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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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