Transcript Sophia Yarosh - ActionResearchProjects

Solving Word Problems
through Illustration
Sophia Yarosh
Seminar in Applied Theory and Research I
Ed. 703.22, Spring 2008
Table of Contents:
1.
2.
3.
4.
5.
6.
7.
8.
Statement of the problem
Review of related literature
Statement of the hypothesis
Methods-participants, instruments,
experimental design, procedure
Statistical analyses & graphs
Logical discussion
Logical implications
Threats to internal and external validity
Statement of the Problem:
Elementary School children, particularly with
learning disabilities, have the most trouble
learning word problems when taught only
traditionally. Visual learning and creativity will
help these students when integrated with
mathematics.
Review of the Literature:
Issues in Mathematics:
• Without meaning, there is no frame of reference for the child to relate
the problem to their real life: Chapman, 2006; Clark & Wallace, 2005;
Schurter, 2002; Weber-Russel & LeBlanc, 2004; Burns, 2000
Reading Word Problems:
• Must look at a child’s reading level
• Reading strategies need to be explicitly taught: Clark & Wallace,
2005; Schurter, 2002; Forsten, 2004
• Text structure, vocabulary, and the purpose: Clark & Wallace, 2005;
Schurter, 2002; Forsten, 2004
• Solving strategies should be modeled, such as drawing a picture, making a
model, as one would do in real-life context: Burns, 2000
Which is Best? Teaching Styles for All Kinds of Learners:
Learning through the abstract/ traditional teaching:
• Explicit instruction: Kroesbergen, Van Luit & Maas, 2004
Learning through the concrete/student centered learning:
Theorists : learning by doing
• Dr. Maria Montessori: Lillard, 2005
• Jean Piaget: Weber-Russel & LeBlanc, 2004; Herrera & Owens, 2001
Dr. Howard Gardner - Multiple Intelligences show our learning styles:
Heacox, 2002
• Creative responses:
– Keep focused, engaged, and in attendance.
– Motivate achievement: Boldt & Brooks, 2006; Robin & Muller, 2006
Cons: Art projects do not improve reading strategies essential for word
problems: Burger & Winner, 2000; Hickman and Huckstep, 2003
Art and its Role in Math:
• Through creativity, children best learn mathematics: Biller, 1994;
Forsten, 2004; Edens & Potter, 2001, 2007; Mann, 2006
• Use of visual images means higher mathematical problemsolving: van Garderen, 2006
• Descriptive drawing: learn processes of organization, selection,
and integration of cognitive processes: Edens & Potter, 2001
• Visuals clarify verbal texts: Edens & Potter, 2001
Research Hypotheses:
 Hr1: Math illustration instructional method will
increase the problem solving skills of 20 Fourth
graders.
 Hr2: Math illustration instructional method will
motivate students to better understand problem
solving skills.
Methods:
• Participants – 18 4th grade students in a mixed-age classroom
• Instruments – consent form, questionnaire, pretest, lesson plan,
posttest
• Quasi experimental design
• Non Equivalent Control Group Design
• Two groups are pretested, exposed to a treatment (X), and
posttested (O).
• Symbolic Design: O X1 O
•
O X2 O
• Procedure – students complete questionnaire
– administer the pretest
– give lessons to experimental group, then control group
– administer posttest
Mode- 4th Grade Questionnaire Graph 1
Results: 1= strongly agree; 4= strongly disagree
3.5
3
2.5
2
1.5
1
0.5
0
Q11
Q13
Q14
Q15
Q16
Q17
Q19
Q23
Q24
Q25
Experimental group
2
2
2
2
2
1
1
3
2
3
Control group
2
2
1
2
1
1
1
2
1.5
1
Questionnaire
Posttest Scores
Correlation between Creative Projects in Math and
Posttest Graph 2
100
90
80
70
60
50
40
30
20
10
0
Experimental Group
Control Group
0
X1
X2
1
2
3
4
Mode of Survey Question #25
5
Posttest- Experimental Group - Bell Curve
9
8
Students
7
6
5
4
3
2
1
0
10
20
30
40
50
Posttest Scores
60
70
80
90
100
Posttest - Control Group - Bell Curve
9
8
Students
7
6
5
4
3
2
1
0
10
20
30
40
50
60
Posttest Scores
70
80
90
100
Results – Statistical Analyses:
No correlation between the pretest and posttest for the experimental group (X1):
•
Line of best fit: results showed the strength of direction as a negative correlation
coefficient, .rxy = -0.590
No correlation between the pretest and posttest for the control group (X2):
• Line of best fit: results showed the strength of direction as a negative correlation
coefficient, .rxy = -0.462
Survey question #25: Do you enjoy doing creative projects for math? How did this affect the
posttest?
