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Blackboard Learn Weighted Column Equations

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Michael Prais
Michael Prais

The equations used by the Blackboard Learn Grade Center for Weighted (Calculated) Columns is not the typical weighted sum of given grades and weighted sum of possible grades.

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Weighted Total Grade Calculation Equations Blackboard Learn Grade Center 17 September 2014 Weighted Total Grade Calculations in the Blackboard Learn Grade Center 1
Total Score Calculations in General Total Possible Score = PossibleScore1 + PossibleScore2 +... Total Given Score = GivenScore1 + GivenScore2 +... Given Fraction of the Total Possible Scores = Total Given Score / Total Possible Score ( 1) Given Percentage of the Total Possible Scores = 100 x Given Fraction of the Total Possible Scores 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 2
Total Score Calculations in General Given Percentage of the Total Possible Scores = 100 x [(GivenScore1 + GivenScore2 + ...) / (PossibleScore1 + PossibleScore2 + ...)] = 100 x (Total Given Score / Total Possible Score) Ratio of Total Given Scores to Total Possible Scores 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 3
Weighted Score Calculations in General Total Weighted Possible Score = [ Weight1 x PossibleScore1 + Weight2 x PossibleScore2 + ... ] /( Weight1 + Weight2 + ) Total Weighted Given Score = [ Weight1 x GivenScore1 + Weight2 x GivenScore2 + ... ] /( Weight1 + Weight2 + ) Given Fraction of the Weighted Possible Scores = Total Weighted Given Score / Total Weighted Possible Score ( 1) Given Percentage of the Weighted Possible Scores = 100 x Given Fraction of the Possible Weighted Scores17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 4
Some Shorthand for Score Calculations GivenScore1 = GS1 GivenScore2 = GS2 PossibleScore1 = PS1 PossibleScore2 = PS2 Given Score Scaled by its Possible Score = GS1/PS1 ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 5
Weighted Score Calculations in General Total Weighted Possible Score = ( W1 x PS1 + W2 x PS2 + ... ) / (W1 + W2 + ) = The Whole (The Maximum Possible) Total Weighted Given Score = ( W1 x GS1 + W2 x GS2 + ... ) / (W1 + W2 + ) = The Part Given Given Fraction of the Weighted Possible Scores = The Part Given / The Whole = (W1 x GS1 + W2 x GS2 + ...) / (W1 x PS1 + W2 x PS2 + ...) ( 1) Given Percentage = 100 x Given Fraction 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 6
Given Percentage of the Weighted Possible Score Calculations in BbLearn Given Fraction of the Weighted Possible Score in BbLearn = [ Weight1 x ( GivenScore1 / PossibleScore1 ) + Weight2 x ( GivenScore2 / PossibleScore2 ) + ... ] /( Weight1 + Weight2 + ) = [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ] /( W1 + W2 + ) ( 1) Given Percentage in BbLearn = 100 x Given Fraction in BbLearn 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 7
Given Percentage of the Weighted Possible Score Calculations in BbLearn The Given Percentage of the Weighted Possible Score in BbLearn is NOT a Fraction of any Whole. = 100 x [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ] /( W1 + W2 + ) 100 x (W1 x GS1 + W2 x GS2 + ) / (W1 x PS1 + W2 x PS2 + ...) It is the Weighted Total of the Given Scores Scaled by the Possible Scores. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 8
The Sum of Weighted Ratios is not the Ratio of Weighted Sums. 1 咋1 1 + 2 咋2 2 1 咋1 + 2 咋2 1 1 + 2 2 1 + 2 = 1 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 9
The Given Percentage of the Weighted Possible Scores in BbLearn Is: [ W1 x (GS1/PS1) + W2 x (GS2/PS2) + ... ]/(W1+W2+) Defined without a sense of the Given Part of a Possible Whole A weighted sum of scaled scores ( 1) A numerical fraction, that is, a number less than one, but not a physical fraction, that is, the ratio of two physical quantities Unwittingly, used as a Percentage in BbLearn 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 10
The Given Percentage of the Weighted Possible Scores in BbLearn Is NOT the same quantity that most people would calculate as the Given Percentage of the Weighted Possible Scores Does ranks students in the same order as the true Given Percentage of the Weighted Possible Scores If you are going to use the weighted scores from BbLearn, make sure you tell your students how to calculate them. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 11
Given the Way Bb Learn Calculates the Given Percentage of the Weighted Possible Scores, How Does Bb Learn Calculate the Total Weighted Given Score? 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 12
Total Weighted Given Score Calculation in BbLearn Total Weighted Given Score in BbLearn = Given Fraction of the Weighted Possible Scores" in BbLearn x Total Weighted Possible Score where: Total Weighted Possible Score = ( Weight1 x PossibleScore1 + Weight2 x PossibleScore2 + ... ) / ( Weight1 + Weight2 + ) = ( W1 x PS1 + W2 x PS2 + )/(W1 + W2 + ) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 13
