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Reverse+multiple choice+method--presentation 6-feb12

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• Reverse+multiple choice+method--presentation 6-feb12

1. 1. Reverse Multiple-ChoiceMethod (RMCM)Indu M. AnandMathematics DepartmentUniversity of Massachusetts – LowellAMCOA Conference, February 9, 2012
2. 2. RMCM -- The MethodReverse Multiple-Choice Method: Presents content for Teaching orTesting Introduced in Patent No. US7,033,182 Uses multiple-choice question format Formalizes reinforcement &explanation Harnesses power of “wrong” answers
3. 3. RMCM -- The Method (contd)Requires examinee to: (i) examine each answer choice in thecontext of the query; (ii) identify key information that makesthe answer correct or incorrect; then, (iii) change the given facts to make anincorrect answer choice the "correct"answer to changed query.
4. 4. RMCM Method (contd)… Correct answer,  no modification For a “wrong” answer choiceExaminee:-- Must examine answer choice Must understand why answer isincorrect Must communicate why it is incorrect More efficient than Open format /essay May be automated for grading
5. 5. How it works – Examinee‟sview…Examinee, typically, is asked: To select correct answer Then -- select one (or more) wrong answer change the query so thatselected wrong answer is thecorrect answer for changed query Modification criteria may be provided
6. 6. How it works – RMCM Question Question is key data structure of system. Components of the Question object are:◦ Query – “Narrative” + Call of the question◦ Answer choices – Multiple , One correctothers incorrect RMCM Questions:◦ May be written from the scratch, or◦ May be developed from other multiple-choice questions◦ Stored in persistent databanks ofquestions
7. 7. RMCM Question (contd)◦ Special features of RMCM question:◦ Fact Objects (FO‟s) = Facts / segmentsof the query on which the answer turns;FO = True or False for an answerchoice, depending on its relevance toanswer choice◦ Fact Object Values (FV‟s) – Valuesassigned to relevant FO‟s for original ormodified query.
8. 8. Structure…Test QuestionQueryAnswerChoiceBodyCallFactObject FactValueValue Score11..*1..*
9. 9. RMCM Question - StructureAnswer Choices should be closelyrelated1Answer choiceFO/FV2 53 Query 4
10. 10. How it works – Examiner‟sview… Select incorrect answer choicesstrategically in order to -- Emphasize the facts provided in thequestion Identify “Fact Objects” for eachanswer choice; Provide “Fact Values” of the “True”Fact Objects ( for each answer choice) Provide score / partial score for eachFO for each answer choice
11. 11. RMCM – Examiner‟s view(contd)Examiner must: Define the Objectives for the questionFigure out what concept to assess Know where and how students miss theconceptForm answer choices around common errors Work BackwardsCorrelate facts / segments in query witherrors Determine importance of each FOApportion relative credit for the facts /segments
12. 12. How it works – System viewThe RMCM system: Assists Examiner with◦ Editorial support to write or import questions;◦ Selecting “Fact Objects” for an answer choicewith (proprietary) segmentation software;◦ Maintaining FO/FV databases, and creditgeneration databases◦ Generating computer-assisted queries Assists Examinee with navigation
13. 13. How it works System view(contd) Compare Examinee‟s answers with Examiner‟sdata◦ Identifying FO‟s for selected wrong answerchoice +◦ Fact Values for (True) FO‟s for selected wronganswer Calculate score for question based oncomparison◦ Identification, or not, of correct answer; and◦ Identification of FO‟s for selected wrong answer◦ Fact Values for FO‟s for the selected wrong
14. 14. How the system works – Logic I
15. 15. How the system works – Logic II
16. 16. Example 1What is the area of a rectangle withsides 3 and 4?A. 5B. 12C. 14D. 16E. 9
17. 17. Screen mock up for Example1
18. 18. Screen mock up continued
19. 19. Screen mock up continued
20. 20. Screen mock up continued
21. 21. Example 2Divide and simplify the expression:(10) 2 =(A) 8(B) 2 2(C) 5(D) 2 5(E) 2 3 This question is taken from REA‟s SAT preparation guidebook (1990)
22. 22. Example 2 (contd) Correct answer is C. (A) would be the correct answer forthe expression: (10-2); (B) would be correct for theexpression: 2 * ( 5 - 1 ); (D) would be correct for theexpression: (10 * 2); (E) would be correct for theexpression:(10 + 2).
23. 23. Example 3
24. 24. Example 3 (contd)What is the current in the 4 Ω resistorwhile switch S is open?(A) Is correct if 12 V is changed to 0 V;(B) Is the correct answer;(C) Is correct if 12 V is changed to 24 V;(D) Is correct if 12 V is changed to 40 V;(E) I correct if 12 V is changed to 60 V.
