Transcript Slide 1

Analyzing Student
Responses to a Multiple
Representation Problem
Tara Bartiromo and Eugenia Etkina
February 17, 2010
AAPT Winter Meeting
Washington, DC
NSF DRL-0733140
Context of Study
Curriculum used: Physics Union Mathematics
High Schools implemented Kinematics Module
Participants: 167 high school students
Test Problem: Qualitative kinematics problem, far
transfer1, open-ended, requires multiple representations
Focus: Students’ solutions to test problem (not
curriculum)
Barnett & Ceci (2002).
Test Problem
Two small metal balls are dropped from the same
height, but the second ball is dropped a little later than
the first one. When the second ball is released, the
vertical distance between the balls is 2.0 cm.
Use your knowledge of how objects fall to predict what
will happen to the distance between the balls as the
balls fall.
Explain your prediction using a motion diagram (dot
diagram), a position-versus-time graph, and
mathematically.
Far transfer problem according to Barnett and Ceci (2002).
Scientific Abilities Rubric*: Motion Diagram
Missing
(0)
No motion
diagram is
constructed.
An Attempt
(1)
Needs Some
Improvement
(2)
Acceptable
(3)
Diagram does
not represent
motion properly,
either spacing of
the dots or the
directions and
length of v
arrows or delta v
arrows does not
match the
motion.
Diagram has no
errors but is
missing one key
feature: dots that
represent
position, or
velocity arrows,
or delta v
arrows.
The diagram
contains no
errors in dots, v
arrows, or delta
v arrows and it
clearly describes
the motion of the
object.
* Etkina, E., Van Heuvelen, A., White-Brahmia, S., Brookes, D.T., Gentile, M., Murthy, S. Rosengrant, D., and Warren, A. (2006).
Research on Representations
Experts:
Qualitative/quanti
tative
reasoning1,2,
variety of
representations1,
fluent
translators2.
Goals of
Education
Novices:
Representation
use?2,
representations
are instructiondependent4,5,
quality of
representation4,
5,6
1. Van Heuvelen (1991); 2. Kozma & Russell (1997); 3. Kohl & Finkelstein (2008); 4. De Leone, & Gire, (2005); 5.
Rosengrant, Van Heuvelen, & Etkina (2009); 6. Kohl & Finkelstein (2007); 7. Meltzer (2005); 8. . Dufresne,
Gerace, & Leonard (1997).
Sample
Response
StudentStudent
Understanding?
Student Understanding?
What evidence is enough to
demonstrate student
understanding (of a concept, a
problem, etc.)?
80,0%
Evidence of Student Understanding:
Single Representation
70,0%
% Students who
Answered
Correctly
60,0%
50,0%
40,0%
%Students who
Answered
Partially Correctly
30,0%
20,0%
% Students who
Answered
Incorrectly
10,0%
0,0%
Prediction
Written
Explanation
Sample: 167 Students
Motion
Diagram
Graph
Using Prediction as a Grading Criteria
Correct
Incorrect/Missing
Prediction (74)
Prediction (93)
Correct Motion
Diagram
41.9%
23.7%
Incorrect Motion
Diagram
58.1%
76.3%
Correct
Prediction (74)
Incorrect/Missing
Prediction (93)
Correct Graph
48.6%
23.7%
Incorrect Graph
51.4%
76.3%
Consistency and Correctness of
Representations
60,0%
Consistent
50,0%
40,0%
Consistent and
Correct
30,0%
20,0%
10,0%
0,0%
MD and Graph
MD and
Graph and
Prediction & MD, Graph, & MD, Graph,
(150)
Equation (75) Equation (76) Other Reps.
Prediction Prediction, &
(133)
(119)
Equation (59)
Summary
Assessing any single representation for correctness leads to
very different results1.
Student understanding is multi-dimensional and can only be
discovered when students need to use multiple
representations to solve a problem2.
Fluent translation (i.e. consistency) between representations
needs to be fostered but is not sufficient.
1. Kohl & Finkelstein (2006); 2. Lesh, Post, & Behr. (1987).
Implications
As researchers, we base our judgment of student
understanding on superficial criteria. As scientists we should
look for more evidence.
There are simple ways of probing deeper to obtain more
evidence of student understanding
Additionally assess students using a more complex problem
that requires students to use and reason with multiple
representations (not in isolation on multiple problems).
Lesh, Post, & Behr. (1987).
For More Information:
 http://pum.rutgers.edu
 http://www.islephysics.net
 http://paer.rutgers.edu/scientificabilities/
Email: [email protected]
References:
1.E. Etkina, and A. Van Heuvelen, in Research-Based Reform of University Physics (2007), Vol. 1, WWW Document,
(http://www.compadre.org/Repository/docu ment/ServeFile.cfm?ID=4988&DocID=239).