Shouldnt these Similar Quantities be Calculated the Same Way? Total Weighted Possible Score = ( W1 x PS1 + W2 x PS2 + )/(W1 + W2 + ) in Bb Learn and in General Total Weighted Given Score = ( W1 x GS1 + W2 x GS2 + ) / (W1 + W2 + ) in General but NOT in Bb Learn! 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 14
Weighted Given Score Calculation in BbLearn Total Weighted Given Score in General = ( W1 x GS1 + W2 x GS2 + ) / (W1 + W2 + ) Total Weighted Given Score in BbLearn = Given Fraction of the Total Weighted Possible Score x Total Weighted Possible Score = [W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ...] ( 1) x (W1 x PS1 + W2 x PS2 + ) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 15
Weighted Given Score Calculations in BbLearn The Total Weighted Given Score calculated in BbL from the Given Percentage of the Weighted Possible Scores calculated in BbL should NOT be used because it is NOT an accurate indicator of this quantity and should NOT be used in subsequent Grade Center calculations because it is NOT a Sum of the Weighted Given Scores! 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 16
Inconsistencies in BbLearn Definitions The Given Fraction (Percentage) of Weighted Possible Scores in BbLearn is NOT defined (or equal to) a ratio of a given part to the maximum possible (the whole). The Total Weighted Given Scores is NOT defined in the same form as the Total Weighted Possible Scores, so the defined given part is not part of the defined whole. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 17
Calculations with Categories 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 18
Calculations with Categories in BbLearn Scores in Categories are automatically combined in two available ways: "Equal" (sized using scaled scores) "Proportional" ( to what? using unscaled scores) Given Score Scaled by its Possible Score = GS1/PS1 ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 19
Scores in Categories Combined Equally Default Score = (GS1/PS1 + GS2/PS2 + ) / N ( 1) x (PS1 + PS2 + ) / N Fraction = (GS1/PS1 + GS2/PS2 + ) / N ( 1) Scaled ScoresNot Scores--are Equally Combined. Each Scaled Score has a maximum value of 1. Unfortunately, the percentage is not calculated as the ratio of a part to a whole. Inconsistently, this Score calculation is the same as the Percentage calculation for Weighted Columns. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 20
When all Possible Scores in a Category are Equal The Given Score for the Category is the Average of the Given Scores. Equally Combined Score = (1/N) (GS1 + GS2 + ) The Given Fraction of Possible Scores of the Category is the Given Fraction of Possible Scores of the Category in General. Equally Combined Fraction = (GS1 + GS2 + ) / (N x PS) PS1 + PS2 + = N x PS Equally Combined Percentage = 100 x Fraction 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 21
Scores in Categories Combined Proportionally Score = (GS1 + GS2 + ) / N Fraction = (GS1 + GS2 + ) / (PS1 + PS2 + ) ( 1) This is the same calculation used for Total Columns. These are physically reasonable quantities except for the division by N to give an average. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 22
When all Possible Scores in a Category are Equal The Given Score for the Category is the Average of the Given Scores. Proportionally Combined Score = (1/N) (GS1 + GS2 + ) The Given Fraction of Possible Scores of the Category is N times the Given Fraction of Possible Scores of the Category in General. Proportionally Combined Fraction = (GS1 + GS2 + ) / (N x PS) ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 23
Weighted Score Calculations in BbLearn Could Be Less Problematic BbLearn should calculate weighted scores using general (simple) weighted sums of Given or Possible Scores. Given Fractions (Percentages) of Weighted Possible Scores should be simple ratio of the Weighted Given Scores over the Weighted Possible Scores. The default combination of scores in categories should also be a simple sum of scoresnot an average. Instructors wishing to weight Given Fractions of Possible Scores can easily do so by adjusting weights. An alternative (flagged) combination of scores in categories and in weighted calculations could combine Given Fractions of Possible Scores. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 24
Weighted Score Calculations in BbLearn Could Be Less Problematic You cannot use Categories to automatically sum the Given Scores in a Category without first somehow scaling them. Bb Learn needs a way to do calculations with all raw scores by default and with scaled scores as an option. + W1 (GS1/PS1 + ) + scaled scores + W1 (GS1 + )/(PS1 + ) + scaled categories + W1 (GS1 + ) + unscaled scores and categories 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 25
Michael G. Prais, Ph.D. Academic Computing and Communication Center University of Illinois at Chicago mgprais@uic.edu 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 26

