Scoring an Ordered List
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ABCDEFGHIJKLMNOPQRSTUVWXYZAA
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FAWNFAWNJACOBJACOBDannyKevinAmyBeckyPeggyKatrinaDavidDavid
Joanthan
SethJessie
Ann Marie
JimbobVictoria
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Score
(Counting Inversions)
(Counting Inversions - Then Calculating Probability)
First thought, look at how many moves needed to put it in correct order (can move adjacent numbers in one step), subtract that from 8.
1 for each in correct position
Sum of distance from correct position - will have to convert somehow so closer is higher score
I did what David did, but divided it by 8 and subtracted it from (the highest score)
Ordering, especially with fractions, is an important understanding. My scoring scheme informs students that they know it or they don't. If they don't we (the student and I, sometimes the whole class) take steps to understand the mistakes.
Group numbers into collections that can be rotated to be ascending without gaps (like (123)(564)(78)). Subtracts number of groups from nine (because correct is 1 group) and subtracts number of rotations within groups.
Similar to Jessie - I see 7 possible groups (1,2)(2,3)(3,4)(4,5)(5,6)(6,7)(7,8) where the consecutive order is correct. I would base the score on these.
Generally I mark this type of thing out of 2. Student scores 1 for one error and 0 for everything else.
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12345678880818782
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Set A12453786256.8571428577.97797664256428704340
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Set B1278645323.754.2857142865.1218255324332185.750433.50
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Set C1235784633.756.5714285717.9434526326543106.750433.50
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Set D4132578600.756.2857142867.8753975114510106.750213.50
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Set E47186325003.4285714292.8781752113000264.750100.50
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Set F1234578656.57.4285714297.998413762677547.506561
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Set G6812345702.254.8571428576.404966215250225.250543.50
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Set H8761234501.252.8571428571.595045214050304.250642.50
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Set I1237856435.55.7142857147.5652786325543126.505430
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Set J4512687301.755.1428571434.3805565114410185.7503220
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Set K8765432170007032407010
15
Don't think I like my method, scores are too high!out of 4out of 7
Generally I mark this type of thing out of 2. Student scores 1 for one error and 0 for more than one error. More than one error means we have more work to do.
16
What if someone exactly reverses the order, do they get a zero, or something else since this seems like a problem reading directions.
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