To CG or to HDG A Comparative Study
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unit1When I think of people in this world who have really made a difference, I think of my parents. They were truly saints among ordinary people.I was one of the ten children my parents adopted. They rescued(挽救)each of us from a life of poverty(贫穷) and loneliness(孤独). They were hardly able to restrain(克制)themselves from bringing home more children to care for. If they had had the resources(资源)they certainly would have.Most people do not realize how much they appreciated (感激) someone until they pass away(大多数人都不知道他们有多么感激一个人,直到那个人去世). My sisters and brothers and I did not want this to happen before we uttered(说)the words "Thank you" to our parents(我的妹妹和弟弟和我都不想在我们对父母说谢谢你之前让这件事发生).Although we have all grown up and scattered(散落) about the country, we got back together to thank our parents. My brother Tom undertook(从事,承担)the task of organizing the event. Every Friday night, Mom and Dad have had the ham dinner special at the same restaurant for the last twenty years. That is where we waited without their knowing. When we first caught a glimpse(瞥一眼) of them coming across the street, we all hid underneath(在…之下) a big table. When they entered, we leapt(跳出来) out and shouted, "Thank you, Mom and Dad." My brother Tom presented (提供)them with a card(办法,手段,妙计)and we all hugged(拥抱). My Dad pretended(假装) that he had known we were under the table all along.1.无论你是多么富有经验的演说家,无论你做了多么充分的准备,你都很难在这样嘈杂招待会上发表演讲(no matter how)No matter how experienced a speaker you are, and how well you have prepared your speech, you will have difficulty making a speech at such a noisy reception.2.就像吉米妹妹的朋友都关心吉米一样,吉米也关心他们(just as )Just as all his sister’s friends cared about him, Jimmy cared about them.3.汽车的生产商在新车的几处都印有汽车识别号码,以便帮助找回被盗车辆Car manufacturers stamp a vehicle identification number at several places on new cars to help track down stolen vehicles.4.老师回来时你敢告我状的话,我就不再和你说话了If you dare tell on me when the teacher gets back I won’t say a word to you any more.5.有些老年人愿意独自过日子,但大多数老人选择和儿女一起生活(on one’s own)Some elderly people prefer to live on their own while the great majority choose to live with their children.6.现在需要面对的事情是:如何筹集创建公司所需的资金(reckon with)Here is something that needs to be reckoned with: how to get the necessary finances to establish the company.unit2Women who exercise regularly need to be careful with what they eat. Researchers have found evidence(证据,迹象) that even moderate(适度的) exercise can result in losing iron. They said that women who exercise regularly, especially in endurance(耐久) activities, typically lose iron. In order to prevent this from becoming a problem(为了防止这成为问题), it is important that those women consume more meat(吃肉) or take supplements(补充)to replace (取代) the iron lost. Those who do not bother to get plentiful amounts of iron (嫌麻烦不愿意获得大量铁的人) may begin to feel weak and tired. "If you can get the recommended daily allowance(按定量供给)of iron in your diet(如果你能每天服用推荐铁的含量), you will probably perform better," said one diet specialist. "One shortcoming(缺点) of taking iron pills is that the pill form is not well absorbed(专心致志,全神贯注) and can sometimes make you sick. It is preferable(可取的) that you try to remedy(治疗) the deficiency(缺点)by getting more iron-rich meats(红肉) in your diet."There are ways to help your body store(储存)away(一直在做…) the ironit takes in. By getting plenty of Vitamin C, your body is able to process(处理), or use, the iron better. Researchers acknowledge(承认,声明)that everyone's body is different and the problem will be less serious for some. Because it is impossible to decide whether or not this could be a problem for you, health specialists say(健康专家说) it is advisable(明智的) to check your iron levels. Even when you can't feel it, you may still have a problem.1.被告是位年仅30岁的女子,她坚持称自己无罪(use an appositive)使用同位语The defendant, a woman of only 30, kept insisting on her own innocence(无罪).2.总体来看,枣、豆类以及一些多叶的绿色蔬菜是最好的铁质来源(use an absolute tructure)使用独立主格结构All tings considered, dates, beans and some leafy green vegetables are the best sources of iron.3.正餐时不供应饮料,饮料会影响消化No beverages are served with meals because they interfere with digestion.4.考虑到那个地方受欢迎的程度,提前订旅馆是明智的Taking the popularity of the region into consideration, it is advisable to book hotels in advance.5.服药后若有呕吐感,请立即停止服用并尽快咨询医生If you have a feeling of wanting to throw up after taking this drug, stop taking it immediately and consult your doctors as soon as possible.6.总结这次讨论时,他说双方都要好好考虑怎样以最有效的方法来解决这一问题Summing up the discussion, he said both parties should consider the most effective way to solve the problem.unit3While many private schools are focusing more on values(重视), public schools are moving toward testing standards. The national government demands(需要)academic(学术上的) success and tests are taken as a key measurement(量度;份量,尺寸;) for a school's performance(表现). Schools with low test scores face penalties(惩罚) such as a reduction(减少) in money to run(经营)their schools. And, even individual teachers are being graded on(分级) how they're preparing their students for these tests."We have concentrated(集中的,全神贯注的) too much on teaching the kidshow to take these tests," commented(评论)one elementary school teacher(初中老师). "We should be providing a more comprehensive(综合的,全面的)curriculum (课程) to these kids. We should be cultivating(改善,培养)leadership and curiosity(领导能力和好奇心). Unfortunately, there is never time."One school principal remarked(重要的评论), "It's true that it would be beneficial(有益的) to our kids if they were getting better scores on the subjects being tested. The trouble is that in poorer areas of the city like ours, kids start school less equipped(被装备) to perform(工作) well. We have many obstacles(障碍)to overcome(战胜,压倒) before we can teach them basic subjects. All schools are not alike(同样地) , so they shouldn't be tested that way.""The goal is to improve performance in schools that are not providing(提供) their students with tools for success," said one government official. He admits(承认), however, that he is having a hard time convincing faculty(说服全体教职员工) and teachers this plan will work.1.在思维方面,与他的行为一样,他是非常传统的(use “as” with the meaning of “in the way that , in the manner(方法)that ,like”.)In his thinking, as in his behavior, he is very traditional.2.教师一旦同意接受新的教学计划。
英语人教版选必二u4作文英文回答:In the realm of language learning, the acquisition of English proficiency occupies a pivotal position in contemporary education. Its global prominence as a lingua franca has fueled an insatiable demand for individuals proficient in its communication. However, the path to English mastery is often fraught with challenges and complexities, demanding a multifaceted approach to overcome the linguistic barriers that impede progress.Recognizing the significance of developing effective English communication skills, educators have devised an array of pedagogical strategies tailored to cater to the diverse learning needs of students. Among these, the communicative approach has emerged as a transformative force, prioritizing authentic language use in real-life contexts. This approach emphasizes the practicalapplication of language, immersing learners in meaningfulinteractions that foster their communicative competence.Furthermore, the incorporation of digital technologies in English language instruction has revolutionized the learning experience. Online platforms and interactive resources provide learners with unprecedented access to authentic materials, enabling them to engage with English content in a variety of formats, such as videos, podcasts, and social media. These interactive experiences empower learners to connect with native speakers and expand their exposure to the language, fostering a deeper understanding of its nuances and complexities.While the communicative approach and digital technologies have been instrumental in advancing English language learning, the role of grammar remains indispensable. Grammar provides the structural framework that underpins language comprehension and production. A solid foundation in grammar enables learners to construct grammatically correct sentences, communicate clearly and effectively, and avoid common errors that can hinder understanding.In addition to formal instruction, immersion inEnglish-speaking environments through travel, study abroad programs, or online language exchange platforms can significantly enhance language proficiency. Exposure to native speakers allows learners to experience the language in its natural context, absorbing its rhythms, intonations, and subtle cultural nuances. Such immersive experiences provide learners with invaluable opportunities to practice their speaking, listening, and comprehension skills, accelerating their progress towards fluency.However, the path to English proficiency is not without its obstacles. Language learners often encounter challenges stemming from cultural differences, interference from their native language, and a lack of motivation. Cultural differences can lead to misunderstandings and communication breakdowns, while interference from one's native language can hinder the acquisition of correct pronunciation and grammar. Additionally, maintaining motivation throughout the learning process can be challenging, especially when progress is slow or plateaus occur.Overcoming these challenges requires a combination of perseverance, resilience, and effective language learning strategies. Learners must embrace a growth mindset, viewing setbacks as opportunities for learning rather thanobstacles to success. Active participation in class,regular practice outside of the classroom, and setting realistic goals can help maintain motivation and foster a sense of accomplishment.In conclusion, the quest for English proficiency is a multifaceted endeavor that necessitates a holistic approach encompassing communicative strategies, digital technologies, grammar instruction, immersion experiences, and adetermined mindset. By embracing these diverse elements, learners can navigate the complexities of English language learning and emerge as confident and effective communicators.中文回答:英语作为当今教育界备受重视的语言,其全球通用语的地位催生了对英语熟练掌握人才的旺盛需求。
