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1 Problem-Based Cooperative Learning Karl Smith Civil Engineering ksmith@umn.edu http://www.ce.umn.edu/people/faculty/smith Estimation Exercise

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Formal Cooperative Learning 1.Jigsaw 2.Peer Composition or Editing 3.Reading Comprehension/Interpretation 4.Problem Solving, Project, or Presentation 5.Review/Correct Homework 6.Constructive Academic Controversy 7.Group Tests

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3 Challenged-Based Learning Problem-based learning Case-based learning Project-based learning Learning by design Inquiry learning Anchored instruction John Bransford, Nancy Vye and Helen Bateman. Creating High-Quality Learning Environments: Guidelines from Research on How People Learn

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4 Professor's Role in Formal Cooperative Learning 1.Specifying Objectives 2.Making Decisions 3.Explaining Task, Positive Interdependence, and Individual Accountability 4.Monitoring and Intervening to Teach Skills 5.Evaluating Students' Achievement and Group Effectiveness

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5 Decisions,Decisions Group size? Group selection? Group member roles? How long to leave groups together? Arranging the room? Providing materials? Time allocation?

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Formal Cooperative Learning Task Groups Perkins, David. 2003. King Arthur's Round Table: How collaborative conversations create smart organizations. NY: Wiley.

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7 Problem Based Cooperative Learning Format TASK: Solve the problem(s) or Complete the project. INDIVIDUAL: Estimate answer. Note strategy. COOPERATIVE: One set of answers from the group, strive for agreement, make sure everyone is able to explain the strategies used to solve each problem. EXPECTED CRITERIA FOR SUCCESS: Everyone must be able to explain the strategies used to solve each problem. EVALUATION: Best answer within available resources or constraints. INDIVIDUAL ACCOUNTABILITY: One member from your group may be randomly chosen to explain (a) the answer and (b) how to solve each problem. EXPECTED BEHAVIORS: Active participating, checking, encouraging, and elaborating by all members. INTERGROUP COOPERATION: Whenever it is helpful, check procedures, answers, and strategies with another group.

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Technical Estimation Exercise TASK: INDIVIDUAL: Quick Estimate (10 seconds). Note strategy. COOPERATIVE: Improved Estimate (~5 minutes). One set of answers from the group, strive for agreement, make sure everyone is able to explain the strategies used to arrive at the improved estimate. EXPECTED CRITERIA FOR SUCCESS: Everyone must be able to explain the strategies used to arrive at your improved estimate. EVALUATION: Best answer within available resources or constraints. INDIVIDUAL ACCOUNTABILITY: One member from your group may be randomly chosen to explain (a) your estimate and (b) how you arrived at it. EXPECTED BEHAVIORS: Active participating, checking, encouraging, and elaborating by all members. INTERGROUP COOPERATION: Whenever it is helpful, check procedures, answers, and strategies with another group.

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9 Group Reports Number of Ping Pong Balls –Group 1 –Group 2 –... Strategy used to arrive at estimate – assumptions, model, method, etc.

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Model 1 (lower bound) let L be the length of the room, let W be its width, let H be its height, and let D be the diameter of a ping pong ball. Then the volume of the room is V room = L * W * H, and the volume of a ball (treating it as a cube) is V ball = D 3, so number of balls = (V room ) / (V ball ) = (L * W * H) / (D 3 ).

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Model 2 (upper bound) let L be the length of the room, let W be its width, let H be its height, and let D be the diameter of a ping pong ball. Then the volume of the room is V room = L * W * H, and the volume of a ball (treating it as a sphere) is V ball = 4/3 πr 3, so number of balls = (V room ) / (V ball ) = (L * W * H) / (4/3 π r 3 ).

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Model 1 (V room / D 3 ball ) B Lower Bound Model 2 (V room / (4/3 πr 3 ball )) B Upper Bound Upper Bound/Lower Bound = 6/π ≈ 2 How does this ratio compare with 1.The estimation of the diameter of the ball? 2.The estimation of the dimensions of the room?

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13 Real World Model World Model V r /V b Calc

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15 Problem-Based Learning Problem posed Identify what we need to know Learn it Apply it START Subject-Based Learning Told what we need to know Learn it Given problem to illustrate how to use it START Normative Professional Curriculum: 1.Teach the relevant basic science, 2.Teach the relevant applied science, and 3.Allow for a practicum to connect the science to actual practice.

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16 Problem-Based Learning (PBL) Problem-based learning is the learning that results from the process of working toward the understanding or resolution of a problem. The problem is encountered first in the learning process B Barrows and Tamlyn, 1980 Core Features of PBL Learning is student-centered Learning occurs in small student groups Teachers are facilitators or guides Problems are the organizing focus and stimulus for learning Problems are the vehicle for the development of clinical problem- solving skills New information is acquired through self-directed learning

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Group Processing Plus/Delta Format Plus (+) Things That Group Did Well Delta ( ∆) Things Group Could Improve

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18 Cooperative Learning is instruction that involves people working in teams to accomplish a common goal, under conditions that involve both positive interdependence (all members must cooperate to complete the task) and individual and group accountability (each member is accountable for the complete final outcome). Key Concepts Positive Interdependence Individual and Group Accountability Face-to-Face Promotive Interaction Teamwork Skills Group Processing

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Modeling Modeling in its broadest sense is the cost-effective use of something in place of something else for some cognitive purpose (Rothenberg, 1989). A model represents reality for the given purpose; the model is an abstraction of reality in the sense that it cannot represent all aspects of reality. Any model is characterized by three essential attributes: (1) Reference: It is of something (its "referent"); (2) Purpose: It has an intended cognitive purpose with respect to its referent; (3) Cost-effectiveness: It is more cost- effective to use the model for this purpose than to use the referent itself. Rothenberg, J. 1989. The nature of modeling. In L.E. Widman, K.A. Laparo & N.R. Nielson, Eds., Artificial intelligence, simulation and modeling. New York: Wiley

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Modeling Heuristics Ravindran, Phillips, and Solberg (1987): 1.Do not build a complicated model when a simple one will suffice. 2.Beware of molding the problem to fit the technique. 3.The deduction phase of modeling must be conducted rigorously. 4.Models should be validated prior to implementation. 5.A model should never be taken too literally. 6.A model should neither be pressed to do, nor criticized for failing to do, that for which it was never intended. 7.Beware of overselling a model. 8.Some of the primary benefits of modeling are associated with the process of developing the model. 9.A model cannot be any better than the information that goes into it. 10.Models cannot replace decision makers.

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An essential aspect of modeling is the use of heuristics. Although difficult to define, heuristics are relatively easy to identify using the characteristics listed by Koen(1984): (1) Heuristics do not guarantee a solution; (2) Two heuristics may contradict or give different answers to the same question and still be useful; (3) Heuristics permit the solving of unsolvable problems or reduce the search time to a satisfactory solution; (4) The heuristic depends on the immediate context instead of absolute truth as a standard of validity. A heuristic is anything that provides a plausible aid or direction in the solution of a problem but is in the final analysis unjustified, incapable of justification, and fallible. It is used to guide, to discover, and to reveal. Koen, Billy V. 1984. Definition of the engineering method. Washington, DC: ASEE.

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Heuristics are also a key part of the Koen's definition of the engineering method: The engineering method is the use of heuristics to cause the best change in a poorly understood situation within the available resources (p. 70). Typical engineering heuristics include: (1) Rules of thumb and orders of magnitude; (2) Factors of safety; (3) Heuristics that determine the engineer's attitude toward his or her work; (4) Heuristics that engineers use to keep risk within acceptable bounds; and (5) Rules of thumb that are important in resource allocation.

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