Glenn Ledder Department of Mathematics University of Nebraska-Lincoln [email protected] Assessment Using Online Assignment Management Systems.

Glenn LedderDepartment of MathematicsUniversity of [email protected]

Assessment Using Online Assignment Management

Systems

1. Defining the terms

2. OAM advantages and disadvantages

3. Low-maintenance administration

4. Accurate and reproducible results

5. Getting meaningful results

Assessment Using Online Assignment Management

Systems

Defining the Terms

“Assessment”

• Conflicting meanings

“Assessment”


– General meaning: measuring academic success in any context

“Assessment”



– Specific meaning: measuring academic success in a broad context

“Assessment”



– Specific meaning: measuring academic success in a broad context

(larger than a single course)

• Dictionary definition:– “assess”: to determine the importance, size,

or value of– “evaluate”: to determine or fix the value of

Assessment vs Evaluation

• Dictionary definition:– “assess”: to determine the importance, size,

or value of– “evaluate”: to determine or fix the value of

• Connotation:– “assessment” usually emphasizes the making

of summary judgments– “evaluation” usually emphasizes the

measurement of quantitative value



• Assessment:– measuring knowledge and understanding

• Evaluation:– measuring achievement


• Assessment:– measuring knowledge and understanding

– used for placement

• Evaluation:– measuring achievement

– used to determine course grades


• Assessment:– measuring knowledge and understanding– used for placement

• Evaluation:– measuring achievement– used to determine course grades

• Test: an instrument used for assessment, evaluation, or both

OAM Advantages and

Disadvantages

OAM Advantages/Disadvantages

+ Immediate grading

(no wait for grading or machine scoring)


+ Immediate grading

+ General purpose testing center

(no need for direct faculty involvement)


+ Immediate grading


– Administrative difficulties

(How do you maintain the database?)


+ Immediate grading



+ Algorithmic Q’s and symbolic A’s

(individual answers, no prompts)


+ Immediate grading



+ Algorithmic Q’s and symbolic A’s

– Difficulties in writing questions

(How to avoid tricky, picky, sticky?)

Low-Maintenance Administration


• Lots of instructors and proctors– Should require minimal knowledge



• One or two faculty manage the system– Should require minimal time



• One or two faculty manage the system– Should require minimal time

• Questions are “permanent.”

• Student records are “transient.”

106 COURSE

•Question banks•Gateway exam•Practice assignments

The 106 COURSE data is “permanent.” The only regular changes are to the Gateway exam dates.Maintained by faculty manager.

The Math 106 EDU folder structure

The Math 106 EDU folder structure

106 COURSE

•Question banks•Gateway exam•Practice assignments

106 CLASS•Question banks•Gateway exam•Practice assignments

•Student records

The 106 COURSE data is “permanent.” The only regular changes are to the Gateway exam dates.Maintained by faculty manager.

Students register for their own 106 CLASS. Tests are inherited. Student records are local.Maintained by individual instructors/proctors.

Accurate and Reproducible Results

Reproducibility

• Tests should measure something.

– The test has to yield consistent results in multiple administrations for a single student.

Reproducibility



• But questions must change when a test is given at different times.

– This is especially important for evaluations.

Reproducibility

• Use template problems to get a great variety of answers.

• Use template problems to get uniformity of content and difficulty.

• Group problems into categories that are consistent in content and difficulty.

The Math 106 Gateway Exam

1. Elementary functions: xn, sin(ax), cos(ax), tan(ax), eax, ln x, nx

2. Products 3. Quotients 4. Compositions

5. Compositions of compositions

6. Products with a composite factor

7. Compositions of products

8. Quotients with an embedded composition

9. Quotients with an embedded product

10. Functions defined by equations

10 questions, 8 correct to pass

Category 4 - Compositions

A, C, N > 0; B ≠ 0; K ≠ 0, 1;

The algorithm chooses 5 random integers satisfying certain requirements.


A, C, N > 0; B ≠ 0; K ≠ 0, 1;

X = t, u, v, w, x, y, z;

The algorithm randomly chooses an independent variable.


