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Problem-based Learning, Collaborative Learning, Problem-solving and Use of Cases to Enhance Learning: What's it all about? Alice Cassidy Centre for Teaching and Academic Growth, the University of British Columbia Last updated: July, 2005 Problems and cases are often complex, real world and interdisciplinary with no one correct answer In 1915, John Dewey, an educational theorist argued that "… education is not an affair of 'telling' and being told, but an active and constructive process" that requires "direct and continuous occupations with things." Further, for these occupations (or experiences) to be educational, they required reflection to transform them into knowledge (Dunne and Brooks, 2004) Taxonomy of Significant Learning: Kinds of Knowledge (Fink, 2003) • • • • • • Foundational Application Integration Human dimension Caring Learning Recall information and ideas Critical, creative, practical thinking Connect ideas and information Learn about oneself and others Develop new feelings, interests, values Become more self-directed Higher order thinking skills Good problems and cases should challenge students to achieve higher-level critical thinking Too often, students view learning as remembering facts, terms and definitions in order to answer questions on tests Many students seem to lack the ability or motivation to go beyond factual material to a deeper understanding of course material In Bloom's Taxonomy, cognitive levels along with parallel student activities are arranged from lower (simple - 1, 2) to complex (higher - 5,6) Problems and cases should strive to induce students to learn at the higher levels Bloom's Cognitive Level Student Activity Evaluation Making a judgment based on a pre-established set of criteria Synthesis Producing something new or original from component parts Analysis Breaking material down into its component parts to see interrelationships/hierarchy of ideas Application Using a concept or principle to solve a problem Comprehension Explaining/interpreting the meaning of material Knowledge Remembering facts, terms, concepts, definitions, principles References: Bloom, B (1956) Taxonomy of Educational Objectives, New York: McKay Fink, D (2003) Creating Significant Learning Experiences San Francisco: Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Jossey-Bass Dunne, D and K Brooks (2004) STLHE Green Guide No Teaching with Cases Halifax, Canada The Society for Teaching and Learning in Higher Education General Resources: Centre for Teaching and Academic Growth, UBC http://www.tag.ubc.ca/links/topics.php The Society for Teaching and Learning in Higher Education (join the excellent listserve to share ideas, resources and queries) http://www.mcmaster.ca/stlhe/index.html Collaborative Learning Collaborative learning is a form of instruction that involves learners working together to accomplish a common goal (Felder and Brent, 1994) It incorporates collaboration as a philosophy of interaction, where learners are responsible for their learning actions, and respect the abilities and contributions of their peers (Panitz) A related technique is Cooperative Learning (Johnson, Johnson and Holubec, 1994) They describe conditions for it to occur: • Positive interdependence – sink or swim together, responsible for ensuring that everyone learns • Individual accountability and responsibility to achieve group goals – each member is responsible for contributing a fair share to group success • Group reflection and processing – to determine what was helpful, not helpful, how to improve on effectiveness • Skills: interpersonal and group – requires trust, communication, acceptance and support of each other and resolution of conflicts • Face-to-face interaction – encouraging and facilitating each others’ efforts to achieve task or reach goals References: Felder, R.M., and Brent, R (1994) Cooperative Learning in Technical Courses: Procedures, Pitfalls, and Payoffs ERIC Document Reproduction Service, ED377038 http://www.ncsu.edu/felder-public/Papers/Coopreport.html Johnson E.W., Johnson, R.T., and Holubec, E.J (1994) The New Circles of Learning: Cooperation in the Classroom and School Alexandria: Association of Supervision and Curriculum Development Panitz, T Collaborative versus cooperative learning – A comparison of the two concepts which will help us understand the underlying nature of interactive learning http://home.capecod.net/~tpanitz/tedsarticles/coopdefinition.htm Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Learning in Groups The Tuckman Model of Group/Organization Formation Bruce W Tuckman is an educational psychologist who first described the four stages of group development in 1965 Tuckman described the four distinct stages that a group can elicit as it comes together and starts to operate The process can be subconscious, although an understanding of the