25. 25. Example 3 & Discussion Other variants possible with differentsets of Fact Objects; e.g., Resistors with other resistance values;or Changes of both resistance andvoltage. One interesting case is where a FactObject is “Switch S is open or closed.” In general, FO holds information –may be numeric or non-numeric Examples: Mathematical operation;Word order in a sentence; Sequenceof lab activity
26. 26. Example 4 – Math wordproblem* The sophomore class plans to sell T-shirts with the school‟s name on them.The cost of each T-shirt alone is \$3.50,and the printing cost of each shirt is\$0.75. If the class plans on selling eachprinted T-shirt for \$11, what expressioncan you use to calculate the class profitfor selling n printed T-shirts? A. 11.00 – (3.50 + 0.75)n B. 11.00n – (3.50 + 0.75) C. 11.00 – 3.50 – 0.75n D. (11.00 – 3.50 – 0.75)n* From 2001 MCAS test for 10th grade
27. 27. Example 4; non-numeric FO The sophomore class plans to sell T-shirts with the school‟s name on them.The cost of each T-shirt alone is\$3.50, and the printing cost of eachshirt is \$0.75. If the class plans onselling each printed T-shirt for\$11, what expression can you use tocalculate the class profit for selling nprinted T-shirts? A. 11.00 – (3.50 + 0.75)n B. 11.00n – (3.50 + 0.75) C. 11.00 – 3.50 – 0.75n D. (11.00 – 3.50 – 0.75)n
28. 28. Non-numeric FO highlighted The sophomore class plans to sell T-shirts with the school‟s name on them.The cost of each T-shirt alone is\$3.50, and the printing cost of eachshirt is \$0.75. If the class plans onselling each printed T-shirt for\$11, what expression can you use tocalculate the class profit for selling nprinted T-shirts? A. 11.00 – (3.50 + 0.75)n B. 11.00n – (3.50 + 0.75) C. 11.00 – 3.50 – 0.75n D. (11.00 – 3.50 – 0.75)n
29. 29. Other question FO‟shighlighted The sophomore class plans to sell T-shirts with the school‟s name on them.The cost of each T-shirt alone is\$3.50, and the printing cost of eachshirt is \$0.75. If the class plans onselling each printed T-shirt for \$11,what expression can you use tocalculate the class profit for selling nprinted T-shirts? A. 11.00 – (3.50 + 0.75)n B. 11.00n – (3.50 + 0.75) C. 11.00 – 3.50 – 0.75n D. (11.00 – 3.50 – 0.75)n
30. 30. Examiner‟s selection & save ofFO The sophomore class plans to sell T-shirts with the school‟s name on them.The cost of each T-shirt alone is\$3.50, and the printing cost of eachshirt is \$0.75. If the class plans onselling each printed T-shirt for \$11,what expression can you use tocalculate the class profit for selling nprinted T-shirts? A. 11.00 – (3.50 + 0.75)n B. 11.00n – (3.50 + 0.75) C. 11.00 – 3.50 – 0.75n D. (11.00 – 3.50 – 0.75)nselling each printed T-shirt
31. 31. RMCM query modifications… A: Change „selling each printed shirt‟ to„selling all printed shirts.‟ B: Change „cost of each T-shirt‟ to „cost of allT-shirts,‟ and change „printing cost of eachshirt‟ to „printing cost of all shirts.‟ C: Change „cost of each T-shirt‟ to „cost of allT-shirts,‟ and change „selling each printedshirt‟ to „selling all printed shirts.‟ D: (may indicate that student lacksunderstanding of the material tested and maylead to complete loss of credit for thequestion).
32. 32. Another RMCM embodiment ofExample 4… Examinee Task:◦ choose an answer that you believeis incorrect.◦ find facts /segments from LIST, sothat chosen incorrect answerbecomes correct answer tochanged question◦ LIST: --„cost of each T-shirt;‟„alone;‟ „\$3.50;‟ „printing cost ofeach shirt;‟ „\$0.75;‟ „selling eachprinted shirt;‟ „\$11;‟ „profit;‟ „selling nprinted shirts‟
33. 33. ◦ LIST: „cost of each T-shirt;‟ „alone;‟„\$3.50;‟ „printing cost of each shirt;‟„\$0.75;‟ „selling each printed shirt;‟„\$11;‟ „‟profit;‟ „selling n printedshirts.‟Expected answers: A: „selling each printed shirt.‟ B: „cost of each T-shirt‟ and „printing cost of eachshirt.‟ C: „cost of each T-shirt‟ and „selling each printedshirt.‟ D: (test-taker lacks understanding of subject
34. 34. Wrap up - Advantages of RMCM Multiple-choice format used forRMCM:-- Allows context definition economically Questions may be reused Scoring may be automated Other advantages of automation e.g.computer-aided generation of queries Forces analysis/ compares / contrastsof similar and related concepts
35. 35. Wrap up - Disadvantagesmitigated by RMCM Unlike traditional Multiple-choiceRMCM: Discourages answering without carefulreading Encourages analysis of questions Finds depth of student‟s learning Databank of questions has lastingvalue
36. 36. Disadvantages of open format/essay mitigated by RMCM◦ Encourages identification of context◦ Discourages padding of answerswith irrelevant writing◦ More efficient◦ Computer-aided assessmentpossible
37. 37. Invitation If you would like to get involved -- Effort is underway to:◦ Assemble groups of educators / others◦ Assemble RMCM Questions databanks◦ Develop self-study courses◦ Develop instructor-led coursesYou are also invited to contribute to furtherdesign and development of RMCMsoftware
38. 38. Thank You!ContactIndu M. Anand indu_m_anand@yahoo.com indu_anand@uml.edu