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On our site OnSolver.com presented a large number of task in mathematics that you can solve online free of charge on a variety of topics: calculation of integrals and derivatives, finding the sum of the series, the solution of differential equations, etc. The main features of our website is easy to find the required task, completeness submitted online calculators and availability of a detailed solutions to all the problems with all the explanations necessary to understand solutions. Now you do not need to look for the right solution on the Internet: user-friendly menu allows you to quickly switch between tasks.

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

• Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
• Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
• Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
• Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
• Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
• SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

• Identify and define the problem
• Consider possible solutions
• Evaluate options
• Choose the best solution
• Implement the solution
• Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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Game Central

Xbox Live Goes Down in Nearly Seven-Hour Outage

By Todd Spangler

Todd Spangler

NY Digital Editor

• Abigail Disney Says She’s Halting Donations to Democrats ‘Unless and Until’ President Biden Drops Out: ‘The Stakes Are Far Too High’ 12 hours ago
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UPDATE, 7/2, 9:01 p.m. ET: Microsoft said it resolved the technical problems that had knocked out Xbox Live for nearly seven hours. “Users should no longer be encountering issues signing in to Xbox Live and services,” the Xbox Support account on X posted at 8:49 p.m. ET. “Thank you for your patience, game on!”

Xbox Live, Microsoft’s multiplayer gaming and digital media network, was suffering a major outage Tuesday as thousands of users reported problems accessing it.

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Other Microsoft-operated services, including Minecraft and the Microsoft Store, also had a high level of user error reports on Downdetector.

The official Xbox Support account on X posted at 2:55 pm. ET, “We are aware that some users have been disconnected from Xbox Live. We’re investigating!” The message directed users to the Xbox status page — which eventually was updated to say that a major outage of the “Account & profile” service was reported at 2:07 p.m. ET. “You may not be able to sign-in to your Xbox profile, may be disconnected while signed in, or have other related problems,” the message on the Xbox status page said. “Features that require sign-in like most games, apps and social activity won’t be available.”

Microsoft requires users to have an Xbox Live account (which is free to set up) to play games online and access other experiences on the Xbox console, Windows PC and Xbox mobile apps.

Xbox Live users took to social media to vent about the technical problems:

@XboxSupport what’s happening? Can’t log in. Can’t watch YT, can’t play games… whatsup xbox /microsoft 😭?? — keep swimming (@lostislander00) July 2, 2024

@XboxSupport Xbox Live is apparently so broken right now that I can’t even report that it’s down pic.twitter.com/38oRux850n — KirstenHeffron.bsky.social (@KirstenHeffron) July 2, 2024

@XboxSupport any reason why this is happening? It’s been 20 minutes and I still can’t log in. I logged in fine this morning. Also I can’t register the outage on the Microsoft website 🤬 pic.twitter.com/A0XuNaP6N6 — Chris Topher (@topbottom23) July 2, 2024

@XboxSupport is there a problem with Xbox live right now? I’ve reset my XSX a couple times and I keep getting this error. pic.twitter.com/GZGZeVxI5n — Jeff J (@MYTHODDIKAL) July 2, 2024

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Xbox Live Suffers Widespread Outage, Xbox Support 'Investigating'

Services have returned after a seven-hour outage..

Update: Xbox Live services are available once again. Xbox has not commented on the cause of the outage but has since confirmed the users should be able to use the service again.

Users should no longer be encountering issues signing in to Xbox Live and services. Thank you for your patience, game on! https://t.co/jw7EOmyyoL — Xbox Support (@XboxSupport) July 3, 2024

Xbox Live was unavailable for approximately seven hours.

Xbox Live is currently down, affecting thousands of gaming fans.

Players who attempted to log into their accounts this afternoon found they were unable to sign in and play games as usual. Microsoft describes the incident as a “major outage” on its official Xbox Live status page . The company says troubles with its service began just after 2 p.m. ET, with the website Downdetector reporting a peak of more than 38,000 individual outage reports around 3 p.m. ET.

