Addressing Student Misconceptions of Addressing Student Misconceptions of Atwood’s Machine: Review of a Research Atwood’s Machine: Review of a Research

Based MethodBased Method

Beth Dietz, Madison Park TVHS Beth Dietz, Madison Park TVHS

Christina Yee, Charlestown HSChristina Yee, Charlestown HS

June 1, 2004June 1, 2004

Journal Article:Journal Article: ““Research as a guide for teaching introductory mechanics: An illustration in the Research as a guide for teaching introductory mechanics: An illustration in the

context of Atwood’s machine” McDermott, L. Department of Physics, University context of Atwood’s machine” McDermott, L. Department of Physics, University of Washington, Seattle, Washington. of Washington, Seattle, Washington. Am. J. PhysAm. J. Phys 62 (1) Jan. 1994 62 (1) Jan. 1994

modified

Main Ideas:Main Ideas:

1) Teachers must know misconceptions in order to 1) Teachers must know misconceptions in order to target learning experiences to have students gain target learning experiences to have students gain more understanding. Misconceptions can be identified more understanding. Misconceptions can be identified through research.through research.

2) Research can be used to create changes in intro 2) Research can be used to create changes in intro physics curriculum to enhance effectiveness of physics curriculum to enhance effectiveness of instruction.instruction.

3) Research must guide the design of curriculum to 3) Research must guide the design of curriculum to be effective. be effective.

Example: Atwood’s MachineExample: 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 used to learn about Newton’s Laws for a system with

two objects, where the motion of one affects the two objects, where the motion of one affects the motion of the other. motion of the other.

Often find the acceleration of the blocks and tension Often find the acceleration of the blocks and tension in the string (which is massless and inextensible).in the string (which is massless and inextensible).

Isolate bodies, draw FBDs,apply 2Isolate bodies, draw FBDs,apply 2ndnd Law and derive Law and derive equations for unknown variables. equations for unknown variables.

Research Study: Test GroupResearch Study: Test Group

Written test to 3 different classes of Written test to 3 different classes of calculus-based physics students.calculus-based physics students.

Students had studied Newton’s Laws, Students had studied Newton’s Laws, analyzed textbook problems, analyzed textbook problems, experienced an experiment in class and experienced an experiment in class and homework questions.homework questions.

Question Asked?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).

Typical Student ResponsesTypical Student Responses

Typical Student ResponsesTypical Student Responses

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 2. Tension pulls in two directions with 2 weights, only

one with wall. 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 force4. The wall did not exert a force Also some thought tension in string was 0 N because Also some thought tension in string was 0 N because

it was canceled out by vector addition. it was canceled out by vector addition.

Main Concept: Tension in a StringMain Concept: Tension in a String

““There was widespread inability to distinguish tension There was widespread inability to distinguish tension from weight. So led to misunderstanding that it is not from weight. So led to misunderstanding that it is not the weight of the one block that acts directly on the the weight of the one block that acts directly on the other—but rather the force exerted by the string.” other—but rather the force exerted by the string.” p.47p.47

Most students did not infer the relative magnitudes of Most students did not infer the relative magnitudes of weights and tension from direction of acceleration. weights and tension from direction of acceleration.

Students also did not recognize that force on the Students also did not recognize that force on the sliding block does not affect hanging block in sliding block does not affect hanging block in modified case.modified case.

modified

Misconception Break-Down:Misconception Break-Down:LinguisticLinguistic

The term “Tension” creates student The term “Tension” creates student confusion.confusion.

Why? Why? Daily use= tautness Daily use= tautness Confusion between scalar and vector Confusion between scalar and vector

– Force exerted on object by stringForce exerted on object by string– Magnitude of this forceMagnitude of this force

Misconception Break-Down:Misconception Break-Down:GeneralGeneral

1.1. Isolation of systemsIsolation of systems

2.2. Identification of forcesIdentification of forces

3.3. 33rdrd law force pairing law force pairing

4.4. Recognizing that Recognizing that FFnetnet determines determines

accelerationacceleration

Conclusion of Research:Conclusion of Research:

Teaching Atwood’s machine is pointless if students Teaching Atwood’s machine is pointless if students believe there are 2 acceleration and 2 tensions!believe there are 2 acceleration and 2 tensions!

