# nguyen-aapt-s09

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Individual Teaching/Learning g
Interviews to Facilitate Student
Problem Solving
P bl    S l i
Dong-H i N
D                 N. S j R b ll
Dong-Hai Nguyen & N Sanjay Rebello
Physics Education Research Group
Kansas State University

AAPT Summer Meeting 2009
Ann Arbor, MI – July 27th 2009
Arbor

This work is supported in part by NSF grant 0816207
1
Objective and Research Questions
Objective: Facilitate students’ transfer of
Objective
bl       l i     kill            bl
problem solving skills across problems off
different contexts and representations

Questions:
Research Questions
What kinds of difficulties do students have when solving
problems different contexts and representations?
How does the sequence in which problems of different
contexts and representations are presented to students
affect their performance?
What kinds of scaffolding may help students overcome
those diffi lti ?
th     difficulties?
2
Methodology
Teaching/Learning Interviews1
Calculus-based physics volunteers (N = 20)
Each participant was interviewed 4 times during semester.
in-class exam.
Each interview came after an in class exam
Each interview, the students were:
• Asked to solve three problems:
problem: a p
Original p
g                problem from most recent exam
Graphical problem: part of info. given as graph
p        part
Functional problem: p of info. g  given as function
• Asked to think aloud while solving problems.
Given verbal hi t whenever unable t proceed.
• Gi       b l hints h          bl to       d
3
1Engelhardt,   et. al. 2003
Examples of Interview Problems
Original problem in Interview 2

4
Examples of Interview Problems
Functional problem in Interview 2
F   ti   l    bl   i I t    i

5
Examples of Interview Problems
Graphical
problem in
Interview 2

6
Results : Difficulties
GRAPH: unable to process information from the graph
provided.
FUNCTION: inappropriate interpretation or use of the
function given.
PRINCIPLE: inappropriate use of physical principles.
QUANTITY: incorrect use, calculations, and units of physical
Q                      ,             ,              p y
quantities.
y                         p          g
FORMULA: incorrectly recalls a formula or interpret meaning
of formulae/expressions.
p y      q
VALUE: uses incorrect value of physical quantities.
MATH: unable to manipulate mathematical processes.
errors.
CALCULATION: simple calculation errors
7
Results: Hints
GRAPH: enables students to read off and process
information from the graph provided.
QUANTITY: helps students plan a strategy to find desired
quantities using the info. given (e.g. graph, function), or to
decide which quantities are applicable in each situation.
MATH: questions on meaning of mathematical notations and
operators.
PRINCIPLE: enables students to determine the appropriate
principle to use.
INFO: asks students to take a more careful look at the
problem statement to gather necessary data.
FORMULA: helps students understand the meaning of a
formula or an equation.
CALCULATION: helps students recognize and correct simple
8
calculation errors.
LTIES PER
# OF DIFFICUL     P
STUDEENT

0
1
2
3

NCIPLE
PRIN

ANTITY
QUA

RMULA
FOR

VALUE
V

ORIGINAL
MATH

GRAPHICAL
FUNCTIONAL
G
GRAPH
DIFFICULTIES: G-F SEQUENCE

CTION
FUNC

CALC
E
ERROR
9
LTIES PER
# OF DIFFICUL     P
STUDEENT

0
1
2
3

E
PRINCIPLE

QUA    Y
ANTITY

ORMULA
FO    A

E
VALUE

ORIGINAL
H
MATH

GRAPHICAL
FUNCTIONAL
H
GRAPH
DIFFICULTIES: F-G SEQUENCE

NCTION
FUN    N

CALC
ERRORR
10
Results :
Sequencing Effect
Representational aspect

sequence:
G-F sequence most
difficulties with graph

sequence:
F-G sequence minor
difficulty with function

Students’ transfer occurs
FG
more easily in the F-G
sequence than in the G-F
sequence.
11
Results :
S      i Eff t
Sequencing Effect
Contextual aspect
p
(from Original to 2nd problem

Graphical:
From Original to Graphical
minor difficulties with
principle and quantities.

F       O i i l to Functional:
F    ti
From Original t Functional    l
some difficulties with
principle and significant
difficulties with quantities.

12
Conclusions
Students           bl to i t       t h i l       i
St d t were unable t interpret physical meaning of     f
mathematical operators and processes.
• Thus had difficulties solving problems in graphical and
functional representations.
When the context of the problem changed, could not relate
the new problem to the original problem.
Thus h d diffi lti id tif i th        i i l     d
• Th had difficulties identifying the principle and
physical quantities needed to solve the new problem
The sequence of problems affected their performance:
• Representational Change: Easier when Functional problem
i presented b f
is                  Graphical  bl
t d before G hi l problem.
• Contextual Change : Harder when accompanied by
representational change from Numerical to Graphical
13
THANK YOU

14

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