2024年成人高考成考英语(高起专)复习试卷及解答参考一、语音知识(本大题有5小题,每小题2分,共10分)1、Choose the word that has the same pronunciation as the word “elephant.”A. elephantB. elephantC. elephantD. elephantAnswer: BExplanation: The word “elephant” is pronounced as /ˈɛl.ɪ.fɑːnt/. Among the options provided, “elephant” in option B is pronounced the same as the original word.2、Select the word that has the opposite meaning of “increase.”A. increaseB. increaseC. decreaseD. decreaseAnswer: CExplana tion: The word “increase” means to make larger or greater. The wordthat has the opposite meaning is “decrease,” which means to make smaller or less. Among the options, “decrease” in option C is the correct answer.3、The word “communicate” is pronounced as:A. /kəˈmjuːnɪkeɪt/B. /kəˈmjuːnɪkeɪt/C. /kəˈmjuːniːkeɪt/D. /kəˈmjuːniːkeɪt/Answer: AExplanation: The correct pronunciation of “communicate” is /kəˈmjuːnɪkeɪt/. The “c” in “communicate” is not hard, as it does not precede a double vowel.4、Which of the following words has the correct pronunciation?A. “Environment” - /ɪnˌvaɪrənˈmeɪnt/B. “Education” - /ˌɛdʒuˈkeɪʃən/C. “Imagine” - /ɪˈmædʒɪneɪt/D. “Compass” - /kəˈmæpəs/Answer: BExplanation: The correct pronunciation of “education” is /ˌɛdʒuˈkeɪʃən/. The “e” in “education” is long, as it is followed by a “g” which is silent. The other options have mispronounced vowels or consonants.5、The sentence “She always has a smile on her face” emphasizes that sheis always __________.A. cheerfulC. nervousD. sadAnswer: A. cheerfulExplanation: The word “always” in the sentence indicates a constant state or behavior. The phrase “has a smile on her face” suggests that she is in a good mood or happy, which is best described by the word “cheerful.” The other options do not accurately capture the positive connotation of the sentence.二、词汇与语法知识(本大题有15小题,每小题2分,共30分)1、Choose the correct word or phrase to complete the sentence below.The_______of the meeting was quite impressive.A. atmosphereB. audienceC. attendanceD. occasionAnswer: CExplanation: The correct answer is “attendance” because it refers to the number of people who were present at the meeting. The other options do not fit the context of the sentence.2、Select the word that does not belong in the following list.A. enthusiasticC. exhaustedD. alertAnswer: CExplanation: The word “exhausted” does not belong in the list because it is an adjective that describes someone who is very tired, whereas “enthusiastic,” “energetic,” and “alert” all describe someone who is full of energy or has a positive, watchful attitude.3、Choose the word that best completes the sentence.The teacher___________the students to be quiet during the examination.A. requestedB. suggestedC. orderedD. recommendedAnswer: C. orderedExplanation: The correct choice is “ordered” because it indicates a direct command or instruction from the teacher. The other options, while they could be used in some contexts, do not convey the same level of authority or necessity as “ordered” does in this sentence.4、Complete the sentence using the correct form of the verb in parentheses.If you________(be) more careful, you would not have made so many mistakes.A. areB. wereC. will beD. had beenAnswer: B. wereExplanation: The correct form of the verb to use in this sentence is “were,” which i s the past subjunctive form of “to be.” The sentence is expressing a hypothetical situation, which is a situation that is not real but is being considered for the sake of argument. The past subjunctive is used to describea condition that is not true but could have been or would have been.5、Choose the word that best completes the sentence.The professor___________the students’ questions eagerly.A. ignoredB. addressedC. neglectedD. overlookedAnswer: B. addressedExplanation: The correct word to complet e the sentence is “addressed,” which means to speak to or write to someone formally or officially. The professor is expected to address the students’ questions, not ignore, neglect, or overlook them.6、Complete the sentence with the correct form of the verb in parentheses.They___________(be) discussing the project when the meeting was called toorder.A. wereB. had beenC. have beenD. isAnswer: A. wereExplanation: The correct form of the verb is “were,” which is the past continuous tense. The sentence describes an action that was happening at a specific past time (when the meeting was called to order), so the past continuous tense is appropriate. The other options are incorrect because they do not match the context or the tense required.7、Choose the word that best completes the sentence.The teacher was surprised by the student’s_ability to understand complex concepts.A)surpriseB)surprisedC)surprisingD)surpriseablyAnswer: C) surprisingExplanation: The correct answer is “surprising” because it is the adjective form that describes the student’s ability. “Surprise” is a noun, “surprised” is the past participle form of the verb, and “surpriseably” is not a word.8、Complete the sentence with the correct form of the given verb in brackets.They (be) (not) aware of the changes that (take) place in the company last month.A)wereB)areC)wasD)beAnswer: A) wereExplanation: The correct answer is “were” because the subject “they” is plural, and the past perfect tense “had taken” indicates that the cha nges occurred before the awareness of them. Therefore, “were” is the correct past tense form of “be.”9.Choose the word that best completes the sentence.I can’t believe how____________changes have occurred in this small town over the past decade.A)numerousB)rapidC)suddenD)gradualAnswer: D) gradualExplanation: The sentence is describing changes that have occurred over a period of time, suggesting a process that was not immediate or extreme. “Gradual” fits this context best, indicating changes that happen slowly over time.10.Select the correct form of the verb to complete the following sentence.The professor___________us a detailed outline of the research project before the deadline.A)gaveB)has givenC)will giveD)is givingAnswer: B) has givenExplanation: The sentence implies that the action of giving the outline has already occurred before the deadline. The present perfect tense (“has given”) is used to describe actions that have a present relevance or result.11.Choose the correct word to complete the sentence:The manager was_about the new project, but the team was confident.A)apprehensiveB)optimisticC)indifferentD)enthusiasticAnswer: A) apprehensiveExplanation: The correct answer is “apprehensive” because it means feeling or showing anxiety or fear about something, which fits the context of the manager being concerned about the new project. The other options do not convey the same sense of worry or anxiety.12.Select the word that is closest in meaning to the underlined word:The teacher’s_appr oach to teaching made the subject much more engaging.A)traditionalB)innovativeC)passiveD)objectiveAnswer: B) innovativeExplanation: The underlined word “innovative” means introducing new methods or ideas. The sentence suggests that the teacher’s approach was different and made the subject more engaging. The word “traditional” would imply a more conventional method, “passive” would suggest a lack of interest, and “objective” would imply a neutral approach, none of which fit the context as well as “innovative.”13.Choose the word that best completes the sentence.The company’s new policy has been widely __________, with both positive and negative reactions.A. criticizedB. implementedC. supportedD. rejectedAnswer: B. implementedExplanation: The correct word here should reflect that the policy has been put into effect. “Implemented” means to carry out or put into effect, which fits the context. “Criticized” would imply there are negative reactions,“supported” would imply positive reactions, and “rejected” wo uld imply outright refusal, none of which fully capture the act of the policy being put into practice.14.Select the correct form of the verb to complete the sentence.She_______(go) to the market every morning, but now she has a car.A. used to goB. uses to goC. used goD. uses goAnswer: A. used to goExplanation: The correct phrase to use in this context is “used to” followed by the base form of the verb, which indicates a past habit or practice that has since changed. “Used to go” is the correc t past simple form that indicates a habit in the past. The other options are grammatically incorrect or do not convey the intended meaning.15.Choose the correct word or phrase to complete the sentence.The professor___________the students to study hard for the exam.A. advisedB. recommendedC. suggestedD. proposedAnswer: B. recommendedExplanation: The correct answer is “recommended” because it is the most appropriate word to express the professor’s advice. “Advised,” “suggested,” and “proposed” can also mean giving advice or suggestions, but “recommended”is often used in a more formal context, such as in an academic setting.三、完形填空(30分)Passage:In the small town of Willow Creek, there was once a charming old library that stood at the heart of the community. The library was a hub of learning and culture, where people of all ages would gather to read, discuss, and exchange ideas. The librarian, Mrs. Thompson, was known for her warm smile and vast knowledge of books. She had been working at the library for over 30 years and was deeply loved by everyone in the town.One day, the town’s mayor announced that the library was in danger of closing due to budget cuts. The community was shocked and immediately rallied to save their beloved library. They organized a series of events, including a book sale, a bake sale, and a benefit concert, to raise funds.The most successful event was the “Willow Creek Reads” program, where local authors were invited to read to the children and talk about their writing process. The children were excited and inspired, and the adults were reminded of the power of books to bring people together.As the days went by, more and more people began to donate books and moneyto the library. Mrs. Thompson was overwhelmed by the outpouring of support from the community. She knew that the library would not only survive but thrive.One evening, as Mrs. Thompson was organizing a new shelf of donated books, she noticed a mysterious note tucked inside one of the books. The note read, “To Mrs.Thompson, from the Friends of Willow Creek Library. We hope these books bring you joy and continue to inspire the community.”Mrs. Thompson smiled, knowing that the spirit of the library was alive and well.Blanks:1.The library in Willow Creek was a___________of learning and culture.2.Mrs. Thompson was___________for her warm smile and vast knowledge of books.3.The town’s mayor announced that the library was in___________due to budget cuts.4.The community___________to save their beloved library.5.The most successful event was the___________program.6.The children were___________and inspired by the local authors.7.The adults were___________of the power of books to bring people