Students have difficulty with concepts of tension and Students have difficulty with concepts of tension and acceleration that need to be addressed prior to acceleration that need to be addressed prior to “practice problems” done on their own.“practice problems” done on their own.

Group work, interaction and analysis during the Group work, interaction and analysis during the tutorial sessions provided more conceptual insight tutorial sessions provided more conceptual insight than lecture (regardless of the quality of the lecturer).than lecture (regardless of the quality of the lecturer).

AnswerAnswer new methods new methods

New Way to Teach Atwood’s New Way to Teach Atwood’s MachineMachine

The use of The use of tutorialtutorial sessions, which are: sessions, which are: Student-centered with emphasis on Student-centered with emphasis on

conceptsconcepts Pre-tests and highly structured worksheets Pre-tests and highly structured worksheets

guide students through reasoning tasksguide students through reasoning tasks Instructor’s role is to conduct q&a with Instructor’s role is to conduct q&a with

studentsstudents Students find their own answers and build Students find their own answers and build

their own knowledge. their own knowledge.

Pretest given to 100 students about role Pretest given to 100 students about role of string with the following set up:of string with the following set up:

Assume string is massless. B is greater Assume string is massless. B is greater mass than A.mass than A.

Research on tutorialResearch on tutorial

B A2 1

Pre-Test Question #1Pre-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.85 stated accelerations were equal.–15 used dynamical arguments that the Forces 15 used dynamical arguments that the Forces

exerted by the two strings were equal and so the exerted by the two strings were equal and so the accelerations be different because of the different accelerations be different because of the different masses. masses.

Pre-test question given to 450 students Pre-test question given to 450 students and still 15% incorrect reasoning.and still 15% incorrect reasoning.

B A2 1

Pre-Test Question #2Pre-Test Question #2

Compare the force exerted by string 1 Compare the force exerted by string 1 on A with the force exerted by string 2 on A with the force exerted by string 2 on B. on B.

Results (out of 100 students)Results (out of 100 students)–40% stated Force of string 1 was greater.40% stated Force of string 1 was greater.

–40% used 240% used 2ndnd Law, since a Law, since a11=a=a22, then due to mass , then due to mass

difference, string 2 would have greater force.difference, string 2 would have greater force.–20% Force exerted by 1&2 were equal. Students did 20% Force exerted by 1&2 were equal. Students did

not take into account external vs. internal forces. not take into account external vs. internal forces.

B A2 1

Looking at friction and way strings Looking at friction and way strings transmit force.transmit force.

Belief that a string transmitted force Belief that a string transmitted force applied to one object unchanged to the applied to one object unchanged to the other object.other object.

50% of students claimed that force of 2 50% of students claimed that force of 2 on A was equal to frictional force on A was equal to frictional force exerted on B. exerted on B.

Students believed frictional force on B Students believed frictional force on B acted directly on A.acted directly on A.

Feel Good About Physics ‘cause even Feel Good About Physics ‘cause even physicists mess up!physicists mess up!

Pretest was given to 20 graduate Pretest was given to 20 graduate physics students.physics students.

100% agreed accelerations were same.100% agreed accelerations were same. 60% argued correctly that force of 1 on 60% argued correctly that force of 1 on

A was greatestA was greatest Many FBDs were incorrect.Many FBDs were incorrect. Same general problems as UG class.Same general problems as UG class.

There must be a better way!There must be a better way!

In use of tutorial class, develop In use of tutorial class, develop questions from simple to complex questions from simple to complex systems. systems.

Use methodology of Use methodology of elicit, confront and elicit, confront and reassure.reassure.

Make explicit the steps to understanding Make explicit the steps to understanding that students fail to do on their own. that students fail to do on their own.