stages can help a group reach effectiveness more quickly and less painfully The four stages are: Forming, Storming, Norming, and Performing In a group environment, students learn how to achieve their education goals by setting expectations, group ground rules, and/or learning contracts Reference: The Tuckman Model of Group/Organization Formation http://www.wujs.org.il/activist/leadership/manual/hadracha/group_behaviour.shtml More Resources: The Learning Contract http://www.ncl.ac.uk/n&yphm/manual/contracts.htm Stages of Group Development http://www.chimaeraconsulting.com/tuckman.htm Gibbs, G (1995) Learning in Teams: A Tutor Guide Oxford: The Oxford Centre for Staff Development This manual is designed to help tutors (instructors) to plan the productive use of student teams and to support their operation in ways which are more likely to develop the kinds of team skills which students need whatever they after they have finished studying It also addresses tricky issues such as the assessment of teams, the formation of teams and the design of appropriate tasks and assignments for teams Team-based Learning Team-based learning is a powerful instructional strategy that brings together student responsibility for learning basic course concepts, readiness assessment procedures that provide rich and rapid feedback for both individuals and teams, and opportunities for student teams to apply course concepts to problem solving assignments The readiness assessment process allows instructor to focus classroom sessions on the application and analysis of course concepts, rather then the delivery of course content The readiness assurance process consists of: Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Assigned readings - Exposes students to essential course concepts Individual testing Team testing - Same evaluation instrument as individual test During team tests students orally elaborate their understanding, defend, strengthen or adjust their schemata related to key course concepts Team feedback - Team reflection and discussion of troublesome concepts identified in results of team tests Instructor feedback - Opportunity to address misconceptions and troublesome concepts Two features distinguish Team-Based Learning from other forms of teaching with small groups and make it an especially powerful form of teaching and learning: (TBL Homepage) "TEAMS" are distinct from and more powerful than "GROUPS" • • • • When a teacher initially puts students into a group, the students are a "group," not a "team." As the students begin to trust each other and develop a commitment to the goals and welfare of the group, they become a team When they become a cohesive team, the team can things that neither a single individual nor a newly-formed group can Team-based learning starts with groups and then creates the conditions that enable them to become teams Course Examples: *** need to add in Brent MacLaine's example from UPEI - see Team learning Explanation doc Mechanical Engineering 223, Mechanical Design and Civil Engineering 400, Construction Management Contact: Jim Sibley These courses, which take place in fixed-seating, tiered lecture theatres, have enrollments of 115 students Jim reports that the first year of using TBL had great results, with students dispersing and collecting their team folder of Scantron (bubble sheet) forms during class time, and working to complete them (for the readiness assessment procedures) with great energy 3rd year Psychology of Sports (this example comes from a member of the TBL listserve, who teaches at Towson University in Maryland: Instructor: Karla Kubitz ) Excerpt from course assignment: The purpose of the assignment is to provide you with the opportunity to integrate and apply what you have learned about the group/ environment-related tools (i.e., the theories, models, etc in chapters 5-10) in the sport psychology toolbox There will be four parts to this assignment Integrative Individual Assignment Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Integrative Team Assignment Peer-evaluation Self-evaluation (the Team Self-evaluation and the individual One Minute Paper) Reference: Team-based Learning Homepage http://atlas.services.ou.edu/idp/teamlearning/index.htm More Resources: Michaelsen, L.K., Knight, A.B., and Fink, L.D (2002) Team-based Learning: A Transformative Use of Small Groups Westport: Praeger Sibley, Jim 2005 Team-based Learning: An alternative to lecturing in large class settings Sneak Preview of Tapestry (Newsletter of the Centre for Teaching and Academic Growth), University of British Columbia Download PDF from: http://www.tag.ubc.ca/resources/tapestry/index.php Case-based Learning In case-based learning, students are given a realistic statement, scenario, and/or case relevant to the course Students often apply what they learned from previous courses or their current courses to work through the case