Though a select few have shared that they’ve been able to eventually sign into Xbox Live, Microsoft says the sign-in issues affect Xbox Series X | S, Xbox One, and Xbox 360 consoles as well as mobile devices, web services, cloud gaming, backward compatibility, and Xbox on Windows. No explanation for the outage has been shared, but in the meantime, Microsoft said in an X/Twitter post that it is investigating the issue while directing concerned players to head to its status page for updates.

Our investigation is taking longer than expected, thank you for your patience and reports! We'll continue to update here and on our status page, https://t.co/kQKp1MgssY https://t.co/nNYKQKZcxL — Xbox Support (@XboxSupport) July 2, 2024

“You may not be able to sign-in to your Xbox profile, may be disconnected while signed in, or have other related problems,” the status page says at the time of this story’s publication. “Features that require sign-in like most games, apps and social activity won't be available.”

A widespread Xbox Live outage means there are thousands of gamers with questions and time on their hands. Many have them quickly took to social media to share memes while looking for answers. Although they’re all in the same boat as they wait for Microsoft to chime in with good news, many are just happy to see they aren’t the only ones faced with gaming downtime.

me checking twitter to make sure Xbox live is down for others as well, and it's not just me pic.twitter.com/aqfbXn4KX0 — 𝕏epyal 🇨🇾🇬🇷 (@xepyal) July 2, 2024

Everyone rushing to Twitter/X to see if Xbox Live is down. pic.twitter.com/w2sBW6nRCn — Andrew Stow (@AndrewStow23969) July 2, 2024

My Minecraft Horse waiting for me to return because Xbox Live is down 🥲 @XboxSupport pic.twitter.com/2OLIoq2A1D — Garrett ✨ (@gxrrettmxrtinez) July 2, 2024

We’ll update this story when Microsoft has an update on the status of Xbox Live. In the meantime, you can check out the recently confirmed Xbox Game Pass lineup for July 2024 . You can also see our IGN Live interview with CEO Phil Spencer , where we learned more about the company’s plans for the future.

Michael Cripe is a freelance contributor with IGN. He started writing in the industry in 2017 and is best known for his work at outlets such as The Pitch, The Escapist, OnlySP, and Gameranx.

Be sure to give him a follow on Twitter @MikeCripe.

Game# 33 : Jul 6, 2024

In this article.

Number Line

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
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• Middle School Math Solutions – Simultaneous Equations Calculator Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions...

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• Open access
• Published: 02 July 2024

Online-to-offline combined with problem-based learning is an effective teaching modality in the standardized residency training of nephrology

• Junxia Wu 1 ,
• Zhida Chen 1 ,
• Mhd Alaa Alhendi 2 ,
• Lina Zhu 1 &
• Kunling Ma 1  

BMC Medical Education volume  24 , Article number:  712 ( 2024 ) Cite this article

65 Accesses

Metrics details

The online-to-offline (O2O) teaching method is recognized as a new educational model that integrates network learning into offline classroom education, while problem-based learning (PBL) is a teaching modality that guides students to apply acquired theoretical knowledge to solve practical problems. However, implementing O2O combined with PBL has not been extensively explored in nephrology residency training. This study aims to explore the efficacy of O2O combined with PBL in the standardized residency training of nephrology by comparing it with the traditional lecture-based teaching (LBT).

Sixty residency trainees who participated in the standardized training of internal medicine in the nephrology department of the Second Affiliated Hospital of Zhejiang University School of Medicine were equally allocated into O2O combined with PBL (O2O/PBL) or the LBT group demographically matched. Examinations of theory, practice skills, clinical thinking and teaching satisfaction surveys were utilized to assess the teaching effects of the two groups.

Participants from the O2O/PBL group outperformed those from the LBT group in the examination of theory (81.233 ± 9.156 vs. 75.800 ± 7.009, mean ± SEM), practice skills (104.433 ± 3.569 vs.100.316 ± 4.628, mean ± SEM) and clinical thinking (88.933 ± 4.473 vs. 86.667 ± 3.844, mean ± SEM). There was no significant difference in the teaching satisfaction between the two groups.

