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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

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

Glenn Ledder

[email protected]

general principles
General Principles
  • Minimize student hassles
  • Avoid multiple choice
  • Avoid unnecessary details
  • Minimize instructor commitment
avoid unnecessary details
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
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 commitment1
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
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
Online Examinations
  • Choose the right material.
  • Set high standards, allow retakes
  • Use problems with randomized data
  • Sort problems into categories
choose the right material
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
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
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
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
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
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 material1
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
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
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
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
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
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
“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
The UNL Calc I Question Banks
  • Limits
  • The Derivative
  • The Definite Integral
  • Differentiation Techniques
limits
Limits
  • Numerical experiments
  • Limits by factoring
  • Continuity
  • Limits at infinity
  • Behavior at infinity
  • The concept of the limit
the derivative
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
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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