Excerpted from Dunne and Brooks (1994): Origins of the Case Method: Harvard Law School - 1870 • Real law cases used to illustrate rules of law • Students placed in roles of the parties and “think in the discipline” • Promotes judgment on part of students Harvard Business School - 1908 • Based on the Law model Perceived benefits at the time • Learning anchored in reality and based on experience • Situations multi-dimensional and often ambiguous • Students must make trade-offs between conflicting influences • In discussing the case with others, must confront your own assumptions and values More Resources: The Centre for Excellence in Teaching at the University of Southern California has an excellent collection of on-line resources on case-based learning, Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 http://www.usc.edu/programs/cet/resources/casebased/ Dunne, David and Kim Brooks (2004) STLHE Green Guide No Teaching with Cases Halifax, Canada The Society for Teaching and Learning in Higher Education (Order through STLHE at: http://www.mcmaster.ca/stlhe/publications/green.guides.htm) Course Examples: Nursing 410, Exploring Avenues of Nursing Practice, Instructor: Marion Clauson Excerpt from an in-class assignment: Perinatal Loss – Worksheet Maria Lewis, a primipara is admitted to your postpartum unit after delivering a stillborn baby boy at 38 weeks, due to a true knot in the cord Maria and her husband, John are very distraught and they can’t believe this is happening to them Part a) What is unique or different about loss during the perinatal period as compared to loss during other life crises b) Can you think of differences in how Maria and John would react if this had been an early pregnancy loss (i.e., miscarriage)? Communications 125 British Columbia Centre for International Education http://www.bccie.bc.ca/bccie/clients&partners/Publications.asp This course uses case studies to model interview and cultural history techniques Learning through Scenarios and Role Plays Course Examples: Human Kinetics 461 and 471: Prevention of Sports Injuries Instructors: Rob Lloyd-Smith and Jack Taunton This course came to our attention in TAG from a student taking it who spoke of how real-life it was Pairs of students have unique cases, which are actual cases at the Sports Medicine Clinic at UBC, including full charts on the patients One example is "Achilles Tendonitis in 48-year old male basketball player." Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Students then come to meet with the sports medicine doctors who are instructing the course With student taking on the role of the doctor, and doctor taking on the role of patient, the student asks questions and makes notes on how to proceed They then discuss the case and how the student might proceed if they were treating the patient for real Students, in pairs, then write up the case, following guidelines for the profession, and lead a joint presentation with Student responsible for: Abstract, Introduction, Case Study, Investigation, Diagnosis, References and Student responsible for: Discussion, Prevention, Conclusion The paper is worth 30%, the joint case presentation work 20% and a final examination is worth 50% of the course grade Business Administration 236: Accounting Computer Applications Instructor: Michelle Nicholson, Business Administration Michelle uses a simulated set of actual client files to teach accounting software First year Management Principles Instructor: Kerry Rempel, Business Administration Efficiency and Effectiveness Assignment Active and Experiential Learning • • • • Involve students with the material (individually, pairs, groups) Use a variety of formats, materials, modes: Learning styles, Multiple Intelligences Model the content or process Find a way for learners to “experience” it More Resources: Cameron B.J (1999) STLHE Green Guide No Active Learning Halifax, Canada The Society for Teaching and Learning in Higher Education (Order through STLHE at: http://www.mcmaster.ca/stlhe/publications/green.guides.htm) TAG On-Line Resources http://www.tag.ubc.ca/links/Topics/ActiveLearning.php Tutor-dedicated Problem-based Learning What is PBL? Medical educators at McMaster University pioneered, or reinvented, problem-based learning, in Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 about 1969 Also called problem-stimulated learning, PBL has been defined as: "A learning method based on the principle of using problems as a starting point for the acquisition and integration of new knowledge." H S Barrows, 1982 PBL is a learning environment in which the problem drives the learning That is, before students learn some knowledge they are given a problem The problem is posed so that the students discover that they need to learn some new knowledge before they can solve the problem Posing the problem before learning tends to motivate students They know why they are