GC for Linear Algebra Exam (ATCM2010).pdf

7/25/2019 GC for Linear Algebra Exam (ATCM2010).pdf

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Linear Algebra Examination

Victor TanDepartment of Mathematics

National Universit of Sin a ore

ATCM 2010 GC for Linear Algebra Examination


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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


n ngs.


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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

-

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

-

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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Number of students using GC for this part: 21


help for this part: 22


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GC has improved your performance in this exam.

Agree 12

Disagree 24

Not sure 27

NA 10



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Without GC, you will perform equally well in this exam

.

Agree 48

Disagree 7

Not sure 18



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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


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?


es


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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


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GC for Linear Algebra Exam (ATCM2010).pdf