2.Etkina, E., Van Heuvelen, A., (2006, 2001), Investigative Science Learning Environment
3.Etkina, E., Van Heuvelen, A., White-Brahmia, S., Brookes, D.T., Gentile, M., Murthy, S. Rosengrant, D., and Warren, A. (2006)
Developing and assessing student scientific abilities. Physical Review. Special Topics, Physics Education Research. 2, 020103.
4.Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem
solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Erlbaum.
5.Rosengrant, D. Van Heuvelen, A., & Etkina, E. (2009). Do students use and understand free-body diagrams? Phys. Rev. Special Topics –
PER, 5, 010108.
6.Meltzer, D. E. (2005). Relation between students’ problem-solving performance and representational format. Am. J. Phys., 73, 463-478.
7.Kohl, P. B., & Finkelstein, N. D. (2005). Student representational competence and self-assessment when solving physics problems. Phys.
Rev. Special Topics – PER, 1, 010104.
8.Kohl, P. B., & Finkelstein, N. D. (2006). Effects of representation on students solving physics problems: A fine-grained characterization.
Phys. Rev. Special Topics – PER, 2, 010106.
9.Kohl, P. B., & Finkelstein, N. D. (2007). Strongly and weakly directed approaches to teaching multiple representation use in physics. Phys.
Rev. Special Topics – PER, 3, 010108.
10.Kohl, P. B., & Finkelstein, N. D. (2008). Patterns of multiple representation use by experts and novices during physics problem solving.
Phys. Rev. Special Topics – PER, 4, 010111.
11.De Leone, C. J., & Gire, E. (2005). Is instructional emphasis on the use of non-mathematical representations worth the effort? In Heron,
P., McCullough, L., and Marx, J. (Eds.), 2005 Physics Education Research Conference, 818, Salt Lake City, Utah, p. 45-48.
12.Kozma, R., & Russell, J. (1997). Multimedia and understanding: Expert and novice responses to different representations of chemical
phenomena. Journal of Research in Science Teaching, 34, 949-968.
13.Dufresne, R., Gerace, W., Leonard, W. (1997). Solving physics problems with multiple representations. The Physics Teacher, 35, 270275.
14.Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn? A taxonomy for far transfer. Psychological Bulletin,
128, 612-637.
Percent of Students who Included each
Representation
100,0%
90,0%
80,0%
70,0%
60,0%
50,0%
40,0%
30,0%
20,0%
10,0%
0,0%
Prediction
Sample: 167 Students
Written
Explanation
Motion
Diagram
Graph
Equations
Sample PUM Activity
12.8
An object moves horizontally. The equations below
represent its motion mathematically. Describe the actual
motion that these two equations together might describe.
1)v(t) = +20 m/s + (-2 m/s2)t
2)x(t) = -200 m + (+20 m/s)t + ½(-2 m/s2)t2
a) Describe the motion in words and sketch the process
represented in the two mathematical expressions above.
b) Draw a motion diagram
c) Draw a position-versus-clock reading graph and a
velocity-versus-clock reading graph.
Sample PUM Activity
12.2
Use the Moving
Man PHET
simulation.
The man is walking initially at 0.75
m/s towards his home starting from the position of 7m to the left
of the origin. At this point, he begins to increase his velocity at a
rate of 0.2 m/s every second.
a) Write an expression for the man’s position as a function of time.
b) Create a position vs. time and velocity vs. time graph for this
function.
c) Before you continue with the simulation, check for consistency
between the representations. How do you know they are
consistent?
Multiple-Representation-Related Goals of
Education
Want students to:
Represent
processes for qualitative and quantitative
understanding1.
Use
variety of representations to solve problems8.
Flexibly
translate between representations2.
1. Van Heuvelen (1991); 2. Kozma & Russell (1997); 3. Kohl & Finkelstein (2008); 4. De Leone, & Gire, (2005); 5.
Rosengrant, Van Heuvelen, & Etkina (2009); 6. Kohl & Finkelstein (2007); 7. Meltzer (2005); 8. Dufresne, Gerace,
& Leonard (1997).
Using Explanation as a Grading Criteria
Correct
Incorrect/Missing
Explanation (14) Explanation (111)
Correct Motion
Diagram
71.4%
24.3%
Incorrect Motion
Diagram
28.6%
75.7%
Correct
Incorrect/Missing
Explanation (14) Explanation (111)
Correct Graph
64.3%
27.0%
Incorrect Graph
35.7%
73.0%
Sample
Response
StudentStudent
Understanding?
Student Understanding?