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Using EDU In Calculus

- General principles
- Online examination principles
- Online instruction principles
- The UNL Calc I Question Banks

Glenn Ledder

General Principles

- Minimize student hassles
- Avoid multiple choice
- Avoid unnecessary details
- Minimize instructor commitment

Avoid unnecessary details

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

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

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

Find the derivative of 4xcos(ex2).

Minimize instructor commitment

- MASTER – 106
- Question banks
- Gateway exam
- Practice assignments

- MASTER – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments

The data in the Master folders is “permanent.” The only regular changes are to the assignment dates.

- CLASS – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments
- Student records

Each 106A class file is used for one section only. All assignments are inherited. Students register for their

own class.

Minimize instructor commitment

- MASTER – 106
- Question banks
- Gateway exam
- Practice assignments

- MASTER – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments

Instructor Jobs

- demonstrate the system
- change dates as needed
- review student work
- download grades

- CLASS – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments
- Student records

Math 106 EDU folder structure

- MASTER – 106
- Question banks
- Gateway exam
- Practice assignments

- MASTER – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments

- CLASS – 106
- Question banks
- Gateway exam
- Practice assignments
- Assignments
- Student records

- CLASS – 106A
- Question banks
- Gateway exam
- Practice assignments
- Assignments
- Student records

Online Examinations

- Choose the right material.
- Set high standards, allow retakes
- Use problems with randomized data
- Sort problems into categories

Choose the right material

- Use paper exams for questions that demand partial credit and questions where the answer is an integral, a graph, or an explanation.
- Use online exams for routine computations where retakes minimize the need for partial credit.

High standards and retakes

- The big advantage of online testing is its capability to be delivered to students individually.
- Students learn more when expectations are higher.
- Students need repetition to achieve high standards. Retakes make up for loss of partial credit.

Randomization and categories

- Template problems yield a great variety of answers.
- Template problems allow uniformity of content and difficulty.
- Categories should be consistent in content and difficulty

The Math 106 Gateway Exam

10 questions, 8 correct to pass

- 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

Category 4 - Compositions

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=sinAX,cosAX,tanAX

T=e-CX+B,eKX+BX

U=Ae-CX+B,AeKX+BX,AlnX,ANX

F=sqrt(P),sqrt(S),sqrt(T), SN,TN,lnQ,lnCS,eQ,eCS, sinQ,cosQ,sinU,cosU

38templates, each with 7independent variables

and at least one parameter

Online Instruction

- Choose the right material
- Use matched sets of questions
- Use a question hierarchy
- Use a mastery protocol
- Give minimal credit for assignments
- Provide a short time window

Choose the right material

- Use online assignments to teach skills and build concepts.
- Use class time to teach ideas, work on multi-step problems, discuss techniques, etc.
- Write test questions based on online assignments.

Use a question hierarchy

Success rates should be 40-90%.

- Higher than 90% -- question too easy
- Lower than 40% -- use easier question to bridge the gap

Best learning comes from success that builds on previous success.

A question hierarchy

Topic: derivatives of quotients with powers of trig functions

3-2cos x

4+7sin2x

Goal: ——–—

1-5cos x

5+3sin x

3-2cos x

4+7sin2x

3x

3+4sin x

——–—

——–—

——–—

Use matched sets of questions

Find the (exact) x coordinate of the global minimum of f(x)=3x3+bx2+cx on [-1,1].

Case 1:

global min at critical point

Case 2:

global min at endpoint

Use a mastery protocol

Students must complete each question successfully, on any number of attempts.

Principal benefit: Students repeat only those questions they get wrong.

Sessions can be given a hierarchical structure.

Give minimal credit

% of students who complete

ass’nm’t

2 pts out of 600 – 75% completion

<1 pt out of 700 – 30% completion

0 pts – about 2% completion

% of course grade per assignment

NO PAY --- NO PLAY

“Grade inflation”

- Higher grades are not a problem if they are really earned. The real problem to be avoided is standards deflation.
- I have 30 2-pt assignments, with 42 of 60 for a C. 60 points is not enough to allow a student to pass the course with a D exam average.

The UNL Calc I Question Banks

- Limits
- The Derivative
- The Definite Integral
- Differentiation Techniques

Limits

- Numerical experiments
- Limits by factoring
- Continuity
- Limits at infinity
- Behavior at infinity
- The concept of the limit

The Derivative

- Concept and definition
- Graphs of derivatives
- Power functions and sums
- Tangent lines and linear approximations
- L’Hopital’s rule
- Critical points
- Absolute extrema
- Local extrema
- Optimization

The Definite Integral

- Computing sums
- Estimating area
- Limits of sums
- Definite integrals from graphs
- Antiderivatives
- Graphs of antiderivatives
- The fundamental theorem
- Derivatives of definite integrals
- Displacement and average value

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