Solving Word Problems through Illustration

1. Solving Word Problems through Illustration Sophia Yarosh Seminar in Applied Theory and Research I Ed. 703.22, Spring 2008

2. Table of Contents: • 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 8. Threats to internal and external validity

3. 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.

4. 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 Review of the Literature:

5. 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

6. 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

7. 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.

8. 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: OX1 O • O X2 O • Procedure – students complete questionnaire • administer the pretest • give lessons to experimental group, then control group • administer posttest

15. 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.

16. 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’.

17. 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%

18. 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

19. 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.

20. Implications: • Posttest may be too hard • Researcher normally teaches older students • Need more time and research to support action research study

21. 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