More Related Content

Blackboard Learn Weighted Column Equations

  • 1. Weighted Total Grade Calculation Equations Blackboard Learn Grade Center 17 September 2014 Weighted Total Grade Calculations in the Blackboard Learn Grade Center 1
  • 2. Total Score Calculations in General Total Possible Score = PossibleScore1 + PossibleScore2 +... Total Given Score = GivenScore1 + GivenScore2 +... Given Fraction of the Total Possible Scores = Total Given Score / Total Possible Score ( 1) Given Percentage of the Total Possible Scores = 100 x Given Fraction of the Total Possible Scores 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 2
  • 3. Total Score Calculations in General Given Percentage of the Total Possible Scores = 100 x [(GivenScore1 + GivenScore2 + ...) / (PossibleScore1 + PossibleScore2 + ...)] = 100 x (Total Given Score / Total Possible Score) Ratio of Total Given Scores to Total Possible Scores 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 3
  • 4. Weighted Score Calculations in General Total Weighted Possible Score = [ Weight1 x PossibleScore1 + Weight2 x PossibleScore2 + ... ] /( Weight1 + Weight2 + ) Total Weighted Given Score = [ Weight1 x GivenScore1 + Weight2 x GivenScore2 + ... ] /( Weight1 + Weight2 + ) Given Fraction of the Weighted Possible Scores = Total Weighted Given Score / Total Weighted Possible Score ( 1) Given Percentage of the Weighted Possible Scores = 100 x Given Fraction of the Possible Weighted Scores17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 4
  • 5. Some Shorthand for Score Calculations GivenScore1 = GS1 GivenScore2 = GS2 PossibleScore1 = PS1 PossibleScore2 = PS2 Given Score Scaled by its Possible Score = GS1/PS1 ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 5
  • 6. Weighted Score Calculations in General Total Weighted Possible Score = ( W1 x PS1 + W2 x PS2 + ... ) / (W1 + W2 + ) = The Whole (The Maximum Possible) Total Weighted Given Score = ( W1 x GS1 + W2 x GS2 + ... ) / (W1 + W2 + ) = The Part Given Given Fraction of the Weighted Possible Scores = The Part Given / The Whole = (W1 x GS1 + W2 x GS2 + ...) / (W1 x PS1 + W2 x PS2 + ...) ( 1) Given Percentage = 100 x Given Fraction 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 6
  • 7. Given Percentage of the Weighted Possible Score Calculations in BbLearn Given Fraction of the Weighted Possible Score in BbLearn = [ Weight1 x ( GivenScore1 / PossibleScore1 ) + Weight2 x ( GivenScore2 / PossibleScore2 ) + ... ] /( Weight1 + Weight2 + ) = [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ] /( W1 + W2 + ) ( 1) Given Percentage in BbLearn = 100 x Given Fraction in BbLearn 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 7
  • 8. Given Percentage of the Weighted Possible Score Calculations in BbLearn The Given Percentage of the Weighted Possible Score in BbLearn is NOT a Fraction of any Whole. = 100 x [ W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ... ] /( W1 + W2 + ) 100 x (W1 x GS1 + W2 x GS2 + ) / (W1 x PS1 + W2 x PS2 + ...) It is the Weighted Total of the Given Scores Scaled by the Possible Scores. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 8
  • 9. The Sum of Weighted Ratios is not the Ratio of Weighted Sums. 1 咋1 1 + 2 咋2 2 1 咋1 + 2 咋2 1 1 + 2 2 1 + 2 = 1 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 9
  • 10. The Given Percentage of the Weighted Possible Scores in BbLearn Is: [ W1 x (GS1/PS1) + W2 x (GS2/PS2) + ... ]/(W1+W2+) Defined without a sense of the Given Part of a Possible Whole A weighted sum of scaled scores ( 1) A numerical fraction, that is, a number less than one, but not a physical fraction, that is, the ratio of two physical quantities Unwittingly, used as a Percentage in BbLearn 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 10
  • 11. The Given Percentage of the Weighted Possible Scores in BbLearn Is NOT the same quantity that most people would calculate as the Given Percentage of the Weighted Possible Scores Does ranks students in the same order as the true Given Percentage of the Weighted Possible Scores If you are going to use the weighted scores from BbLearn, make sure you tell your students how to calculate them. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 11
  • 12. Given the Way Bb Learn Calculates the Given Percentage of the Weighted Possible Scores, How Does Bb Learn Calculate the Total Weighted Given Score? 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 12
  • 13. Total Weighted Given Score Calculation in BbLearn Total Weighted Given Score in BbLearn = Given Fraction of the Weighted Possible Scores" in BbLearn x Total Weighted Possible Score where: Total Weighted Possible Score = ( Weight1 x PossibleScore1 + Weight2 x PossibleScore2 + ... ) / ( Weight1 + Weight2 + ) = ( W1 x PS1 + W2 x PS2 + )/(W1 + W2 + ) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 13