learning the new knowledge Learning in the context of the need-to-solve-a-problem also tends to store the knowledge in memory patterns that facilitate later recall for solving problems PBL utilizes student groups, but each group member is also responsible for independent research Further, instructor scaffolding is considerably less direct in problem-based learning than in other constructivist models such as anchored instruction Students are allowed to struggle and induct their own mental model of course concepts with only occasional "life-lines" from the instructor when concept processing falls off-track Problem-based learning is most similar to case-based instruction, but in its purest form, PBL is more open-ended In PBL, students are confronted with an ill-structured problem that mirrors real-world problems Well chosen problems encourage students to define problems, identify what information is needed, and engage in solution generation and decision making In PBL, the self-directed study occurs in small groups of 6-8 students with the aid of a facilitator, or tutor It is the tutor's role to guide the students through the problems, and to provide them with ongoing formative evaluation Although PBL uses tutorial groups, the learning is essentially an individual process, and each person is responsible for the acquisition of knowledge The tutorial is where learning issues are developed and information is shared, discussed and integrated back into the problem In addition, it is a place where clarification of concepts can occur as well as a place to share useful resources Each individual is responsible for his/her own learning, and for making sure the tutorial meets his/her own needs More Resources: Centre for Teaching and Academic Growth, UBC http://www.tag.ubc.ca/links/Topics/Problem-basedLearning.php Educational Technologies, Virginia Tech http://www.edtech.vt.edu/edtech/id/models/index.html The Effectiveness of Problem-based Learning (PBL) in Preparing Dental Students for Clinical Treatment Planning http://www.dentistry.ubc.ca/Personnel/walton/project3.html Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 Art History, University of Delaware http://www.udel.edu/pbl/ Agricultural Sciences, UBC http://www.agsci.ubc.ca/learningcentre/resources.htm FNH 313, Microorganisms in Food Systems www.agsci.ubc.ca/courses/fnh/313/FNH313.syllabus.pdf FNH 250, Nutrition: Concepts and Controversies (On-line) http://det.cstudies.ubc.ca/detsite/CourseOfferings/FNH.html FNH 472, Nutrition Assessment www.agsci.ubc.ca/courses/fnh/370/FNH370.syllabus.pdf FNH 475, Advanced Topics in Clinical Nutrition www.agsci.ubc.ca/courses/fnh/475/FNH475.syllabus.pdf FNH 497, Sports Nutrition Student Directed Seminars www.agsci.ubc.ca/courses/fnh/497/FNH497B.syllabus.pdf AGRO 461, Applied Agroecology www.agsci.ubc.ca/courses/agro/461/AGRO461.syllabus.pdf Landscape Architecture http://www.agsci.ubc.ca/landscape_architecture/our_program/html/unique_format.html Psychiatry, UBC http://www.psychiatry.ubc.ca/undergrad/PBL.htm Faulty of Medicine, UBC http://www.health-sciences.ubc.ca/desd/faculty.html A Study on Tutors' Expertise and Student Learning http://www.health-sciences.ubc.ca/desd/exp-tut-learn.html Validity of PBL Tutors' Summative Assessment http://www.health-sciences.ubc.ca/desd/tut-valid.html Students' Evaluation of Expert Vs Non-Expert PBL Tutors http://www.health-sciences.ubc.ca/desd/expert-tutors.html Educational and Counseling Psychology, and Special Education, UBC EPSE 513, Seminar in Developmental Disabilities Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 http://www.ecps.educ.ubc.ca/courses/archive/00s/EPSE_513.htm EPSE 549, Seminar in Autism http://www.ecps.educ.ubc.ca/courses/archive/00W/EPSE_549.htm Office of Distance Education and Technology (On-line Courses), UBC Pathology 417 http://det.cstudies.ubc.ca/detsite/CourseOfferings/outlinePATH417.html Microbiology 410 www.microbiology.ubc.ca/pdfs/micb410.PDF MEDG 530, Human Genetics www.medgen.ubc.ca/courses/mggp/MEDG%20530%202005.pdf Special Topics Problem-based Learning in Large Classes http://chemeng.mcmaster.ca/pbl/pbl.htm Learning through Inquiry Learning through inquiry is based on a self-directed, question-driven search for understanding An absolutely essential feature of this conception of inquiry is the explicit formation of a set of questions that provide a framework for research Inquiry can be carried out by students working as individuals or in small groups The approach can be the format for an entire course or for just part of a course The principal steps of inquiry are: the students explores a subject or theme and chooses a focus for the research; a central research question for inquiry is formulated; the student develops a plan of research, based on critical questioning and the attempt to anticipate findings; and these research findings are brought to bear on the central question The