Using EDU In Calculus

1. General principles

2. Online examination principles

3. Online instruction principles

4. The UNL Calc I Question Banks

Glenn Leddergledder@math.unl.edu

General Principles

• Minimize student hassles

• Avoid multiple choice

• Avoid unnecessary details

• Minimize instructor commitment

Avoid unnecessary details

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

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

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

Find the derivative of 4x cos (ex2).

Minimize instructor commitment

MASTER – 106

•Question banks•Gateway exam•Practice assignments

MASTER – 106A•Question banks•Gateway exam•Practice assignments

•Assignments

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 theirown class.

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

Minimize instructor commitment

MASTER – 106

•Question banks•Gateway exam•Practice assignments

MASTER – 106A•Question banks•Gateway exam•Practice assignments

•Assignments

CLASS – 106A•Question banks•Gateway exam•Practice assignments•Assignments

•Student records

Instructor Jobs• demonstrate the system• change dates as needed• review student work• download grades

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

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

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

F = sqrt(P), sqrt(S), sqrt(T), SN, TN, ln Q, ln CS, eQ, eCS, sin Q, cos Q, sin U, cos U

38 templates, each with 7 independent 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

3-2 cos x

4+7 sin2 xGoal: ——–—

3x

3+4 sin x

1-5 cos x

5+3 sin x

3-2 cos x

4+7 sin2 x——–— ——–— ——–—

Use matched sets of questions

Find the (exact) x coordinate of the global minimum of f(x) =3 x3+b x2+c x 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 course grade per assignment

% of students who completeass’nm’t

NO PAY --- NO PLAY

0 pts – about 2% completion

<1 pt out of 700 – 30% completion

2 pts out of 600 – 75% completion

“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

1. Limits

2. The Derivative

3. The Definite Integral

4. Differentiation Techniques

Limits

1. Numerical experiments

2. Limits by factoring

3. Continuity

4. Limits at infinity

5. Behavior at infinity

6. The concept of the limit

The Derivative

1. Concept and definition2. Graphs of derivatives3. Power functions and sums4. Tangent lines and linear approximations5. L’Hopital’s rule6. Critical points7. Absolute extrema8. Local extrema9. Optimization

The Definite Integral

1. Computing sums2. Estimating area3. Limits of sums4. Definite integrals from graphs5. Antiderivatives6. Graphs of antiderivatives7. The fundamental theorem8. Derivatives of definite integrals9. Displacement and average value