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Problem-based learning

Problem-based learning (PBL) is a teaching method in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes. This includes knowledge acquisition, enhanced group collaboration and communication.

The PBL process was developed for medical education and has since been broadened in applications for other programs of learning. The process allows for learners to develop skills used for their future practice. It enhances critical appraisal, literature retrieval and encourages ongoing learning within a team environment.

The PBL tutorial process often involves working in small groups of learners. Each student takes on a role within the group that may be formal or informal and the role often alternates. It is focused on the student's reflection and reasoning to construct their own learning.

The Maastricht seven-jump process involves clarifying terms, defining problem(s), brainstorming, structuring and hypothesis, learning objectives, independent study and synthesising. In short, it is identifying what they already know, what they need to know, and how and where to access new information that may lead to the resolution of the problem.

The role of the tutor is to facilitate learning by supporting, guiding, and monitoring the learning process. The tutor aims to build students' confidence when addressing problems, while also expanding their understanding. This process is based on constructivism. PBL represents a paradigm shift from traditional teaching and learning philosophy, which is more often lecture-based.

The constructs for teaching PBL are very different from traditional classroom or lecture teaching and often require more preparation time and resources to support small group learning.

Meaning
Wood (2003) defines problem-based learning as a process that uses identified issues within a scenario to increase knowledge and understanding. The principles of this process are listed below: The Maastricht 7-jump involves seven steps, which are:
 * 1) Learner-driven self-identified goals and outcomes
 * 2) Students do independent, self-directed study before returning to larger group
 * 3) Learning is done in small groups of 8–10 people, with a tutor to facilitate discussion
 * 4) Trigger materials such as paper-based clinical scenarios, lab data, photographs, articles or videos or patients (real or simulated) can be used
 * 5) The Maastricht 7-jump process helps to guide the PBL tutorial process
 * 6) Based on principles of adult learning theory
 * 7) All members of the group have a role to play
 * 8) Allows for knowledge acquisition through combined work and intellect
 * 9) Enhances teamwork and communication, problem-solving and encourages independent responsibility for shared learning - all essential skills for future practice
 * 10) Anyone can do it as long it is right depending on the given causes and scenario

 * 1) discuss the case and make sure everyone understands the problem
 * 2) identify the questions that need to be answered to shed light on the case
 * 3) brainstorm what the group already knows and identify potential solutions
 * 4) analyse and structure the results of the brainstorming session
 * 5) formulate learning objectives for the knowledge that is still lacking
 * 6) do independent study, individually or in smaller groups: read articles or books, follow practicals or attend lectures to gain the required knowledge
 * 7) discuss the findings

History
The PBL process was pioneered by Barrows and Tamblyn at the medical school program at McMaster University in Hamilton in the 1960s. Traditional medical education disenchanted students, who perceived the vast amount of material presented in the first three years of medical school as having little relevance to the practice of medicine and clinically based medicine. The PBL curriculum was developed in order to stimulate learning by allowing students to see the relevance and application to future roles. It maintains a higher level of motivation towards learning, and shows the importance of responsible, professional attitudes with teamwork values. The motivation for learning drives interest because it allows for selection of problems that have real-world application.

Problem-based learning has subsequently been adopted by other medical school programs adapted for undergraduate instruction, as well as K-12. The use of PBL has expanded from its initial introduction into medical school programs to include education in the areas of other health sciences, math, law, education, economics, business, social studies, and engineering. PBL includes problems that can be solved in many different ways depending on the initial identification of the problem and may have more than one solution.

In 1974, Aalborg University was funded in Denmark and all the programs (engineering, natural and social sciences) were based on PBL. The UNESCO Chair in Problem-Based Learning in Engineering Education is at Aalborg University. Currently its roughly 20,000 students still follow PBL principles.

Advantages
There are advantages of PBL. It is student-focused, which allows for active learning and better understanding and retention of knowledge. It also helps to develop life skills that are applicable to many domains. It can be used to enhance content knowledge while simultaneously fostering the development of communication, problem-solving, critical thinking, collaboration, and self-directed learning skills. PBL may position students to optimally function using real-world experiences. By harnessing collective group intellect, differing perspectives may offer different perceptions and solutions to a problem. Following are the advantages and limitations of problem-based learning.

Enhance student-centred learning
In problem-based learning the students are actively involved and they like this method. It fosters active learning, and also retention and development of lifelong learning skills. It encourages self-directed learning by confronting students with problems and stimulates the development of deep learning.

Upholds lifelong learning
Problem-based learning gives emphasis to lifelong learning by developing in students the potential to determine their own goals, locate appropriate resources for learning and assume responsibility for what they need to know. It also greatly helps them better long term knowledge retention.

Prominence on comprehension not facts
Problem-based learning focuses on engaging students in finding solutions to real life situations and pertinent contextualized problems. In this method discussion forums collaborative research take the place of lecturing.

In-depth learning and constructivist approach
PBL fosters learning by involving students with the interaction of learning materials. They relate the concept they study with everyday activities and enhance their knowledge and understanding. Students also activate their prior knowledge and build on existing conceptual knowledge frameworks.

Augments self-learning
Students themselves resolve the problems that are given to them, they take more interest and responsibility for their learning. They themselves will look for resources like research articles, journals, web materials, text books etc. for their purpose. Thus it equips them with more proficiency in seeking resources in comparison to the students of traditional learning methods.

Better understanding and adeptness
By giving more significance to the meaning, applicability and relevance to the learning materials it leads to better understanding of the subjects learnt. When students are given more challenging and significant problems are given it makes them more proficient. The real life contexts and problems makes their learning more profound, lasting and also enhance the transferability of skills and knowledge from the classroom to work. Since there is more scope for application of knowledge and skills the transferability is increased. It will be also very helpful to them not only to visualise what it will be like applying that knowledge and expertise on their field of work or profession.

Reinforces interpersonal skills and teamwork
Project based learning is more of teamwork and collaborative learning. The teams or groups resolve relevant problems in collaboration and hence it fosters student interaction, teamwork and reinforces interpersonal skills. like peer evaluation, working with group dynamic etc. It also fosters in them the leadership qualities, learn to make decision by consensus and give constructive feed back to the team members etc.

Self-motivated attitude
Researchers say that students like problem-based learning classes rather than the traditional classes. The increase in the percentage of attendance of students and their attitude towards this approach itself makes it very clear that they are self-motivated. In fact it is more fascinating, stimulating and one of the good learning methods because it is more flexible and interesting to students. They enjoy this environment of learning for it is less threatening and they can learn independently. All these aspects make students more self-motivated and they pursue learning even after they leave the school or college.

Enriches the teacher-student relationship
Since the students are self-motivated, good teamwork, self-directed learning etc. the teachers who have worked in both traditional and project based learning formats prefer project based learning. They also feel that problem-based learning is more nurturing, significant curriculum and beneficial to the cognitive growth of the student.

Higher level of learning
The PBL students score higher than the students in traditional courses because of their learning competencies, problem solving, self-assessment techniques, data gathering, behavioral science etc. It is because they are better at activating prior knowledge, and they learn in a context resembling their future context and elaborate more on the information presented which helps in better understanding and retention of knowledge. In medical education, PBL cases can incorporate dialogue between patients and physicians, demonstrate the narrative character of the medical encounter, and examine the political economic contributors to disease production. PBL can serve as a platform for a discursive practices approach to culture that emphasizes the emergent, participant-constructed qualities of social phenomena while also acknowledging large-scale social forces.

Disadvantages
According to Wood (2003), the major disadvantage to this process involves the utilization of resources and tutor facilitation. It requires more staff to take an active role in facilitation and group-led discussion and some educators find PBL facilitation difficult and frustrating. It is resource-intensive because it requires more physical space and more accessible computer resources to accommodate simultaneous smaller group-learning. Students also report uncertainty with information overload and are unable to determine how much study is required and the relevance of information available. Students may not have access to teachers who serve as the inspirational role models that traditional curriculum offers.

Time-consuming
Although students generally like and gain greater ability to solve real-life problems in problem-based learning courses, instructors of the methodology must often invest more time to assess student learning and prepare course materials, as compared to LBL instructors. Part of this frustration also stems from the amount of time dedicated to presenting new research and individual student findings regarding each specific topic, as well as the disorganised nature of brain-storming

Traditional assumptions of the students
The problem of the problem-based learning is the traditional assumptions of the students. Most of the students might have spent their previous years of education assuming their teacher as the main disseminator of knowledge. Because of this understanding towards the subject matter students may lack the ability to simply wonder about something in the initial years of problem-based learning.

Role of the instructor
The instructors have to change their traditional teaching methodologies in order to incorporate problem-based learning. Their task is to question students' knowledge, beliefs, give only hints to correct their mistakes and guide the students in their research. All these features of problem-based learning may be foreign to some instructors; hence they find it difficult to alter their past habits.

Pupil's evaluation
The instructors have to adapt new assessment methods to evaluate the pupils' achievement. They have to incorporate written examinations with modified essay questions, practical examinations, peer and self assessments etc. Problem-based has also been considered slightly more favourable to female participants, whilst having equivocal impacts on their male counterparts when compared to lecture based learning.

