• 検索結果がありません。

Student Evaluating an Online Lunchtime Foreign Culture Course in ITM

N/A
N/A
Protected

Academic year: 2022

シェア "Student Evaluating an Online Lunchtime Foreign Culture Course in ITM"

Copied!
12
0
0

読み込み中.... (全文を見る)

全文

(1)

Student Evaluating an Online Lunchtime Foreign Culture Course in ITM

Robson, GRAHAM

Abstract

The Faculty of International Tourism Management (ITM) has been active in promoting English education in its curriculum. A recent additional to that curriculum has been the adoption of out of class work, a point system designed to make first year students more autonomous and develop their interest in English. As part of out of class work, the ITM English teachers have worked to create a series of culture-based lectures. Due to the pandemic, these four foreign culture-based lectures were delivered via a pre-recorded live premier online through YouTube. This study sets out to address the attitudes and academic approaches of students toward these lectures. In the autumn 2020 semester, 126 first years who attended the live version of at least two of these lectures responded to a 20-item questionnaire. The results show very positive feedback towards the lectures, and the author concludes with factors affecting the success of these lectures.

Introduction

The Faculty of International Tourism Management (ITM) has been active in promoting English education in its curriculum. This is important to work towards the global goals set by Toyo University, after becoming a recipient of Super Global funds from the Japanese Ministry of Education. Part of this commitment involves work outside the classroom, partly because of the lack of time allotted to compulsory English in the curriculum, but also to foster both autonomy in the faculty’s learners, as well as a fascination for foreign cultures outside of Japan. The latter along with ability to deal with different situations, and strong English proficiency, are three needs recognized by the Japanese government that go towards the creation of international human resources (グローバル人材, Global Human Resource Development Committee (2010)).

One project that the ITM has embarked on over the past two years is its out of class work. This has been part of a first year English Communication class as an additional 10% credit, requiring students to submit ten pieces of work they have undertaken outside the class, such as watching Ted Talks, or using apps to study English. Part of out of class work has also been the creation of lunchtime sessions. (hereafter referred to as LS). Again, the goal of LS is to provide a means for ITM students to engage with English outside of class by listening to lectures provided by faculty English teachers. LS exist for first and second years, the latter have an opportunity to increase their overall grade score for compulsory

(2)

English classes in the second year by attending a number of these lectures.

Due to the Corona pandemic situation, and avoiding face-to-face classes, the first- and second-year’s LS were moved online. For the first years, the focus of this paper, there were four lunchtime sessions provided, roughly around the pace of once every two weeks during the autumn 2020 semester. His paper will outline the LS, provide a rationale for their implementation, and report on results of a survey of what first year students that took part in the sessions thought about them.

What are the LS?

For the LS in the autumn 2020 semester, teachers provided culture-based lectures lasting around 40 minutes on topics such as the English language, Hawaiian culture and cultural appropriation in English.

These videos were streamed live through YouTube. This platform was chosen as it allows a maximum number of students to watch the session at once, a problem inherent in systems available through the university intranet. Teachers pre-recorded their talks on PowerPoint and added voiceover and subtitles before the videos received their premiers. They were further advertised in class and on the university intranet system, encouraging student participation. Students who attended could receive both TGL points (a university-wide system recognizing efforts in English study) based on the number of sessions they attended, and could also write a report based on a question posed by the presenter in the presentation that could go towards credit for out of class work. During the presentation, presenters were logged into a YouTube channel offering extra information through the chat function, and fielding any questions from students (students needed to login into a Google account to post questions to the presenter). Finally, the videos were left on the intranet system so students who did not attend the premier could watch them (and enjoy them and / or use them to write reports).

Rationale for LS

When looking for reasons why students are drawn to attend seminars outside of the class, it is necessary to investigate the underlying motivational constructs that could lead students to engage in or avoid such situations. One of the main models that addresses motivation in second language is Self- Determination theory (SDT). This theory looks at how different types of motivation are derived from the reasons or goals that bring forth a particular action. The main distinction in SDT theory is between Intrinsic Motivation, or goal-oriented behavior that involves doing something because it is inherently interesting or enjoyable,” and Extrinsic Motivation, which is goal-oriented behavior characterized by

“doing something that leads to a separable outcome” (Ryan & Deci, 2000, p. 55). Studies in Japan have also shown that the SDT theory is both viable and inherent in student goals (Kimura, Nakata &

Okumura, 2001; Ogane & Sakamoto (1999) and Otoshi & Heffernan, (2011). Whatever the motivation students have for attending the LS needs to be identified.

