Using EDU In Calculus

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# Using EDU In Calculus - PowerPoint PPT Presentation

Using EDU In Calculus. General principles Online examination principles Online instruction principles The UNL Calc I Question Banks. Glenn Ledder [email protected] General Principles. Minimize student hassles Avoid multiple choice Avoid unnecessary details

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Using EDU In Calculus
• General principles
• Online examination principles
• Online instruction principles
• The UNL Calc I Question Banks

Glenn Ledder

[email protected]

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
• 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 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

• 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