The current study shows the positive impact of O2O combined with PBL approach on standardized residency training in nephrology without reducing teaching satisfaction.

Peer Review reports

China has established a system of national standardized medical residency training since 2014, affecting the health of its 1.4 billion people [ 1 ]. The Chinese government stated that by 2020, all new medical graduates must first complete residency training in an accredited program before working as attending physicians [ 2 ]. Residents are required to finish 33 months of training in different departments within internal medicine in order to complete their training. Moreover, 2 months are arranged for the nephrology department rotations according to the new standards for the internal medicine curriculum [ 1 ]. However, nephrology training has been facing a challenging phase, with difficulty in attracting prospective residents. Factors such as lower income, greater complexity compared to other specialties, and relatively limited job opportunities in some parts of the country may all be significant contributing factors. Therefore, improving teaching methods could potentially render nephrology easier to understand and could hopefully enhance recruitment to the field [ 3 ]. Thus, it is very important to develop new teaching methods to improve the teaching efficiency of nephrology in the standardized residency training.

The advent of the COVID-19 pandemic has necessitated a transition from the offline face-to-face teaching model to the online model as a measure to mitigate the congregation and subsequent transmission of the virus. Due to its efficiency and immediacy, online live teaching is highly regarded by a substantial number of educators [ 4 ]. Ding Talk serves as critical software extensively utilized for office work and online teaching, particularly during the COVID-19 pandemic in China [ 5 ]. The online-to-offline (O2O) teaching method is emerging as an innovative educational model that integrates network learning into offline classroom education in the post-epidemic era [ 6 ], which has been applied to advanced mathematics education and yields exceptional outcomes [ 4 ].

Problem-based learning (PBL) is recognized as an effective, active learning strategy that offers various benefits to students [ 7 , 8 ]. It is characterized as an innovative teaching method that is problem-based, student-centered, and teacher-guided, which directs students to apply their acquired theoretical knowledge to resolve practical challenges [ 9 , 10 , 11 , 12 , 13 , 14 ]. This approach has been successfully implemented in both the standardization training for ultrasonography residents as well as in undergraduate medical education [ 15 , 16 ]. However, the integration of online-to-offline combined with problem-based learning has not been well explored in the education of nephrology in the standardized residency training. Thus, the aim of this study is to explore the effect of O2O combined with the PBL teaching method in the standardized residency training of nephrology.

Participants

A total of 60 internal medicine trainees, ranging in age from 23 to 30 years, were voluntarily enrolled from the nephrology department of the Second Affiliated Hospital of Zhejiang University School of Medicine. These trainees underwent a standardized internal medicine training program in the nephrology department, which spanned from August 1, 2022, to April 30, 2023.

Study design

Following informed consent, participants were divided into two distinct groups: the traditional lecture-based teaching (LBT) group and the O2O combined with PBL (O2O/PBL) teaching group. The LBT group comprised 30 trainees, including 10 males and 20 females. And the O2O/PBL group comprised 30 trainees, including 8 males and 22 females (Table  1 ).

The training instructors of the two groups are all attending nephrologists who have worked for at least 3 years in the nephrology department of the Second Affiliated Hospital of Zhejiang University School of Medicine. And they are regularly trained by educators who are proficient in O2O/PBL and the LBT teaching methods and have passed regular assessments according to the new standards for residency training of internal medicine. Both groups of residency trainees participated in the teaching activities of the nephrology department, such as residency training lectures, case discussions, and teaching rounds. The teaching content was formulated according to the residency training teaching syllabus in China. The study was carried out following the flowchart as demonstrated in Fig.  1 .