together.8.More and more people began to___________books and money to the library.9.Mrs. Thompson was___________by the outpouring of support from the community.10.The note was a___________from the Friends of Willow Creek Library.11.Mrs. Thompson smiled, knowing that the spirit of the librarywas___________and well.Questions:11.What was the note a___________from the Friends of Willow Creek Library?A)InvitationB)ComplaintC)Thank youD)ApologyAnswer:C) Thank you四、阅读理解(本部分有5大题,每大题9分,共45分)第一题Read the following passage and answer the questions that follow.The Internet has revolutionized the way we communicate, access information, and conduct business. With just a few clicks, we can connect with people from all over the world, access a vast amount of information, and even conduct transactions online. However, along with these benefits, the Internet has also brought about various challenges and risks. One of the most significant risks is the potential for cybercrime, which includes hacking, identity theft, and phishing.1.What is one of the major risks associated with the use of the Internet?A. Improved communicationB. Access to a vast amount of informationC. Potential for cybercrimeD. Increased business opportunities2.What are some examples of cybercrimes mentioned in the passage?A. Hacking, identity theft, and phishingB. Improved communication and access to informationC. Increased business opportunitiesD. Reduced need for physical interaction3.How does the Internet impact the way we conduct business?A. It reduces the need for physical interactionB. It increases the potential for cybercrimeC. It provides a platform for global communication and transactionsD. It eliminates the need for traditional banking and financial servicesAnswers:1.C2.A3.C第二题Passage:The rapid development of technology has greatly influenced the way people communicate. Social media platforms have become an integral part of daily life,allowing individuals to connect with others across the globe. However, this shift in communication has raised concerns about the impact on face-to-face interactions and the potential loss of traditional social skills.One of the most popular social media platforms is Instagram, which is known for its focus on visual content. Users can share photos, videos, and stories, and follow others who share similar interests. While Instagram can be a great way to stay connected with friends and discover new things, it also has its downsides.A recent study found that excessive use of Instagram can lead to feelings of loneliness and depression. The constant comparison with others’ seemingly perfect lives can create a sense of inadequacy. Additionally, the platform’s algorithm can create a filter bubble, where users are only exposed to content that aligns with their existing beliefs and interests, thus limiting their exposure to diverse perspectives.Despite these concerns, many people find Instagram to be a valuable tool for networking and personal growth. It can provide a platform for artists, writers, and entrepreneurs to showcase their work and connect with potential audiences. Moreover, it can be a source of inspiration and motivation, as users are exposed to the achievements and stories of others.Questions:1、What is the main topic of the passage?A) The benefits of using social media platforms.B) The negative effects of Instagram on social interactions.C) The history of social media platforms.D) The role of technology in modern communication.2、Which of the following is NOT mentioned as a potential negative effect of using Instagram?A) Feelings of inadequacy.B) Limited exposure to diverse perspectives.C) Improved communication skills.D) Increased feelings of loneliness and depression.3、What is the author’s attitude towards Instagram?A) Highly critical.B) Indifferent.C) Positive and supportive.D) Ambiguous.Answers:1、B) The negative effects of Instagram on social interactions.2、C) Improved communication skills.3、D) Ambiguous.第三题Reading Passage:In the small town of Greenfield, there was a long-standing tradition of the annual Greenfield Festival. The festival, which took place every autumn, broughttogether local artists, musicians, and performers from around the region. It was a time for celebration, a showcase of local talent, and a chance for the community to come together and enjoy the arts.One of the highlights of the festival was the “Greenfield Talent Show,” where local residents could audition to perform. This year, the talent show had a special twist: the winner would receive a scholarship to study music at a prestigious music school in the nearby city of Bluewater.Word Count: 102Questions:1、What is the main purpose of the Greenfield Festival?A) To promote tourism in GreenfieldB) To bring the community together and celebrate local artsC) To raise funds for charityD) To promote agricultural products2、Which event at the festival was of particular interest to this year’s participants?A) The art exhibitionB) The music concertC) The Greenfield Talent ShowD) The local craft fair3、What reward did the winner of the Greenfield Talent Show receive?A) A cash prizeB) A trip to the nearby cityC) A scholarship to study musicD) A trophyAnswers:1、B) To bring the community together and celebrate local arts2、C) The Greenfield Talent Show3、C) A scholarship to study music第四题Reading ComprehensionRead the following passage and answer the questions that follow.The rise of e-commerce has revolutionized the way people shop and has had a significant impact on traditional brick-and-mortar stores. Online shopping has become increasingly popular due to its convenience and the vast variety of products available. However, this shift has also brought about challenges and changes in the retail industry.One of the main advantages of e-commerce is the convenience it offers. Customers can shop from the comfort of their own homes at any time of the day or night. This eliminates the need to travel to physical stores and wait in long queues. Additionally, online platforms often provide detailed product descriptions, customer reviews, and even virtual try-ons, which can help customers make more informed purchasing decisions.Despite these benefits, e-commerce has also presented challenges fortraditional retailers. Many have had to adapt to the changing landscape by investing in their online presence and offering competitive pricing and customer service. However, some have struggled to keep up and have been forced to close their doors.The retail industry is also witnessing a shift in consumer behavior. Customers are becoming more environmentally conscious and are increasingly looking for sustainable and ethical products. This has led to a rise ineco-friendly shopping options and a decline in demand for fast fashion.1.What is the main advantage of e-commerce mentioned in the passage?A) Competitive pricingB) ConvenienceC) Eco-friendly optionsD) Detailed product reviews2.How has e-commerce affected traditional brick-and-mortar stores?A) They have become more profitable.B) They have had to adapt and invest in online presence.C) They have seen a significant increase in foot traffic.D) They have closed down due to increased competition.3.What is the trend in consumer behavior mentioned in the passage?A) Customers are looking for more affordable products.B) Customers are becoming more environmentally conscious.C) Customers are preferring fast fashion over sustainable options.D) Customers are no longer interested in online shopping.Answers:1.B) Convenience2.B) They have had to adapt and invest in online presence.3.B) Customers are becoming more environmentally conscious.第五题Read the following passage and answer the questions that follow.In recent years, there has been a growing interest in online education. This shift is primarily due to the convenience and flexibility it offers to students. Online courses allow individuals to learn at their own pace, from any location, and often at a lower cost compared to traditional in-person classes. However, despite these advantages, online learning also comes with its own set of challenges.One of the main concerns is the potential for reduced social interaction. In traditional classrooms, students have the opportunity to engage with their peers and professors, which can enhance their learning experience. Online students, on the other hand, may feel isolated and disconnected from the academic community. This can lead to a lack of motivation and engagement in the course material.Another challenge is the need for self-discipline. Online courses require students to be self-motivated and organized. Without the structure of a traditional classroom, students must set their own schedules and manage their time effectively. This can be difficult for some individuals, especially thosewho are accustomed to the routine of attending classes on campus.Despite these challenges, many online learners find that the benefits outweigh the drawbacks. They appreciate the ability to work around their other commitments, such as full-time jobs or family responsibilities. Additionally, online courses often provide access to a wider range of resources and expertise than traditional courses.1.The primary reason for the growing interest in online education is:a) the opportunity for social interactionb) the flexibility and convenience it offersc) the lower cost compared to traditional in-person classesd) the access to a wider range of resources2.What is one of the main concerns mentioned about online learning?a) The convenience of learning at one’s own paceb) The potential for reduced social interactionc) The lower cost of online coursesd) The increased access to expertise3.According to the passage, which of the following is a challenge for online learners?a) The ease of engaging with peers and professorsb) The need for self-discipline and organizationc) The lower cost of online coursesd) The ability to work around other commitmentsAnswers:1.b) the flexibility and convenience it offers2.b) The potential for reduced social interaction3.b) The need for self-discipline and organization五、补全对话(本大题有5小题,每小题3分,共15分)第一题A: Excuse me, could you help me with some English vocabulary?B: Sure, I’d be happy to. What would you like to know about?A: I need to expand my vocabulary for the college entrance exam. Can you suggest some useful words for an “Adult Higher Education” (AHLE) English test?B: Absolutely! Here are a few words and phrases that are often included in such exams:1.(______) - a higher level of education beyond high school.2.