Cognitive load
Sweller and others published a series of studies over the past twenty years that is relevant to problem-based learning, concerning cognitive load and what they describe as the guidance-fading effect. Sweller et al. conducted several classroom-based studies with students studying algebra problems. These studies have shown that active problem solving early in the learning process is a less effective instructional strategy than studying worked examples (Sweller and Cooper, 1985; Cooper and Sweller, 1987). Certainly active problem solving is useful as learners become more competent, and better able to deal with their working memory limitations. But early in the learning process, learners may find it difficult to process a large amount of information in a short time. Thus the rigors of active problem solving may become an issue for novices. Once learners gain expertise the scaffolding inherent in problem-based learning helps learners avoid these issues. These studies were conducted largely based on individual problem solving of well-defined problems.

Sweller (1988) proposed cognitive load theory to explain how novices react to problem solving during the early stages of learning. Sweller, et al. suggests a worked example early, and then a gradual introduction of problems to be solved. They propose other forms of learning early in the learning process (worked example, goal free problems, etc.); to later be replaced by completions problems, with the eventual goal of solving problems on their own. This problem-based learning becomes very useful later in the learning process.

Many forms of scaffolding have been implemented in problem-based learning to reduce the cognitive load of learners. These are most useful to enable decreasing ("fading") the amount of guidance during problem solving. A gradual fading of guidance helps learners to slowly transit from studying examples to solving problems. In this case backwards fading was found to be quite effective and assisting in decreasing the cognitive load on learners.

Evaluation of the effects of PBL learning in comparison to traditional instructional learning have proved to be a challenge. Various factors can influence the implementation of PBL: extent of PBL incorporation into curriculum, group dynamics, nature of problems used, facilitator influence on group, and the motivation of the learners. There are also various outcomes of PBL that can be measured including knowledge acquisition and clinical competence. Additional studies are needed to investigate all the variables and technological scaffolds, that may impact the efficacy of PBL.

Demands of implementing
Implementing PBL in schools and Universities is a demanding process that requires resources, a lot of planning and organization. Azer discusses the 12 steps for implementing the "pure PBL"
 * 1) Prepare faculty for change
 * 2) Establish a new curriculum committee and working group
 * 3) Designing the new PBL curriculum and defining educational outcomes
 * 4) Seeking Advice from Experts in PBL
 * 5) Planning, Organizing and Managing
 * 6) Training PBL facilitators and defining the objectives of a facilitator
 * 7) Introducing Students to the PBL Program
 * 8) Using 3-learning to support the delivery of the PBL program
 * 9) Changing the assessment to suit the PBL curriculum
 * 10) Encouraging feedback from students and teaching staff
 * 11) Managing learning resources and facilities that support self-directed learning
 * 12) Continuing evaluation and making changes (pg. 809-812)

Cultural difference: Asia
Some of the reported difficulties in implementing PBL in these schools include poor participation and difficulty in getting students involved in discussions, due possibly to their Asian reticence. One school reported that students felt that they were compelled to speak as they were being assessed. Some students reported not having enough confidence to seek information independently without guidance from their teachers. The students also found it very time-consuming to seek information themselves, as they still had to cope with the requirements of the traditional curriculum of attending lectures. Some students had difficulty with the language if the PBL discussions were conducted in English, as it was not their working language.

Constructivism
Problem-based learning addresses the need to promote lifelong learning through the process of inquiry and constructivist learning. PBL is considered a constructivist approach to instruction because it emphasizes collaborative and self-directed learning while being supported by tutor facilitation. Yew and Schmidt, Schmidt, and Hung elaborate on the cognitive constructivist process of PBL:
 * 1) Learners are presented with a problem and through discussion within their group, activate their prior knowledge.
 * 2) Within their group, they develop possible theories or hypotheses to explain the problem. Together they identify learning issues to be researched. They construct a shared primary model to explain the problem at hand. Facilitators provide scaffolding, which is a framework on which students can construct knowledge relating to the problem.
 * 3) After the initial teamwork, students work independently in self-directed study to research the identified issues.
 * 4) The students re-group to discuss their findings and refine their initial explanations based on what they learned.

PBL follows a constructivist perspective in learning as the role of the instructor is to guide and challenge the learning process rather than strictly providing knowledge. From this perspective, feedback and reflection on the learning process and group dynamics are essential components of PBL. Students are considered to be active agents who engage in social knowledge construction. PBL assists in processes of creating meaning and building personal interpretations of the world based on experiences and interactions. PBL assists to guide the student from theory to practice during their journey through solving the problem.

Supporting evidence
Several studies support the success of the constructivist problem-based and inquiry learning methods. One example is a study on a project called GenScope, an inquiry-based science software application, which found that students using the GenScope software showed significant gains over the control groups, with the largest gains shown in students from basic courses.

One large study tracked middle school students' performance on high-stakes standardized tests to evaluate the effectiveness of inquiry-based science. The study found a 14 percent improvement for the first cohort of students and a 13 percent improvement for the second cohort of students. The study also found that inquiry-based teaching methods greatly reduced the achievement gap for African-American students.

A systematic review of the effects of problem-based learning in medical school on the performance of doctors after graduation showed clear positive effects on physician competence. This effect was especially strong for social and cognitive competencies such as coping with uncertainty and communication skills.

Another study from Slovenia looked at whether students who learn with PBL are better at solving problems and if their attitudes towards mathematics were improved compared to their peers in a more traditional curriculum. The study found that students who were exposed to PBL were better at solving more difficult problems; however, there was no significant difference in student attitude towards mathematics.

Malaysia and Singapore
In Malaysia, an attempt was made to introduce a problem-based learning model in secondary mathematics, with the aim of educating citizens to prepare them for decision-making in sustainable and responsible development. This model called Problem-Based Learning the Four Core Areas (PBL4C) first sprouted in SEAMEO RECSAM in 2008, and as a result of training courses conducted, a paper was presented at the EARCOME5 conference in 2010, followed by two papers during the 15th UNESCO-APEID conference in 2011.

In Singapore, the most notable example of adopting PBL pedagogy in curriculum is Republic Polytechnic, the first polytechnic in Singapore to fully adopt PBL across all diploma courses.

Medical schools
Several medical schools have incorporated problem-based learning into their curricula following the lead of McMaster University Medical School, using real patient cases to teach students how to think like a clinician. More than eighty percent of medical schools in the United States now have some form of problem-based learning in their programs. Research of 10 years of data from the University of Missouri School of Medicine indicates that PBL has a positive effect on the students' competency as physicians after graduation.

In 1998, Western University of Health Sciences opened its College of Veterinary Medicine, with curriculum based completely on PBL.

In 2002, UC Berkeley – UCSF Joint Medical Program (JMP), an accredited five year Master of Science/Medical Doctorate Program housed at University of California, Berkeley School of Public Health, began offering a 100% case based curriculum to their students in their pre-clerkship years. The curriculum integrates the basic and preclinical sciences while fostering an understanding of the biological, social, and moral contexts of human health and disease. The students spend their last two clerkship years at University of California, San Francisco.

Ecological economics
The transdisciplinary field of ecological economics has embraced problem-based learning as a core pedagogy. A workbook developed by Joshua Farley, Jon Erickson, and Herman Daly organizes the problem-solving process into (1) building the problem base, (2) analyzing the problem, (3) synthesizing the findings, and (4) communicating the results. Building the problem base includes choosing, defining, and structuring an ecological economic problem. Analysis is breaking down of a problem into understandable components. Synthesis is the re-integration of the parts in a way that helps better understand the whole. Communication is the translation of results into a form relevant to stakeholders, broadly defined as the extended peer community. (a concept developed in Post-normal science).

Other outcomes
One of the aims of PBL is the development of self-directed learning (SDL) skills. In Loyens, Magda & Rikers' discussion, SDL is defined as "a process in which individuals take the initiative...in diagnosing their learning needs, formulating goals, identifying human and material resources, choosing and implementing appropriate learning strategies, and evaluating learning outcomes". By being invited into the learning process, students are also invited to take responsibility for their learning, which leads to an increase in self-directed learning skills. In Severiens and Schmidt's study of 305 first year college students, they found that PBL and its focus on SDL led to motivation for students to maintain study pace, led to social and academic integration, encouraged development of cognitive skills, and fostered more study progress than students in a conventional learning setting. PBL encourages learners to take a place in the academic world through inquiring and discovery that is central to problem-based learning.

PBL is also argued as a learning method that can promote the development of critical thinking skills. In PBL learning, students learn how to analyze a problem, identify relevant facts and generate hypotheses, identify necessary information/knowledge for solving the problem and make reasonable judgments about solving the problem.

Employers have appreciated the positive attributes of communication, teamwork, respect and collaboration that PBL experienced students have developed. These skills provide for better future skills preparation in the ever-changing information explosion. PBL curriculum includes building these attributes through knowledge building, written and interpersonal interactions and through the experience of the problem solving process.

Computer-supported collaborative learning
Computer-supported PBL can be an electronic version (ePBL) of the traditional face-to-face paper-based PBL or an online group activity with participants located distant apart. ePBL provides the opportunity to embed audios and videos, related to the skills (e.g. clinical findings) within the case scenarios improving learning environment and thus enhance students' engagement in the learning process. Comparing face-to-face setting with strict online PBL, the group activities play the key role in the success of the social interaction in PBL. Online PBL is also seen as more cost-effective. Collaborative PBL has been shown to improve critical thinking scores as compared with individual PBL, and increased students' achievement levels and retention scores.

