1. Addressing Student Misconceptions of Atwood’s Machine: Review of a Research Based Method Beth Dietz, Madison Park TVHS Christina Yee, Charlestown HS June 1, 2004

2. Journal Article: “Research as a guide for teaching introductory mechanics: An illustration in the context of Atwood’s machine” McDermott, L. Department of Physics, University of Washington, Seattle, Washington. Am. J. Phys 62 (1) Jan. 1994 “Research as a guide for teaching introductory mechanics: An illustration in the context of Atwood’s machine” McDermott, L. Department of Physics, University of Washington, Seattle, Washington. Am. J. Phys 62 (1) Jan. 1994 modified

3. Main Ideas: 1) Teachers must know misconceptions in order to target learning experiences to have students gain more understanding. Misconceptions can be identified through research. 2) Research can be used to create changes in intro physics curriculum to enhance effectiveness of instruction. 3) Research must guide the design of curriculum to be effective.

4. Example: Atwood’s Machine used in typical introductory physics course. used in typical introductory physics course. used to learn about Newton’s Laws for a system with two objects, where the motion of one affects the motion of the other. used to learn about Newton’s Laws for a system with two objects, where the motion of one affects the motion of the other. Often find the acceleration of the blocks and tension in the string (which is massless and inextensible). Often find the acceleration of the blocks and tension in the string (which is massless and inextensible). Isolate bodies, draw FBDs,apply 2 nd Law and derive equations for unknown variables. Isolate bodies, draw FBDs,apply 2 nd Law and derive equations for unknown variables.

5. Research Study: Test Group Written test to 3 different classes of calculus-based physics students. Written test to 3 different classes of calculus-based physics students. Students had studied Newton’s Laws, analyzed textbook problems, experienced an experiment in class and homework questions. Students had studied Newton’s Laws, analyzed textbook problems, experienced an experiment in class and homework questions.

6. Question Asked? (a)(b) Students were asked to compare the tension in the string at position (a) vs. the tension of the string at position (b).

7. Typical Student Responses

8. 50% identified the force at (a) and (b) to be the same. 50% identified the force at (a) and (b) to be the same. Misconceptions: Misconceptions: 1. Tension in string with 2 weights, 2x greater. 1. Tension in string with 2 weights, 2x greater. 2. Tension pulls in two directions with 2 weights, only one with wall. 2. Tension pulls in two directions with 2 weights, only one with wall. 3. Tension force was sum of forces at end of string. 3. Tension force was sum of forces at end of string. 4. The wall did not exert a force 4. The wall did not exert a force Also some thought tension in string was 0 N because it was canceled out by vector addition. Also some thought tension in string was 0 N because it was canceled out by vector addition.

9. Main Concept: Tension in a String “There was widespread inability to distinguish tension from weight. So led to misunderstanding that it is not the weight of the one block that acts directly on the other—but rather the force exerted by the string.” p.47 “There was widespread inability to distinguish tension from weight. So led to misunderstanding that it is not the weight of the one block that acts directly on the other—but rather the force exerted by the string.” p.47 Most students did not infer the relative magnitudes of weights and tension from direction of acceleration. Most students did not infer the relative magnitudes of weights and tension from direction of acceleration. Students also did not recognize that force on the sliding block does not affect hanging block in modified case. Students also did not recognize that force on the sliding block does not affect hanging block in modified case. modified

10. Misconception Break-Down: Linguistic The term “Tension” creates student confusion. The term “Tension” creates student confusion. Why? Why? Daily use= tautness Daily use= tautness Confusion between scalar and vector Confusion between scalar and vector –Force exerted on object by string –Magnitude of this force

11. Misconception Break-Down: General 1. Isolation of systems 2. Identification of forces 3. 3 rd law force pairing 4. Recognizing that F net determines acceleration

12. Conclusion of Research: Teaching Atwood’s machine is pointless if students believe there are 2 acceleration and 2 tensions! Teaching Atwood’s machine is pointless if students believe there are 2 acceleration and 2 tensions! Students have difficulty with concepts of tension and acceleration that need to be addressed prior to “practice problems” done on their own. Students have difficulty with concepts of tension and acceleration that need to be addressed prior to “practice problems” done on their own. Group work, interaction and analysis during the tutorial sessions provided more conceptual insight than lecture (regardless of the quality of the lecturer). Group work, interaction and analysis during the tutorial sessions provided more conceptual insight than lecture (regardless of the quality of the lecturer). Answer  new methods Answer  new methods

13. New Way to Teach Atwood’s Machine The use of tutorial sessions, which are: The use of tutorial sessions, which are: Student-centered with emphasis on concepts Student-centered with emphasis on concepts Pre-tests and highly structured worksheets guide students through reasoning tasks Pre-tests and highly structured worksheets guide students through reasoning tasks Instructor’s role is to conduct q&a with students Instructor’s role is to conduct q&a with students Students find their own answers and build their own knowledge. Students find their own answers and build their own knowledge.