  • 14. Shouldnt these Similar Quantities be Calculated the Same Way? Total Weighted Possible Score = ( W1 x PS1 + W2 x PS2 + )/(W1 + W2 + ) in Bb Learn and in General Total Weighted Given Score = ( W1 x GS1 + W2 x GS2 + ) / (W1 + W2 + ) in General but NOT in Bb Learn! 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 14
  • 15. Weighted Given Score Calculation in BbLearn Total Weighted Given Score in General = ( W1 x GS1 + W2 x GS2 + ) / (W1 + W2 + ) Total Weighted Given Score in BbLearn = Given Fraction of the Total Weighted Possible Score x Total Weighted Possible Score = [W1 x (GS1 / PS1) + W2 x (GS2 / PS2) + ...] ( 1) x (W1 x PS1 + W2 x PS2 + ) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 15
  • 16. Weighted Given Score Calculations in BbLearn The Total Weighted Given Score calculated in BbL from the Given Percentage of the Weighted Possible Scores calculated in BbL should NOT be used because it is NOT an accurate indicator of this quantity and should NOT be used in subsequent Grade Center calculations because it is NOT a Sum of the Weighted Given Scores! 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 16
  • 17. Inconsistencies in BbLearn Definitions The Given Fraction (Percentage) of Weighted Possible Scores in BbLearn is NOT defined (or equal to) a ratio of a given part to the maximum possible (the whole). The Total Weighted Given Scores is NOT defined in the same form as the Total Weighted Possible Scores, so the defined given part is not part of the defined whole. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 17
  • 18. Calculations with Categories 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 18
  • 19. Calculations with Categories in BbLearn Scores in Categories are automatically combined in two available ways: "Equal" (sized using scaled scores) "Proportional" ( to what? using unscaled scores) Given Score Scaled by its Possible Score = GS1/PS1 ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 19
  • 20. Scores in Categories Combined Equally Default Score = (GS1/PS1 + GS2/PS2 + ) / N ( 1) x (PS1 + PS2 + ) / N Fraction = (GS1/PS1 + GS2/PS2 + ) / N ( 1) Scaled ScoresNot Scores--are Equally Combined. Each Scaled Score has a maximum value of 1. Unfortunately, the percentage is not calculated as the ratio of a part to a whole. Inconsistently, this Score calculation is the same as the Percentage calculation for Weighted Columns. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 20
  • 21. When all Possible Scores in a Category are Equal The Given Score for the Category is the Average of the Given Scores. Equally Combined Score = (1/N) (GS1 + GS2 + ) The Given Fraction of Possible Scores of the Category is the Given Fraction of Possible Scores of the Category in General. Equally Combined Fraction = (GS1 + GS2 + ) / (N x PS) PS1 + PS2 + = N x PS Equally Combined Percentage = 100 x Fraction 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 21
  • 22. Scores in Categories Combined Proportionally Score = (GS1 + GS2 + ) / N Fraction = (GS1 + GS2 + ) / (PS1 + PS2 + ) ( 1) This is the same calculation used for Total Columns. These are physically reasonable quantities except for the division by N to give an average. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 22
  • 23. When all Possible Scores in a Category are Equal The Given Score for the Category is the Average of the Given Scores. Proportionally Combined Score = (1/N) (GS1 + GS2 + ) The Given Fraction of Possible Scores of the Category is N times the Given Fraction of Possible Scores of the Category in General. Proportionally Combined Fraction = (GS1 + GS2 + ) / (N x PS) ( 1) 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 23
  • 24. Weighted Score Calculations in BbLearn Could Be Less Problematic BbLearn should calculate weighted scores using general (simple) weighted sums of Given or Possible Scores. Given Fractions (Percentages) of Weighted Possible Scores should be simple ratio of the Weighted Given Scores over the Weighted Possible Scores. The default combination of scores in categories should also be a simple sum of scoresnot an average. Instructors wishing to weight Given Fractions of Possible Scores can easily do so by adjusting weights. An alternative (flagged) combination of scores in categories and in weighted calculations could combine Given Fractions of Possible Scores. 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 24
  • 25. Weighted Score Calculations in BbLearn Could Be Less Problematic You cannot use Categories to automatically sum the Given Scores in a Category without first somehow scaling them. Bb Learn needs a way to do calculations with all raw scores by default and with scaled scores as an option. + W1 (GS1/PS1 + ) + scaled scores + W1 (GS1 + )/(PS1 + ) + scaled categories + W1 (GS1 + ) + unscaled scores and categories 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 25
  • 26. Michael G. Prais, Ph.D. Academic Computing and Communication Center University of Illinois at Chicago mgprais@uic.edu 17 September 2014 Weighted Total Grade Calculations in Blackboard Learn 26