Schematic demonstration of the process of teaching activities. In the traditional LBT model, residency trainees were exposed to new materials in class through lecture delivered by the instructor in the classroom. While residency trainees in O2O/PBL model were exposed to the material prior to class and involved in problem-based learning mode with study groups during the class via face-to-face teaching by Ding Talk broadcast. Live playback of the classes was available after class for repeated viewing to reinforce learning outcomes. O2O/PBL: Online-to-offline combined with problem-based learning; LBT: lecture-based teaching

The teaching process of O2O/PBL group involved the following: Uploading pre-class materials: including online teaching materials such as operation and theoretical courses, putting forward specific clinical problems, and guiding trainees to self-study before class. The theoretical courses referred to the related cases and summary of knowledge points of the classes in the format of slideshows. Each trainee was expected to take about 30 min to preview these materials, and the amount of online work was comparable to the time needed to review course material with the LBT group. The operation courses referred to the practice skills videos and instructions on how to perform urinary catheterization and physical checkups in nephrology. While for the LBT group, urinary catheterization was taught by bedside demonstration. They were also encouraged to self-study before the class and practice after class but with no problem-based discussion and teaching videos. In the LBT group there were no additional learning materials before the class.

During the course, trainees were divided into study groups by the instructor, each consisting of 2 to 3 trainees. They discussed the problems raised before the class, shared their own opinions, and the teacher gave feedback and summarized the questions. In each class, smart electronic screens were employed as teaching media in the classroom, and Ding Talk live broadcast started during offline classroom teaching. After the course, playback of the live broadcast of the classes was available for repeated watching to reinforce learning outcomes. The teaching process of the LBT group was as follows: trainees were encouraged to preview relevant textbooks, guidebooks and references before class, and the instructors carried out traditional classroom teaching according to the teaching syllabus. The knowledge points covered in the LBT group addressed the same teaching content as those covered in the O2O/PBL group. Furthermore, the stated learning objective for the LBT group was identical to that of the O2O/PBL group. Finally, the instructors were led to summarize and answer questions. During the class, there were no Ding Talk live broadcasts. The students were allowed to ask questions during the lectures, but no problems were proposed during the LBT classes. Both groups of trainees participated in ward work normally, including receiving inpatients, completing physical examinations, writing medical records, and observing clinical operations according to the outline of the standardized training of internal medicine.

Assessment system

After the rotation of the nephrology department, trainees of both groups participated in examinations, which included theoretical knowledge, practical skills and clinical thinking, according to the outline of residency training of nephrology. The examination results were employed as objective evaluation indicators. The full score of the theory and clinical thinking examination is 100 points, while the practical skills exam has a full score of 110 points. The theoretical examinations were formulated by the residency training secretary of the nephrology department and underwent a rigorous review by internal medicine educators (Additional file 1 ). The practical skills examination focused on the proficiency in urinary catheterization. During the clinical thinking examination, trainees were tasked with randomly selected case studies which they analyzed to summarize their medical histories, to give diagnosis, and the differential diagnosis, as well as to propose treatment strategies and interventions. An examiner will score the candidates’ professional knowledge, humanistic, professional quality, and communication ability. The entire examination process was supervised by the residency training secretary of the nephrology department and the supervisory committee of the medical residency training program, ensuring adherence to the established standards [ 2 , 17 ].

All residency trainees who participated in the study were invited to complete an anonymous survey online (Additional file 2 ) [ 18 ]. The trainees from both the traditional LBT group and O2O/PBL group were respectively assessed via questionnaires to evaluate their subjective perceptions of different teaching methods. The questionnaire covered five aspects: overall teaching satisfaction, learning difficulty, learning interest, classroom atmosphere and knowledge points consolidation. The questionnaire was assessed using a five-point scale, where a score of 1 indicated “very satisfied” and a score of 5 denoted “very dissatisfied”, with intermediate values representing “relatively satisfied”, “generally satisfied”, and “not very satisfied” [ 19 , 20 ].

Data evaluation and statistical analysis

SPSS 22.0 was utilized for statistical analysis of the theoretical scores, practical skills scores, clinical thinking scores, and teaching satisfaction survey items. All measurement data were represented by (mean ± standard deviation). Normal tests were conducted on the data, and the test scores were in line with the normal distribution, whereas the teaching satisfaction survey items were not in line with the normal distribution. An independent sample t-test [ 21 ] was applied for test scores and a chi-square test was utilized for comparison of teaching satisfaction between the two groups. P  < 0.05 was considered as statistically significant, P >0.05 was considered as not significant. All analytical methods were conducted in accordance with relevant guidelines and regulations.