Along with motivation, students need a modicum of autonomy. Being that students are not in the

(3)

classroom, and away from supervision of the teacher, students need to be responsible enough to attend.

In second language research, learner autonomy has been defined as an ability to take charge of one’s own learning”, and to and to have “the responsibility for all the decisions concerning all aspects of this learning, (Holec 1981, p.3). Inherent in this responsibility are the capacity for applying metacognitive abilities like to reflecting, monitoring, and planning, (Holec 1981; Little, 2006) and also an affective dimension (Little, 2006), as well as attitudes towards taking responsibility for learning (Dickinson, 1993.)

The above studies work on the assumption of learner autonomy having perceived importance in the context of second language setting, but in the context of foreign language settings the view of autonomy may be different from the image espoused from Europe and the West. Littlewood (2000) makes the point that different pedagogies should be established for different learning contexts. In Asian countries like China and Japan, education demands obedience, deference to authority (p.31). On top of this, Herriman (2007) cites problems of learning English through the medium of Japanese, and because of the concentration on grammar study with in learning English, English becomes something to be studied, and not used. Herriman adds that the “… teacher is the expert and students perceive the situation in this way and expect it to be that way” (p. 144). On the face of it, these situations appear to provide little leeway for autonomy.

Rather than reject outright the notion of autonomy in Asia, some researchers like Littlewood (1999) have begun to rethink the concept. He believes that Japanese have the same capacity for autonomy as their western counterparts, but he makes a distinction between proactive autonomy, which is espoused in the West and consists of learners setting goals, selecting methods and making personal agendas, and reactive autonomy that does not mean learners set their own directions, but once direction is initiated, learners can organize resources to reach learning goals (p. 75). This can include such learner activities as learning new vocabulary through a phone application or taking part in the LS. In a study at ITM, Hardy (2017) found that students display autonomy provided that the teacher sets the basic overall aims of assignments like projects,

The topic of the lunchtime sessions can be described loosely as cultural, with each teacher introducing something from their own culture. When teaching culture to non-natives, Seelye’s (1988) identifies seven goals. These include helping raise students awareness of conventional behavior exhibited in the target culture and to generate interest about the target culture with the goal of fostering empathy for people in that target culture. Both of these goals are kept in mind, particularly, the second one, when designing materials for the LS.

Further, it is hoped to wean students off the printed word, and have them become more used to accessing technology. Technology, through Internet platforms like YouTube, provide students with authentic materials to watch and connect with at their free will. As Japan moves slowly towards globalization, integrating culture into students’ learning is seen as an important second and foreign language learning goal (Thanasoulas, 2001), so it is worthwhile adding this element to the ITM curriculum via popular platforms like YouTube.

(4)

To add to the previous point, Japan is the midst of a pandemic, so face-to-face lessons cannot be relied upon to facilitate LS. The YouTube format allows easy access for any students who wants to watch the sessions. Further, these sessions were recorded offering authentic texts for students to listen to afterwards. This is particularly important as students should be exposed to language that they meet in the real world as much as possible (Rogers & Medley, 1988). So it can be said that the use of authentic materials can be very motivating for students as it provides a link to the outside world (Edge, 1996).

Native speakers take it for granted to watch movie or dramas over an extended period of time, something that non-native speakers find incredibly difficult to do.

To aid comprehension, teachers recorded their own videos texts for the sessions. In this way, the teachers could adjust their talking by speaking slower, and offering repetition where students might have some difficulty understanding. Indeed, some see the way that teachers talk as paramount to student comprehension (Walsh, 2002). Having teachers use authentic materials helps to engage students in authentic cultural experiences. And using videos that show culture from other countries has the dual benefit of being entertaining but also being beneficial for language learning. This paper has set the following research questions:

1. What are student attitudes and approaches toward the LS?

2. What other factors affecting the success of LS?

Methods

Participants

To answer the research questions, this survey employed a survey of first years who took the English Communication course in the autumn semester of 2020, and were thus; required to do out of class work, with lunchtime session being one way for students to collect points for that system. Students who had attended at least two of the four live events were identified and approached as they would be representative of good practice as far as taking part in the sessions went. There were 126 participants in this study, coming from a variety of proficiency levels within the English Communication course as determined by a TOEIC listening score from the start of April 2020.

