By Susan Allen 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 ID: 393231
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Slide1
The Role of Visual Prompts in Solving Mathematical Word Problems
By Susan AllenSlide2
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.Slide3
Problem
The majority of studies
on diagrams are
focused on student-constructed
diagrams.
L
ittle
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.Slide4
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.Slide5
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.Slide6
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 abilitySlide7
Design
5 total survey questions after the word problem2 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.Slide8
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?Slide9
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
?Slide10
Instruments
Survey (same for both groups):
1. How old are you?
2. What is your gender?
a
. Male
b
. Female c. No response3. 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 meSlide11
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!)Slide12
Results
B
y 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
Group
Correct
(%)
Incorrect (%)
Total
Control
(no diagram)
1 (14.3%)
6 (85.7%)
7
Experimental (diagram)
5 (83.3%)
1 (16.7%)
6
Total
6
7
13
Group
Correct
(%)
Incorrect (%)
Total
Control
(no diagram)
2 (14.3%)
12 (85.7%)14Experimental (diagram)10 (83.3%)2 (16.7%)12Total121426Slide13
Results: Survey
Overall, how difficult was this problem for you?
*
no one answered “very
difficult” α=0.05 x²
=.
07
df=2 p = 0.966How 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
Group
Not difficult at all
A little difficult
Somewhat difficult
Total
Control (no diagram)
1 (14.3%)
4 (57.1%)
2 (28.6%)
7
Experimental
(diagram)
1 (16.7%)
3 (50%)
2 (33.3%)
6
Total
2
7
4
13
Group
OneTwoAll threeTotalControl (no diagram)1 (14.3%)
1 (14.3%)
5 (71.4%)
7
Experimental (diagram)
02 (33.3%)4 (66.7%)6Total 13913Slide14
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
T
his 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