Cooperative Group Problem Solving Chris Meyer christopher. meyer@tdsb. on. ca York Mills C. I.
Brought to You by. . . • Pat and Ken Heller of the University of Minnesota • Outstanding, free, online resource • http: //groups. physics. umn. edu/physed/Research/CGPSintro. htm
Context-Rich Problems • Situations presented in colloquial language, almost as a story • Challenge: identify the physics ideas at work • Challenge: identify the important information • Challenge: no “plug'n'chug” solutions
Group Format • Problems are more difficult than a single person could handle • Group roles assigned • Planning, explanation and discussion are critical
Roles - Manager • Direct the sequence of steps. • Keep your group “on-track”. • Make sure everyone in your group participates. • Watch the time spent on each step. "Let's come back to this later if we have time. “ "We need to move on to the next step. “ "Chris, what do you think about this? ”
Recorder / Checker • Act as a scribe for your group. • Check for understanding of all members. • Make sure all members of your group agree on plans and actions. • Make sure names are on group products. "Do we all understand this diagram? “ "Explain why you think that. “ "Are we in agreement on this? "
Speaker / Skeptic • Speak on behalf of your group in class discussions • Help your group avoid coming to agreement too quickly. • Make sure all possibilities are explored. • Suggest alternative ideas. "What other possibilities are there? “ "Let's try to look at this another way. “ "I'm not sure we're on the right track. "
The Process Problem Statement A: The Picture B: The Question C: The Plan D: The Work E: The Results
The Physics Challenge • • • Add in the physical world! Physical objects need to be explored / measured The final result is physically verified
Your Challenge! The Washer Drop Your group will be given a length of string, five washers and some tape. Your challenge is to attach the five washers such that when you release the string and the washers hit the ground, there is a steady succession of sounds. clink-clink-clink. Not clink. … clink ……. . . clink, clink.
A: The Picture • Draw a clear diagram showing what’s happening • Attach important information using simple phrases • Make measurements • Attach unknowns if possible • Indicate coordinate system and sign convention • Complete? Problem statement is discarded Problem Statement A: The Picture B: The Question C: The Plan D: The Work E: The Results
A. The Picture all washers released from rest, v 1=0 t 4 length of string, Δd 4 = 4. 15 m gravity, ag = 9. 80 m/s 2 + t 3 Δd 3 = ? t 2 Δd 2 = ? Starts just above ground t 1 Δd 1 = ?
B: The Question • Create a specific physics question that will give the answer to the problem. • Indicate which quantities will allow you to answer the question. Problem Statement A: The Picture B: The Question C: The Plan D: The Work E: The Results
B. The Question What are the displacements from the three middle washers to the bottom of the string such that the time intervals between each washer hitting the ground are equal? Δd 1, Δd 2, Δd 3 = ?
C: The Plan Problem Statement A: The Picture • List the important physics concepts or ideas involved in the solution. • Outline the key steps involved in solving the problem • List any useful “textbook” equations and relationships B: The Question C: The Plan D: The Work E: The Results
C. The Plan Key concepts and ideas Key steps Key equations and relationships • Washers accelerate uniformly due to gravity. • Washers start from rest • Big 5 equations valid • Find time for whole string to drop, divide into 4 equal intervals. • Use intervals to find position of each washer above the ground. ΔΔd = vit + ½at 2
D: The Work • Create the specific equations you will use – write them down with a simple statement explaining what you are doing. • Perform the algebraic work first, whenever practical. • Verify the units of derived expressions Problem Statement A: The Picture B: The Question C: The Plan D: The Work • No number crunching yet! E: The Results
D. The Work Find the time for the top washer to drop: Find the other time intervals: Determine the displacements of the middle washers:
E: The Results • Substitute numbers into your manipulated equations and calculate a result. • State the final answer in response to the question you created. • Write brief statements explaining why the answer seems reasonable in size, direction and units. Problem Statement A: The Picture B: The Question C: The Plan D: The Work E: The Results
E. The Results The washers should be positioned 0. 26 m, 1. 04 m and 2. 33 m from the bottom of the string.
Reasonable size, units, direction? Size: The values are smaller than the full length and create successively larger displacements from the bottom. This makes sense for a series of accelerating objects. Units: The unit is metres, which is appropriate for displacements. Direction: All displacements were positive - meaning downwards, which makes sense for falling washers.
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