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Linear Algebra Examination
Victor TanDepartment of Mathematics
National Universit of Sin a ore
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AbstractIn the teaching of a first undergraduate course in Linear Algebra, the
.
students are solving linear algebra problems, it is very likely thatthey will need to perform tedious computation like matrix
.
(GC) are capable of performing these computations. However, not
all undergraduate students (in my university) are equipped with GC,
scientific calculators for their examinations. During a recent
semester, I allowed a special group of students to use GC and
res r c e e res o e s u en s o use sc en c ca cu a ors ur ngthe same examination. I studied and compared the examination
results of the two groups of students. In this talk, I will present my
ATCM 2010 GC for Linear Algebra Examination
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Overview Usage of GC in Singapore Schools
Pre-University
University
Course description
Students rofile
Assessments
Students Feedback Survey Exam results
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Usage of GC in Singapore Schools
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Introduced to all JC students in the first year
Most JCs use TI-84 Plus
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Usage of GC in Singapore Schools
Not commonly used in math classes
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University lecturers are not familiar with GC
Alternative software available
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Linear Algebra Course in NUS
Offered in both semester 1 and 2
~
Mainly for math major and science students
Systems of linear equations. Matrices. Determinants.
Euclidean n-space. Subspaces. Linear independence.
Basis and dimension. Rank of a matrix. Orthogonalityand orthonormal bases. Eigenvalues and eigenvectors.
Dia onalization. Linear transformations.
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Linear Algebra Course in NUSStudents profile (Semester 2)
Undergraduate students Math Major
Non-Math Science students
Non-Science students
H3 students
Selected from JC students based on their
math results
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Linear Algebra Course in NUSAssessment
Any calculatorsMATLAB
Practice Sessions Lab Sessions
Mid-Term Exam
Final Exam
Only scientific calculators
(traditionally)
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Linear Algebra Course in NUS
Should students be allowed to use GC duringexam?
Will students who use GC during exam have
an advanta e over students who dont?
Is it possible to set an exam that is fair to all
students with or without using GC?
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Linear Algebra Course in NUSAssessment
Any calculatorsMATLAB
Practice Sessions Lab Sessions
Mid-Term Exam
Final Exam
Only scientific calculators
(traditionally)
H3 students: graphing calculators are allowed
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Linear Algebra Course in NUSUsage of GC in Linear Algebra
Reduced row echelon form Matrix multiplication
Determinant
Inverse matrix
Elementary row operations
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Students FeedbackPost mid-term exam survey
75 H3 students
27 did not use the GC42 used the GC
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 21
ATCM 2010 GC for Linear Algebra Examination
help for this part: 22
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 2
ATCM 2010 GC for Linear Algebra Examination
help for this part: 3
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 6
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help for this part: 9
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 4
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help for this part: 6
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 6
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help for this part: 14
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 0
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help for this part: 5
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 2
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help for this part: 9
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Students FeedbackPost mid-term exam survey
Number of students using GC for this part: 14
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help for this part: 14
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Students FeedbackPost mid-term exam survey
GC has improved your performance in this exam.
Agree 12
Disagree 24
Not sure 27
NA 10
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Students FeedbackPost mid-term exam survey
Without GC, you will perform equally well in this exam
.
Agree 48
Disagree 7
Not sure 18
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Students FeedbackPost mid-term exam survey
Do you think that GC is necessary for this exam?
.
Yes 15
No 44
Not sure 14
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Students Feedback It takes a long time to key in matrices in GC
an use or ques ons w un nowns
manual calculation can be faster for small matrices
still need to be shown
GC may discourage us to practice the Gaussian
SC is equally capable (as GC)
Do not know how to use GC for matrix calculation
No time to use Save time in performing Gaussian Elimination
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s a goo oo or error c ec ng
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Concluding RemarksQuestions
Should students be allowed to use GC during
exam?
They can be allowed to use GC
Will students who use GC during exam havean a van age over s u en s w o on
Not significant
Is it possible to set an exam that is fair to allstudents with or without using GC?
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Concluding Remarks
Post final exam survey
ompar son etween an un ergra
Comparing the performance of H3students with and without using GC
Allowin under rad to use GC in exam
Prepare the H3 students on the use of
ATCM 2010 GC for Linear Algebra Examination