Comparative analysis of the test score

The theoretical score of O2O/PBL group was 81.233 ± 9.156, and that of the LBT group was 75.800 ± 7.009. The practical skills score of O2O/PBL group was 104.433 ± 3.569, and that of the LBT group was 100.316 ± 4.628. The clinical thinking score of the O2O/PBL group was 88.933 ± 4.473, and that of the LBT group was 86.667 ± 3.844. The differences were all statistically significant ( P  < 0.05), as shown in Table  2 . We also performed an ANOVA test and obtained similar results to the independent sample t-test for the three test scores between the two groups (Additional file 3 ).

Comparative analysis of questionnaire results

In this study, a total of 60 questionnaires were distributed and all 60 were received. The questionnaire survey revealed that in the O2O/PBL group, 17 people were very satisfied, 11 people were relatively satisfied, 2 people were generally satisfied, and the satisfaction rate was 93.33%; in the LBT group, 17 people were very satisfied, 11 people were relatively satisfied, 2 people were generally satisfied, and the overall satisfaction rate was 93.33%. Teaching satisfaction survey showed no statistical difference in overall teaching satisfaction, learning difficulty, learning interest, classroom atmosphere, and knowledge points consolidation, as shown in Fig.  2 ( P  > 0.05).

Comparison of teaching satisfaction evaluation. A Chi-square test was employed for comparison between groups, P >0.05 was considered as not significant. NS: not significant

In the post-epidemic era, the single online or offline teaching method cannot meet the needs of medical education. The teaching platform is very important for developing online teaching activities as it serves as a bridge connecting teachers and students while carrying various teaching resources [ 6 , 22 ]. A smart screen with access online was provided by the Second Affiliated Hospital of Zhejiang University School of Medicine for teaching, meeting, and remote consultation. Ding Talk and smart screens make it convenient to start a live stream while conducting face-to-face teaching in the classroom. Live playback of the classes was available after class for repeated viewing to reinforce learning outcomes.

Nephrology is a comprehensive and highly practical discipline which is an important part of standardized residency training in internal medicine. Nephrology education is a demanding, complex and often frustrating task. Therefore, the implementation of innovative teaching methods is crucial for enhancing teaching quality and strengthening students’ learning initiative and enthusiasm [ 21 , 23 , 24 , 25 , 26 ].

The O2O teaching method refers to an innovative teaching method that integrates online with offline teaching, which both have the advantage of the ease and efficiency of online education and the environmental experience of offline education. It has been proven that the O2O teaching method has relatively powerful and outstanding practical and social characteristics [ 27 , 28 ]. PBL teaching method is student-centered, combined with specific cases [ 10 ]. It also stimulates students’ subjective initiative in learning through pre-class learning, in class group discussion, and self-study after class. The PBL approach has gained substantial traction in the realm of clinical education due to its effectiveness in enhancing clinical thinking and practical skills [ 29 , 30 ].

Based on these theories and experiences, we combined O2O and PBL teaching methods into the residency training of internal medicine of nephrology, utilizing smart electronic screen as the teaching medium, distributing pre-class and after-class learning materials through Ding Talk network platform, assigning pre-class and after-class homework, initiating Ding Talk live broadcast during face-to-face teaching session, and facilitating students’ discussions on clinical problems raised by instructors in study groups. The teacher summarized the questions, gave feedback and answered questions raised by the students. Finally, a statistical analysis was conducted on the students’ theoretical scores, practical skills scores, and clinical thinking assessment scores (Fig.  1 ). We found that the test scores of the O2O combined PBL teaching group were higher than those of the traditional teaching group, and the difference was statistically significant (Table  2 ). Furthermore, the teaching satisfaction of two groups of students was investigated. There was no statistically significant difference between the two groups, and the complaint rate did not increase (Fig.  2 ). These findings suggest that the O2O combined PBL teaching method was more effective than the traditional lecture-based teaching because it can significantly improve the learning effect of residency trainees without reducing teaching satisfaction. This study showed that the O2O combined PBL teaching method is promising and could be promoted in the standardized residency training of nephrology.