(______) - a system of post-secondary education that allows working adults to earn degrees.3.(______) - a person who is studying or has studied at a college or university.4.(______) - a course or program of study that leads to a degree or certification.5.(______) - a test taken by students to gain admission to a college or university.A: Great, thanks! What should I write in the blank spaces?B:1.(______) - A higher level of education beyond high school.2.(______) - A system of post-secondary education that allows working adults to earn degrees.3.(______) - A person who is studying or has studied at a college or university.4.(______) - A course or program of study that leads to a degree or certification.5.(______) - A test taken by students to gain admission to a college or university.答案:1.Degree2.Adult Higher Education (AHLE)3.College student4.Curriculum5.Admission test解析:1.Degree - This word is used to describe a higher level of education, which is a key concept in the context of college education.2.Adult Higher Education (AHLE) - This specific term refers to the system that caters to working adults who wish to pursue further education.3.College student - This phrase describes someone who is currently or has been enrolled in a college or university.4.Curriculum - This word refers to the courses or program of study that an educational institution offers.5.Admission test - This term refers to the test that students must take to be admitted to a college or university, which is a common requirement for higher education.第二题1.A: I’m sorry, but I can’t help you with that right now.B: Why not?A: Because I’m currently in a meeting.B: Oh, I see. Well, can I leave you a message?A: Certainly, you can.B: Thank you. I’ll just write down my number and call you back after the meeting.A: That sounds good.B: Is there anything specific you need help with?A: Yes, actually. I need some information about the new software package our company is considering.B: Of course. Let me check if I have that information available.A: Alright, take your time.B: I should be able to find it for you. Just a moment, please.A: No problem.B: There we go. I have the information you need.A: Great, thanks. Can you send it to my email?B: Absolutely. I’ll send it over right now.A: Perfect. I appreciate your help.B: You’re welcome. Feel free to call back if you need anything else.A: Will do. Have a good meeting.B: You too. Goodbye.1.A: I’m sorry, but I can’t help you with that right now.B: Why not?A: Because I’m currently in a meeting.B: Oh, I see. Well, can I leave you a message?A: Certainly, you can.B: Thank you. I’ll just write down my number and call you back after the meeting.A: That sounds good.B: Is there anything specific you need help with?A: Yes, actually. I need some information about the new software package our company is considering.B: Of course. Let me check if I have that information available.A: Alright, take your time.B: I should be able to find it for you. Just a moment, please.A: No problem.B: There we go. I have the information you need.A: Great, thanks. Can you send it to my email?B: Absolutely. I’ll send it over right now.A: Perfect. I appreciate your help.B: You’re welc ome. Feel free to call back if you need anything else.A: Will do. Have a good meeting.B: You too. Goodbye.答案:解析:The correct continuation of the dialogue is B because it maintains the context of the original message and provides a logical progression of the conversation. It addresses the initial reason for the inability to assist and then moves on to offering a solution (leaving a message) and asking for further details about the assistance needed. The dialogue then proceeds with the person finding the information, offering to send it via email, and concluding with a friendly farewell.第三题A: Excuse me, I’m looking for the English section of the Adult College Entrance Examination. Can you help me?B: Sure, follow me. You need to go to the second floor and then turn right. The English section is located in Room 202.A: Oh, okay. Thank you. By the way, what time does the exam start?B: The exam will begin at 9:00 a.m. sharp. Make sure you arrive 30 minutes early to get settled.A: Got it. I’ll be there on t ime. One more thing, is there a specific roomfor the English exam?B: Yes, it’s Room 202 as well. You’ll see a sign indicating the English section.A: Perfect. Thanks again for your help.B: You’re welcome. Good luck with your exam!Answer:B: Yes, it’s Room 202 as well. You’ll see a sign indicating the English section.Explanation:In this dialogue, the student is asking for directions to the English section of the exam. The answer to the question is found in the response by the staff member. They confirm that the English exam is held in Room 202, as indicated by a sign, providing clear information to the student.第四题A: Excuse me, I seem to have misplaced my calculator. Can you help me find it?B: Sure, where do you think you might have left it?A: I was working on this problem for our math class, and I think I might have left it on the desk.B: Okay, let’s check the desk first. Is this the one you’re looking for?A: No, that’s not it. It was smaller and black.B: Alright, let’s look over there by the window. Do you see anything that。
The Journey of Acquisition: More Preciousthan the DestinationIn the realm of knowledge, the quest for wisdom often outshines the wisdom itself. The process of acquiring knowledge, a labyrinthine journey that demands curiosity, perseverance, and an open mind, is often more valuable than the knowledge itself. This assertion holds true not only in academic pursuits but also in the day-to-day experiences of life.The allure of knowledge lies not just in the facts and figures but in the exploration of ideas, the challenges faced, and the lessons learned. Each step of the journey, whether it's a eureka moment or a frustrating dead end, contributes to our growth and understanding. The process itself is an education, shaping our perspectives and equipping us with the tools necessary to navigate the complexities of the world.Moreover, the process of acquiring knowledge isiterative and ongoing. It's a dynamic dance between curiosity and discovery, where new information challenges old beliefs, and vice versa. This continuous cycle oflearning and unlearning is crucial for intellectual growth and the cultivation of critical thinking skills.In the academic world, the process of acquiring knowledge is often more rewarding than simply absorbing facts. The journey involves delving into texts, engaging with peers, and thinking critically about the information presented. This active engagement with knowledge not only enhances comprehension but also fosters a deeper understanding of the subject matter.Outside the classroom, the process of acquiring knowledge is equally, if not more, important. It involves trial and error, experimentation, and the embrace of uncertainty. This process, often messy and unpredictable,is vital for personal growth and the development of resilience. It teaches us to be adaptable, resourceful, and innovative in the face of challenges.Additionally, the process of acquiring knowledge is often more enjoyable than the destination itself. The journey is filled with surprises, insights, and moments of clarity that make the pursuit of knowledge an exciting and rewarding adventure. The sense of accomplishment andfulfillment derived from this process is often more satisfying than simply acquiring the knowledge itself.In conclusion, the process of acquiring knowledge is more precious than the knowledge itself. It is a transformative experience that shapes our perspectives, enhances our understanding, and fosters personal growth.The journey, filled with challenges, insights, and momentsof discovery, is an adventure that is both rewarding and enjoyable. As we embark on this journey, we must cherishthe process and embrace the unknown, as it is through this process that we truly learn and grow.**获取知识之旅:比终点更重要**在知识的领域中,对智慧的追求往往比智慧本身更加耀眼。
托福写作范文:是否应该强制高中学生学习音乐题目:Do you agree or disagree with the following statement?All students should be required to study art and music in secondary school. Use specific reasons to support your answer.范文:The term “art” has various definitions. It refers to the conscious use of skill and creative imagination especially in the production of aesthetic objects. It also means the works so produced. Sometimes it is used as the synonym of fine arts while in other case it refers to one of the fine arts. In the following discussion, it is defined as one of the fine arts. Under this definition, it is unreasonable to require all secondary school students to learn it and music.The first prerequisite to answer the question whether all secondary students must study art and music is the purpose of secondary school teaching and learning. The second is the functions of music and art in the life of a secondary school student. Besides, if the art and music is compulsory in the secondary school curriculum, we will focus on how to teach them or how to help students study the specific art and music.What is the purpose of the secondary school? In China, it is no more than teaching students the tricks to crack the nut of National Matriculation Tests (NMT), or the college entrance or admission examination. Parents emphasize nothing more than the possibility for their children to earn a high score in these tests, which finally dictates the fate of a student. If the candidate outnumbers all other rivals in NMT, he or she will have the opportunity to enter a leading university such as Peking University. And if a candidate is admitted by such higher education organizations, she or he will be able to live a relative comfortable and convenient life in future. The consequence of NMT means everything to a secondary school student. It means the career, job, salary, house, car, and even a decent husband or wife. Therefore, in China, it is abhorred to force secondary school students to learn music and art because both of them are not in the list of NMT.The purpose of secondary school in the USA or European countries might be strikingly different from the Chinese version. I learn that the secondary school students also have to sit some tests such as SAT or SSAT, but the results are not weighed much.In this case, it might be reasonable to ask students to learn music and art. However, it is yet presumptuous to claim that all students must learn because each individual student has his or her distinct interest and the right to choose what to learn.Unlike the engineering courses or medicine courses that prepare students for a better career, art and music function in the deeper world of human spirit. The impacts of learning art and music are on the cultivation of human personality, aesthetic taste, and characteristic development. Therefore, theoretically speaking, it benefits students who learn. Nevertheless, neither education organization, nor teachers, nor parents, nor the educators have a far reaching vision to encourage students to study art and music. Instead, art and music today have been degraded as nothing different from commodities that help people earn money. Consequently, it is not feasible to ask all students to study music and art.If we consider this issue more profoundly, we find it is impossible to list music and art as compulsory in secondary school curriculum.。