Start with pre-test on simple system:Start with pre-test on simple system:

No friction present. Students asked to No friction present. Students asked to compare the magnitude of all forces.compare the magnitude of all forces.

Steps to understanding Steps to understanding Atwood’s MachineAtwood’s Machine

A B

11StSt pretest was difficult. Why? pretest was difficult. Why?

Incorrect use of Newton’s 3Incorrect use of Newton’s 3rdrd Law (F Law (FABAB>F>FBABA))

Assumption that FAssumption that FABAB=F=Fhandhand

Next step: use question with friction present and blocks moving Next step: use question with friction present and blocks moving at constant velocity.at constant velocity. Students asked to draw separate FBDsStudents asked to draw separate FBDs Focus on agent that exerts force, body it acts onFocus on agent that exerts force, body it acts on Then they are asked to rank magnitude of horizontal forcesThen they are asked to rank magnitude of horizontal forces Students realize FStudents realize Fhandhand must overcome frictional forces of both blocks must overcome frictional forces of both blocks

so it must be greatest in magnitude.so it must be greatest in magnitude.

Looking at the situation with clear steps helps build acceptance of Looking at the situation with clear steps helps build acceptance of Newtonian view of external forces on object affecting its motion.Newtonian view of external forces on object affecting its motion.

Building Understanding Step #2Building Understanding Step #2

Pre-test question #2: Two bodies connected by Pre-test question #2: Two bodies connected by inextensible string.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 Compare a in #1 with #2. Students come up with aaAA=a=aBB. .

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.The separation between the objects must remain the same.

B A

Building Understanding re: Tension ScenarioBuilding Understanding re: Tension Scenario

B A

Mass ≠ 0

Building Understanding re: Tension ScenarioBuilding 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:

B R A

FRBx FRBx FARx FARx Fhand

Rank Magnitude of ForcesRank Magnitude of Forces

To rank forces must use 2To rank forces must use 2ndnd Law Law FFARAR – F – FBRBR= M= MRRa if Ma if MR R ≈ 0 then:≈ 0 then:

FFAR AR = F= FBRBR

Newton’s 3Newton’s 3rdrd Law: F Law: FARAR = F = FRARA

FFBRBR=F=FRB RB and soand so

FFRARA=F=FRBRB

Rank Magnitude of ForcesRank Magnitude of Forces

Students see more than 1 force on A.Students see more than 1 force on A. Those who did not include FThose who did not include Fhandhand earlier are forced to do so. earlier are forced to do so. Students realize that FStudents realize that Fhand hand must overcome Fmust overcome FRARA so it must be so it must be

greater.greater. FFhandhand>F>FRARA = F = FARAR > F > FBRBR=F=FRBRB

********************************************************************************** Why use of massless strings? What are the consequences of Why use of massless strings? What are the consequences of

massless string?massless string? FFARAR-F-FBRBR = 0 then F = 0 then FARAR= F= FBRBR

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 A taut, massless string exerts equal and opposite forces at both

ends.ends.

Tension and force exerted on objectsTension and force exerted on objects

Picture block & rope cutPicture block & rope cut

Cutting stringsCutting strings Tension in a taut, massless string is Tension in a taut, massless string is

equal to force it exerts on objects it equal to force it exerts on objects it connects.connects.

Atwood’s Vertical MachineAtwood’s Vertical Machine

Students now understand:Students now understand: (1) for an inextensible string the (1) for an inextensible string the

acceleration will be the same for the two acceleration will be the same for the two objects it connects.objects it connects.

(2) Massless string the tension is the (2) Massless string the tension is the same at both ends. same at both ends.

Ignore pulley issues.Ignore pulley issues.

Atwood’s Vertical Machine Atwood’s Vertical Machine Pre-testPre-test

Predict the motion if system released.Predict the motion if system released.

– Most students correctly guessed that heavier weight Most students correctly guessed that heavier weight would move down and lighter weight up.would move down and lighter weight up.

