Investigating Variations in Problem-Solving Strategies for Solving Linear Equations Kuo-Liang Chang and Jon R. Star, Michigan State University

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Investigating Variations in Problem-Solving
Strategies for Solving Linear EquationsKuo-Liang
Chang and Jon R. Star, Michigan State University
To investigate variations in students strategy
development, this study engages students in
problem-solving interviews, which have been
widely used in research on mathematical problem
solving (e.g., Star, 2001 Hunting, 1997).
Specifically, study participants were prompted to
share and explain their ideas before and after
they solved problems. Data from these
problem-solving interviews were used to identify,
categorize and analyze students developmental
changes of strategies in problem solving.
Table 1 An example of sophistication of
students utterances
These categories include the consistency between
utterances and written strategies, relations
between actions and subgoals, goal-subgoal
structure, certainty of utterances, speed of
utterances, students justification of strategy
choice (e.g., quickest, most accurate, more
familiar). Together these categories were
aggregated to provide a measure of the
sophistication of students utterances.
Utterance
More Sophisticated So you can get all the xs on one side and all the regular numbers on the other (S1051)
Less Sophisticated Right here I used the EXPAND step, right here I used the MOVE step (S1003)
Results There are three main results. First,
students utterances got more sophisticated as
they gained problem solving experience. Students
gradually increased the detail and rationale
included in their descriptions of strategies as
they engaged in more problem-solving practice. As
Table 1 illustrates, sophistication often
involved mentioning the purposes of ones
actions, as opposed to a mere listing of actions.
Second, students written strategies got more
sophisticated as their utterances got more
sophisticated. Several students changed or added
new written strategies when their utterances
displayed more detail about their choices on
problem-solving strategies. Third, students
became more successful problem solvers (getting
more correct answers) as their written strategies
and utterances became more sophisticated.
Students with more sophisticated utterances had
13 more correct answers than those with less
sophisticated utterances for the three
problem-solving sessions.
References Catrambone, R. (1998). The subgoal
learning model creating better examples so that
students can solve novel problems. Journal of
Experimental Psychology General, 127(4),
355-376. Hunting, R. P. (1997). Clinical
interview methods in mathematics education
research and practice. Journal of Mathematical
Behavior, 16(2), 145-165. Star, J. R. (2001).
Re-conceptualizing procedural knowledge
Innovation and flexibility in equation solving.
Unpublished doctoral dissertation, University of
Michigan, Ann Arbor.
Method Videotaped problem-solving interviews
were conducted with twenty-three 6th grade
students (12 males and 11 females). Students
participated for a total of five hours over five
consecutive days. Each student was given a
pretest, twenty minutes of instruction, three
one-hour videotaped problem solving sessions, and
a posttest. In each of the three one-hour
problem-solving sessions, students were asked a
series of questions as they solved linear
equations, including prompts to explain their
choice of problem-solving strategies.
Analysis Of particular interest here is the
level of sophistication of students utterances
relating to their written strategies. In order to
analyze variations in students strategies (as
evidenced by students utterances), several
coding categories were employed.
Contact Information Jon R. Star, jonstar_at_msu.edu
Kuo-Liang Chang, changku3_at_msu.edu. College of
Education, Michigan State University, East
Lansing, Michigan, 48824. This poster can be
downloaded at www.msu.edu/jonstar.