TPO53托福阅读Passage1原文及答案解析如今大家在进行托福备考时TPO托福模考软件信任是大家用的最多的工具了,对于托福成果的提升是特殊有关怀的今日我在这里整理了TPO53托福阅读Passage1原文文本+题目+答案解析来共享给大家,希望对大家托福听力备考有关怀。
TPO53托福阅读Passage1原文文本Questions About A Drama ClassListen to a conversation between a student and his drama professor.Professor: Hi Robert. So hows your paper going?Robert: Pretty well. Its a lot of work, but I’m getting into it, so I dont mind. I’ll probably have some questions for you in the next week or so.Professor: Okay. Glad to hear you’re progressing so well.Robert: Um… There was something you said at the end of the lecture on Tuesday, something about there not really being any original plays.Professor: There’s no such thing as an original play. Yes. Thats the direct quote from Charles Mee.Robert: Mee… thats with two “e”s, right?Professor: Yep. M-E-E. Youll probably be hearing a lot about him. Hes becoming a pretty famous playwright.Robert: Yeah,well, I’ve been thinking about his quote. I mean there must be some original plays out there.Professor: I’ll grant that hes overstating things somewhat. But the theater does have a long tradition of borrowing. Take Shakespeare. Like most writers of his day, he borrowed plots from other sources unabashedly. And the ancient Greeks, all the plays they wrote were based on earlier plays, poems and myths.Robert: And borrowing applies to plays being written nowadays, too?Professor: To some extent, yes. Mee, for example, hes made a career out of remaking plays, one of which we’ll be studying soon. It’s called Full Circle and Mee based it on an earlier play by a German playwright.Robert: Oh Full Circle… Wasnt that based on the Caucasian Chalk Circle?Professor: Thats right.Robert: I remember hearing about that play from my acting coach.Professor: Okay. Well, the Caucasian Chalk Circle was based on a play by yet another German playwright, someone who was fascinated by the ancient literatures of China, India and Persia, and many of his works were adapted from those literatures, including his version of the Chalk Circle which was based on an early Chinese play.Robert: So this Full Circle play, by Charles Mee, the one were going to study, its like the third or fourth remake. Wow… And we complain that Hollywood keeps making the same movies over and over again.Professor: Well, part of what Mee’s trying to do is drive home the point that: One, theater’s always a collaborative effort.Robert: Well, yeah, the playwright, the director, the actors, people have to work together to produce a play.Professor: Yes, of course. But Mee means historically. The dramatic literature ofearly periods is hugely influential in shaping later dramatic works.Robert: So its like when the playwright bases a play on a previous playwrights theme or message.Its like theyre talking to each other, collaborating. Uh, just not at the same time right?Professor: Exactly. And the second point Mees trying to make, I think, is that its legitimate to retell an old story in a new way, in a way that’s, uh… more in line with contemporary concerns. So when playwrights reinvent or update an earlier play, it shouldnt be construed as a lack of imagination or an artistic failure.TPO53托福阅读Passage1题目Question 1 of 5Why does the man go to see the professor?A. To discuss a play he heard aboutB. To get feedback on a paper he is writingC. To ask about a point made in classD. To get information about an acting coachQuestion 2 of 5Why does the professor mention Shakespeare and the ancient Greek playwrights?A. To support her statement that some original plays do existB. To show that playwrights historically have used themes from earlier playsC. To point out that Shakespeare was greatly influenced by ancient Greek playsD. To give examples of playwrights whose plays have inspired later playwrightsQuestion 3 of 5What does the professor imply about the play Full Circle by Charles Mee?A. It served as the basis for a Hollywood film.B. It is indirectly based on a Chinese play.C. It has influenced a more recent play.D. It uses themes from ancient Greek literature.Question 4 of 5What two points does Charles Mee make about playwriting? Click on 2 answersA. Rewriting old plays to deal with modern issues is a respectable practice.B. Playwrights should preserve as much of the original as possible when updating an older play.C. Older plays tend to show more imagination than newer plays.D. In a way, modern playwrights work with playwrights of the past.Question 5 of 5What does the man imply when he says this:A. He thinks the professor misunderstood his point.B. He has written some original plays himself.C. He doubts that what Charles Mee said is true.D. He has read some original plays by Charles Mee.TPO53托福阅读Passage1解析正确答案:C题目解析:此题定位到原文:Robert: Um… There was something you said at the end of the lecture on Tuesday, something about therere not really being any originalplays. 此处原文的大意是:学生提到教授上节课说其实没有完全原创的戏剧。
The Journey of Acquisition: The Process Overthe PrizeIn the realm of knowledge, the quest for wisdom often outweighs the wisdom itself. It is not merely about accumulating facts or regurgitating information, but rather a transformative journey that shapes our perspectives and refines our understanding of the world. The process of acquiring knowledge, rather than the knowledge itself,holds the key to personal growth and intellectual development.The quest for knowledge is an adventure that ignitesour curiosity and spurs us to explore. It is the quest that takes us from the known to the unknown, from familiarity to mystery. In this journey, we encounter new ideas, challenges, and perspectives that stretch our thinking and broaden our horizons. This process, filled with exploration and discovery, is what makes knowledge truly valuable.The process of acquiring knowledge is iterative and dynamic, involving constant questioning, reflection, and refinement. It is about asking why, challenging assumptions, and seeking deeper understandings. It is about criticallyexamining information, weighing evidence, and making informed decisions. This iterative process not only enhances our understanding of a subject but also cultivates our critical thinking and problem-solving skills.Moreover, the process of acquiring knowledge is often more rewarding than the knowledge itself. The sense of accomplishment and growth that comes from overcoming challenges, understanding complex concepts, and piecing together information is invaluable. The journey, filled with ups and downs, triumphs and failures, is what truly shapes our character and defines our intellectual capabilities.Additionally, the process of acquiring knowledge is collaborative and shared. It involves seeking wisdom from others, engaging in discussions, and collaborating with peers. This collaborative process not only enhances our understanding but also fosters a sense of community and belonging. It is through this process that we learn to appreciate diverse perspectives, embrace diversity, and work towards common goals.In conclusion, while knowledge itself is indeed valuable, the process of acquiring it holds even greater significance. It is the journey that shapes our perspectives, broadens our horizons, and cultivates our intellectual capabilities. It is the process that ignites our curiosity, spurs our exploration, and drives our growth. Therefore, let us cherish the journey of acquisition and embrace the process over the prize, as it is in thisjourney that we truly find wisdom and fulfillment.**获取知识的过程:过程重于结果**在知识的领域中,追求智慧的过程往往比智慧本身更为重要。
托福写作备考必备10大常考话题整理托福写作考试大家平时都是如何进行练习的呢?相信大家都会通过官方真题Official、机经的真题来练习。
这里的题目可以有很多,你有没有精选一些重点备考的题目呢?小编在这里为大家整理了托福写作考试常见的10类话题整理,大家在备考时可以重点放在这些题目中去练习。
下面大家就跟小编一起来练习起来吧。
托福写作备考必备10大常考话题整理1、动物类一直以来采取防止动物和植物免于灭绝太少了,尽管人们已经注意到这个问题了很长时间。
为什么人们没能改善这种状况吗?你有什么建议吗?Far too little has been done to prevent animals and plants from dying out, although people have noticed this problem for a long time. Why have people failed to improve this situation? What are your suggestions?2、教育类i.一些人认为教育孩子完全会使他们受益。
其他人认为聪明的孩子应该分开教学,给予特别的课程。
讨论双方的观点,给你自己的意见。
i. Some people believe that educating children altogether will benefit them. Others think intelligent children should be taught separately and given special courses. Discuss both views and give your own opinion.ii.如今,越来越多的毕业生无法找到工作。
讨论在年轻人和成年人之间不断上升的失业率的原因,给出解决方案。
ii. Today, more school leavers are unable to find jobs. Discuss the causes of rising unemployment among young adults and suggest any solutions.3、全球化影响现有一个对于增加国家之间的商业和文化联系给国家的身份所带来的影响的分歧。