X = t, u, v, w, x, y, z; A,C,N>0; B≠0; K≠0,1

P = XN+B, XN+BX

Q = AXN+B, AXN+BX, sqrt(X)+B

S = sin AX, cos AX, tan AX

T = e -CX+B, eKX+BX

U = Ae -CX+B, AeKX+BX, A ln X, ANX

The algorithm randomly creates functions P, Q, S, T, U, using some of the chosen integers.


X = t, u, v, w, x, y, z; A,C,N>0; B≠0; K≠0,1

P = XN+B, XN+BXQ = AXN+B, AXN+BX, sqrt(X)+BS = sin AX, cos AX, tan AXT = e

-CX+B, eKX+BXU = Ae

-CX+B, AeKX+BX, A ln X, ANX

F1 = sqrt(P), sqrt(S), sqrt(T)

F2 = SN, TN

F3 = ln Q, ln CS

F4 = eQ, eCS

F5 = sin Q, cos Q, sin U, cos U

The algorithm chooses one of 5 functions based on prior elements.There are 38 templates, each with 7 independent variables and at least one parameter

Reproducibility



Accuracy

• Tests should measure what they were intended to measure.

Accuracy


– Questions should have to be done right to be counted right.

Accuracy


– Questions should have to be done right to be counted right.

– Students who can do what the test is supposed to measure should get a good score.

Counted right → Done right

• Savvy test takers can do well on multiple choice tests even when they don’t understand the material.



• For calculations, students should have to type in the answer.



• For calculations, students should have to type in the answer.

• For conceptual questions, use multiple selection. (Which of the following…)

Can do → Good score

• Tricky: Misinterpretation or small mistakes account for many wrong answers.



Find the derivative of cos e2x

and

Find the derivative of e-2 cos x

are tricky




and


are tricky, compared to

Find the derivative of e2 cos x




and


are tricky, compared to

Find the derivative of e2 cos x

The problem is meant to test the chain rule, not elementary algebra.


• Picky: Too many details connect minor errors with wrong answers.

Find the derivative of cos2(2x+3)+ 4 sin x.

Find the derivative of 4x5-2x cos (ex2).




Find the derivative of cos2(2x+3).


Find the derivative of ex5 cos (ex2).




Find the derivative of cos2(2x+3).


Find the derivative of ex5 cos (ex2).

The simpler problems are hard enough.


• Sticky: Difficulties in transferring answer from paper to computer.

Find the derivative of —–. ————2x2

x+34x(x+3)-2x2

(x+3)2



Find the derivative of —–. ————

Find the derivative of —– at x = 2. —

2x2

x+34x(x+3)-2x2

(x+3)2

2x2

x+33225



Find the derivative of —–. ————

Find the derivative of —– at x = 2. —

2x2

x+34x(x+3)-2x2

(x+3)2

2x2

x+33225

Type 4x(x+3)-2x2 / (x+3)2, get 2x2

(x+3)24x(x+3)- ———

Getting Meaningful Results

Accuracy


Getting Meaningful Results


• What should OAM evaluations and assessments be intended to measure?

Don’t give up paper evaluations


• Use paper exams for questions that demand partial credit and questions where the answer is an integral, a graph, or an explanation.



• Use OAM evaluation for routine computations and basic concepts.



• Use OAM evaluation for routine computations and basic concepts.

• Testing takes time and effort. Decide what is important and then create the test to match.

• Set high standards and allow retakes.

Do give up paper assessments


• Assess routine computations and basic concepts.


• Assess routine computations and basic concepts.

• Expect very few retakes. Qualified students should pass on the first try.

• Provide necessary formulas online or as a printed supplement. Test conceptual understanding and knowledge, not memory for trivia.

Glenn Ledder Department of Mathematics University of Nebraska-Lincoln [email protected] Assessment Using Online Assignment Management Systems.

Documents

achievement slide

prompts slide

minimal knowledge slide

broad context slide

minimal time slide

single course slide

meaningful results assessment

placement evaluation