• .rxy = -0.627, no correlation for the experimental group
• .rxy = -0.566, no correlation for the control group
Experimental group posttest: mean is 80%; mode is 0; median is 83%
– The Standard Deviation from the mean was +/- 10.5
– Seven of the nine scores, 78%, are one standard deviation from the mean.
Control group posttest: mean is 79%; mode is 88%; median is 78%
– The Standard Deviation from the mean was +/- 7.0
– Five of the nine scores, 56%, are one standard deviation from the mean.
Discussion:
•
Dr. Howard Gardner - Multiple Intelligences show our learning styles:
Heacox, 2002
– The child chose the strategy that works best for them
– 2 children whose scores went down might have benefitted from
illustration, exposed to more options
•
Reading strategies need to be explicitly taught
Text structure, vocabulary, and the purpose: Clark & Wallace, 2005;
Schurter, 2002; Forsten, 2004
•
Literal translation without thinking of meaning of problem: Jitendra, Griffin,
Deatline-Buchman, & Sczesniak, 2007; Jonassen, 2003
-While solving word problems, children were stuck by words such as ‘dozen’
and ‘double’.
• Although there is little empirical research in support of this, no
concrete evidence that art & math help develop better
understanding: Hickman and Huckstep, 2003
– Experimental group: mean 62% pretest; mean 80% posttest
– Control group: mean 61% pretest; mean 79% posttest
• Learning by traditional teaching through explicit instruction
(Kroesbergen, Van Luit & Maas, 2004) or learning by doing (Lillard,
2005; Weber-Russel & LeBlanc, 2004; Herrera & Owens, 2001)
-Both groups increased their posttest scores by 18 points
• Children, especially with learning difficulties (LD), have trouble with
multiple cognitive processes: Jitendra et. al., 2007; Kroesbergen,
Van Luit, & Maas, 2004; Gonzalez & Espinel, 2002
– Might require direct, explicit instruction: Kroesbergen, Van Luit, &
Maas, 2004
• Student with ADD, his scores went down from 88% to 70%
• Without meaning, there is no frame of reference for the child to
relate the problem to their real life: Chapman, 2006; Clark &
Wallace, 2005; Schurter, 2002; Weber-Russel & LeBlanc, 2004;
Burns, 2000
– Both groups were better able to better understand the context of
word problems when it related to their life.
• Visuals clarify verbal texts & descriptive drawing: learn processes of
organization, selection, and integration of cognitive processes:
Edens & Potter, 2001
-When working on word problem about stacks of blocks, drawing
them was only way for children to really understand and visualize
problem
– Pretest did not affect posttest
– No correlation between creative activities in math, as seen by survey,
and posttest, yet mode of data was conflicting
• Through creativity, children best learn mathematics: Biller, 1994;
Forsten, 2004; Edens & Potter, 2001, 2007; Mann, 2006
• Use of visual images means higher mathematical problem-solving:
van Garderen, 2006
–
–
–
–
Posttest scores for both groups: negative skew
Experimental group: 78% the normal distribution of the Bell Curve.
Higher percentage of the scores resembles a normal population.
Control group: 56% within the normal distribution of the Bell Curve.
Implications:
• Posttest may be too hard
• Researcher normally teaches older students
• Need more time and research to support action research
study
Threats to Internal Validity:
• Statistical regression
• Mortality
• Selection-maturation interaction
• Instrumentation
• Testing sensitization
• Multiple group threats
• History
Threats to External Validity:
• Pretest-X treatment interaction
• Generalizable conditions
• Ecological validity
• Reactive arrangements/participant effects