Education systems around the world vary significantly,with the differences between Eastern and Western education being particularly notable.These differences can be seen in educational philosophies,teaching methods,and the overall goals of the education systems.Philosophical DifferencesIn Western countries,education is often seen as a means to foster individualism and creativity.Students are encouraged to think critically,question authority,and express their unique perspectives.The Western educational philosophy values the development of the whole person,focusing on intellectual,social,and emotional growth.In contrast,Eastern education systems,particularly in countries like China,Japan,and South Korea,tend to emphasize conformity,respect for authority,and the importance of tradition.The educational philosophy in these countries often revolves around the idea of collective success and the pursuit of academic excellence.Students are expected to adhere to strict discipline and work diligently towards achieving high scores in standardized tests.Teaching MethodsThe teaching methods in Western education are generally more studentcentered.Teachers often use a variety of teaching strategies,such as projectbased learning,group discussions, and handson activities,to engage students and encourage them to take an active role in their learning.This approach is designed to stimulate curiosity and promote a deeper understanding of the subject matter.On the other hand,Eastern education systems typically employ a more teachercentered approach.Lessons are often delivered in a lecture format,with teachers providing the bulk of the information and students expected to absorb and memorize the content.There is a strong emphasis on rote learning and the mastery of factual knowledge. Assessment and EvaluationIn Western education,assessment is often more holistic and includes a variety of methods, such as essays,presentations,and practical demonstrations.Grades are not the sole measure of a students success,and there is a greater focus on the development of skills and competencies.Eastern education systems,however,place a heavy emphasis on standardized testing.Highstakes exams,such as the Gaokao in China or the college entrance exams in South Korea,play a critical role in determining a students future educational and career opportunities.As a result,there is a strong incentive for students to focus on test preparation and achieve high scores.Curriculum and Subject MatterThe curriculum in Western education is often more diverse and flexible.Students have the opportunity to choose from a wide range of subjects and electives,allowing them to explore their interests and develop a broad base of knowledge.In Eastern education,the curriculum is typically more rigid and focused on core subjects such as mathematics,science,and language.There is less emphasis on subjects like art, music,and physical education,which are often viewed as less important in the pursuit of academic success.ConclusionWhile both Eastern and Western education systems have their merits,they also face challenges.Western education must balance the promotion of individualism with the need for students to acquire a solid foundation of knowledge.Eastern education,on the other hand,must strive to foster creativity and critical thinking without sacrificing academic rigor.Ultimately,the ideal education system would likely incorporate elements from both Eastern and Western approaches,promoting a balance between individual expression and collective achievement,creativity and discipline,and intellectual development and practical skills.。
托福写作解析:比较对比句怎么写写作中最主要的三种句型:因果论证句、比较对比句和假设条件句。
下面就来看一下比较对比句具体该怎么写!托福写作解析:比较对比句怎么写Movies: serious or entertaining?Therefore, the merits(advantage) encompassed within serious movies far outweigh those of entertaining movies.Adervertising is the main cause of unhealthy eating habits.In reality, compared with other sources of negative influences, advertising only plays a small role. the eating habits are formed on the basis of many complicated factors.Therefore, it is rash to consider it a major cause of those unhealthy eating habits.Compared with A, B...中的A和B是两个同类的事物托福写作句型赏析:一句话三种逻辑名句欣赏:There has been an implicit assumption that because electric cars do not burn fossil fuels, they are clearer for the environment and safer for people, but that does not take into account how the electricity they use is generated.解析:这句话比较长,但逻辑主干还是比较简单:There has been an assumption that A, but that does not take into account B.有一个假设A,但这并没有考虑到BA 是assumption 的具体内容,B 是考虑的内容,即= take B into accountA=because electric cars do not burn fossil fuels, they are clearer for the environment and safer for people1) A 是 assumption 的同位语2)electric cars 电动汽车3)burn fossil fuels 燃烧化石燃料4)safe 在这里的意思是[not likely to lead to any physical harm or danger ] 不损害健康的整个A的意思是:因为电动汽车不燃烧化石燃料,因此它们对环境更清洁,对人们更无害。
J Sci Comput(2012)51:183–212DOI10.1007/s10915-011-9501-7To CG or to HDG:A Comparative StudyRobert M.Kirby·Spencer J.Sherwin·Bernardo CockburnReceived:27January2011/Revised:26May2011/Accepted:27May2011/Published online:1July2011©Springer Science+Business Media,LLC2011Abstract Hybridization through the border of the elements(hybrid unknowns)combined with a Schur complement procedure(often called static condensation in the context of con-tinuous Galerkin linear elasticity computations)has in various forms been advocated in the mathematical and engineering literature as a means of accomplishing domain decomposi-tion,of obtaining increased accuracy and convergence results,and of algorithm optimiza-tion.Recent work on the hybridization of mixed methods,and in particular of the discontin-uous Galerkin(DG)method,holds the promise of capitalizing on the three aforementioned properties;in particular,of generating a numerical scheme that is discontinuous in both the primary andflux variables,is locally conservative,and is computationally competitive with traditional continuous Galerkin(CG)approaches.In this paper we present both imple-mentation and optimization strategies for the Hybridizable Discontinuous Galerkin(HDG) method applied to two dimensional elliptic operators.We implement our HDG approach within a spectral/hp element framework so that comparisons can be done between HDG and the traditional CG approach.We demonstrate that the HDG approach generates a global trace space system for the unknown that although larger in rank than the traditional static condensation system in CG, has significantly smaller bandwidth at moderate polynomial orders.We show that if one ignores set-up costs,above approximately fourth-degree polynomial expansions on triangles Work of R.M.Kirby accomplished while on sabbatical at Imperial College London.Work of B.Cockburn accomplished in part while visiting the Research Institute of Mathematical Sciences,Kyoto University,Kyoto,Japan,as part of a Single Semester Leave from the Universityof Minnesota.R.M.Kirby( )School of Computing,Univ.of Utah,Salt Lake City,UT,USAe-mail:kirby@S.J.SherwinDepartment of Aeronautics,Imperial College London,London,UKe-mail:s.sherwin@B.CockburnSchool of Mathematics,Univ.of Minnesota,Minneapolis,MN,USAe-mail:cockburn@and quadrilaterals the HDG method can be made to be as efficient as the CG approach, making it competitive for time-dependent problems even before taking into consideration other properties of DG schemes such as their superconvergence properties and their ability to handle hp-adaptivity.Keywords High-orderfinite elements·Spectral/hp elements·Discontinuous Galerkin method·Hybridization·Domain decomposition1IntroductionGiven a particular scientific or engineering problem of interest,the current computational science and engineering practitioner has at his or her disposal a large array of numerical methodologies from which to choose to tackle the problem.The choice of which method to employ is normally not made solely by one selection criterion such as asymptotic conver-gence rate,but rather upon a host of different competing criteria including numerical proper-ties,geometricflexibility,robustness,time-to-implement,and computational cost.The pur-pose of this paper is to examine in the context of(symmetric second-order)elliptic partial differential equations(PDEs)two commonly used numerical techniques—the continuous Galerkin(CG)method and the discontinuous Galerkin(DG)method—and to provide guid-ance as to why one might select to use one versus the other when run-time versus afixed error tolerance is the major discriminating criterion.The literature concerning the continuous Galerkin(CG)methods,and in particular the finite element method(FEM),is vast.We refer the interested reader to[35,50–52]for com-prehensive discussions of the formulation and implementation of the method,and to[30, 37,42,48]for extensions to high-order(polynomial-enriched)finite elements.The salient feature of thefinite element method for elliptic problems with respect to this work is that the FEM method provides a continuous,piecewise polynomial approximation of the solu-tion which minimizes the residual of the solution in the integral sense.It is considered the mainstay numerical technique against which to make both accuracy and computational cost evaluations.On the other hand,the discontinuous Galerkin(DG)methods[20]provide what some consider to be a compact high-order extension of thefinite volume method in a way similar to how high-order or spectral/hp elements[37,48]extend standardfinite elements. Like thefinite element method,the DG methodology allows for a dual path to convergence through both elemental‘h’and polynomial‘p’refinement by providing a discontinuous, piecewise polynomial approximation of the solution that similarly minimizes the residual in the integral sense.In the overview of the development of the discontinuous Galerkin method [27]there is a succinct discussion of the merits of this compact extension offinite volumes; see also[15,16].In the context of diffusion problems,there are many different DG choices as presented in[3,4]within a unified framework.Since the inception of DG methods for elliptic problems,there have been speculations made as to whether DG methods can be made more computationally efficient than CG meth-ods.That is,for a given error tolerance,can the run-time necessary to compute a DG solu-tion be made more efficient than what is required tofind a corresponding CG solution.This speculation has been fueled by the claim that although a DG solution has more degrees of freedom than a corresponding CG solution on the same mesh and at the same polynomial degree(due to not enforcing inter-element continuity and therefore not removing global degrees of freedom),the corresponding linear system that one generates is more weakly coupled and hence more amenable to various optimization techniques.DG advocates of-ten highlight the fact that as one increases the polynomial degree per(geometric)element,the number of degrees of freedom in the volumetric interior of an element increases more rapidly than the degrees of freedom on element boundaries,and hence,in spite of the extra degrees of freedom the DG methodology becomes more efficient for high-degree polyno-mial approximations.Advocates of the CG method have always pointed to the fact that,in addition to the lower degree of freedom count due to constraining the solution at the el-ement boundaries,years of employing CG methods have led to a tremendous number of optimization techniques—not least among them static condensation—that,combined with the approximation properties of CG methods for elliptic problems,makefinite elements a very tenable choice.Until recently,domain decomposition and optimization techniques that exploit the de-coupling of local and global degrees of freedom have only been