– http://www.msu.edu/user/brechtjo/physics/atwood/athttp://www.msu.edu/user/brechtjo/physics/atwood/atwood.htmlwood.html

– They showed different magnitudes for the forces They showed different magnitudes for the forces exerted by the strings. Typical incorrect FBD shown exerted by the strings. Typical incorrect FBD shown below:below:

Draw Correct FBD for Vertical AtwoodDraw Correct FBD for Vertical Atwood

Values are given for weights of 4N and 6N. Students Values are given for weights of 4N and 6N. Students asked to find Fasked to find Fnetnet and a for each weight. and a for each weight.

Still problem with 2 masses, 2 accelerations---Still problem with 2 masses, 2 accelerations---students needed to be reminded of effect of string on students needed to be reminded of effect of string on motion.motion.

Students used past info to remember that Students used past info to remember that accelerations must be equal. Recheck FBD’s and accelerations must be equal. Recheck FBD’s and correct themselves in practice.correct themselves in practice.

Can infer that a must be in between weight of both Can infer that a must be in between weight of both blocks and less than free fall. blocks and less than free fall.

Effectiveness of TutorialEffectiveness of Tutorial

Compared 3 UG physics classesCompared 3 UG physics classes All classes used same text, lecturers, All classes used same text, lecturers,

content in the same ordercontent in the same order 2 classes had 4 lectures/week, 1 had 3 2 classes had 4 lectures/week, 1 had 3

lectures + 1 tutorial session/weeklectures + 1 tutorial session/week Assessment of all groups via 3 Assessment of all groups via 3

examination questions.examination questions.

Sliding Block has m=100g and hanging block B has a mass of 200g. An object of 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 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.C when they are released. Consider with friction and without friction.

Assessment: Exam Question #1Assessment: Exam Question #1

C

A

CB

Assessment: Exam Question #1 ResultsAssessment: Exam Question #1 Results

For Friction situation: 100% of 3 classes were correct in C For Friction situation: 100% of 3 classes were correct in C reaching bottom first.reaching bottom first.

No Friction situation: No Friction situation: Tutorial: 70% predict C hit first

Previous Tutorials (not this one): 55% predict C firstPrevious 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 Tutorial students could express the constraint of the T up on Block B, which led them to the correct answer.B, which led them to the correct answer.

Non-tutorial students “seemed unaware of the upward force Non-tutorial students “seemed unaware of the upward force exerted by string on B”exerted by string on B”

Assessment: Exam Question #2Assessment: Exam Question #2

In this case, how does the tension in the string change when the block A is In this case, how does the tension in the string change when the block A is released?released?

C

A

CB

Assessment: Exam Question #2 ResultsAssessment: Exam Question #2 Results

Common incorrect answer was tension would not change because Common incorrect answer was tension would not change because only change taking place was with Block A. Failure to recognize only change taking place was with Block A. Failure to recognize that within system, one change can affect all parts. 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.There was less tendency to treat blocks and string independently.

Assessment Exam Question #3Assessment Exam Question #3

A AC CB

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.

Assessment Exam Question #3: Results Part 1Assessment Exam Question #3: Results Part 1

Tutorial Class:

90% drew correct FBD; 70% idenified correct 3rd 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 3rd Law pairs

60% had Fc>Fb>Fa

Assessment Exam Question #3: Results Part 2Assessment 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.

Conclusions from Research Project:Conclusions from Research Project:

Much better performance with tutorial on FBDs, identifying 3Much better performance with tutorial on FBDs, identifying 3rdrd Law Law Pairs, and qualitative analysisPairs, and qualitative analysis

More time spent on concepts without initial math the better the More time spent on concepts without initial math the better the results on exams.results on exams.

**Numerous encounters with material fights deeply held **Numerous encounters with material fights deeply held uncertainties.uncertainties.

Teachers role is to move students from passive recipients to active Teachers role is to move students from passive recipients to active learners (tell them that from the beginning).learners (tell them that from the beginning).

Intro Physics should help students identify what they do and do not Intro Physics should help students identify what they do and do not know and what is a scientific explanation.know and what is a scientific explanation.