Student Sense-Making on Homework in a Sophomore Mechanics ...
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QR Student Sense-Making on Homework in a Sophomore Mechanics Course Kelby T. Hahn, Paul J. Emigh, MacKenzie Lenz, and Elizabeth Gire Limiting Case: Takes a limit of a variable of interest, typically the limit to 0 or ∞ Student example of using limiting case to analyze an equation of the velocity as a function of mass for a rocket with linear air resistance. Special Case: Chooses a specific value for a variable of interest, like 0 or π Student example of using special case to analyze an equation of the velocity as a function of mass for a rocket with linear air resistance. Cases Fundamental Dimensions: Uses fundamental dimensions of quantities (length, mass, and time) Student example of using fundamental dimensions to analyze the Lagrangian of a free particle. States Dimensions: States the units/dimensions were correct without justification Units: Uses units of physical quantities (grams, meters, seconds, etc.) Compound Dimensions: Describes quantities as having dimensions of acceleration, energy, etc. Student example of using compound dimensions to analyze the Lagrangian of a free particle. Dimensions Research Question What sense-making strategies do students use when given an open-ended prompt to do sense-making? 2 nd Way Compares answer using 2 solution methods Visualization Understands the solution through figures, diagrams, graphs, etc. Algebra States that the answer is correct because the algebra was done correctly Assumptions Checks for consistency between the answer and assumptions made at the beginning of the solution Reasonable Magnitude States or argues why the magnitude of the answer is reasonable No Sense-Making Does the problem but does not answer the sense-making prompt Strategy Identification Identifies potential sense-making strategies but doesn’t implement them Research Methods Data: • Homework solutions from 29 students • Coded 825 student responses to open-ended sense-making prompts on Homework 4-8 Homework 4-7 Sense-Making Prompt Ex. “Find the equation of motion (acceleration) of the bead. Use at least two sense-making strategies to make sense out of this equation.” Homework 8 Sense-Making Prompt Ex. “Be sure to do some sense-making around your result.” Instructional Context Techniques of Theoretical Mechanics: • 10 weeks, 50 min. meetings, 3 times a week • Classical mechanics: Newtonian, Lagrangian, and Hamiltonian techniques • Special relativity • Spring 2017 - Taught by author EG Sense-Making: Sense-making while solving physics problems involves coordinating the use of algebraic symbols with conceptual understandings, understandings of geometric relationships, and intuitions about the physical world. • Treated on equal footing with the physics content goals • Included on syllabus, exams, in-class discussions, and homework ✓ Prescribed sense-making prompts on Homework 1-3, 9, & 10 ✓ Open-ended sense-making prompts on Homework 4-8 Prior Knowledge Explains how answer is connected to conceptual understanding Student example of using conceptual connection to analyze the constraint force, λ found through undetermined Lagrange multipliers, of a particle confined to the surface of a cylinder. Conceptual Connection Checks that the sign of the answer makes sense with their coordinate system Student example of using sign to analyze the Lagrangian of a bead on a rotating rod. Sign Analyzes if and how the answer depends on certain physical quantities (a) Equations of motion (b) Student example of using functional dependence to analyze the equations of motion seen in part (a), of a spherical pendulum. Functional Dependence References C. Singh, Am. J. Phys. 70 (2002). D. Hammer, Phys. Teach. 27, 664 (1989). A. R. Warren, Phys. Rev. ST Phys. Educ. Res. 6, 020103 (2010), 10.1103/PhysRevSTPER.6.020103 J. Tuminaro and E. F. Redish, Phys. Rev. ST Phys. Educ. Res. (2007). M. Lenz and E. Gire, in PERC Proceedings (2016). B. Rosenshine and C. Meister, Ed. Lead. (1992). J. R. Taylor, Classical Mechanics (University Science Books, 2005). T. Dray, Geometry of Special Relativity (A. K. Peters, 2012). Acknowledgements We would like to thank the students who volunteered to participate in this study and the Oregon State Physics Education Research Group. Authority Checks answer in the back of the book or some other outside authority 2% <1% <1% 2% 7% 18% 18% <1% 1% 3% <1% 3% 14% 4% 2% 2% 17% 4% Compares answer to real world experiences or knowledge form a previous course Student example of using prior knowledge to analyze the Lagrangian of a spherical pendulum.
Transcript of Student Sense-Making on Homework in a Sophomore Mechanics ...