Instrument

The survey in this paper consists of 20 items divided into four main sections. The first section deals with the content, the second with how students approached the LS, the third relates to motivational issues surrounding the LS and the last section deals with miscellaneous items connected to LS the author wanted to check at the time of researching. The items were both designed from scratch and revised from other studies (Otoshi & Hefferman, 1999; Hardy, 2017). The students were required to choose one of four responses that best described their position. Each statement requires one of four levels of agreement (from strongly disagree to strongly agree), with no middle option. There was also one open item (11b).

To generate this survey, the author first created it in English and with the support of a Japanese colleague

(5)

translated those items into Japanese. The version seen by the students is in Appendix A.

Procedure

The request for undertaking the Japanese version of the questionnaire was sent to those students identified as having taken part in more than two LS around the tenth week of the autumn semester 2020. This was after the last of the four lunchtime sessions had finished. The purposes were explained along with the survey and it was further stated that the data were for research purposes and that students decision to take the questionnaire was voluntary and would in no way affect their grades. The survey was removed two weeks later in week 12 of the semester.

As well as recording the means of the 20 items, further analysis addressed differences between the lower and higher halves of the data set, as determined by their TOEIC listening scores. The decision to concentrate on differences between the groups with differing listening abilities was made to establish how students in differing English ability groups approached the task and what they thought about the LS. The differences were determined by a percentage value between lower and higher data sets, and those greater than +/-8% were included in the results.

Results

The results are presented in the four sections from the survey.

Content Issues of LS

The results in the first section are encouraging as seen in Table 1. Students were able to follow the pace of the videos, and mainly understood the content. Surprisingly, there were no differences between the upper and lower group on item 2. Students did well despite the use of no Japanese in the videos. All the presenters spoke at a slower pace, with lots of repetition and highlighting of key words and points, making comprehension easier for students. Lastly, on the whole, students found the content to be authentic, an important criterion for cultural topics. Interestingly, the lower level believed it was more authentic than the higher level, a result which seems to suggest that the content was somehow more applicable to students in that group.

Table 1. Content issues of LS (n=126)

Item M

1 I found the pace of the LS to be appropriate 3.25

2 I mostly understood the content of the LS 2.92

3 I felt the English I listened to in the lunchtime session was authentic 3.25 L>H

(6)

Participants’ approach to LS

The results for this section are seen in Table 2, and these deal with how students engaged with the LS.

Items 4 and 5 deal with the use of captions. One the amendments that was made to each video was the availability of captions. It required students to click a button to bring them up, and most students followed those instructions, and indeed, the captions made the videos easier to understand.

Table 2. Participants approach to LS (n=126)

Item M

4 I used the captions / subtitles when watching the LS 3.33 5 The captions / subtitles helped my understanding of the LS 3.52 6 I watched the recorded version as well as watching the live version 3.14 H>L 7 While listened I tried to take notes as often as possible? 3.05 H>L 8 I checked unknown words I encountered during the LS 2.79 H>L 9 I submitted a report for out of class work after for each LS 2.98 H>L 10 I posted a question to the presenter during the LS 1.21 11a I wanted to post a question to the presenter during the LS 2.05 H>L 11b Please supply more details about your 11a answer

Item 6 shows that students are also taking advantage of watching videos after the live event. It would be good to think that students are using this opportunity to recheck information to deepen their understanding and to enable them to write reports. Items 7 and 8 show, that on the whole, respondents have a reasonable level of study skills: taking notes and checking unknown words. Item 9 also recorded high results and appeared to show that students are working to understand the video so they can submit in report form for out of class points. However, there was a clear difference between higher and lower groups on items 6-9. It appears that the higher level data set are approaching this session in a manner in line with the expectations associated with this kind of activities more so than the lower data set.

The last three items 10, 11a and 11b address students posting questions to the speaker. It was hoped students would post questions to make the sessions livelier, to increase their own knowledge, give support to the presenter and as a way of creating learner autonomy. However, very few actually posted in any of the sessions, and 11a results show there was little wish to do so. Table 3 reveals why students did not post questions. The highest number of instances was that following the videos was difficult enough and students did not have time or ability to post a question. This might explain the difference between lower and higher groups for this item. Also featuring high were technical issues such as not having a YouTube (Google) account enabling the holder to post. The next two results are a little discouraging in that given the opportunity students could not think of or did not want to post a question.

It was expected that students’ interests would be peaked by the topics and lead them to find out more.

Other significant results show reasons related to not having a clear enough understanding of the video, and cultural issues such as the feeling of embarrassment in posting a question that others would see.