above excerpt is from Hudspith, B., and Jenkins, H (2001) STLHE Green Guide N0 Teaching the Art of Inquiry Halifax, Canada: The Society for Teaching and Learning in Higher Education Course Examples: Chemistry 121, Structural Chemistry and Chemistry 123, Physical and Organic Chemistry: From the URL below, you can link to the lab components, which are taught via inquiry Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 10 http://www.chem.ubc.ca/courseware/courseware.shtml First year Environmental Sciences (200+ students) at McMaster University Lectures are delivered using a series of questions; draw on expertise of class to start to answer question, and to discuss how to find answer More Resources: Centre of Leadership in Learning, McMaster University http://www.mcmaster.ca/cll/inquiry/inquiry.resources.htm A list of resources on inquiry learning can be found here Information ranges from general broad definition of inquiry-based learning to specific topics such as group formation, problem writing, and examples in specific fields Project-based Learning Students participate in projects and, whatever the discipline of the course, they often practise an interdisciplinary array of skills from such fields as math, language, fine arts, science, and technology for process and/or content More Resources: Project-based Learning, University of Calgary http://www.ucalgary.ca/~kmkahler/67910/projectbased/ Project-based Learning, University of Kansas http://pblchecklist.4teachers.org/ Project-based Learning http://www.techlearning.com/db_area/archives/TL/2003/01/project.html Project-based Learning, Roskilde University http://www.ruc.dk Course Examples: Business Administration 128: Computer Applications (a required course) Instructor: Michelle Nicholson, Business Administration Michelle uses a case style term project to ensure that students apply the skills they have learned using a textbook Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 11 2nd year (graduating year) course: Capstone Design Project Instructor: Iain Cameron, Mechanical Engineering Technology Students work in teams to carry out design projects Teacher Preparation course for teachers of English as an Additional Language Instructor: Yan Guo, University of Calgary Students integrate language, content, and skills through projects Guided Design Guided design involves active learning and sustained participation in small groups Students are explicitly led through steps to solve problems and reach logical decisions The process is an active one requiring student participation and involvement at each step Problems, often real world situations, may be solved during scheduled class times Small-group work occurs in the presence of the instructor, who provides feedback and encouragement as students proceed through each step of the thinking process More Resources: Cameron, B.J (1999) STLHE Green Guide No Active Learning Halifax, Canada: The Society for Teaching and Learning in Higher Education Wales, C.E., Nardi, A.H., and Stager, R.A (1986) Professional Decision-making Morgantown, WV: West Virginia Center for Guided Design Wales, C.E., Nardi, A.H., and Stager, R.A (1987) Thinking Skills: Making a Choice Morgantown, WV: West Virginia Center for Guided Design Other Real-life Connections: Theory+Practice, Current Events, Community Service Learning… Community Service Learning is a method under which students learn and develop through thoughtfully organized service that: • • • • is conducted in and meets the needs of a community and is coordinated with an institution of higher education, and with the community; helps foster civic responsibility; is integrated into and enhances the academic curriculum of the students enrolled; and includes structured time for students to reflect on the service experience More Resources: Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 12 Center for Community Partnerships, the University of Pennsylvania http://www.upenn.edu/ccp/educate.shtml Center for Community Service-Learning, The California State University http://www.csun.edu/~ocls99/ Find out more about the Learning Exchange's Reading Week Community Service Learning Projects at Course Example: Biology 345: Human Ecology Instructor: Alice Cassidy Course Aims: Through this course, I hope to give you an opportunity to learn more about, and gain a greater appreciation of our natural world and the many ways that humans play a part in it The course is framed around basic concepts of ecology, such as ecosystems, biodiversity and cycles in nature We also focus on basic science skills, such as field observations and inquirybased learning, that are also useful in other disciplines! We'll study current events and issues, both local and global A group project will include community service, whereby your actions and knowledge can make a real difference Much of the course content will come out of what you are