There are two limitations to our study. One is that we conducted the study only in our institution with a relatively small number of learners. Another limitation is that we assessed only the short-term results of this teaching approach via test scores. But our research provides a foundation for the O2O combined PBL teaching method to be conducted as an effective teaching method and applied in other institutions with more learners. Further studies are needed to investigate the long-term benefits of this teaching approach for internal medicine training in nephrology such as educational policy making and even career development in China and other countries in the future.

In summary, by comparing the learning effect of O2O/PBL and LBT in residency training of nephrology, we believe that O2O/PBL teaching method can provide a better teaching method for residency training of nephrology, which can fully mobilize students’ learning initiative and achieve better learning results.

Data availability

The related materials including teaching materials, examination materials, and teaching satisfaction surveys were kept in hard copies in the nephrology department of the Second Affiliated Hospital of Zhejiang University, School of Medicine. The original datasets of the study are available from the corresponding author on reasonable request.

Abbreviations

Online-to-offline combined with problem-based learning

lecture-based teaching

Lio J, Ye Y, Dong H, Reddy S, McConville J, Sherer R. Standardized residency training in China: the new internal medicine curriculum. Perspect Med Educ. 2018;7(1):50–3.

Article   Google Scholar  

Lio J, Dong H, Ye Y, Cooper B, Reddy S, Sherer R. Standardized residency programs in China: perspectives on training quality. Int J Med Educ. 2016;7:220–1.

Calderon KR, Vij RS, Mattana J, Jhaveri KD. Innovative teaching tools in nephrology. Kidney Int. 2011;79(8):797–9.

Peng W, Wang S. Online-offline teaching for Bio-pharmaceutical Students during the COVID-19 pandemic: the Case Study of Advanced Mathematics in Application-oriented universities of China. Front Public Health. 2022;10:911117.

Xu T, Gao Q, Ge X, Lu J. The relationship between social media and professional learning from the perspective of pre-service teachers: a survey. Educ Inf Technol (Dordr) 2023:1–26.

Zhao X, Xue W. From online to offline education in the post-pandemic era: challenges encountered by international students at British universities. Front Psychol. 2022;13:1093475.

Roche M, Adiga IK, Nayak AG. PBL trigger design by medical students: an effective active learning strategy outside the Classroom. J Clin Diagn Res. 2016;10(12):JC06–8.

Google Scholar  

Burgess A, Roberts C, Ayton T, Mellis C. Implementation of modified team-based learning within a problem based learning medical curriculum: a focus group study. BMC Med Educ. 2018;18(1):74.

Dolmans D, Loyens SMM, Marcq H, Gijbels D. Deep and surface learning in problem-based learning: a review of the literature. Adv Health Sci Educ Theory Pract. 2016;21(5):1087–112.

Stentoft D. Problem-based projects in medical education: extending PBL practices and broadening learning perspectives. Adv Health Sci Educ Theory Pract. 2019;24(5):959–69.

Wosinski J, Belcher AE, Durrenberger Y, Allin AC, Stormacq C, Gerson L. Facilitating problem-based learning among undergraduate nursing students: a qualitative systematic review. Nurse Educ Today. 2018;60:67–74.

Al-Azri H, Ratnapalan S. Problem-based learning in continuing medical education: review of randomized controlled trials. Can Fam Physician. 2014;60(2):157–65.

Hung W, Dolmans D, van Merrienboer JJG. A review to identify key perspectives in PBL meta-analyses and reviews: trends, gaps and future research directions. Adv Health Sci Educ Theory Pract. 2019;24(5):943–57.

Alrahlah A. How effective the problem-based learning (PBL) in dental education. A critical review. Saudi Dent J. 2016;28(4):155–61.

Wang Q, Li H, Pang W. From PBL tutoring to PBL coaching in undergraduate medical education: an interpretative phenomenological analysis study. Med Educ Online. 2016;21:31973.