(7)

Table 3. responses given to question 11B - (n=118)

Approximate responses No. of instances

Difficult to post and concentrate at same time 36

No YouTube account 18

Could not think of question 27

Did not want to ask question 11

Understood enough to not ask question 12

Feeling of embarrassment 9

Did not login to a google account 4

did not know how to 4

Privacy issue 3

Did not like content 2

Busy eating lunch 2

Motivation surrounding LS

The third section focuses on motivation for the LS as is shown in Table 4. The first encouraging result is that students are taking part in the LS events to both learn about other cultures and increase their knowledge. Still also high in endorsement was to challenge students’ English. The other alternative of attending LS merely to get credit was lower showing that students have less of a need to satisfy externally imposed goals and instead may have more goals attached to personal development. Lastly, also as encouraging is the desire to take part in something resembling LS in the second year.

Table 4. motivation issues surrounding LS (n=126)

Item M

12 I was interested to learn more about other cultures through LS 3.36 13 My main motivation for joining the LS was to gain credit 2.56 14 My main motivation for joining the LS was to challenge my English

comprehension 3.06

15 My main motivation for joining the LS was to increase my knowledge 3.24 16 I would like to take part in similar LS in the future 3.08

Other issues related to LS

The last section is a collection of miscellaneous items. First, the item 17 result appears to show that teachers have been active in promoting the LS in class. Although information does appear on the school intranet introducing each event, the teacher is pivotal in pushing students to attend. The next item seems to mirror results for item 12 that shows how important students think learning about other cultures is.

Item 19 saw somewhat of different between higher and lower groups in the regular submission of out of class activities in general. Not only LS, but other activities like watching YouTube give students an interesting variety of activities that caters to different tastes and learning styles. However, lower level learners in this data set are less regular with their submission it seems, so some action is required in

(8)

making students see the benefit of regular progress in English. The last item is a little disappointing and seems to show that students have not been so proactive in attending other events. This may be as a result of fewer events being held because of the pandemic, or that students are not getting information in the correct way, but it could also be apathy in attending such events.

Table 5. Other issue related to LS (n=126)

Item M

17 My teacher promoted the LS in class 3.58

18 Adding foreign culture into the ITM curriculum is important 3.33 19 I usually submit regular work for the out of class activities other than the LS 2.90 H>L

20 I attend other events / lectures organized by ITM 1.94

Discussion

From the results, the research questions can now be addressed:

1. What are student attitudes and approaches toward the LS?

For the sample in this study, it appears respondents have positive attitudes towards the LS, believing them to be both authentic and interesting. However, this sample does not account for all the 374 students in the first year. Students in this sample attended at least twice, another 100 students at least attended once, and the number of views on the video left on the intranet after each session, reached between 100- 300 views. It’s clear that even if students are not watching the LS live, they are consuming them in some way.

Generally, the students were also interested in studying foreign culture, and were intrinsically motivated to watch the sessions as shown by the result showing the main purposes for watching were for increasing knowledge and challenging English and less so for merely attaining credit. Having intrinsically-motivated students is very important in an English program, and events similar to these need to be further offered to cater to different tastes. However, as Robson (2015) discovered far from extrinsic motivation producing negative consequences, it might be a necessary reality for Japanese students as they enter the Japanese job market after graduation.

Lastly, these events, and the out of class work in general are used to develop English ability, an interest in other cultures and also to build autonomy. It is hoped that helping students to find ways of enjoying English is important in helping to build a deeper connection with English. However, it is clear that work need to be done to engage student’s autonomous learning. It is very well to keep leading students to English, but at some point students need to take the initiative themselves and seek out ways to enjoy English on their own. Scholars have stated developing autonomous learning could be one of the most important goals in the educational field (Sakai & Takagi, 2009). To this end, behaviors that are encouraged in class can go a long way to promoting autonomy. One such behavior is reflection, a

(9)

process in which learners reassess learning habits (Benson, 2013). Currently, students write reports after the LS, and as part of this, students should be encouraged to share their feelings about how they did and how they could do better in both written reports and class discussions. These actions may help to engage the students more in the process of learning.

2. What other factors affecting the success of LS?

Through this study a number of factors have come to light that can affect the success of LS. Firstly, the technology of YouTube allows for captions that make comprehension better. It also helps that all of the speakers spoke slower and used repetitions. No Japanese was used at all in the LS. If students can comprehend these, it could be motivating for them. Further, lessons learned from the changes in teaching delivery style due to the recent pandemic have shone a spotlight on the utility of online lessons, a result found by the author in a study of student’s reactions to online learning during the 2020 pandemic (Robson, 2021). These events don’t require students to attend en mass, with students consuming the content potentially anywhere. This offers a new avenue for effective English language education within the faculty.