available to the CG method and hence made any comparison between CG and DG methods unrealistic.How-ever,the recent introduction of a static-condensation-amenable DG method—the hybridiz-able discontinuous Galerkin(HDG)method[22]—now makes a realistic comparison pos-sible.The HDG method is a DG method that can be rendered hybrid since its numer-ical trace of the scalar variable,λ,can be expressed as the only globally coupled un-known;see the definition of a hybrid method in[14,p.421].It is the ability to hybridize the formulation that makes it possible to implement CG and HDG solvers in very similar ways.In this paper,we present both implementation and optimization strategies for the HDG method applied to a two-dimensional model elliptic problem.We implement our HDG ap-proach within a spectral/hp element framework so that comparisons can be done between HDG and the traditional CG approach.We demonstrate that the HDG approach generates a global system for the approximation on the boundaries of the elements that although larger in rank than the traditional static condensation system in CG,has significantly smaller band-width at moderate polynomial degrees.We show that,if one ignores set-up costs above ap-proximately fourth-degree polynomial expansions on triangles and quadrilaterals the HDG method can be made as efficient as the CG approach,making it attractive for time-dependent problems.1.1BackgroundLet us provide a brief a review of the relevant literature related to the HDG method,with a particular emphasis on its connection with the traditional concept of static condensation as used infinite elements.Hybridization wasfirst introduced back in1965as a technique to efficiently implement and solvefinite element approximations for linear elasticity[32].Roughly speaking,the idea consists in expressing the unknowns in terms of the hybrid unknownλin an element-by-element fashion;the functionλis called hybrid because it is defined only on the boundaries of the elements.The original variables are subsequently eliminated,giving rise to a global system of equations involving onlyλ.In1985,it was noted[2]that the hybrid unknownλsuper-converged to a projection of the solution for the hybridized version of the mixed method of Raviart-Thomas(RT) for symmetric second-order elliptic problems[41].This observation was then used to con-struct a means of enhancing the accuracy of thefinite element approximation by using a local post-processing[2].Similar post-processing results were obtained for the so-called Brezzi-Douglas-Marini(BDM)mixed method in[9].Variations on post-processing have been proposed in[8,33,46,47]and an extension to the Hellan-Herrmann-Johnson method in[28].In2004,hybridized RT and BDM methods of arbitrary order were revisited and a weak formulation for the hybrid unknownλwas found[17];see[13]for the lowest order RT method.This weak formulation allowed for a new,effective assembly of the matrix equa-tion for the degrees of freedom ofλ.It also allowed for establishing unsuspected relations between the RT and BDM methods and opened the way for the devising and analysis of new,variable-degree versions of those methods[18].Soon after,the above approach was extended to produce a unifying framework for the hy-bridization of mixed,discontinuous and continuous Galerkin methods[22].All the methods in this framework were such that the only globally coupled unknown was an approximation to the scalar variable on the boundaries of the elements,λ.In fact,when dealing with the RT and BDM methods,the characterization ofλis exactly the one previously obtained in[17], and,when dealing with the CG method,the way of obtainingλcoincides with the traditional static condensation procedure.In this paper,we take advantage of this unifying framework to compare the CG and a particular HDG method,the so-called LDG-H method;see[22].In carrying out the com-parison,we will attempt to balance the effects of the different advantages of these methods. Thefirst issue to take into account in this balance is that for a given polynomial degree and a given mesh,the unknownλfor the CG method has less degrees of freedom than the un-knownλfor the HDG method.The competing second issue is that the corresponding global stiffness matrix of the CG method contains a higher degree of information coupling due to interactions between the vertex degrees of freedom not present in the HDG method,making it possibly less amenable to optimization than its HDG counterpart.The third competing issue is that both the approximations to the scalar variable and its gradient given by the CG method converge with one order less than the locally post-processed approximation to the scalar variable and the approximate gradient provided by the HDG method for simplices; see[19,23,26].(This is unlike all the DG methods considered in the unified analysis of DG methods[4],which provide approximations converging with the same orders than the CG method.)A typically cited disadvantage of the CG method,namely,that it does not provide an approximation of the gradient whose normal component is single valued on the bound-aries of the elements,can now be overcome[24]by using an L2-like global projection.It is hence not considered here as a competing issue.To the best knowledge of the authors,the only comparison of the CG and HDG methods was carried out in[21],for a convection-diffusion-reaction model problem in a diffusion-dominated regime.This paper however only considers up to third-order polynomial expan-sions and considers counting non-zero matrix entries as a reflection of computation time rather than any direct timing comparisons.To end,let us point out that if the stabilization function of the h-version of the HDG method are taken to be of order one,the method converges with optimal convergence orders when using simplicial elements.However,if the stabilization function is taken to be of order 1/h,the method looses one order of convergence in both the locally post-processed approx-imation to the scalar variable and the approximate gradient;see[23,26].A similar effect is produced when instead of takingλin the space of discontinuous functions,it is taken in a subspace of continuous functions;see[25].The resulting methods,introduced in[45],were called the embedded discontinuous Galerkin(EDG)methods,and have a stiffness matrix for λwith a sparsity structure identical to that of the statically condensed CG method.A similar idea prompted the introduction of the so-called multi-scale discontinuous Galerkin(MDG) method[10,36].The EDH and MDG methods coincide in many cases.1.2OutlineThe paper is organized as follows.In Sect.2we present the CG method and outline the pro-cess of static condensation.We then use this as the model to mimic for the presentation of the DG methods and their hybridization.In Sect.3,the discretization provided by the result-ing HDG method is expressed in terms of a matrix representation which is more amenable to numerical implementation.Once the elemental building blocks are in place,we present in Sect.4the approach which is used to assemble the linear system which one solves for the trace-space degrees of freedom.In Sect.5we then proceed to discuss the patterns and algorithms that one might employ when trying to optimize the construction and assembly of the HDG system.In Sect.6we present a comparison of our HDG implementation against a CG implementation within the same code base,Nektar++.We then conclude in Sect.7by discussing the pros and cons of the HDG approach as revealed through this implementation and comparison study.2Formulation of the Building BlocksIn this section we introduce the CG and HDG methods for the following elliptic diffusion problems with mixed Dirichlet and Neumann boundary conditions:−∇2u(x)=f(x)x∈ ,(1a)u(x)=g D(x)x∈∂ D,(1b)n·∇u(x)=g N(x)x∈∂ N,(1c) where∂ D∪∂ N=∂ and∂ D∩∂ N=∅.The formulation above can be generalized in many ways which can be treated in a similar manner.For example,by considering a diffusion tensor which is given by a symmetric positive definite matrix and by adding convection and reaction terms.In order to stress the similarities between the HDG methods and the well-known CG method,we proceed as follows.In Sect.2.3wefirst highlight how to restructure the standard weak global formulation of the CG method to a weak formulation that captures the static condensation procedure.In doing so we introduce a set of local problems needed to express the degrees of freedom inside the element in terms of the degrees of freedom on the border of the element,and then,we provide the global formulation used to determine the degrees of freedom on the border of the elements.In Sect.2.4we then mimic this procedure to define the HDG methods.In other words, starting from the original global weak formulation of the HDG methods,we show how to define a static condensation procedure.Thus,we consider a set of local problems to express the approximation inside each element in terms of the approximation at its border,and then we provide a global formulation with which we determine the approximation on the border of the elements.From this perspective,both the CG and HDG methods can be viewed as following the same pipeline:construction of a collection of elemental(local)operators which are then ju-diciously assembled through a static-condensation-aware procedure to yield a global system whose solution determines the degrees of freedom on the boundary of the elements.This boundary system is significantly smaller than the full system one would solve without em-ploying the Schur-complement(the linear algebra underpinning of the static-condensationprocedure)of the corresponding assembled global system.Once the solution has been ob-tained on the boundaries of the elements,the primary solution over each element can be determined independently through a forward-application of the elemental operators.How-ever before proceeding we first define the partitioning of the domain in Sect.2.1and the finite element spaces in Sect.2.2.2.1Partitioning of the DomainWe begin by discretizing our domain.We assume T ( )is a two-dimensional tessellation of .(Note that although we will describe things in terms of two-dimensions for the pur-poses of this paper,all mathematical formulations trivially extend to three dimensions.)Let e ∈T ( )be a non-overlapping element within the tessellation such that if e 1=e 2then e 1∩ e 2=∅.By N el ,we denote the number of elements (or cardinality)of T ( ).Let ∂ edenote the boundary of the element e (i.e.