MATH 152 MATLAB Labs - Retention Experiment
Students of MATH 152, Winter term 2007/08, completed 6 MATLAB-based computer labs. To
assess their learning of basic MATLAB commands the following question was given as part of
the final exam in April 2008
Math 152 April Final Exam:
Q11. The following MATLAB commands were typed in, followed by <enter>:
• A = [[1 2 2];[2 1 2];[2 2 1]];
• x = [1 1 1];
• y = [1 2 3];
What will be the result of the following MATLAB commands, followed by <enter>:
(a) x.*y
(b) x*y
(c) x*y’
(d) A*x’
(e) A\x’
Recall that in MATLAB, the symbol <’> denotes transpose. Hint: one of the
commands above will lead to an error message. For this case, describe why an error
occurs.
Data Analysis
# of students enrolled = 648
# of exams recorded = 543 (84%)
Q11 (out of 5)
mean 2.43 – 48.6%
st dev 1.34 – 26.8%
Exam (out of 60)
mean 37.9 – 63.2%
st dev 12.6 – 21%
Math 152 April 2008 Final Exam
1
0.9
0.8
Total % score
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
% Score in Q11
0.8
1
Retention Experiment:
To measure retention of basic MATLAB commands learned in MATH 152 computer labs run in
Jan-April 2008, questions involving MATLAB were added to the Mech 220 review quiz.
The quiz was given on Aug 25 2008 to all students entering the Mech 2 program in Mechanical
Engineering. MATLAB was not listed as a possible topic covered in the quiz. No marks were
associated with these questions.
Five questions were added to the quiz. The first three questions were nearly identical to Q11 (a)
(b) (c) given in the MATH 152 April 2008 Final Exam:
Mech 220 Review Quiz: Q29 –30 -31
29. The following MATLAB commands were typed in, followed by <enter>
X=[1 1 1];
Y=[1 2 3];
what is the output of X.*Y followed by <enter>?
a) 6
b) 1 2 3
c) 1 4 6
d) error message
e) 1
1
1
30. For the same X and Y as in question 29, what is the output of X*Y followed by <enter>?
a) 6
b) 1 2 3
c) 1 4 6
d) error message
e) 1 1 1
31. For the same X and Y as in question 29, what is the output of X*Y' followed by <enter>?
a) 6
b) 1
2
3
c) 1 4 6
d) error message
e) 1
1
1
Data Analysis:
# of students who wrote quiz = 82
# of students who wrote quiz and Math 152 final exam = 66
# of students in comparison set = 58 (71%)
Q29-31 (out of 3)
all students
comparison set
Mean 1.1 – 38%
mean 1.31 – 44%
St dev 1 – 34%
st dev 1 – 33%
152 Final Exam Q11 a,b,c (out of 3)
comparison set
mean 2 – 68%
st dev 0.8 – 26%
Comparison set (Q29-31)
math 152 final
1.2
mech 220 quiz
% score
1
0.8
0.6
0.4
0.2
Comparison Set (Q29-31)
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
1
0
math 152 final
mech 220 quiz
1.2
% score
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
Two more questions involving MATLAB were added to the Mech 220 quiz.
Note: Because of the nature of Q11.e in the Math 152 final exam (open question, high failure
rate due to algebra computation errors) a direct comparison with Q32 below is not possible.
Mech 220 review Quiz: Q32-33
32. Which of the following lines of MATLAB commands, followed by <enter>, would you
type in to compute the solution of the following linear system
x_1 + 2 x_2 + 2 x_3 = 1
2 x_1 +
x_2 + 2 x_3 = 1
2 x_1 + 2 x_2 +
x_3 = 1
a) A=[1 2 2; 2 1 2; 2 2 1];
B=[1 1 1];
A\B
b) A=[1:2:2; 2:1:2; 2:2:1];
B=[1 1 1];
A\B
c) A=[1 2 2; 2 1 2; 2 2 1];
B=[1 1 1];
A\B'
d) A=[1 2 2; 2 1 2; 2 2 1];
B=[1 1 1];
B\A
e) A=[1 2 2; 2 1 2; 2 2 1];
B=ones(1,3);
A/B
33. Suppose the variable A is defined as a 3x3 matrix with random entries. What is the output
of the following MATLAB script?
for i = [1:3]
A(i,:)=A(i,:)/A(i,1)
end
a)
b)
c)
d)
e)
each entry of A is divided by the entry in the first row and first column
the first column of A is divided by the entry in the first row and first column
each row of A is divided by the first entry in that row
the first column of A is divided by the last entry of the first row
each columnn of A is divided by the first entry in that column
Data Analysis
Q32-33 (out of 2)
All students
Mean 0.74 – 37%
St dev 0.65 – 32%
comparison set
36%
32%
Effects of Computer Labs
# of students who did not attend Math 152 computer labs in Jan-April 2008: 16
Scores
all questions (out of 5)
Mean 1.44 – 29%
St dev 0.9 – 18%
All Students
All questions
Q29-31
Q32-33
Not in Math152 (Jan08)
All questions
Q29-31
Q32-33
Mean
St Dev
37%
38%
37%
24%
34%
32%
29%
25%
34%
18%
31%
30%