For the instructors, instructional design principles for the instructors regarding the design and development of online PBL must include collaborative characteristics. For example, the scheduling must be conducive to collaborative activities. Additionally, instructors should ensure that the problems should be relevant to real-life experiences, and the nature of solutions and problem contexts. Furthermore, a sound technological infrastructure is paramount.

History of online PBL
The establishment and application of PBL in teaching and training started as early as in the 1960s. As instructional technology developed over time coupled with the emergence of the internet in the mid-1990s, online education became popular gaining huge attention from organizations and institutions. However, the use of PBL in complete online education does not seem as established based on the relatively scarce references available in the literature. In 2001, the University of Southern Queensland (USQ) was one of the first few faculties that utilized a learning management system (LMS) to facilitate collaboration and group problem-solving. The result showed the significant impact of online PBL on the learning outcomes of students in many aspects including enhancing their communication skills, problem-solving skills and ability to work as a team. The most successful feature of the LMS in terms of user rate was the discussion boards where asynchronous communications took place. Technology has advanced for another decade since then and it should help us take online PBL to a greater height as many more activities such as synchronous online meetings have been made readily available today on numerous platforms. The key focus here is to examine how technology can further facilitate the effective use of PBL online by zooming into the learner needs in each phase of PBL.

Collaborative tools
The first, and possibly most crucial phase in PBL, is to identify the problem. Before learners can begin to solve a problem, all members must understand and agree on the details of the problem. This consensus forms through collaboration and discussion. With online learning on the rise, it is important that learners can engage in collaborative brainstorming and research through the use of technology. Technology allows for groups to collaborate synchronously or asynchronously from anywhere in the world; schedules and geography no longer prevent collaboration in PBL. Today, there is a plethora of tools available to promote group collaboration online, each with unique strengths and limitations. Learning management systems and cloud-based solutions are the two most popular and accessible technological solution for online collaboration. Learning management systems, such as Canvas, Edmodo, Moodle, Schoology, and itslearning, provide schools and classrooms collaborative tools to support synchronous and asynchronous communication and learning.

The learning management systems (LMS) allow for supervision and support by the course administrator or professor. One limitation of these systems is their availability; most LMS are restricted by course enrollment. Students must be enrolled in a particular course or subscribe to a specific class to gain access to the tools and content stored in the system. Cloud-based solutions on the other hand, such as Google Apps, OneNote, and the Office 365 suit offer collaborative tools outside the traditional education setting. Educators of all kinds (K-12 schools, colleges, and universities, vocational training, HR training teams, etc.) can access these cloud-based solutions and collaborate with anyone around the world by simply sharing a link. These tools range in availability from free with an email account to subscription costs based on the suit purchased. In addition to potential financial limitations, these cloud-based systems are always as secure or private as an LMS that requires course enrollment. Both LMS and cloud-based solutions present learners with opportunities to collaborate in a variety of ways while brainstorming the meaning of the problem and developing a plan for research and future collaboration.

Research tools
Once the problem has been identified, learners move into the second step of PBL: the information gathering phase. In this phase, learners research the problem by gathering background information and researching potential solutions. This information is shared with the learning team and used to generate potential solutions, each with supporting evidence. The most popular online tool for gathering information today is Google, but there are many other search-engines available online. Free search engines, such as Google, Yahoo, or Bing, offer access to seemingly countless links to information. While these research tools provide ample sources of potential information, the quantity can be overwhelming. It also becomes difficult to identify quality sources without adding filters and higher-level search strategies when using these broad search-engines. Libraries are a more selective option and often offer online-databases, but typically require an account or subscription for online access to articles and books. Wolframalpha.com is a smart search-engine with both free and subscription level access options. Wolfram claims to be more than a platform for searching the web, rather, "getting knowledge and answers... by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods."

Presentation tools
The third most important phase of PBL is resolving the problem, the critical task is presenting and defending your solution to the given problem. Students need to be able to state the problem clearly, describe the process of problem-solving considering different options to overcome difficulties, support the solution using relevant information and data analysis. Being able to communicate and present the solution clearly is the key to the success of this phase as it directly affects the learning outcomes. With the help of technology, presentation has been made much easier and more effective as it can incorporate visual aids of charts, pictures, videos, animations, simulations etc. Ideas and connections between ideas can be clearly demonstrated using different tools. Microsoft PowerPoint 2016, Apple Keynote, Prezi, and Google Slides are among the top-rated presentation applications of 2017.

These popular presentation tools have their distinctive features and advantages over one another and can be summarized into three broad types. The first type has almost everything a presenter needs, ranging from tables, charts, picture tools, animations, video tools, add in functions and so forth. Such tools can replace many authoring tools as more complicated functions such as creating simulations, drag and drop etc. are all made possible. Hence, the presentation can be made highly interactive, engaging and compatible with most devices. The best examples are Microsoft PowerPoint and Apple Keynote. However, one drawback is that such tools often come at a subscription charge and need to be installed locally on devices. Both PowerPoint and Keynote point more towards the standard form of slide by slide presentations. Prezi represents the second major type of tools with a storytelling style and less traditional or structured form of presentation that allows one to zoom in and out of any part of the screen. These tools are generally web-based and have collaborative functions of value-add for the PBL process. Nevertheless, this type of tools also charge subscription fees based on privilege levels. The third broad type of tools would be the web-based ones free of charge with less fanciful effects, allowing access to presentations collaboratively online anytime. Google Slides is such an option which is easy to use. Though it has less functions, it offers the convenience of being available anytime anywhere on any online device. This type can be effective when students have limited time to prepare for their presentations as it removes many technical difficulties such as arranging for face-to-face meetings, installing the presentation tool or the time needed to learn to create the presentation. Students can spend more time on meaningful discussions about their problem and solution instead of the presentation itself.

P5BL approach
P5BL stands for People, Problem, Process, Product and Project Based Learning.

The P5BL approach was a learning strategy introduced in Stanford School of Engineering in their P5BL laboratory in 1993 as an initiative to offer their graduate students from the engineering, architecture and construction disciplines to implement their skills in a "cross-disciplinary, collaborative and geographically distributed teamwork experience". In this approach, which was pioneered by Stanford Professor Fruchter, an environment across six universities from Europe, the United States and Japan along with a toolkit to capture and share project knowledge was developed. The students (people) from the three disciplines were assigned a team project that works on solving a problem and delivering an end-product to a client.

The main stress of this approach is to have an inter-disciplinary integrated development of deliverables, in order to improve the overall competency and skills of the students. P5BL mentoring is a structured activity that involves situated learning and constructivist learning strategies to foster the culture of practice that would extend beyond the university campus to real life. P5BL is all about encouraging teaching and learning teamwork in the information age, by facilitating team interaction with professors, industry mentors and owners who provide necessary guidance and support for the learning activity.

Key advantages of this method are that it familiarizes students with real world problems and improves their confidence in solving these. It also improves their networking skills, thereby establishing rapport with key persons of the industry. They also learn, in an educational setting, the value of teamwork. The method also creates in them an appreciation of interdisciplinary approach.

The approach however needs due consideration of the mentoring provided to the students. Appropriate scaffolding should be done by the mentors to ensure that students are successful in attaining their project goals to solve the problem. Communication between the team should also be open and constructive in nature for achieving the necessary milestones.

title: Problem-based learning


text:
Talk:Ludovico Sforza

Images
This article has way too many images for its length. If it's not expanded, the two that aren't of il Moro should be removed. ɱў ɭ ĩє What did I do http://bits.wikimedia.org/skins-1.5/common/images/button_sig.pngwrong 23:43, 27 March 2007 (UTC)

 * One image that should go is the one that shows La Belle Ferrionare as definitively Lucrezia. It's simply not known which woman in the Duke of Milan's househeld is depicted.Levalley (talk) 04:20, 11 November 2009 (UTC)

 * As it's been awhile and no dissent, I'm making that edit.--LeValley 03:26, 11 April 2010 (UTC)

 * Cecilia was driven out of the house after Ludovico's marriage with Beatrice (and married off to some other guy). The portrait went with her. Beatrice would not have just sat around on her thumbs watching Leonardo paint some other mistress.  Exact date on the painting is unknown, but it appears to be after Beatrice married Ludovico.  Cecilia's portrait was later referred to by Beatrice's sister (who apparently did get to see it, prompting her to beg Leonardo to paint one of her).  She wrote directly to Cecilia to ask it be sent to her.  It's a nice legend (that Sforza was so powerful he forced his wife to accept his gumare's, but not supported by fact.). And I want to see an English language citation on the book burning issue. An academic history of Milan in that period or a well-researched bio of Ludovico will do. We have several here at home - no mention of this incident.--LeValley 03:36, 11 April 2010 (UTC)

The mulberry tree
The mulberry tree was on his blason because of his name, not vice versa. —Preceding unsigned comment added by 72.229.184.19 (talk) 05:22, 14 December 2007 (UTC)

Moro
There seems to be an exclusively Anglo-Saxon dispute about the meaning of the attribute "il moro". Well, "il moro" in italian does not just mean "the moor". More simply it is the masculine equivalent of "brunette". Every many that is not just straight blonde can be called "moro". So moro in his case might just very likely- and very simply - refer to his jet black hair. --141.151.247.85 (talk) 03:22, 6 April 2008 (UTC)

