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					                     g
 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



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