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The Role of Visual Prompts in Solving Mathematical Word Problems By Susan Allen

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Problem One of the most common strategies to help students in mathematics is visualization. The belief is that diagrams make word problems easier for students by making the abstract concepts more concrete and easier for students to identify.

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Problem The majority of studies on diagrams are focused on student- constructed diagrams. Little research has been done on presented diagrams (despite their ubiquitous existence in math classes, textbooks, and standardized tests). Research is necessary to determine whether students are, in fact, more able to solve word problems when presented with a diagram. Shedding light on the usefulness of presented diagrams in math will further educators’ understanding of how to make mathematical concepts more accessible to students.

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Hypotheses Participants who are presented with a diagram will score higher on a math assessment than those presented with no diagram. Participants who are presented with a diagram will report lower levels of perceived difficulty, as well as higher levels of confidence in their own answers, than those not presented with a diagram.

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Sample Participants were all graduate students enrolled in EDU738 at Salem State University. 14 total volunteers (7 in control group, 7 in experimental group) One volunteer did not participate in the study, so there were 7 respondents in the control group and 6 in the experimental group. Of the 13 respondents, 12 were female and 1 was male. Participants ranged in age from 24-45.

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Design Participants were randomly assigned to either the control group or the experimental group. They were emailed a link to their respective group’s survey on Survey Monkey. Control group: Word problem with no diagram Experimental group: Word problem with diagram Both groups were asked to complete the word problem to the best of their ability

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Design 5 total survey questions after the word problem 2 demographic questions (gender and age) 3 questions about the word problem—these questions asked about the difficulty, participants’ confidence in their responses, and whether or not they felt the diagram (if one was provided) was helpful.

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Instruments Word problem for control group: Josh has a rug in the center of his bedroom floor. Both the bedroom and the rug are in the shape of a rectangle. Josh’s bedroom is 13 feet wide and 11 feet long. The rug is 2 feet away from the bedroom wall on all four sides. a. What is the area, in square feet, of the entire floor? b. What is the perimeter, in feet, of the rug? c. What is the area, in square feet, of the part of the floor not covered by the rug?

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Instruments Word problem for experimental group: Josh has a rug in the center of his bedroom floor. Both the bedroom and the rug are in the shape of a rectangle. Josh’s bedroom is 13 feet wide and 11 feet long. The rug is 2 feet away from the bedroom wall on all four sides. a. What is the area, in square feet, of the entire floor? b. What is the perimeter, in feet, of the rug? c. What is the area, in square feet, of the part of the floor not covered by the rug?

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Instruments Survey (same for both groups): 1. How old are you? 2. What is your gender? a. Male b. Female c. No response 3. Overall, how difficult was the word problem for you? a. not difficult at all b. a little difficult c. somewhat difficult d. very difficult 4. How many of the 3 questions do you feel you answered correctly? a. none b. one c. two d. all three 5. How did the provided diagram affect your ability to answer the questions? a. There was no diagram/I did not see a diagram b. The diagram made the problem more difficult for me c. The diagram had no affect on my ability to solve the problem d. The diagram made the problem easier for me

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Results Question 1 not analyzed: all but one participant answered correctly Everyone who answered #2 correctly also answered #3 correctly Everyone in the experimental group indicated that the diagram made the problem easier to solve. Everyone in the control group indicated that they did not see a diagram (because there wasn’t one!)

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Results By individual: α=0.05 x²=6.1978 df=1 p = 0.0128 By total # of responses α=0.05 x²=12.396 df=1 p = 0.0004 GroupCorrect (%)Incorrect (%)Total Control(no diagram)1 (14.3%)6 (85.7%)7 Experimental (diagram)5 (83.3%)1 (16.7%)6 Total6713 GroupCorrect (%)Incorrect (%)Total Control(no diagram)2 (14.3%)12 (85.7%)14 Experimental (diagram)10 (83.3%)2 (16.7%)12 Total121426

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Results: Survey Overall, how difficult was this problem for you? *no one answered “very difficult” α=0.05 x²=.07 df=2 p = 0.966 How many of the three questions do you feel you answered correctly? *no one answered “none” α=0.05 x²=1.38 df=2 p = 0.5016 GroupNot difficult at allA little difficultSomewhat difficultTotal Control (no diagram)1 (14.3%)4 (57.1%)2 (28.6%)7 Experimental (diagram) 1 (16.7%)3 (50%)2 (33.3%)6 Total27413 GroupOneTwoAll threeTotal Control (no diagram)1 (14.3%) 5 (71.4%)7 Experimental (diagram)02 (33.3%)4 (66.7%)6 Total13913

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Implications The superior performance of the experimental group could possibly be attributed to the presence of the diagram This theory is supported by the fact that everyone in the experimental group indicated that the diagram made it easier This would imply that visualization is a helpful tool for solving word problems A possible explanation for the lack of difference in perceived difficulty and confidence

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