14. Pretest given to 100 students about role of string with the following set up: Pretest given to 100 students about role of string with the following set up: Assume string is massless. B is greater mass than A. Research on tutorial BA 21

15. Pre-Test Question #1 Compare the acceleration of B with A. Compare the acceleration of B with A. Results (out of 100 students) Results (out of 100 students) –85 stated accelerations were equal. –15 used dynamical arguments that the Forces exerted by the two strings were equal and so the accelerations be different because of the different masses. Pre-test question given to 450 students and still 15% incorrect reasoning. Pre-test question given to 450 students and still 15% incorrect reasoning. BA 21

16. Pre-Test Question #2 Compare the force exerted by string 1 on A with the force exerted by string 2 on B. Compare the force exerted by string 1 on A with the force exerted by string 2 on B. Results (out of 100 students) Results (out of 100 students) –40% stated Force of string 1 was greater. –40% used 2 nd Law, since a 1 =a 2, then due to mass difference, string 2 would have greater force. –20% Force exerted by 1&2 were equal. Students did not take into account external vs. internal forces. BA 21

17. Looking at friction and way strings transmit force. Belief that a string transmitted force applied to one object unchanged to the other object. Belief that a string transmitted force applied to one object unchanged to the other object. 50% of students claimed that force of 2 on A was equal to frictional force exerted on B. 50% of students claimed that force of 2 on A was equal to frictional force exerted on B. Students believed frictional force on B acted directly on A. Students believed frictional force on B acted directly on A.

18. Feel Good About Physics ‘cause even physicists mess up! Pretest was given to 20 graduate physics students. Pretest was given to 20 graduate physics students. 100% agreed accelerations were same. 100% agreed accelerations were same. 60% argued correctly that force of 1 on A was greatest 60% argued correctly that force of 1 on A was greatest Many FBDs were incorrect. Many FBDs were incorrect. Same general problems as UG class. Same general problems as UG class.

19. There must be a better way! In use of tutorial class, develop questions from simple to complex systems. In use of tutorial class, develop questions from simple to complex systems. Use methodology of elicit, confront and reassure. Use methodology of elicit, confront and reassure. Make explicit the steps to understanding that students fail to do on their own. Make explicit the steps to understanding that students fail to do on their own.

20. Start with pre-test on simple system: Start with pre-test on simple system: No friction present. Students asked to compare the magnitude of all forces. No friction present. Students asked to compare the magnitude of all forces. Steps to understanding Atwood’s Machine AB

21. 1 St pretest was difficult. Why? Incorrect use of Newton’s 3 rd Law (F AB >F BA ) Incorrect use of Newton’s 3 rd Law (F AB >F BA ) Assumption that F AB =F hand Assumption that F AB =F hand Next step: use question with friction present and blocks moving at constant velocity. Next step: use question with friction present and blocks moving at constant velocity. Students asked to draw separate FBDs Students asked to draw separate FBDs Focus on agent that exerts force, body it acts on Focus on agent that exerts force, body it acts on Then they are asked to rank magnitude of horizontal forces Then they are asked to rank magnitude of horizontal forces Students realize F hand must overcome frictional forces of both blocks so it must be greatest in magnitude. Students realize F hand must overcome frictional forces of both blocks so it must be greatest in magnitude. Looking at the situation with clear steps helps build acceptance of Newtonian view of external forces on object affecting its motion. Looking at the situation with clear steps helps build acceptance of Newtonian view of external forces on object affecting its motion.

22. Building Understanding Step #2 Pre-test question #2: Two bodies connected by inextensible string. Pre-test question #2: Two bodies connected by inextensible string. Compare Pre-test #1 with #2 set up: Compare Pre-test #1 with #2 set up: Compare a in #1 with #2. Students come up with a A =a B. Compare a in #1 with #2. Students come up with a A =a B. How do you know if a and v of two objects are equal? How do you know if a and v of two objects are equal? –The separation between the objects must remain the same. B A

23. Building Understanding re: Tension Scenario B A Mass ≠ 0

24. Building Understanding re: Tension Scenario Students are asked to isolate A, B and Rope from each other to help students recognize force of rope. Students guided through some problems: Asked for horizontal comp. Of forces on A,R and B: BRA F RBx F ARx F hand

25. Rank Magnitude of Forces To rank forces must use 2 nd Law To rank forces must use 2 nd Law F AR – F BR = M R a if M R ≈ 0 then: F AR – F BR = M R a if M R ≈ 0 then: F AR = F BR F AR = F BR Newton’s 3 rd Law: F AR = F RA Newton’s 3 rd Law: F AR = F RA F BR =F RB and so F BR =F RB and so F RA =F RB F RA =F RB

26. Rank Magnitude of Forces Students see more than 1 force on A. Students see more than 1 force on A. Those who did not include F hand earlier are forced to do so. Those who did not include F hand earlier are forced to do so. Students realize that F hand must overcome F RA so it must be greater. Students realize that F hand must overcome F RA so it must be greater. F hand >F RA = F AR > F BR =F RB F hand >F RA = F AR > F BR =F RB ***************************************** ***************************************** Why use of massless strings? What are the consequences of massless string? Why use of massless strings? What are the consequences of massless string? F AR -F BR = 0 then F AR = F BR F AR -F BR = 0 then F AR = F BR No net force is needed to accelerate a massless string. No net force is needed to accelerate a massless string. A taut, massless string exerts equal and opposite forces at both ends. A taut, massless string exerts equal and opposite forces at both ends.

