Assessment is Important Need for Value-Added . . . Current Approaches to . . . Towards More Adequate Natural Idea: Using . . . Linear Dependence . . . Value-Added How to Determine the . . . Case of Interval . . . Teacher Assessments: Appendix: Case of . . . How Intervals Can Help Title Page ◭◭ ◮◮ Karen Villaverde 1 and Olga Kosheleva 2 ◭ ◮ 1 Department of Computer Science Page 1 of 16 New Mexico State University Las Cruces, NM 88003, USA Go Back kvillave@cs.nmsu.edu Full Screen 2 Department of Teacher Education Close University of Texas at El Paso El Paso, TX 79968, USA Quit olgak@utep.edu
Assessment is Important 1. Assessment is Important Need for Value-Added . . . • Objective: improve the efficiency of education. Current Approaches to . . . Natural Idea: Using . . . • Important: to assess this efficiency, i.e., to describe this Linear Dependence . . . efficiency in quantitative terms. How to Determine the . . . • This is important on all education levels: Case of Interval . . . – elementary schools Appendix: Case of . . . – middle schools Title Page – high schools ◭◭ ◮◮ – universities ◭ ◮ • Quantitative description is needed because Page 2 of 16 – it allows natural comparison of different strategies Go Back of teaching and learning Full Screen – and selection of the best strategy. Close Quit
Assessment is Important 2. Need for Value-Added Assessment Need for Value-Added . . . • Traditional assessment: by the amount of knowledge Current Approaches to . . . that the students have after taking this class. Natural Idea: Using . . . Linear Dependence . . . • Example: the average score of the students on some How to Determine the . . . standardized test. Case of Interval . . . • Comment: this is actually how the quality of elemen- Appendix: Case of . . . tary/high school classes is now estimated in the US. Title Page • Limitation: the class outcome depends ◭◭ ◮◮ – not only on the quality of the class, but ◭ ◮ – also on how prepared were the students when they Page 3 of 16 started taking this class. Go Back • A more adequate assessment should estimate the added Full Screen value that the class brought to the students. Close Quit
Assessment is Important 3. Current Approaches to Value-Added Assessment Need for Value-Added . . . and their Limitations Current Approaches to . . . • Main idea: subtracting the outcome from the input. Natural Idea: Using . . . Linear Dependence . . . • Example: subtract How to Determine the . . . – the average grade after the class (on the post-test) Case of Interval . . . – the average grade on similar questions asked before Appendix: Case of . . . the class (on the pre-test). Title Page • Comment: the existing techniques take into account ◭◭ ◮◮ additional parameters influencing learning. ◭ ◮ • Main limitation: actually, the amount of knowledge Page 4 of 16 learned depends on the initial knowledge. Go Back • Additional limitation: the assessment values come from Full Screen grading, and are therefore somewhat imprecise. Close Quit
Assessment is Important 4. Natural Idea: Using Interval Techniques Need for Value-Added . . . • Reminder: assessments are imprecise, we usually only Current Approaches to . . . know bounds on the actual amount of knowledge. Natural Idea: Using . . . Linear Dependence . . . • Conclusion: it is natural to use interval techniques to How to Determine the . . . process the corresponding values. Case of Interval . . . • In this paper: we describe how to the use interval tech- Appendix: Case of . . . niques. Title Page • Result: interval techniques help us overcome both lim- ◭◭ ◮◮ itations of the existing value-added assessments. ◭ ◮ Page 5 of 16 Go Back Full Screen Close Quit
Assessment is Important 5. Traditional Approach: Reminder Need for Value-Added . . . • Reminder: the post-test result y depends on the pre- Current Approaches to . . . test result x as y ≈ x + a : Natural Idea: Using . . . Linear Dependence . . . y ✻ How to Determine the . . . � Case of Interval . . . � 1 � � Appendix: Case of . . . � � � � Title Page � � � � ◭◭ ◮◮ � � � ◭ ◮ � � � � � Page 6 of 16 � � � a � Go Back � Full Screen � ✲ x 0 1 t Close Quit
