solving word problems through illustration sophia yarosh seminar in applied theory and research i...
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Solving Word Problems through
Illustration
Solving Word Problems through
IllustrationSophia Yarosh
Seminar in Applied Theory and Research I
Ed. 703.22, Spring 2008
Sophia Yarosh
Seminar in Applied Theory and Research I
Ed. 703.22, Spring 2008
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Table of Contents:1. Statement of the problem2. Review of related literature3. Statement of the hypothesis4. Methods-participants,
instruments, experimental design, procedure
5. Statistical analyses & graphs6. Logical discussion7. Logical implications8. Threats to internal and
external validity
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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.
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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
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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
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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 problem-solving: 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
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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.
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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
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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.
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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 taughtText 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’.
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• 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%
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• 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
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– 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.
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Implications:
• Posttest may be too hard• Researcher normally teaches older students• Need more time and research to support action research study
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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