Lin ZM, Hong YR, Liu CM, Luo ZY, Zhang Y, Xie XJ, Huang PT. PBL teaching in ultrasonography resident standardization training in the COVID-19 pandemic. BMC Med Educ. 2022;22(1):512.

Zhao L, Sun T, Sun BZ, Zhao YH, Norcini J, Chen L. Identifying the competencies of doctors in China. BMC Med Educ. 2015;15:207.

Hampton D, Culp-Roche A, Hensley A, Wilson J, Otts JA, Thaxton-Wiggins A, Fruh S, Moser DK. Self-efficacy and satisfaction with teaching in Online courses. Nurse Educ. 2020;45(6):302–6.

Hashizume CT, Myhre DL, Hecker KG, Bailey JV, Lockyer JM. Exploring the teaching motivations, satisfaction, and challenges of Veterinary Preceptors: a qualitative study. J Vet Med Educ. 2016;43(1):95–103.

Liu YM, Hou YC. Effect of multi-disciplinary teaching on learning satisfaction, self-confidence level and learning performance in the nursing students. Nurse Educ Pract. 2021;55:103128.

Yang F, Lin W, Wang Y. Flipped classroom combined with case-based learning is an effective teaching modality in nephrology clerkship. BMC Med Educ. 2021;21(1):276.

Yu H, Li X. Cultivation of positive psychological quality of College Students’ English Learning under the Online and Offline Teaching Mode during the Epidemic. Front Public Health. 2022;10:929027.

Rondon-Berrios H, Johnston JR. Applying effective teaching and learning techniques to nephrology education. Clin Kidney J. 2016;9(5):755–62.

Shah HH, Jhaveri KD, Sparks MA, Mattana J. Career choice selection and satisfaction among US adult nephrology fellows. Clin J Am Soc Nephrol. 2012;7(9):1513–20.

Jhaveri KD, Sparks MA, Shah HH. Novel educational approaches to enhance learning and interest in nephrology. Adv Chronic Kidney Dis. 2013;20(4):336–46.

Bayefsky SD, Shah HH, Jhaveri KD. Nephrology education for medical students: a narrative review. Ren Fail. 2016;38(7):1151–9.

Zhang X, Zhang B, Zhang F. Student-centered case-based teaching and online-offline case discussion in postgraduate courses of computer science. Int J Educ Technol High Educ. 2023;20(1):6.

Feher A, Veha M, Boros HM, Kovacs B, Kontor E, Szakaly Z. The relationship between online and Offline Information-seeking behaviors for Healthy Nutrition. Int J Environ Res Public Health 2021, 18(19).

Wang B, Zhang M, Zhao Z, Huang Y, Li J, Chen X, Su J, Yi M. Multidimensional evaluation of offline and online education in dermatology teaching during the COVID-19 pandemic in a Chinese teaching hospital: a cross-sectional study. BMC Med Educ. 2023;23(1):195.

Pei L, Wu H. Does online learning work better than offline learning in undergraduate medical education? A systematic review and meta-analysis. Med Educ Online. 2019;24(1):1666538.

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This research is funded by the Second Affiliated Hospital, Zhejiang University School of Medicine under grants no.20220234 and no.20220222.

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Junxia Wu, You Ke, Zhida Chen, Lina Zhu & Kunling Ma

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Junxia Wu participated in the teaching activities, collected the data, analyzed the results and drafted the manuscript; You Ke, Zhida Chen and Lina Zhu participated in the teaching activities, Mhd Alaa Alhendi revised the manuscript and Kunling Ma designed the study. All authors contributed to the critical revision of the paper and approved the final manuscript for publication.

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Wu, J., Ke, Y., Chen, Z. et al. Online-to-offline combined with problem-based learning is an effective teaching modality in the standardized residency training of nephrology. BMC Med Educ 24 , 712 (2024). https://doi.org/10.1186/s12909-024-05675-w

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Received : 11 November 2023

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DOI : https://doi.org/10.1186/s12909-024-05675-w

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