 * I agree.--LeValley 03:25, 11 April 2010 (UTC)

Il moro, la mora
As a matter of fact, il moro IS the name of the tree as all trees (!) in Italian are masculine. It is the fruit that is feminine, therefore la mora. Whoever wrote this should correct it and pay more attention next time. —Preceding unsigned comment added by 89.212.144.123 (talk) 09:53, 16 April 2008 (UTC)

The last supper
It says no-where on the page that he commissioned the last supper (leonardo). I haven't edited a page before so could somebody else do it. —Preceding unsigned comment added by 83.226.97.163 (talk) 08:07, 31 January 2009 (UTC)

 * I'll try. Not only is that information missing from this page (along with a host of other information about Ludovico which is historically as certain as history gets, such as where he died, under what circumstances and where he is buried), but the article confidently states that La Belle Ferrionere is one of his mistresses - something that was made up long after the fact, and which Louvre art historians are very unsure about.  Indeed, it's a subject of so much debate and research, it's ludicrous to state that this is Lucrezia, when the timing of the picture indicates it might be Beatrice herself, beautified by Leonardo (who definitely drew preliminary profile pictures of her, as he did for his other three quarter subjects - look it up!)--LeValley 03:24, 11 April 2010 (UTC)

Disentangling oft-repeated lore from fact
Somewhere, I have good citations for the 2 mistresses named (but not for many mistresses, as in the older version). Further, everything I've read has the two mistresses departing the premises once Beatrice arrived. Leonardo was still in Il Moro's employ at the time of the wedding (obviously), and so knew Beatrice until she died. Did he sneak around and paint the other mistress after the wedding? What's the date on this affair? As stated in the article, Cecilia was Ludovico's mistress before Beatrice, but she was quickly married off and the child she had with Ludovico was raised in her new husband's household. Ludovico kindly gave her quite a nice dowry. The real story is much more interesting than this article makes it seem.--LeValley 03:55, 11 April 2010 (UTC)

Portrait of Beatrice is probably not
See Julia Cartwright's voluminous research in her book, Beatrice D'Este, Duchess of Milan. The hair decorations are not consistent with what Beatrice would have worn, and that it is inconsistent with other portraits of Beatrice - instead, she thinks is Bianca Sforza, his daughter. This article doesn't say, as far as I can tell, who Bianca's mom is (yet another mistress? Where is this information coming from? I want citations!)--LeValley 04:17, 11 April 2010 (UTC)

RESA79: I am conducting research on this portrait since 2,5 years. The majority amongst art historians say it's not a portrait by da Vinci (contemporary: e.g. Kemp, Zöllner). The way the portrait is painted bears similiarities with the "Red Angel with a Lute" in the national Gallery London, for the eyes are painted in a quite similar way. Since the angel was part of the co-production de Predis/da Vinci "Virgin of the Rocks", it is quite difficult to say who painted the angel although the contract says it is de Predis. Morelli was the one who changed the attribution of the portrait from da Vinci to de Predis. One thing is absolutely clear: it is not a portrait of Beatrice d'Este but much more likely of Anna Sforza (compare with http://it.wikipedia.org/wiki/Lucrezia,_Bruto_e_Collatino). There are several portraits of Beatrice d'Este preserved and she looks quite different and by far not so attractive.

Sources:

Lermolieff, Ivan (aka Giovanni Morelli), 1890. Kunstkritische Studien über Italienische Malerei: Die Galerien Borghese und Doria Panfili in Rom. Leipzig: F.A. Brockhaus.

von Bode, Wilhelm, 1889. Ein Bildnis der zweiten Gemahlin Kaiser Maximilians, Bianca Maria Sforza, von Ambrogio de Predis. Jahrbuch der Königlich Preussischen Kunstsammlungen, 10. Bd., 2. H. (1889), pp. 71-79.

von Bode, Wilhelm, 1915. Leonardos Bildnis der jungen Dame mit dem Hermelin aus dem Czartoryski-Museum in Krakau und die Jugendbilder des Künstlers. Jahrbuch der Königlich Preussischen Kunstsammlungen, 36. Bd. (1915), pp. 189-207.

von Bode, Wilhem, 1921. Studien über Leonardo da Vinci. Berlin: G. Grote’sche Verlagsbuchhandlung.

von Liphart, Ernst Friederich, 1912. Kritische Gänge und Reiseeindrücke. Jahrbuch der Königlich Preussischen Kunstsammlungen, 33. Bd. (1912), pp. 193-224.

von Seidlitz, Wilhelm, 1906. Leonardo da Vinci und Ambrogio Preda. Jahrbuch der Kunsthistorischen Sammlungen des Allerhöchsten Kaiserhauses, Band XXVI, Heft I, pp. 1-48.

Kemp, Martin/Cotte, Pascal, 2010. "La Bella Principessa": The Profile Portrait of a Milanese Woman. London: Hodder & Stoughton.

Cartwright, Julia, 1914. Italian Gardens of the Renaissance. London: Smith, Elder & Co.

Cartwright, Julia, 1920. Beatrice d’Este, Duchess of Milan, 1475-1497: A Study of the Renaissance. 8th Ed. London: J.M. Dent & Sons.

Pascal Cotte, Lumiere Technology: http://www.lumiere-technology.com/news/Sforziada%20Owners%20Genealogy.pdf.

The true portrait of Beatrice d'Este is possibly this one:

Lorenzo Costa (Elder), ca. 1490. Beatrice d’Este, oil on wood, cm 46.5 x 35. At: Florence, Galleria degli Uffizi. URL: http://www.polomuseale.firenze.it/catalogo/scheda.asp?nctn=00287160&value=1# (Dec 2012). Please note: the Galleria degli Uffizi lists this portrait as a Ritratto di Barbara Pallavicino of the 1510s by Araldi Alessandro. — Preceding unsigned comment added by RESA79 (talk • contribs) 12:20, 31 May 2013 (UTC)

Just deleted the portrait by de Predis (attr.). This is definitely not Beatrice d'Este. Check the discussion under https://en.wikipedia.org/wiki/Talk:Beatrice_d%27Este#Art_historians_at_Pinocateca.2FBiblioteca_Ambrosiana_say_it.27s_a_Leonardo — Preceding unsigned comment added by RESA79 (talk • contribs) 20:36, 3 January 2014 (UTC)

The infobox dates on his reign are wrong
They have him reigning in the 1700's! Someone reversed some numbers somewhere. I'm not sure I should attempt to edit an info box - but if I can easily grab the dates from the article, I'll try to fix it. Last time I tried an infobox edit, I screwed it up, so there's that.--LeValley 04:23, 11 April 2010 (UTC)

 * Did what I could. Ludovico continued to claim he was Duke of Milan until the bitter end (perhaps his death) but it's specious to claim he was still Duke when the French had deposed and imprisoned him.  In this case, anyway "dates of reign" are ambiguous - even the beginning date is ambiguous, since he was de facto ruler long before the duchy properly went to him.--LeValley 04:30, 11 April 2010 (UTC)

Beatrice's age
She was born in June 1475 and married in January 1491. She was therefore 15. I'm making that change.--LeValley 00:30, 10 May 2010 (UTC)

Odd comma placement may lead to the wrong interpretation?
This sentence confuses me:

"As none of the other Italian states would help, the ruler who had invited the French into Italy four years earlier, Louis, was successful in driving out Ludovico from Milan."

I think it may be due to odd comma placement: it implies that Louis was "the ruler who had invited the French into Italy four years earlier" (instead of Sforza); and it also then starts and ends with disconnected fragments.

I think the correct format should be:

"As none of the other Italian states would help the ruler who had invited the French into Italy four years earlier, Louis was successful in driving out Ludovico from Milan."

The first clause explains the reason for the second clause, and it reads more clearly that way. But I'm not an expert on the subject, so I'm not sure I've got it correct.166.249.96.233 (talk) 16:05, 4 September 2011 (UTC)

Appearance and Personality Section
What's up with this entire section? It reads like hagiography more than anything else - strangely personal and subjective and focused on defending against imputed faults which the reader might not have even been aware of until reading the section. Also leaving aside the content it's got some odd grammar and punctuation mistakes at times too - feels like it was translated from another language, I assume Italian? His wife Beatrice also gets a similarly odd treatment as well in her similarly titled section. I'm not super familiar with Wikipedia but it all feels sorta out of place? 86.16.238.210 (talk) 22:53, 23 October 2021 (UTC)
 * Yes, this set of edits, some of which say they are translated from the Italian (presumably the it:wp bio, or even the sources.). It's not just that section either. Johnbod (talk) 03:23, 24 October 2021 (UTC)

Should "coith" be "coitus"?
I struggle finding any proper references for the word "coith". Could it be a mere misspelling/-reading/-scanning of "coitus"?Elias (talk) 21:51, 1 February 2022 (UTC)

yes, some words are sometimes mistranslated Beaest (talk) 22:06, 1 February 2022 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 23:52, 1 October 2022 (UTC)
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title: Talk:Ludovico Sforza


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User talk:ThwartedEfforts

Hello "ThwartedEfforts" and welcome to Wikipedia. A few tips for you:

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 * Sign talk page entries with ~, which is automatically converted to a name and date.
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Happy wiki'ing! -- Infrogmation 11:33, 10 Nov 2003 (UTC)

Hello from me as well. Maybe you already noticed, I converted your article 419er into a redirect as we already have an article about that topic - we try to avoid having duplicated articles. If your original content of 419er isn't covered by that article yet you may consider re-adding it. andy 11:38, 10 Nov 2003 (UTC)

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October 2007
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 * Whatever. I think it's super great we can have an army of the clueless running around adding tags to pages they don't like the look of, but anyone who guards the content jeopardised by such action is asked to justify what they're doing ThwartedEfforts 13:23, 25 October 2007 (UTC)

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Thanks!
Just read this on the Christian Bale talk page "Had he been born on a plane over the Atlantic, would he be Anglo-Boeing?" Hehe! Made me smile... She'sGotSpies (talk) 14:12, 23 July 2008 (UTC)

Christian Bale
The article has now been protected and hopefully a mediation cabal should be getting involved in the frequent debate over what Christian Bale should be listed as in the lead line. Please air your views on the talk page. Thanks White43 (talk) 11:34, 20 February 2009 (UTC)

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List of cities in Tanzania

This is a list of cities, municipalities, and towns in Tanzania.

title: List of cities in Tanzania


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title: User talk:80.178.8.118


text:
Talk:Adium

Older Revision
This page is just a free advert for the software, it is not an encyclopedia article. I'm going to point it out on votes for deletion, so get your act together or expect to see it gone. It's also not important enough to warrant a link on the Mac OS X page, sorry. GRAHAMUK 11:45, 10 Nov 2003 (UTC)

 * I'm afraid that I don't understand what you dislike about this page. A quick search revealed others quite like it, for other instant messengers: Trillian (instant messenger), Fire (instant messenger), MSN Messenger, AOL Instant Messenger, Yahoo Messenger, iChat, many of which are far more ad-like than this one.

 * If you would like to contact one of the Adium developers, head to http://www.adiumx.com/development.php . Starting with a nice request and suggestions on how to make this entry more encyclopaedic, instead of a hostile demand, would be a great way to improve this entry. -- David dchoby98, Adium Developer

 * Just a note: GRAHAMUK's comment, the one David was referring to, was about a previous version of the page, and Adium has since been rewritten. --bdesham 19:29, 18 Oct 2004 (UTC)

Background
Adium is an open source multi-platform, multi-service instant messaging program available for Mac OS X. Its messaging services implementation is provided by the open source Gaim library, popular on Linux. Adium is a highly customizable IM application, written by a team and community that have clearly taken to the medium and activity of Instant Messaging. It incorporates features resurrected from IRC (eg recalling previous message history), tabbed chat windows borrowed from Mozilla, and altogether original innovations like meta contacts (combining several IM accounts in your contacts list into a single entity).

While lacking in the A/V conferencing features offered by Apple's iChat (the Mac's default IM program), Adium provides an ad-free, fully customizable, and very poweruser-friendly IM experience to Mac users; particularly those that conduct multiple chats simultaneously.

Adium is NOT AdiumX
Adium is a seperate program than AdiumX. AdiumX is the rewrite of Adium. Shouldn't this page talk about the original Adium?

 * For the purposes of this article, we're considering Adium [original] and AdiumX to be two versions of the same program. Breaking the information into two articles wouldn't really leave enough content in either article, IMO. --bdesham 20:16, 18 Dec 2004 (UTC)

 * The above is the correct interpretation. The X is technically a part of the version number, according to the developers.

Version number
The article says that the last release was 0.77 / February 18, 2005, but the official version history says 0.76 (1/30/2005). --Ellmist 06:33, 19 Feb 2005 (UTC)

 * This has been fixed, sometimes that page isn't updated immediately.

Notability
I'm amazed that someone added the Notability template to this page. Adium is one of the "big three" third-party messengers for OS X: Proteus, Fire, Adium. It has well over 5000 users (I think the last estimates were around 30,000 - 40,000) and has been around since OS X 10.0. A Google search for "Adium" (not a common word otherwise) returns over 1 million hits. It is usually considered the most popular multiprotocol messenger for OS X. As a random example, Adium is the only third-party messenger which Google has configuration instructions for on its Gtalk site. Likewise, Gizmo Project's only supported 3rd-party tool is Adium.

Adium has also spawned Growl, another notable piece of software. Do we need additional proof? Incidentally -- why do Fire and Proteus not have a Notability template as well? -- dcclark (talk) 16:24, 23 February 2006 (UTC)

 * I agree. Adium is clearly notable. Removed Notability template. GregChant 19:51, 23 February 2006 (UTC)

 * Just as the the tag said, "please expand the article to establish notability, citing reliable sources. See Notability (software)"  I found no  proof of its notability in the current article. --Perfecto  00:26, 24 February 2006 (UTC)

 * I provided a good bit of evidence about why Adium is notable, but none of it belongs in the article. The article should not cite "over 1 million google hits" or "This is the only OS X messenger which Gtalk references". They are good examples of notability, but they aren't useful in the article itself. Could you suggest what sort of things would sufficiently expand the article for you? Additionally, I mentioned before: why don't Fire or Proteus have similar tags? -- dcclark (talk) 03:36, 24 February 2006 (UTC)

 * I have added the following sentence to the article: "It is now one of the three most popular instant messaging programs for OS X, along with Fire and Proteus." I think this establishes Adium's notability pretty firmly.  (If people feel that the references to the other two programs are inappropriate for the lead paragraph, please feel to change it.) --bdesham  ★  03:55, 24 February 2006 (UTC)

 * See Notability (software) for the inclusion criteria. I've tagged Fire and Proteus now - Do you have more?  BTW, a "three most popular" claim is best served with a citation.  Do you have independent proof?  Cite proof so no one can say you're making things up.  See Verifiability.  --Perfecto  04:00, 24 February 2006 (UTC)
 * I have added (as an example) a link to the SourceForge download statistics. You may notice that the peak was above 100,000 downloads/month, and it is typically around 2000-3000 downloads/month. I still feel that this information does NOT belong on the article page, but I hope it shows you that Adium is indeed notable. Incidentally, you may wish to check out the List of instant messengers -- presumably nearly every messenger there should be questioned for notability. Do note, however, that Adium is listed under "Mainstream". -- dcclark (talk)

 * I further submit these links, which do not belong on the article page, as evidence. Note that adding some of this information would nearly be advertising ("MacWorld says that Adium is top notch!"), and so shouldn't be added:
 * Review at Macworld (Read the whole article as well, Adium is declared "top notch")
 * MacUpdate entry Note the > 100,000 downloads.
 * VersionTracker entry Also > 100,000 downloads
 * Adium forums (as well as related projects) Note > 6000 users
 * I hope that this helps establish the credibility of the article. -- dcclark (talk) 06:31, 24 February 2006 (UTC)

 * Please respect Wikipedia guidelines. These pieces of software are clearly notable. I suggest you become a little bit more familiar with software projects in general before editing these pages. As said previously, Fire, Proteus, and Adium are the three most popular messaging clients for Mac OS X, and have been for several years. Please review the pages submitted by dcclark and remove these notices. GregChant 06:50, 24 February 2006 (UTC)

 * Addendum to the numbers quoted by dcclark above: The previous version of Adium as of this writing, 1.0.1, had 785,543 downloads between its release on 2/16/2007 and the release of 1.0.2 on 3/25/07. Evands 18:51, 25 March 2007 (UTC)

Google Summer of Code?
I thought I read something about Adium being the Google Summer of Code project this summer. Is this correct or was I dreaming? Paul C/T+ 02:25, 10 May 2006 (UTC)

 * It's not the project, just one of the many Summer of Code projects, for this summer. It's not particularly notable unless every other Summer of Code project has a note on its page. -- dcclark (talk) 02:55, 10 May 2006 (UTC)

 * Yeah, when I followed the link after my post I realized this. Oops. But, why would it be more or less notable if every other Summer of Code project was or wasn't listed on its page? We should just be concerned about the Adium page. If the fact that Adium has a SoC project is important for the Adium app, it should be noted on this page. Right? That is what makes sense to me.  Paul C/T+ 23:55, 10 May 2006 (UTC)

 * There are a *lot* of projects taking part in the Summer of Code. I don't think it's a particularly notable thing to be one of those projects, but I wouldn't object to there being a note about it in the article. In addition, many things are important for Adium -- for example, Webkit passing Acid2 or the recent spamminess of ICQ's "web-aware" mode. That doesn't necessarily need to be mentioned in the article, though. -- dcclark (talk) 00:38, 11 May 2006 (UTC)

I wanna know more about this page adium Unicorntkd (talk) 18:22, 5 December 2016 (UTC)

Pronunciation
Can someone add how to pronounce adium?

