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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 - PowerPoint PPT Presentation
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Using EDU In Calculus
1. General principles
2. Online examination principles
3. Online instruction principles
4. The UNL Calc I Question Banks
Glenn [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)+ 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