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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 gledder@math.unl.edu. General Principles. Minimize student hassles Avoid multiple choice Avoid unnecessary details

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Using EDU In Calculus

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  1. Using EDU In Calculus • General principles • Online examination principles • Online instruction principles • The UNL Calc I Question Banks Glenn Ledder gledder@math.unl.edu

  2. General Principles • Minimize student hassles • Avoid multiple choice • Avoid unnecessary details • Minimize instructor commitment

  3. 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).

  4. 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.

  5. 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

  6. 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

  7. Online Examinations • Choose the right material. • Set high standards, allow retakes • Use problems with randomized data • Sort problems into categories

  8. 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.

  9. 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.

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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.

  15. 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.

  16. 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 ——–— ——–— ——–—

  17. 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

  18. 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.

  19. 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

  20. “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.

  21. The UNL Calc I Question Banks • Limits • The Derivative • The Definite Integral • Differentiation Techniques

  22. Limits • Numerical experiments • Limits by factoring • Continuity • Limits at infinity • Behavior at infinity • The concept of the limit

  23. 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

  24. 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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