 * I think it's pronounced "AY-dee-um", if I recall correctly from a messageboard post by one of the developers; I'll look for it and get back about that. – Mipadi 18:30, 3 October 2006 (UTC)

 * Adam, the founder of the project, pronounces it "AY-dee-um". Evan, the lead developer, pronounces it "ADD-ee-um". Most people do whatever they like, there is no official pronunciation. -- dcclark (talk) 21:03, 3 October 2006 (UTC)

 * That information is in the FAQ on the Adium website. WP isn't a mirror for that information. --Colin Barrett 03:54, 10 October 2006 (UTC)
 * On the other hand, many articles do have IPA pronunciations for the article subject. Stale Fries taste better 04:25, 13 June 2007 (UTC)

Skype Protocol
Adium does NOT support Skype protocol, and there's no software which does it so far but Skype itself, I'm gonna remove Skype from the list.Koumed (talk) 01:25, 27 December 2007 (UTC)

Leopard only support starting with the 1.4 beta release
It should be noted that with the release of the 1.4 beta, Adium will now only work with Leopard, and Tiger support will end after version 1.3. I took it upon myself to put that into the article. If theres any problems with that, please write it on this talk page. - Froggy26rk (talk) 4:34, 13 July 2009 (UTC)

To Add? Pidgin Endorsement
due to no packages being compiled for OS X, pidgin endorse adium on their website, as it uses libpurple and is therefor very similar. should this be added, and if so where? Ms.henrick (talk) 16:14, 13 July 2011 (UTC)

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text:
Kittie

Kittie is a Canadian heavy metal band from London, Ontario, formed in 1996 by lead guitarist Fallon Bowman and the Lander sisters, drummer Mercedes and lead vocalist/rhythm guitarist Morgan. Tanya Candler completed the band's early line-up on bass. The Lander sisters have remained the band's sole constant members. Collectively, their material released via independent record labels has sold over two million copies worldwide.

Kittie was chosen as the band name because the name "seemed contradictory". After signing to Ng Records, Kittie released their debut album Spit (1999), which saw a wider release under Artemis Records the following year. The album, which primarily exhibited a nu metal sound, sold at least 600,000 copies in the United States and was certified gold by the RIAA. Kittie's subsequent output, including Oracle (2001) and Until the End (2004), saw the band transition towards a heavier, more aggressive albeit melodic sound featuring characteristics of alternative metal, groove metal and death metal. Neither album was able to replicate the success of Spit, and Kittie parted ways with Artemis Records in 2005.

After leaving Artemis, Kittie created their own label, X of Infamy, and released their fourth album Funeral for Yesterday in 2007. In 2009, the band signed to eOne Music, with who they released In the Black (2009) and I've Failed You (2011), both with bassist Ivana "Ivy" Jenkins. After the release of I've Failed You, Kittie went on an indefinite hiatus and the band's members pursued various other projects. In 2018, a documentary, Kittie: Origins/Evolutions, chronicling the history of the band was released in co-ordination with its 20th anniversary, followed by a one-off reunion concert. In 2022, Kittie reunited to perform at the Blue Ridge Rock and the When We Were Young festivals. Their first album in 13 years, Fire, was released on June 21, 2024, through Sumerian Records.

Formation and early years (1996–2004)
Kittie was formed in September 1996 when drummer Mercedes Lander and guitarist Fallon Bowman met in gym class. Morgan Lander, sister to Mercedes, became the lead vocalist and guitarist after weeks of Fallon and Mercedes jamming. Tanya Candler completed the line-up by joining as the bassist. Kittie recorded their first demos and began playing concerts in 1998. The band performed at Call the Office and the Embassy and signed up for Canadian Music Week in 1999. Kittie approached Jason Wyner, who was second-in-command at NG Records. After Jason saw the band perform live, NG Records signed Kittie in 1999. Kittie initially released their debut album Spit on NG Records on November 13, 1999;  however, shortly after, NG Records was purchased by Artemis Records, and production was halted. Around the same time, Candler left the band and was replaced on bass by Talena Atfield. Artemis subsequently reissued Spit, with different artwork and photographs, on January 11, 2000. It is the band's most successful album, being certified gold by the RIAA. Spit has sold at least 600,000 copies in the United States and at least 40,000 copies in Canada. They supported the album by touring with Slipknot.

Their debut album and supporting tour earned Kittie coverage in Metal Edge, whose readers voted Morgan Lander for "Female Performer of the Year" and Spit in Your Eye for "Home Video of the Year" in the magazine's 2000 Readers' Choice Awards. The band was also voted "New Band of the Year", "Who's Going to be the Next Big Thing", and "Most Underrated Band", earning them a total of five Metal Edge Readers' Choice Awards that year. On July 11, 2000, Kittie made a home-video called Spit in Your Eye which featured interviews of the band and the band playing shows with the band Slipknot. The success of Spit led Billboard to call Kittie "the most successful female band in modern metal" in December 2001.

After returning home from touring, Kittie were tasked by their label with writing their next album in three months. During this time, the band's relationship with Fallon Bowman began to deteriorate; Bowman and Morgan Lander found themselves at creative odds, and their interactions became increasingly argumentative. Bowman ultimately quit the band following an argument at a rehearsal for a radio show on May 28, 2001, and her departure was announced in August 2001. They have since reconciled their differences.

On November 13, 2001, Kittie released their second album Oracle. Sounding more aggressive than Spit, the album features elements of death metal and thrash metal. Morgan Lander noted how the band members were only 14 years old when writing their debut album and said "We haven't written in 4 or 5 years." She acknowledged a change in influence from their early days, stating, "Then we listened to bands like Nirvana, Silverchair, and Alice in Chains. Now we listen to stuff like Cannibal Corpse and Nile." However, the band would continue to write in the same fashion by first composing the music and then using that "as the backdrop behind the vocals." The album Oracle was recorded with Morgan Lander and Jeff Phillips, the latter who worked as Kittie's guitar technician and who filled Fallon's position. The album went on to ship almost 225,000 copies in the United States by 2018. On March 2, 2002, Talena Atfield left the band and was replaced on bass by Jennifer Arroyo. In April 2003, Kittie and Garth Richardson sued Artemis over unpaid royalties of $900,000 and eleven breaches of contract by the label; the dispute was settled out of court in March 2004. In 2004, the group added guitarist Lisa Marx, and Jeff Phillips went to work full-time on his side project, Thine Eyes Bleed. On July 27, 2004, Kittie released their third studio album Until the End.

Departure from Artemis and Funeral for Yesterday (2005–2007)
On March 23, 2005, Morgan Lander reported that both Lisa Marx and Jennifer Arroyo had left the band. Jennifer Arroyo's split was amicable while Lisa Marx's came as a surprise. Morgan cited financial difficulties, which they attributed to Artemis Records' poor promotion of their releases, as the reasons for both members' departures. Lander also revealed that Artemis and the band were in negotiations over whether the band's contract would be renewed, expressing her desire to leave the label. Arroyo confirmed that the split was amicable, and also cited her desire to work outside of Kittie full-time was an additional factor. She would go on to join Billy Graziadei of Biohazard in the band Suicide City.

On March 31, 2005, Kittie announced they had parted ways with Artemis Records due to "a proposed amendment to the recording budget for the pending fourth Kittie album."

In 2005, Kittie added two new members: Tara McLeod on guitar and Trish Doan on bass. In 2005, Morgan and Mercedes Lander's clothing line, Poisoned Black clothing, started. Morgan and Mercedes also appeared briefly in the documentaries Metal: A Headbanger's Journey and Heavy Metal - Louder than Life. On February 7, 2006, Kittie released their Never Again EP through Rock Ridge Music. Also in 2006, vocalist Morgan Lander provided vocals on the song "It Turns to Rust", from the album In the Arms of Devastation, by the Canadian death metal band Kataklysm.

Kittie created their own record label, Kiss of Infamy Records, and used it to release their fourth studio album. The label name was later changed to "X of Infamy" after a cease-and-desist letter from attorneys representing Kiss Catalog Ltd. (the owner of the intellectual property rights pertaining to the musical group Kiss) alleging that the Kiss of Infamy trademark was "confusingly similar" to their client's trademark. Kittie's fourth studio album Funeral for Yesterday was released on February 20, 2007, through their record label. Along with the release of Funeral for Yesterday, Morgan Lander announced that Kittie would release a 45-minute-DVD with the CD. In February 2007, Kittie toured as part of the Funeral for Yesterday Tour alongside Walls of Jericho, 36 Crazyfists, Dead To Fall, and In This Moment. Doan left Kittie following the tour due to her struggles with anorexia athletica-nervosa, which she developed during the recording of Funeral for Yesterday. From July 6 to September 16, 2007, Kittie embarked on another headlining tour of the United States, the Sweet Revenge Tour, with It Dies Today, Silent Civilian, Bring Me the Horizon and Blessed by a Broken Heart. Jeff Phillips filled in on bass for the duration of tour. Soon after, Ivy Vujic officially became the new bass player.

In the Black and I've Failed You (2008–2011)
On August 2, 2008, David Lander, father of band members Morgan and Mercedes and the band's manager, died of a heart attack.

On June 26, 2009, it was announced that Kittie signed to the E1 Music record label. The band's fifth studio album In the Black, was released on September 15, 2009. Videos were shot for two singles, "Cut Throat" and "Sorrow I Know". "Cut Throat" premiered on MTV 2's Headbangers Ball on September 5, 2009, and on the Canadian show Much Loud on September 20, 2009. "Cut Throat" also appeared on the Saw VI Soundtrack released on October 20, 2009, and also in Diary of a Wimpy Kid: Rodrick Rules, released on March 25, 2011. On September 16, 2009, an announcement was made that German label Massacre Records would distribute In the Black in Europe.

