created in the late 13th century (the early Yuan dynasty) which was intended to transliterate all the languages of the Mongol empire such as Tibetan, Uyghur and Chinese into a single writing system. Among all the Chinese hP’ags-pa materials, the primer Bǎijiā xìng 百家姓 [Surnames of the Hundred Families] (BJX) offered us extensive hP’ags-pa syllables and their corresponding Chinese characters. The BJX in hP’ags-pa script has four editions that are currently known to scholars. A careful comparison and examination of the four editions of the BJX text reveals three main types of errors in hP’ags-pa syllables: (1) The misuse of similar-looking letters; (2) Pure clerical errors; and (3) Errors in the transliteration of variant pronunciations. The variant transliterations in the C edition provide some clues to sound changes, including (1) The devoicing of voiced stops and fricatives and (2) The loss of the bilabial nasal coda [m]. Aside from the variant transliterations, the majority of errors are purely graphic and reflect a lack of knowledge about the writing system. An examination of the use of the hP’ags-pa script in the BJX text suggests several potential reasons for the failure of the script to come into common use. These include: (1) A misconception of the nature of the hP’ags-pa writing system; (2) An ineffective learning approach; (3) The discrepancy of phonological categories and phonetic values; and (4) The non-adaptability to the Chinese language.

Abstract The study aims to discuss how English article system is acquired by Mandarin-Chinese speakers at two domains, semantic domain and sentence level, by analyzing oral-story-telling data produced by forty 19-to-20-year old college students in Taiwan (20 males and 20 females), divided into low proficiency and high proficiency levels based on their results of Michigan Listening Comprehension Test. The production data was classified into four semantic types marked by a combination of two universal semantic concepts, specificity and definiteness for the purpose of examining Fluctuation Hypothesis (FH) proposed by Ionin (2004), who argued that L2 access to Universal Grammar by predicting L2 learners without article system will fluctuate between two parameter settings of specificity and definiteness. It is found that overuse of the did occur in [+specificity, -definiteness] contexts where target use is a, particularly for low-level learners. Besides, to closely probe into how L1 Mandarin-Chinese speakers use articles in L2 grammar within Ionin¡¦s framework, a model for linguistic properties marking specificity and definiteness in Chinese was proposed so as to compare the differences between English article system and Chinese classifier system, arguing that the interference of L1 may take place at semantic domain by L1 Mandarin-Chinese speakers. The evidence that the substitution of nage for definite article the in [+specificity, +definiteness] contexts and that of numeral one yige for indefinite article a in only [+specificity, -definiteness] and [-specificity, -definiteness] contexts sheds the light on the possibility of the occurrence of L1 transfer at the semantic domain. As for article use in sentential positions, due to definiteness effect and subject indefinite effect in Chinese, it is predicted that L1 Mandarin-Chinese speakers would drop articles more often in preverbal positions than in postverbal positions. The result showed that low-level learners did drop more articles in preverbal positions than in postverbal positions, but advanced learners showed the contrast, which implies that the beginners are easily governed by the definiteness effect, that is, L1 is at play at the initial state of L2 grammar. Overall, the advanced learners used articles more accurately than the low-level learners did, suggesting that the advanced Mandarin-Chinese L2 English learners may gradually reset the parameter of L2 grammars in acquiring English article system. Furthermore, different error types produced by the participants were classified in the study and provided with theoretical discussion. A surprising finding is that the low-level learners highly misused the Cinderella for Cinderella in the data. Such error production may show the evidence of L2 access to UG since the Cinderella cannot be used in English and there is no determiner the projecting in Chinese proper name. The overuse of the further illustrates the existence of projecting D for L1 Chinese learners. The acquisition rate of article use was measured by SOC (Suppliances in Obligatory Contexts) and TLU (Target-Like-Use). The results showed that the most difficult article use for both proficiency levels is zero article Ø. The advanced learners can use the more accurately than the learners at proficiency level due to the high occurrences of overgeneralization of the by the low-proficiency levels. In general, the result of the current study bears on the issue of accessibility of UG and the possibility of parameter (re-) setting. It is also shown that L1 plays a significant role in L2 article use not only at the semantic domain but also at the sentential level by L1 Mandarin-Chinese speakers, especially for those at the initial state of L2 grammar.

This mixed methods research study centers on learner-learner interactions; thus, contributing to the on-going investigation within negotiation and interaction, computer-mediated-communication and its role in second language learning. The specific aim was to investigate corrective feedback types, incidences, and the relationship between error and feedback type among peers within online synchronous environments in EFL classes in Slovenia, Europe. Interactional characteristics of corrective feedback with learners having a documented special need (SN) also were explored using qualitative analyses. The study encompassed 208 students that were randomly placed into 104 dyads within intact classes of Grades 7, 8, 10, and 11. There were 32 dyads in Grade 7, 16 dyads in Grade 8, 24 dyads in Grade 10, and 32 dyads in Grade 11. Three participants had a documented special need. Quantitative analysis did not reveal statistical significant difference in the incidence of corrective feedb feedback and grade level, the relationship among the type of corrective feedback and grade level, or the relationship between learner error and type of corrective feedback across grade levels. Corrective feedback types were similar to those studied in traditional classroom research (i.e., explicit corrections, recasts, negotiation of form). However, descriptive statistics and qualitative analyses revealed conversational techniques that are specific to text-based online discourses providing insight into interactional characteristics among interactants within a discourse environment that differs both from speech and written texts. Consequently, an additional corrective feedback type emerged from the data, coded as feedback request. The most frequent corrective feedback type provided was explicit corrections. Frequency data revealed that corrective feedback tended to decrease as the grade level increased. Data with SN learners indicated distinctive discourse techniques.Overall, low incidences of corrective feedback and error types might have been affected by the learner's developmental levels, social readiness, and/or psychological readiness (Oliver, 1998), as well as the learner's individual conversational styles and socio-cultural factors. Consequently, further research is warranted in examining these factors. In addition, longitudinal studies are warranted in examining whether online negotiated work lead towards L2 acquisition. Finally, the role of phantom corrective moves when coding qualitative online text data also need to be examined further.

The rapid increase of data volumes makes sampling a crucial component of modern data management systems. Although there is a large body of work on database sampling, the problem of automatically determine the optimal sample for a given query remained (almost) unaddressed. To tackle this problem the authors propose a sample advisor based on a novel cost model. Primarily designed for advising samples of a few queries specified by an expert, the authors additionally propose two extensions of the sample advisor. The first extension enhances the applicability by utilizing recorded workload information and taking memory bounds into account. The second extension increases the effectiveness by merging samples in case of overlapping pieces of sample advice. For both extensions, the authors present exact and heuristic solutions. Within their evaluation, the authors analyze the properties of the cost model and demonstrate the effectiveness and the efficiency of the heuristic solutions with a variety of experiments.