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Reverse+multiple choice+method--presentation 6-feb12
The Reverse Multiple-Choice Method (RMCM) presents content for teaching or testing using a multiple-choice question format. It formalizes reinforcement and explanation by requiring examinees to identify why answers are correct or incorrect, and modify incorrect answers by changing facts to make them correct. This forces analysis and comparison of concepts. RMCM aims to harness the power of "wrong" answers and be more efficient than open-ended questions while allowing automated scoring.
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Reverse+multiple choice+method--presentation 6-feb12
- 1. Reverse Multiple-Choice Method (RMCM) InduM. Anand Mathematics Department University of Massachusetts – Lowell AMCOA Conference, February 9, 2012
- 2. RMCM -- TheMethod Reverse Multiple-Choice Method: Presents content for Teaching or Testing Introduced in Patent No. US 7,033,182 Uses multiple-choice question format Formalizes reinforcement & explanation Harnesses power of “wrong” answers
- 3. RMCM -- TheMethod (contd) Requires examinee to: (i) examine each answer choice in the context of the query; (ii) identify key information that makes the answer correct or incorrect; then, (iii) change the given facts to make an incorrect answer choice the "correct" answer to changed query.
- 4. RMCM Method (contd)… Correct answer, no modification For a “wrong” answer choice Examinee:-- Must examine answer choice Must understand why answer is incorrect Must communicate why it is incorrect More efficient than Open format / essay May be automated for grading
- 5. How it works– Examinee‟s view… Examinee, typically, is asked: To select correct answer Then -- select one (or more) wrong answer change the query so that selected wrong answer is the correct 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 correct others incorrect RMCM Questions: ◦ May be written from the scratch, or ◦ May be developed from other multiple- choice questions ◦ Stored in persistent databanks of questions
- 7. RMCM Question (contd) ◦Special features of RMCM question: ◦ Fact Objects (FO‟s) = Facts / segments of the query on which the answer turns; FO = True or False for an answer choice, depending on its relevance to answer choice ◦ Fact Object Values (FV‟s) – Values assigned to relevant FO‟s for original or modified query.
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- 9. RMCM Question -Structure Answer Choices should be closely related 1 Answer choice FO/FV 2 5 3 Query 4
- 10. How it works– Examiner‟s view… Select incorrect answer choices strategically in order to -- Emphasize the facts provided in the question Identify “Fact Objects” for each answer choice; Provide “Fact Values” of the “True” Fact Objects ( for each answer choice) Provide score / partial score for each FO for each answer choice
- 11. RMCM – Examiner‟sview (contd) Examiner must: Define the Objectives for the question Figure out what concept to assess Know where and how students miss the concept Form answer choices around common errors Work Backwards Correlate facts / segments in query with errors Determine importance of each FO Apportion relative credit for the facts / segments
- 12. How it works– System view The RMCM system: Assists Examiner with ◦ Editorial support to write or import questions; ◦ Selecting “Fact Objects” for an answer choice with (proprietary) segmentation software; ◦ Maintaining FO/FV databases, and credit generation databases ◦ Generating computer-assisted queries Assists Examinee with navigation
- 13. How it worksSystem view (contd) Compare Examinee‟s answers with Examiner‟s data ◦ Identifying FO‟s for selected wrong answer choice + ◦ Fact Values for (True) FO‟s for selected wrong answer Calculate score for question based on comparison ◦ 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 systemworks – Logic I
- 15. How the systemworks – Logic II
- 16. Example 1 What isthe area of a rectangle with sides 3 and 4? A. 5 B. 12 C. 14 D. 16 E. 9
- 17. Screen mock upfor Example 1
- 18. Screen mock upcontinued
- 19. Screen mock upcontinued
- 20. Screen mock upcontinued
- 21. Example 2 Divide andsimplify 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 for the expression: (10-2); (B) would be correct for the expression: 2 * ( 5 - 1 ); (D) would be correct for the expression: (10 * 2); (E) would be correct for the expression: (10 + 2).
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- 24. Example 3 (contd) Whatis the current in the 4 Ω resistor while 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 different sets of Fact Objects; e.g., Resistors with other resistance values; or Changes of both resistance and voltage. One interesting case is where a Fact Object 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; Sequence of lab activity
- 26. Example 4 –Math word problem* 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 each printed T-shirt for $11, what expression can you use to calculate the class profit for 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-numericFO 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 each printed T-shirt for $11, what expression can you use to calculate the class profit for 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
- 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 each shirt is $0.75. If the class plans on selling each printed T-shirt for $11, what expression can you use to calculate the class profit for 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
- 29. Other question FO‟s 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 each shirt is $0.75. If the class plans on selling each printed T-shirt for $11, what expression can you use to calculate the class profit for 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
- 30. Examiner‟s selection &save of 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 each shirt is $0.75. If the class plans on selling each printed T-shirt for $11, what expression can you use to calculate the class profit for 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 selling 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 all T-shirts,‟ and change „printing cost of each shirt‟ to „printing cost of all shirts.‟ C: Change „cost of each T-shirt‟ to „cost of all T-shirts,‟ and change „selling each printed shirt‟ to „selling all printed shirts.‟ D: (may indicate that student lacks understanding of the material tested and may lead to complete loss of credit for the question).
- 32. Another RMCM embodimentof Example 4… Examinee Task: ◦ choose an answer that you believe is incorrect. ◦ find facts /segments from LIST, so that chosen incorrect answer becomes correct answer to changed question ◦ LIST: --„cost of each T-shirt;‟ „alone;‟ „$3.50;‟ „printing cost of each shirt;‟ „$0.75;‟ „selling each printed shirt;‟ „$11;‟ „profit;‟ „selling n printed shirts‟
- 33. ◦ LIST: „costof each T-shirt;‟ „alone;‟ „$3.50;‟ „printing cost of each shirt;‟ „$0.75;‟ „selling each printed shirt;‟ „$11;‟ „‟profit;‟ „selling n printed shirts.‟ Expected answers: A: „selling each printed shirt.‟ B: „cost of each T-shirt‟ and „printing cost of each shirt.‟ C: „cost of each T-shirt‟ and „selling each printed shirt.‟ D: (test-taker lacks understanding of subject
- 34. Wrap up -Advantages of RMCM Multiple-choice format used for RMCM:-- 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 / contrasts of similar and related concepts
- 35. Wrap up -Disadvantages mitigated by RMCM Unlike traditional Multiple-choice RMCM: Discourages answering without careful reading Encourages analysis of questions Finds depth of student‟s learning Databank of questions has lasting value
- 36. Disadvantages of openformat/ essay mitigated by RMCM ◦ Encourages identification of context ◦ Discourages padding of answers with irrelevant writing ◦ More efficient ◦ Computer-aided assessment possible
- 37. Invitation If youwould like to get involved -- Effort is underway to: ◦ Assemble groups of educators / others ◦ Assemble RMCM Questions databanks ◦ Develop self-study courses ◦ Develop instructor-led courses You are also invited to contribute to further design and development of RMCM software
- 39. Thank You! Contact Indu M.Anand indu_m_anand@yahoo.com indu_anand@uml.edu
Editor's Notes
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