In January 2010, Kittie returned to Europe to promote In the Black. Supporting bands on the tour included It Dies Today and Malefice. This tour included dates in Scotland, England, France, Switzerland, Denmark, Belgium, Germany, Italy and the Netherlands. In a January 27, 2010 interview, Morgan Lander revealed that the band was in talks to film a video for the track "Die My Darling". In March 2010, Kittie embarked on another North American tour with God Forbid, Periphery and Gwen Stacy as support. From May through June 2010, Kittie took part in the Happy Daze tour headlined by Insane Clown Posse and featuring Coolio, Kottonmouth Kings and Necro.

Kittie participated in the 2010 Thrash and Burn tour through July and August which also featured Asking Alexandria, Born of Osiris, Evergreen Terrace, Stick to Your Guns, Chelsea Grin, Through the Eyes of the Dead, Impending Doom, Periphery and Greeley Estates. This was followed by a one-month stint as one of the two opening acts on Devildriver's 2010 North American tour.

Kittie's sixth studio album, titled I've Failed You, was released on August 30, 2011. Two videos were released for the songs "We Are the Lamb" and "Empires (Part 2)". In 2011, Mercedes Lander joined the all-female band the Alcohollys featuring former Kittie bassist Tanya Candler.

Documentary, death of Trish Doan, hiatus (2012–2020)
On February 13, 2012, Kittie announced that Ivy Vujic was resigning from the band and that Trish Doan would be returning. On September 7, 2013, Kittie performed at the Spread the Metal Festival at The Opera House in Toronto. The band would enter a period of inactivity following the performance, citing rising costs associated with touring and writing new music. Morgan later noted declining turnouts at the band's shows as a factor, with her and Mercedes both feeling that Kittie had "overstayed [their] welcome" by the time I've Failed You was released. In 2017, Mercedes described Kittie as being on an indefinite hiatus. In spite of their prolonged inactivity, the band did not want to announce that they had broken up. In 2024, McLeod said: "To admit that we were done would have been a really big heartbreak for all of us. None of us wanted to admit that even though we did overstay our welcome. We knew it was inevitable but maybe didn't want to admit it. All of us really gripped onto [Kittie] as a musical identity."

In early 2014, Kittie posted information about a secret project that was in the works to their Facebook page. On March 8, Kittie posted photos on their Facebook and Instagram of past and present members all together in the same room with a camera. On March 28, 2014, Kittie launched an Indiegogo campaign celebrating the impending 20th anniversary of the band, with a DVD documentary featuring past and present members and a tell all book. Their goal of $20,000 was reached in eight hours. The campaign closed on April 28, 2014, with a total amount of $40,525 raised, 203% of the initial goal. Kittie slated Rob McCallum to direct the documentary and Mark Eglinton to help pen the biography.

In April 2015, it was announced that Kittie would tour the United States in June 2015, as part of Ill Niño's the Civil Unrest Tour. However, a month before it could begin, the band dropped out of the tour "due to unforeseen issues with immigration in the USA". In October 2015, Kittie released a cover of David Bowie's "Space Oddity", featured on the Cleopatra Records tribute album A Salute To The Thin White Duke - The Songs Of David Bowie. Morgan, Mercedes and McLeod recorded the cover in a single day in December 2014 at Beach Road Studios with producer Siegfried Meier.

In October 2016, it was announced that drummer/vocalist Mercedes Lander had started a new sludge/doom metal band called the White Swan that released the single "Illuminate". The debut EP, Anubis, was released on November 1, 2016.

On February 11, 2017, bassist Trish Doan died at the age of 31. Doan had moved to Australia in 2013 and had frequently used her social media accounts to speak of her frustrations with depression.

On August 30, 2017, the band announced that they would performing a three-set single concert on October 27, 2017, in their hometown of London, Ontario in the London Music Hall, featuring three different line-up variations made up of both current and former members. The concert marked the launch of their 20-year anniversary documentary, and featured the return of Candler, Bowman, Phillips, Arroyo and Vujic to perform songs from their respective eras. The concert was released on DVD format on March 26, 2019.

On March 30, 2018, the documentary Kittie: Origins/Evolutions, which was filmed prior to the reunion concert, was released on Blu-ray and DVD for the very first time. Like they did with the reunion concert, Atfield and Marx declined to participate; according to Morgan Lander, Atfield was supportive of the documentary, appearing in the initial crowdfunding pitch video, but "didn't think it was the right move for her" to appear. Packaged with the movie was a CD featuring a collection of live performances by the band.

In 2019, Morgan Lander expressed uncertainty about the future of the band, the primary reason being that she didn't feel right moving the band forward without Trish Doan. Several months later, it was announced that Lander had joined the melodic death metal band, Karkaos, as their new lead singer.

In October 2020, Mercedes Lander stated that it was unlikely that Kittie would reunite to perform again without a significant financial offer and the ability to include all of the band's former members. Like her sister, she also stated that she found it difficult to go forward with the band without Doan.

Return to performing, Fire (2021–present)
In late 2021, coinciding with a resurgence in nu metal's popularity, Kittie was contacted by bookers to play several shows, prompting the band to officially end their hiatus in January 2022 with Jenkins rejoining the band on bass. On September 8, 2022, Kittie performed their first show since 2017 at the Blue Ridge Rock Festival at the Virginia International Raceway in Alton, Virginia. In October 2022, Kittie performed on all three days of the When We Were Young festival in Las Vegas, Nevada. After seeing the band perform at the When We Were Young festival, Kittie were signed to Sumerian Records by label head Ash Avildsen and began working on new material in January 2023.

On May 13, 2023, Kittie performed their first new song in 12 years, "Vultures", at the Sick New World Festival in Las Vegas. On November 19, 2023, the band confirmed that they were recording a new album with producer Nick Rasculinecz at Sienna Studios in Nashville, Tennessee. On February 13, 2024, Kittie premiered their first new song in 13 years, "Eyes Wide Open", on Sirius XM's Liquid Metal channel. The following day, the band formally released the song as a single with a music video and announced that they had signed to Sumerian Records. Upon release, Consequence, Exclaim!, Metal Hammer and Revolver listed the song as one of the best of the week. After the release of "Vultures", the band announced that its seventh album, Fire, would be released on June 21, 2024.

Musical style and influences
Kittie has been put under multiple genres of music. They have been categorized as nu metal, alternative metal,  heavy metal,  death metal,    extreme metal, groove metal,  thrash metal, gothic metal, punk, and hard rock. Kittie has often used death metal and black metal vocals in their songs and often had clean singing in those songs as well. On the Spit album, Kittie used screaming, clean singing and rapping. Kittie have been compared to bands such as Pantera, Slayer, and Mudvayne.

Kittie's formative influences were based within the Seattle grunge scene; Morgan Lander has stated that when Kittie made Spit, the band were listening to bands such as Silverchair, Alice in Chains, and Nirvana. Later on, when Morgan joined the band, Kittie transitioned from a grunge band into a nu metal band, taking inspiration from recent releases of the time by Korn, Deftones and Sepultura. When asked about their influences in an interview with Metal Maidens in 1999, the members of Kittie cited Nile, Today Is the Day, Placebo, Far, Weezer, Orgy, Fear Factory, Hole, Tura Satana, Human Waste Project, Babes in Toyland, Misfits, Blondie, and Nasum as influences. With the release of Oracle, Kittie abandoned the nu metal style found on Spit in favour of a more extreme metal sound. In interviews, Morgan has cited Marilyn Manson, Korn, Metallica, Cannibal Corpse, Nile, Carcass, At the Gates, Acid Bath, and Testament as influences on the band.

Kittie is often known for being an all-female band. Kittie's drummer Mercedes Lander said that she wants Kittie to be seen as just a metal band instead of a "girl metal" band saying "You don't call Machine Head a 'boy metal band,' you call them a metal band … Why should they make an exception [for us] just because of the gender? It's almost exactly the same kind of music, except we don't have penises."

Current

 * Morgan Lander – lead vocals, rhythm guitar, piano (1996–present)
 * Mercedes Lander – drums (1996–present), backing vocals (2005–present)
 * Tara McLeod – lead guitar (2005–present)
 * Ivana "Ivy" Jenkins – bass (2007–2012, 2022–present)

Former

 * Fallon Bowman – lead guitar, backing vocals (1996–2001)
 * Tanya Candler – bass, backing vocals (1997–1999)
 * Talena Atfield – bass (1999–2002)
 * Jeff Phillips – lead guitar, backing vocals (2001–2003) bass (2007)
 * Jennifer Arroyo – bass (2002–2005)
 * Lisa Marx – lead guitar (2004–2005)
 * Trish Doan – bass (2005–2007, 2012–2017; died 2017)

Discography
Studio albums
 * Spit (1999)
 * Oracle (2001)
 * Until the End (2004)
 * Funeral for Yesterday (2007)
 * In the Black (2009)
 * I've Failed You (2011)
 * Fire (2024)

title: Kittie


text:
Separable polynomial

In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial.

This concept is closely related to square-free polynomial. If K is a perfect field then the two concepts coincide. In general, P(X) is separable if and only if it is square-free over any field that contains K, which holds if and only if P(X) is coprime to its formal derivative D P(X).