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Student Sense-Making on Homework in a Sophomore Mechanics Course Kelby T. Hahn, Paul J. Emigh, MacKenzie Lenz, and Elizabeth Gire
Limiting Case: Takes a limit of a variable
of interest, typically the limit to 0 or ∞
Student example of using limiting case to analyze
an equation of the velocity as a function of mass
for a rocket with linear air resistance.
Special Case: Chooses a specific value for
a variable of interest, like 0 or π
Student example of using special case to analyze
an equation of the velocity as a function of mass
for a rocket with linear air resistance.
Cases
Fundamental Dimensions: Uses
fundamental dimensions of quantities
(length, mass, and time)
Student example of using fundamental dimensions
to analyze the Lagrangian of a free particle.
States Dimensions: States the
units/dimensions were correct without
justification
Units: Uses units of physical quantities
(grams, meters, seconds, etc.)
Compound Dimensions: Describes
quantities as having dimensions of
acceleration, energy, etc.
Student example of using compound dimensions to
analyze the Lagrangian of a free particle.
Dimensions
Research QuestionWhat sense-making strategies do students use when
given an open-ended prompt to do sense-making?
2nd WayCompares answer using 2 solution
methods
VisualizationUnderstands the solution through
figures, diagrams, graphs, etc.
AlgebraStates that the answer is correct
because the algebra was done correctly
AssumptionsChecks for consistency between the
answer and assumptions made at the
beginning of the solution
Reasonable MagnitudeStates or argues why the magnitude of
the answer is reasonable
No Sense-MakingDoes the problem but does not answer
the sense-making prompt
Strategy IdentificationIdentifies potential sense-making
strategies but doesn’t implement them
Research MethodsData:
• Homework solutions from 29 students
• Coded 825 student responses to open-ended
sense-making prompts on Homework 4-8
Homework 4-7 Sense-Making Prompt Ex.
“Find the equation of motion (acceleration) of
the bead. Use at least two sense-making
strategies to make sense out of this equation.”
Homework 8 Sense-Making Prompt Ex.
“Be sure to do some sense-making around your
result.”
Instructional ContextTechniques of Theoretical Mechanics:
• 10 weeks, 50 min. meetings, 3 times a week
• Classical mechanics: Newtonian, Lagrangian,
and Hamiltonian techniques
• Special relativity
• Spring 2017 - Taught by author EG
Sense-Making:
Sense-making while solving physics problems
involves coordinating the use of algebraic symbols
with conceptual understandings, understandings
of geometric relationships, and intuitions about
the physical world.
• Treated on equal footing with the physics
content goals
• Included on syllabus, exams, in-class
discussions, and homework
✓ Prescribed sense-making prompts on
Homework 1-3, 9, & 10
✓ Open-ended sense-making prompts on
Homework 4-8
Prior Knowledge
Explains how answer is connected to
conceptual understanding
Student example of using conceptual connection to
analyze the constraint force, λ found through
undetermined Lagrange multipliers, of a particle
confined to the surface of a cylinder.
ConceptualConnection
Checks that the sign of the answer makes
sense with their coordinate system
Student example of using sign to analyze the
Lagrangian of a bead on a rotating rod.
Sign
Analyzes if and how the answer depends
on certain physical quantities
(a) Equations of motion (b) Student example of
using functional dependence to analyze the
equations of motion seen in part (a), of a
spherical pendulum.
FunctionalDependence
ReferencesC. Singh, Am. J. Phys. 70 (2002).
D. Hammer, Phys. Teach. 27, 664 (1989).
A. R. Warren, Phys. Rev. ST Phys. Educ. Res. 6, 020103
(2010), 10.1103/PhysRevSTPER.6.020103
J. Tuminaro and E. F. Redish, Phys. Rev. ST Phys. Educ. Res.
(2007).
M. Lenz and E. Gire, in PERC Proceedings (2016).
B. Rosenshine and C. Meister, Ed. Lead. (1992).
J. R. Taylor, Classical Mechanics (University Science Books,
2005).
T. Dray, Geometry of Special Relativity (A. K. Peters, 2012).
AcknowledgementsWe would like to thank the students who volunteered to
participate in this study and the Oregon State Physics
Education Research Group.
AuthorityChecks answer in the back of the book
or some other outside authority
2%
<1%
<1%
2%7% 18%
18%
<1%
1%
3%
<1%
3%
14%4% 2% 2%
17%
4%
Compares answer to real world experiences
or knowledge form a previous course
Student example of using prior knowledge to
analyze the Lagrangian of a spherical pendulum.