Further, skills necessary to take part successfully in LS and indeed for general academic use need to be better isolated and highlighted in regular classes. Note taking and asking questions are very important skills to develop at universities. It is clear that the teachers who promote these events have already bought into the idea. More work is needed in creating optimal conditions for students to benefit further from the LS.

Lastly, these kind of events would not come into effect without the continued support of the English teachers in ITM. Having teachers that understand the benefit of these events, offer their time to give lectures for these events and promote them in their classes is invaluable. It is essential that English teachers in ITM understand their value in promoting English language education.

Conclusion

The results from this study appear to show that the initial purpose of creating LS to increase interest and motivation in English and foreign culture has been met with some success. It is important for students at Japanese universities, and more so ITM students, to develop an understanding of foreign culture as the Japanese inbound tourism market waits for a return to an increase in numbers. However, caution must be taken to not offer the LS without some kind of academic support. Students must understand the need for asking questions, and developing better study skills with any opportunity to interact with English at ITM. The faculty in turn must create more chances for our students to find interesting and relevant content, not just during this pandemic, but for the long-term future.

References

Benson, P. (2013). Teaching and researching autonomy (2nd ed.). New York: Routledge.

(10)

Dickinson, L. (1993). Talking shop: aspects of autonomous learning. ELT Journal, 47 (4), pp. 330-336. doi: 10.1093/ elt/47.4.330

Edge, J. (1996) Essentials of English language teaching. Longman, London

Global Human Resource Development Committee of the Industry-Academia Partnership for Human Resource Development (2010). Develop global human resources through industry-academia-government. Ministry of Economy, Trade and Industry.

Hardy, D. (2017). Measuring the effect of learner attitude and autonomous learning through increasing extracurricular homework tasks. Toyo University Journal of Tourism Studies, 16, 79-95.

Herriman, M. (2007). Autonomous learning in EFL in Japan. The International Journal of Learning. Vol. 14(5), pp. 141- 147. doi: 10.18848/1447-9494/CGP/v14i05/45340

Holec, H. (1981). Autonomy and foreign language learning. Oxford: Pergamon.

Kimura, Y., Nakata, Y., & Okumura, T. (2001). Language learning motivation of EFL learners in Japan: A cross-sectional analysis of various learning milieus. JALT Journal, 23(1), 47-68. Retrieved December 12, 2014, from http://jalt- publications.org/archive/jj/2001a_JJ.pdf#page=47.

Little, D. (2006). Learner autonomy: Drawing together the threads of self-assessment, goal-setting and reflection. ELT Journal. Available from http://archive.ecml.at/mtp2/Elp_tt/Results/DM_layout/00_10/06/06%20Supplementary%20 text.pdf

Littlewood, W. (1999). Defining and developing autonomy in East Asian contexts. Applied Linguistics, 20(1), 71-94. doi:

10.1093/applin/20.1.71

Littlewood, W. (2000). Do Asian students really want to listen and obey? ELT Journal, 54 (1), 31-36.

Ogane, E., & Sakamoto, M. (1999). SEM: relationships among EFL motivation and proficiency factors. In A. Yamashiro (Ed.), TUJ Working papers in applied linguistics–Individual differences in the EFL Context. TUJ: Tokyo, Japan.

Retrieved November 13, 2012, from

 http://www.tuj.ac.jp/tesol/publications/working-papers/vol-14/oganeetal.html.

Otoshi, J., & Heffernan, N. (2011). An analysis of a hypothesized model of EFL students motivation based on self- determination theory. Asian EFL Journal, 13(3), 66-86. Retrieved May 11, 2012, from

 http://www.asian-efl-journal.com/PDF/September-2011.pdf.

Robson, G. (2021). Researching student attitudes of Online class amid Covid-19. Journal of Tourism Studies. Vol 20. Robson, G. (2015). A model of situational constructs accounting for willingness to communicate at a Japanese university.

[Unpublished doctoral dissertation]. Temple University: Tokyo, Japan.

Rogers, C. V., & Medley, F. W. (1988). Language with a purpose: using authentic materials in the foreign language classroom. Foreign Language Annals, 21,(5) 467-478. Doi: 10.1111/j.1944-9720.1988.tb01098.x

Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivation: Classic definitions and new directions. Contemporary Educational Psychology, 25, 54-67. doi:10.1006/ceps.1999.1020

Sakai, S., & Takagi, A. (2009). Relationship between learner autonomy and English language proficiency in Japanese learners. The Journal of Asia TEFL, 6(3), 297-325.

