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

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    • 1. Reverse Multiple-ChoiceMethod (RMCM)Indu M. AnandMathematics DepartmentUniversity of Massachusetts – LowellAMCOA Conference, February 9, 2012
    • 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. 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. 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. 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. 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. 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. Structure…Test QuestionQueryAnswerChoiceBodyCallFactObject FactValueValue Score11..*1..*
    • 9. RMCM Question - StructureAnswer Choices should be closelyrelated1Answer choiceFO/FV2 53 Query 4
    • 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. 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. 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. 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. How the system works – Logic I
    • 15. How the system works – Logic II
    • 16. Example 1What is the area of a rectangle withsides 3 and 4?A. 5B. 12C. 14D. 16E. 9
    • 17. Screen mock up for Example1
    • 18. Screen mock up continued
    • 19. Screen mock up continued
    • 20. Screen mock up continued
    • 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. 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. Example 3
    • 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. 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. 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. 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. 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. 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. 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. 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. 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. ◦ 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. 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. 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. Disadvantages of open format/essay mitigated by RMCM◦ Encourages identification of context◦ Discourages padding of answerswith irrelevant writing◦ More efficient◦ Computer-aided assessmentpossible
    • 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. Thank You!ContactIndu M. Anand indu_m_anand@yahoo.com indu_anand@uml.edu

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