Older definition
In an older definition, P(X) was considered separable if each of its irreducible factors in K[X] is separable in the modern definition. In this definition, separability depended on the field K; for example, any polynomial over a perfect field would have been considered separable. This definition, although it can be convenient for Galois theory, is no longer in use.

Separable field extensions
Separable polynomials are used to define separable extensions: A field extension $K ⊂ L$ is a separable extension if and only if for every $α$ in $L$ which is algebraic over $K$, the minimal polynomial of $α$ over $K$ is a separable polynomial.

Inseparable extensions (that is, extensions which are not separable) may occur only in positive characteristic.

The criterion above leads to the quick conclusion that if P is irreducible and not separable, then D P(X) = 0. Thus we must have
 * P(X) = Q(X p)

for some polynomial Q over K, where the prime number p is the characteristic.

With this clue we can construct an example:
 * P(X) = X p − T

with K the field of rational functions in the indeterminate T over the finite field with p elements. Here one can prove directly that P(X) is irreducible and not separable. This is actually a typical example of why inseparability matters; in geometric terms P represents the mapping on the projective line over the finite field, taking co-ordinates to their pth power. Such mappings are fundamental to the algebraic geometry of finite fields. Put another way, there are coverings in that setting that cannot be 'seen' by Galois theory. (See Radical morphism for a higher-level discussion.)

If L is the field extension
 * K(T 1/p),

in other words the splitting field of P, then L/K is an example of a purely inseparable field extension. It is of degree p, but has no automorphism fixing K, other than the identity, because T 1/p is the unique root of P. This shows directly that Galois theory must here break down. A field such that there are no such extensions is called perfect. That finite fields are perfect follows a posteriori from their known structure.

One can show that the tensor product of fields of L with itself over K for this example has nilpotent elements that are non-zero. This is another manifestation of inseparability: that is, the tensor product operation on fields need not produce a ring that is a product of fields (so, not a commutative semisimple ring).

If P(x) is separable, and its roots form a group (a subgroup of the field K), then P(x) is an additive polynomial.

Applications in Galois theory
Separable polynomials occur frequently in Galois theory.

For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divide the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable (which is the case for every p but a finite number) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.

Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients are polynomials in the coefficients of P, which provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G. For example, if D is the discriminant of P then $$X^2-D$$ is a resolvent for the alternating group. This resolvent is always separable (assuming the characteristic is not 2) if P is irreducible, but most resolvents are not always separable.

title: Separable polynomial


text: User talk:194.82.219.248

title: User talk:194.82.219.248


text:
Óscar Berger

Óscar José Rafael Berger Perdomo ( born 11 August 1946) is a Guatemalan businessman and politician who served as the 46th president of Guatemala from 2004 to 2008. He previously served as mayor of Guatemala City from 1991 to 1999.

Early years and family
Berger was born to an upper-class family with large sugar and coffee holdings. His paternal grandparents were Belgian immigrants. He graduated in law from the private Jesuit Rafael Landívar University.

In 1967, he married Wendy Widmann, also from a land-owning Guatemalan family. He had a son and a grandchild named Juan Pablo Berger.

Political career
In 1985, Berger joined Álvaro Arzú's successful campaign to become mayor of Guatemala City. From January 1991 to June 1999, he was mayor himself. After leaving office, he ran in the 1999 presidential election as the candidate of the National Advancement Party but lost to Alfonso Portillo.

A representative of the industrial and land oligarchy that financed his electoral campaign, Berger was elected with 54.13% of the vote in the presidential election of December 2003, ahead of his rival from the center-left, Alvaro Colom. Only 46% of those registered on the electoral rolls took part in the vote.

Berger's party worked for national reconciliation following the civil war that gripped the country until 1996.

Mayor of Guatemala City (1991-1999)
As university classmates, Berger established a friendship with Álvaro Arzú, with whom they founded the then PAN civic committee, which would later become a political party. With the support of Arzú, Berger won a seat at the Municipal Council of Guatemala City, taking office on January 15, 1986. He would later join different municipal commissions that focused on Sports, Public Health, Agriculture, Livestock, and Food, and also became director of the Municipal Social and Sports Club, one of the most popular soccer clubs in Guatemala.

On May 11, 1989, Berger and Arzú registered the National Advance Party (PAN). The newly formed center-right party would participate and win in the 1990 Guatemalan city mayoral election. Berger would be sworn in as mayor on January 15, 1991, and become re-elected in the 1995 mayoral election.

PAN would also succeed in the 1995 general election, gaining the majority of seats in Congress and qualifying Álvaro Arzú to the second round of the presidential election. Arzú would go on to defeat FRG candidate Alfonso Portillo.

1999 candidacy
During Arzú's presidential term, Berger expressed his interest in running for the presidency. On June 27, 1999, PAN would formalize his candidacy for the 1999 general election. Accordingly, Berger would step down from his mayoral duties and devote his time to the campaign.

Berger would run a campaign focusing on combatting poverty, increasing the country's wage limit, and being tough on organized crime. However, the populist rhetoric delivered by second-time presidential hopeful Alfonso Portillo would have a greater reach with the Guatemalan populace. Berger would go on to lose the second round of the presidential election; many speculated his loss as a punishment for the arrogance of President Arzú and the questionable ways state corporations were privatized during his mandate.

The electoral loss would cause conflict within the PAN party, which would later have a faction of the party leave to form the Unionist Party. During this time, Berger would break his relationship with Arzú, blaming his lousy governance for his defeat against Portillo's FRG party.

2003 candidacy
In the spring of 2002, Berger returned to the political arena with a newly formed conservative political coalition called the Great National Alliance (GANA), encompassing the Patriot Party, the Reform Movement (MR), and the National Solidarity Party (PSN). His association with GANA would cause him to be expelled from PAN. Nevertheless, after seeing a significant lead in the country's polls, Berger would accept GANA's presidential nomination.

The beginning of the 2003 presidential race was marked by the unusual registration of Efraín Ríos Montt as a presidential candidate - despite the constitution prohibiting it - and the extortions and assassinations of prominent political leaders. However, Montt would not have the significant votes to go to the second round, making the election a race between Álvaro Colom, leader of the National Unity of Hope (UNE), and Berger. Running on a campaign of political, economic, and social reform and the explicit support of the country's oligarchs, Berger would win the election with 54% of the vote. His coalition would also win 47 seats in Congress.

Presidency (2004–2008)
The inauguration of Óscar Berger as the 46th president took place on January 14, 2004. In his inaugural speech, Berger promised to continue strengthening government institutions, defend the rule of law, and fight against the impunity of corrupt and violent actors. At the beginning of his presidency, persecution began against former officials of the Portillo administration, which raised a high expectation that the government would dismantle the corrupt structure of the State. However, investigations against the officials halted, which led to Berger's approval ratings plummeting.

Domestic policy
Berger authorized the construction of several highways in Guatemala and the remodeling of the Aurora International Airport. He undertook a reform of the army, recognized the responsibility of the state for war crimes, and appointed Rigoberta Menchu, a figure of the pacifist and indigenous movement, as special ambassador to the presidency. Most of the members of his government, however, were from the oligarchy.

Serious events would also occur that exposed the degree of corruption of several of Berger's officials, such as the PARLACEN Case, the Case of the seizure of the Pavón prison, the bankruptcy of the Coffee and Commerce banks, and the million-dollar robbery at the Aurora Airport. Additionally, Berger would pursue a repressive policy towards the peasant movement. It is in this context that the massacre of Nueva Linda took place in August 2004, in which the police killed nine peasants. A CICIG report published in 2010 accused the government of Óscar Berger of carrying out "social cleansing" operations and ordering extrajudicial executions. Philip Alston, a rapporteur to the United Nations, had already, in 2007, denounced social cleansing operations involving the Guatemalan government.

CICIG
On December 12, 2006, the United Nations and the Government of Guatemala signed an agreement that would institute the International Commission Against Impunity in Guatemala (CICIG), which, after the approval of the Constitutional Court in May 2007, was subsequently ratified by Congress on August 1, 2007. Thus, the CICIG emerged as an independent international body whose purpose was to support the Public Prosecutor's Office, the National Civil Police, and other State institutions in the investigation of the crimes committed by members of the illegal security forces and clandestine security devices, and in general in the actions that tend to the dismantling of these groups.

Hurricane Stan
In October 2005, Guatemala suffered one of the worst natural disasters in its history. The passage through Central America of Hurricane Stan, whose consequences would be even more virulent than those produced years ago by Mitch, sowed chaos in the country, causing hundreds of fatalities and missing persons, as well as an incalculable number of victims.

Such was the degree of destruction generated that Berger declared the "state of public calamity." Berger would also remark in regards to the damage done by Stan: "It's not so bad, poor people are used to living like this."

Foreign policy
In March 2006, Berger would ratify the Central American Free Trade Agreement (CAFTA).

In June 2006, the Berger administration, and the governments of El Salvador, Honduras, and Nicaragua, signed the Central America-4 Free Mobility Agreement, which authorized the free movement of their citizens across borders between the four signatory states without any restrictions or checks.

Post-presidency
Berger's presidency ended on January 14, 2008, upon the inauguration of his successor, Álvaro Colom. The Colom administration would accuse Berger of leaving a floating debt of more than 4 billion quetzals.

title: Óscar Berger