¯ e \ e )and ∂ e i denote an individual edgeof ∂ e such that 1≤i ≤N e b where N e b denotes the number of edges of element e .We thendenote by the set of boundaries ∂ e of all the elements e of T ( ).Finally,we denote by N the number of edges (or cardinality)of .For simplicity,we assume that the tessellation T ( )consists of conforming elements.We say that l is an interior edge of the tessellation T ( )if there are two elements of the tessellation, e and f ,such that l = e ∩ f and the length of l is not zero.We say that l is a boundary edge of the tessellation T ( )if there is an element of the tessellation, e ,such that l = e ∩∂ and the length of l is not zero.In Fig.1,we present a diagram of the domain and elemental tessellation demonstrating the use of our notation.As it will be useful later,let us define a collection of index mapping functions,graphi-cally depicted in Fig.2,that allow us to relate the local edges of an element e ,namely,∂ e 1,...,∂ e N e b,with the global edges of ,that is,with 1,...,N .Thus,since the j -th edge of the element e ,∂ e j ,is the l -th edge l of the set of edges ,we set σ(e,j)=l sothat we can write ∂ e j =σ(e,j).Similarly,since the interior edge l is the intersection of the boundaries of the two elements e and f ,we set η(l,+)=e and η(l,−)=f so that we can write l =∂ η(l,+)∩∂ η(l,−).Here the ±convention is arbitrary.Note that everything we are going to do can be extended to non-conforming discretiza-tions;the definition of the set of edges and index mapping functions will have to be modified accordingly.Also note that the definitions above do not preclude the use of more non-traditional element types (e.g.diamond or hexagonal elements).Fig.1Diagram of the domain(left )and correspondingtessellation (center and right )demonstrating the use of ournotation.Note that thetessellation is a polygonalapproximation consisting ofstraight-sided elements of theoriginal domainFig.2Diagram demonstratingthe use of the index mappingsdescribed in the text2.2The Finite Element SpacesNext,we define thefinite element spaces associated with the partition T( ).To begin,for a two-dimensional problem we setV h:={v∈L2( ):v| e∈P( e)∀ e∈T( )},(2a)h:={τ∈[L2( )]2:τ| e∈ ( e)∀ e∈T( )},(2b)M h:={μ∈L2( ):μ| l∈P( l)∀ l∈ },(2c) where P( l)=S P( l)is the polynomial space over the standard segment,P( e)=T P( e) is the space of polynomials of total degree P defined on a standard triangular region and P( e)=Q P( e)is the space of tensor-product polynomials of degree P on a standard quadrilateral region,defined asS P( l)={s p;0≤p≤P;(x1(s),x2(s))∈ l;−1≤s≤1},T P( e)={ξp1ξq2;0≤p+q≤P;(x1(ξ1,ξ2),x2(ξ1,ξ2))∈ e;−1≤ξ1+ξ2≤0}, Q P( e)={ξp1ξq2;0≤p,q≤P;(x1(ξ1,ξ2),x2(ξ1,ξ2))∈ e;−1≤ξ1,ξ2≤1}. Similarly ( e)=[T P( e)]2or ( e)=[Q P( e)]2.For curvilinear regions the expan-sions are only polynomials when mapped to a straight-sided standard region[37,44].2.3The CG Method and Its Static CondensationIt is well known that the approximation u CG given by the CG method is the element of the space V0hof continuous functions in V h satisfyingu CG=I h(g D)on∂ D,∇v·∇u CG=∂ Nvg N+vf,(3)for all v∈V0h such that v=0on∂ D.Here I h is a suitably defined interpolation operatorwhose image is the space of traces on∂ D of functions in V0h .We next show how to transi-tion from this standard formulation to the formulation that defines the values of u CG on the boundaries of all elements,λ.This is nothing more than the well-known static condensation procedure.Although this procedure is traditionally presented in terms of matrices,here we also present it in terms of weak formulations since in this manner its similarities with the corresponding procedure used in the HDG method will became more clear.To do this,we begin by noting that,if we assume that the functionλ,which belongs to thespace M0h of continuous functions in M h,is known,the equation satisfied by the restrictionof u CG to an arbitrary element e∈T h is the solution of the following local problem:u CG=λon∂ e,(4)e ∇v·∇u CG=evf for all v∈P( e)such that v=0on∂ e.This formulation follows from the standard global formulation of the CG method by taking the test functions v different from zero only on the element e.This implies that,if we define by Uλand by U f the local solutions to(4)when f=0and whenλ=0,respectively (i.e.the homogeneous and heterogeneous solutions),we can writeu CG=Uλ+U f.(5) The discrete problem represented by(4)can also be recast into an elemental matrix problem. To do so,wefirst defineu CG=n φen(x)ˆu CG[n]=nφbn(x)ˆu b[n]+nφin(x)ˆu i[n](6)where theφinare functions which are defined to be zero on the element boundary∂ e andφbnare functions that have support on the element boundaries.The arrayˆu CG[n]holds the degrees of freedom(modes)of the solution;ˆu b[n]andˆu i[n]holds the degrees of freedom (modes)on the boundaries and in the interior,respectively.We next introduceL[n,m]=e∇φn·∇φm,L=L b,b L b,iL i,b L i,i,f[n]=eφn f(7)where the superscripts on the matrix L correspond to the decomposition of the functionsφninto the setsφbn andφin.We can now restate(4)asˆv t Lˆu=ˆv t f(8)where v=nφen(x)ˆv[n].Considering(5),we can express Uλand U f in terms oftheir approximating expansions as follows:Uλ=nφn(x)ˆUλ[n]=nφbn(x)ˆU bλ[n]+n φin(x)ˆU iλ[n]and U f=nφn(x)ˆU f[n]=nφbn(x)ˆU b f[n]+nφin(x)ˆU i f[n].Letλ=n φbn(∂ e)ˆλ[n].By substituting these expressions into(8)and solving forˆUλassumingf=0with known boundaries based uponλ,and solving forˆU f assumingλ=0with known right-hand-side f,we arrive at(respectively):ˆU λ=I−(L i,i)−1L i,bˆλ,ˆUf=000(L i,i)−1f.(9)If we know f andλ(or equivalently f andˆλ)we would be able to construct the solution u CG,and so it therefore remains tofind a way to characterizeλ.It is reasonably straightfor-ward to see thatλis the element of the space M0hsuch thatλ=I h(g D)on∂ D,∇Uμ·∇Uλ=Uμf+∂ NUμg N for allμ∈M0hsuch that Uμ=μon∂ e,(10)where we note that U λis related to λthrough problem (4)when f =0and U μis similarly related to μ.Indeed,to see that the weak formulation (10)holds,insert the expression of the approximate solution u CG given by (5)into the standard formulation of the CG method given by (3),take the test function v to be U μ,and note that we have ∇U f ·∇U μ=0,by definition of the local solutions U f and U μ.This last result can also be demonstrated by evaluating ∇U f ·∇U μ=ˆUf L ˆU μusing the definitions (7)and (9).We can further highlight the connection between (10)and the statically condensed CG problem by considering the elemental contribution to (10)using the matrix form we intro-duced above.We can express the component of problem (10)restricted to element e asˆμt I ,−L b,i (L i,i )−1 L b,b L b,i L i,b L i,iI −(L i,i )−1L i,b ˆλ=ˆμt f b −L b,i (L i,i )−1f i where μ= n φb n (∂ e )ˆμ.Multiplying out this equation then leads us to the standard ele-mental Schur complement formulation of the statically condensed problem for ˆλ:ˆμt L b,b −L b,i (L i,i )−1L i,b ˆλ=f b −L b,i (L i,i )−1f i .(11)In summary,we have seen that the static condensation procedure for the CG method has three main steps:The introduction of the local problems (4)(or equivalently (8)),the defi-nition of the global approximation in terms of its local solutions (6)(see also (9)),and the global formulation for the approximate trace λas given by (10)and (11).Next,we show that a similar procedure can be used to define the HDG methods.2.4The Global Formulation of the DG MethodsFollowing [4],we use the so-called flux formulation to define the DG methods.Thus,we rewrite (1a )in auxiliary or mixed form as two first-order differential equations by introduc-ing an auxiliary flux variable q =∇u .We readily obtain−∇·q =f (x )x ∈ ,(12a)q =∇u(x )x ∈ ,(12b)u(x )=g D (x )x ∈∂ D ,(12c)q ·n =g N (x )x ∈∂ N .(12d)Note that the solution of this first-order system is amenable to approximation by a mixed method ,that is,by a method using approximations for both the scalar variable u and its gra-dient q .This point is explicitly made in [22]when referring to DG methods as discontinuous Galerkin mixed methods.In the unified analysis of DG methods [4],the mixed form of the DG method is called the flux formulation.Note that in most HDG presentations,e.g.,[22,23,26],the flux q is defined as the negative gradient of the primitive solution and not as its gradient,as we do here.This was done to stay close to some examples of physical relevance,like heat flow or Darcy’s flow,but here we prefer to follow [4]and take q to be the gradient of u .The DG method seeks an approximation to (u,q ),(u DG ,q DG ),in the space V h × h ,and determines it by requiring thate ∈T ( )e (∇v ·q DG )d x − e ∈T ( ) ∂ e v(n e · q DG )ds = e ∈T ( )e vf d x ,(13a)e ∈T ( )e (w ·q DG )d x =− e ∈T ( ) e (∇·w )u DG d x + e ∈T ( ) ∂ e (w ·n e ) u DG ds,(13b)for all (v,w )∈V h ( )× h ( ),where the numerical traces u DG and q DG have to be suit-ably defined in terms of the approximate solution (u DG ,q DG ).As discussed in [4],many of the specific DG schemes found in the literature can be characterised by appreciating whatchoices are made for defining u DG and ˜qDG .Let us briefly discuss the choice with which we are concerned in this paper.First,let us assume that we are at an interface between two elements.Then if we require the numerical traces to be (i)linearly dependent on the available left and right values of the primitive u DG and flux values q DG on either side of the interface,(ii)consistent and (iii)singled valued,we find that the numerical traces must be of the formu = 12−C 21·n + u ++ 12−C 21·n − u −−C 22(q +·n ++q −·n −),(14a) q = 12−C 12·n + q ++ 12−C 12·n − q −−C 11(u +n ++u −n −),(14b)where C 11,C 22and C 12,C 21are some scalar and vector parameters to be chosen as to ensure the stability of the method as well as its best possible convergence properties.Note that we have dropped the super-index DG to simplify the notation.On the Dirichlet border ∂ D ,we would then haveu = 12+C 21·n u + 12−C 21·n g D ,(15a) q =q −C 11(u −g D )n ,(15b)and on the Neumann border ∂ N ,u =u −C 22(q ·n +−g N ),(16a) q = 12−C 12·n q + 12+C 12·n g N n .(16b)Next,we apply a procedure similar to the static condensation procedure for the CG method discussed in Sect.2.3.2.5The HDG Methods and Their Local ProblemsWe begin by introducing the local problems.Assuming that the functionλ:= u DG ∈M h ,(17a)is known,for any element e ,from the global formulation of the DG method,that the restriction of the DG solution to the element e ,(u e ,q e )to be the function in P ( e )× ( e )satisfies the following equations:e (∇v ·q e )d x − ∂ e v(n e · q e )ds =e vf d x ,(17b)。