Seelye, H. N. (1988). Teaching Culture. Lincolnwood, IL.: National Textbook Company.

Thanasoulas, D (2001). The Importance of teaching culture in the foreign language. ICAAP(3), 3. Available at https://

radicalpedagogy.icaap.org/content/issue3_3/7-thanasoulas.html

Walsh, S. (2002). Construction or obstruction: teacher talk and learner involvement in the EFL classroom. Language Teaching Research,6(1), 3-23. doi 10.1191/1362168802lr095oa

(11)

Appendix A

(1)全くそう思わない (2)あまりそう思わない (3)そう思う (4)とてもそう思う 1 ランチタイムセッションの進め方が適切だと思う

2 ランチタイムセッションの内容はほぼ理解が出来た 3 ランチタイムセッションの英語は本格的だと感じた

4 ランチタイムセッションを見ている最中キャプション・サッブタイトル(字幕)を見た

5 キャプション・サッブタイトルを見ることによってランチタイムセッションへの自分の理解が深 まった

6 オンデマンド(ライブ)のランチタイムセッションを見たが、後日録画したものをもう一度みた 7 ランチタイムセッションを見ている間、出来るだけ内容をメモした

8 ランチタイムセッションを見ている間、後に知らない単語の意味を調べた 9 ランチタイムセッションのクラス外活動用のレポートを毎回提出した 10 ランチタイムセッションの時にプレゼンターに(チャットで)質問した 11a ランチタイムセッションの時にプレゼンターに質問したかった

11b 11aについての詳細(しなかった理由を述べて)

12 ランチタイムセッションを通じて異文化についてもっと興味を持った 13 ランチタイムセッションに参加する主な理由は成績のためだった

14 ランチタイムセッションに参加する主な理由は英語の理解より深める為だった 15 ランチタイムセッションに参加する主な理由は知識を高める為だった

16 将来ランチタイムセッションのような行事に参加したい 17 先生にランチタイムセッションの参加を授業中に勧められた 18 異文化を国際観光学部のカリキュラムに導入入れるべきです 19 ランチタイムセッション以外のクラス活動は定期的自己します 20 国際観光学部が行っているイベントやセミナに参加します

(12)

国際観光学部でのお昼休み中の

オンライン異文化プログラムの学生による評価について

ロブソン・グライアム

[要旨]

国際観光学部はカリキュラムにおいて英語教育を積極的に推進している。近年、カリキュラムに はクラス外活動の取り組みが含まれるようになった。クラス外活動にはポイントシステムが採用さ れ、新入生を自律的な学習者にさせ、英語に関心を持たせる試みが導入されている。クラス外活動 の一環として、国際観光学部の教員は、異文化に関する一連の英語の講義を行っている。パンデミ ックにより、これらの講義は事前に録画され、YouTube でオンライン配信された。本研究はこれ らの講義に対する学生の態度やアプローチに関して分析したものである。2020 年の秋学期にこの オンライン講義に少なくとも 2 回参加した 126 名の学生が質問紙調査に回答した。結果は、学生は 講義に対して非常に好意的な態度を示していることがわかった。著者は、これらの講義の成功のさ まざまな要因について検討した。

参照

関連したドキュメント

pole placement, condition number, perturbation theory, Jordan form, explicit formulas, Cauchy matrix, Vandermonde matrix, stabilization, feedback gain, distance to

Applications of msets in Logic Programming languages is found to over- come “computational inefficiency” inherent in otherwise situation, especially in solving a sweep of

Shi, “The essential norm of a composition operator on the Bloch space in polydiscs,” Chinese Journal of Contemporary Mathematics, vol. Chen, “Weighted composition operators from Fp,

[2])) and will not be repeated here. As had been mentioned there, the only feasible way in which the problem of a system of charged particles and, in particular, of ionic solutions

This paper presents an investigation into the mechanics of this specific problem and develops an analytical approach that accounts for the effects of geometrical and material data on

discrete ill-posed problems, Krylov projection methods, Tikhonov regularization, Lanczos bidiago- nalization, nonsymmetric Lanczos process, Arnoldi algorithm, discrepancy

Jin [21] proved by nonstandard methods the following beautiful property: If A and B are sets of natural numbers with positive upper Banach density, then the corresponding sumset A +

I think that ALTs are an important part of English education in Japan as it not only allows Japanese students to hear and learn from a native-speaker of English, but it