27. Tension and force exerted on objects Picture block & rope cut Picture block & rope cut Cutting strings Cutting strings Tension in a taut, massless string is equal to force it exerts on objects it connects. Tension in a taut, massless string is equal to force it exerts on objects it connects.

28. Atwood’s Vertical Machine Students now understand: Students now understand: (1) for an inextensible string the acceleration will be the same for the two objects it connects. (1) for an inextensible string the acceleration will be the same for the two objects it connects. (2) Massless string the tension is the same at both ends. (2) Massless string the tension is the same at both ends. Ignore pulley issues. Ignore pulley issues.

29. Atwood’s Vertical Machine Pre-test Predict the motion if system released. Predict the motion if system released. –Most students correctly guessed that heavier weight would move down and lighter weight up. –http://www.msu.edu/user/brechtjo/physics/atwood/at wood.html http://www.msu.edu/user/brechtjo/physics/atwood/at wood.htmlhttp://www.msu.edu/user/brechtjo/physics/atwood/at wood.html –They showed different magnitudes for the forces exerted by the strings. Typical incorrect FBD shown below:

30. Draw Correct FBD for Vertical Atwood Values are given for weights of 4N and 6N. Students asked to find F net and a for each weight. Values are given for weights of 4N and 6N. Students asked to find F net and a for each weight. Still problem with 2 masses, 2 accelerations--- students needed to be reminded of effect of string on motion. Still problem with 2 masses, 2 accelerations--- students needed to be reminded of effect of string on motion. Students used past info to remember that accelerations must be equal. Recheck FBD’s and correct themselves in practice. Students used past info to remember that accelerations must be equal. Recheck FBD’s and correct themselves in practice. Can infer that a must be in between weight of both blocks and less than free fall. Can infer that a must be in between weight of both blocks and less than free fall.

31. Effectiveness of Tutorial Compared 3 UG physics classes Compared 3 UG physics classes All classes used same text, lecturers, content in the same order All classes used same text, lecturers, content in the same order 2 classes had 4 lectures/week, 1 had 3 lectures + 1 tutorial session/week 2 classes had 4 lectures/week, 1 had 3 lectures + 1 tutorial session/week Assessment of all groups via 3 examination questions. Assessment of all groups via 3 examination questions.

32. Sliding Block has m=100g and hanging block B has a mass of 200g. An object of 200g is held at the same height as Block B. Compare the accelerations of B and C when they are released. Consider with friction and without friction. Assessment: Exam Question #1 C A CB

33. Assessment: Exam Question #1 Results For Friction situation: 100% of 3 classes were correct in C reaching bottom first. No Friction situation: Tutorial: 70% predict C hit first Previous Tutorials (not this one): 55% predict C first No tutorial: 45% predicted C first Tutorial students could express the constraint of the T up on Block B, which led them to the correct answer. Non-tutorial students “seemed unaware of the upward force exerted by string on B”

34. Assessment: Exam Question #2 In this case, how does the tension in the string change when the block A is released? C A CB

35. Assessment: Exam Question #2 Results Common incorrect answer was tension would not change because only change taking place was with Block A. Failure to recognize that within system, one change can affect all parts. Class with tutorial:50% recognized that T becomes less than weight of B. Class without tutorial: 25% when B accelerates down, T becomes less than its weight. There was less tendency to treat blocks and string independently.

36. Assessment Exam Question #3 AACC B D 1.Draw FBDs for each of the three blocks, indicate any third law force pairs and rank from (largest  smallest) the magnitude of the net force on each block. 2.Describe any changes in motion of blocks and on the net force on Blocks A and C.

37. Assessment Exam Question #3: Results Part 1 Tutorial Class: 90% drew correct FBD; 70% idenified correct 3 rd Law pairs 98% recognized B and C exert forces opposite to direction of motion 60% had Fc>Fb>Fa Non-Tutorial Class: 30% drew correct FBD; 15% idenified correct 3 rd Law pairs 60% had Fc>Fb>Fa

38. Assessment Exam Question #3: Results Part 2 Tutorial Class: 80% predicted that since overall system mass went down, that acceleration went up. Since A & C remain same mass, their net force has to increase. Non-Tutorial Class: 35% were correct.

39. Conclusions from Research Project: Much better performance with tutorial on FBDs, identifying 3 rd Law Pairs, and qualitative analysis Much better performance with tutorial on FBDs, identifying 3 rd Law Pairs, and qualitative analysis More time spent on concepts without initial math the better the results on exams. More time spent on concepts without initial math the better the results on exams. **Numerous encounters with material fights deeply held uncertainties. **Numerous encounters with material fights deeply held uncertainties. Teachers role is to move students from passive recipients to active learners (tell them that from the beginning). Teachers role is to move students from passive recipients to active learners (tell them that from the beginning). Intro Physics should help students identify what they do and do not know and what is a scientific explanation. Intro Physics should help students identify what they do and do not know and what is a scientific explanation.