Assessment is Important 6. Linear Dependence instead of Addition: Idea Need for Value-Added . . . • Problem: the difference y − x actually changes with x . Current Approaches to . . . Natural Idea: Using . . . • Natural next approximation: y ≈ m · x + a. Linear Dependence . . . • Observation: for f-s f 1 ( x ) = m 1 · x + a 1 and f 2 ( x ) = How to Determine the . . . m 2 · x + a 2 corr. to two teaching strategies, we may have Case of Interval . . . • f 1 ( x 1 ) < f 2 ( x 1 ) for some x 1 and Appendix: Case of . . . • f 1 ( x 2 ) > f 2 ( x 2 ) for some x 2 > x 1 . Title Page ◭◭ ◮◮ • Interpretation: ◭ ◮ – for weaker students, with prior knowledge x 1 < x 2 , the second strategy is better, while Page 7 of 16 – for stronger students, with prior knowledge Go Back x 2 > x 1 , the first strategy is better. Full Screen • Conclusion: the new model provides a more nuanced Close comparison between different teaching strategies. Quit
Assessment is Important 7. Ideal Case: Perfect Learning Need for Value-Added . . . • Ideal case: no matter what the original knowledge is, Current Approaches to . . . the resulting knowledge is perfect, y ≡ 1; then m = 0. Natural Idea: Using . . . Linear Dependence . . . y ✻ How to Determine the . . . Case of Interval . . . � 1 Appendix: Case of . . . � � Title Page � � ◭◭ ◮◮ � ◭ ◮ � � Page 8 of 16 � Go Back � � Full Screen � ✲ x 0 1 t Close Quit
Assessment is Important 8. Example 2: Minimizing Failure Rate Need for Value-Added . . . • Main idea: to avoid failure, we concentrate on the stu- Current Approaches to . . . dents with low x ; then f ( x ) = m · x + a , with m < 1. Natural Idea: Using . . . Linear Dependence . . . y ✻ How to Determine the . . . Case of Interval . . . � 1 Appendix: Case of . . . � � Title Page � ✟ ✟✟✟✟✟✟✟✟✟✟✟✟ ◭◭ ◮◮ � � ◭ ◮ � � a Page 9 of 16 � Go Back � � Full Screen � ✲ x 0 t 1 Close Quit
Assessment is Important 9. Example 3: Emphasis on Strong Students Need for Value-Added . . . • Idea: concentrate most of the effort on top students. Current Approaches to . . . Natural Idea: Using . . . • Result: f ( x ) = m · x + a , with m > 1. Linear Dependence . . . y How to Determine the . . . ✻ Case of Interval . . . ✓ � 1 ✓ Appendix: Case of . . . ✓ � ✓ � Title Page ✓ ✓ � ◭◭ ◮◮ ✓ � ✓ ✓ � ◭ ◮ ✓ � ✓ Page 10 of 16 ✓ � ✓ � ✓ Go Back ✓ � ✓ � Full Screen ✓ a � ✲ Close x 0 1 t Quit
Assessment is Important 10. How to Determine the Coefficients m and a : Ideal Need for Value-Added . . . Case of Crisp Estimates Current Approaches to . . . • We know: pre-test grades x 1 , . . . , x n and post-test grades Natural Idea: Using . . . y 1 , . . . , y n . Linear Dependence . . . How to Determine the . . . • Problem: find m and a for which y i ≈ m · x i + a . Case of Interval . . . n ( y i − ( m · x i + a )) 2 → min � • Least Squares method: m,a . Appendix: Case of . . . i =1 Title Page ◭◭ ◮◮ 88.3 88.7 85.2 120 83 77.4 y = 1.1929x - 22.994 77 ◭ ◮ 100 72.2 71.7 61.7 80 58.7 55.7 Page 11 of 16 60 45.7 43.5 40 Go Back 28.3 20 Full Screen 0 0 20 40 60 80 100 120 Close Quit
Assessment is Important 11. Case of Interval Uncertainty: Analysis Need for Value-Added . . . • Fact: the grade depends on assigning partial credit for Current Approaches to . . . partly correct solutions. Natural Idea: Using . . . Linear Dependence . . . • Known: partial credit is somewhat subjective. How to Determine the . . . • How to avoid this subjectivity: letter grades such as A Case of Interval . . . (corresponding to 90 to 100) are more objective. Appendix: Case of . . . • Conclusion: instead of the exact grade x i , we have an Title Page interval x = [ x i , x i ] of possible grades. ◭◭ ◮◮ • Value-added assessment: describe the dependence y = ◭ ◮ f ( x ) of the outcome grade y on the input grade x : Page 12 of 16 • we consider all the students for whom the input Go Back grade is within the interval x ; Full Screen • then, y = f ( x ) is the set of all possible outcome grades for these students. Close Quit
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