interested in You are invited to consider how ecology ties in to your daily life, and to make connections between ecology and other disciplines I am happy to share more details about my course through email (see top of document for link to my email address.) A thought to leave you with: It has been said that: 67% of our students learn best actively, yet many lectures are passive 69% of our students are visual, yet we often choose primarily verbal material 28% of our students think globally, so we can help them with more on the 'big picture' References: Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 13 Felder, R.M., and Silverman, L.K (1988) Learning and teaching styles in engineering education Engineering Education 78 (7): 674-681, April 1988 Montgomery, S.M Addressing diverse learning styles through the use of multimedia Other resources and discipline-specific ideas: Anthropology Flexible Delivery Initiatives, the University of Queensland http://ublib.buffalo.edu/libraries/projects/cases/ubcase.htm Professor Lesley Jolly describes the use of problem-based learning in he cultural anthropology class Biology Case Examples in Biology http://www.saltspring.com/capewest/pbl.htm An introduction on problem-based learning and 20 case examples in biology can be found here Case Studies in Science (Plant Science), State University of New York at Buffalo http://ublib.buffalo.edu/libraries/projects/cases/ubcase.htm Click to “Plant Science” for five cases in plant sciences HIV 2001, the University of Arizona http://www.biology.arizona.edu/immunology/activities/AIDS2001/main.html This is a case on the spread of HIV A stimulated “web lab” is available to assist learning Business Administration, Case Studies European Case Clearing House http://www.ecch.cranfield.ac.uk/ Business cases developed by the Cranfield School of Management, the London Business School, Harvard, University of Western Ontario, and University of Virginia can be browsed here Online inspection copies are available once registered Harvard Business, Case Method Teaching http://harvardbusinessonline.hbsp.harvard.edu/b01/en/academic/edu_casemethod.jhtml Articles on case-based teaching and over 7,500 cases on a variety of topics (Accounting, Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 14 Finance, Human Resources Management, etc) are available for US$6.50 each Darden Business Publishing, University of Virginia http://store.darden.virginia.edu/ecustomer_enu/start.swe? SWEVI=&_sn=JZ0OkfwMd5U6cyVc1mRU9Kan8vAFRAyiW6vLEyZ3IvM_&SWECmd=Refr esh&SWERF=1&SWEFullRefresh=1&SWEFullRefresh=1 Cases are available for US$3.29 each Education, Instructional Technology and Design, Case Studies University of Virginia http://curry.edschool.virginia.edu/go/ITcases/Site/Casebook/book.html Three completed cases on instructional design are available on-line Psychology Case Studies in Science, State University of New York at Buffalo http://ublib.buffalo.edu/libraries/projects/cases/ubcase.htm Click to ‘Psychology” for 10 sample cases in psychology Social Work, Introductory Course Social Policy and Social Work, Higher Education Academy http://www.swap.ac.uk/learning/PBlearning4.asp Case studies on social policy and links to Social Work Programs using problems and cases in their core curricula can be found here Problem-based Learning What is PBL? How to Set-up? Barriers? Limitations? California State University http://edweb.sdsu.edu/clrit/learningtree/PBL/WhatisPBL.html Follow the links in this page and you will find answers to many commonly asked questions related to PBL Lists of references are also available PBL in Curriculum Development Problem-based Learning, Samford University http://www.samford.edu/pbl/process_currmapping.html This site provides a few tips on what to expect and what not to expect while incorporating PBL in the curriculum Links to two excellent PDF articles on putting PBL into practice are available here Problem-based Learning, De Montfort University http://www.dmu.ac.uk/~jamesa/teaching/pbl.htm Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 15 A short and concise article on what PBL is Tips on how to incorporate a “good” PBL into existing curriculum and course design Developing PBL A Self-checklist http://www.uchsc.edu/CIS/PBLChkList.html A short list for planning and conducting PBL Dealing with Resistant Learners Pike, B., and Arch, D (1997) Dealing with Difficult Participants: 127 Practical Suggestions for Minimizing Resistance and Maximizing Results in Your Presentation San Francisco: JosseyBass Classroom Management Suggestions: http://www.yale.edu/peace/management.htm Problem Students http://www.stanford.edu/dept/CTL/teach/handbook/problem.thml Many thanks to Judy Chan, TAG Graduate Student assistant, for her assistance in the creation and updating of this document Centre for Teaching and Academic Growth, University of British Columbia Last update: June, 2005 16