1. Steven Spurling City College of San Francisco sspurlin@ccsf.edu ftp://advancement.ccsf.edu/general/ModelingAchievement.ppt Modeling Educational Achievement

2. Presentation The importance of the presentation The Achievement Equation Example of Use Persistence Calculation The calculation of Achievement as a double summation. Predicted Achievement with changes in 4 Variables The timeframe issue The pipeline problem A mathematical simplification Summary Scheduling for Achievement

3. The importance of this presentation: Model can be generalized to any educational objective defined by courses with units and grades. Meets the criteria of Occam’s razor. Applies a classical mathematics model to the social sciences. Classical math models are much more explanatory than statistical models. Bi-directional across the equal sign and no error term. Presents an excellent example of Plato’s cave The ARCC report asks the wrong questions. It’s the educational winter, not educational summer. The water is overflowing the river banks.

4. The Equation that Models Achievement a = p (t/us) Where a = Long term educational goal Achievement p = Average Persistence (term-to-term) to goal. t = Total units needed to achieve goal u = Units per term s = Passing rate (course Success) t/us is the number of terms students need to achieve their educational goal.

5. CCSF Students who First Appeared in Credit Academic History 1998 - 2002 (fall and spring starters only) and were tracked through fall 2010 to see how many completed 60 units. N Persist ence Terms Units Taken Units per Term Units Passed Passing Percent Units Needed Terms Needed Predicted Achieve- ment Actual Achieve ment Total72,29980%3.9927.456.8819.3671%6012.367%12%

6. 60+ unit Achievement Calculation Terms needed = total units/((units per term)(passing rate)) = 60/((6.88)(.71)) = 60/4.88 = 12.36 Achievement =.8 12.36 =.07

7. Persistence Calculation Terms at CCSFN Number Remaining Percent Remaining Persist ence 1 27,450 72,299100% 2 11,660 44,84962% 3 6,710 33,18946%74% 4 4,801 26,47937%80% 5 3,755 21,67830%82% 6 3,087 17,92325%83% 7 2,708 14,83621%83% 8 2,244 12,12817%82% 9 1,848 9,88414%81% 10 1,581 8,03611%81% 11 1,350 6,4559%80% 12 1,050 5,1057%79% 13 897 4,0556%79% 14 672 3,1584%78% 15 563 2,4863%79% 16 473 1,9233%77% 17 346 1,4502%75% 18 281 1,1042%76% 19 211 8231%75% 20 154 6121%74% 21 131 4581%75% 22 98 3270%71% 23 72 2290%70% 24 45 1570%69% 25 36 1120%71% 26 28 760%68% 27 14 480%63% 28 13 340%71% 29 5 210%62% 30 6 160%76% 31 4 100%63%

8. What’s the Average Persistence over 12.36 semesters? P= ((1.00)(.62)(.74)(.8)(.82)(.83)(.83)(.82)(.81)(.81)(.80)(.79)) ( 1/12) =.8 This is the geometric Mean. If the last term is zero, the whole persistence rate is zero.

9. Achievement of the 60 Unit Completion Goal Summed Over Passing Rate Interval Rounde d Units Passed PercentIntervalN % of Total Persist enceTermsUnits Units per Term Units Passed Passed % Units Needed Terms Needed Predicted Achieve ment Contrib ution to Total Actual Achieve ment 00-.04 13,79119%0%1.245.744.620.010%608639.940% 0.1.05-.14 1,1492%0%3.2722.9172.3910%6082.130% 0.2.15-.24 1,5072%0%3.9328.17.155.620%6042.130% 0.3.25-.34 2,9444%0%3.8626.436.857.9330%6029.190% 0.4.35-.44 2,6784%81%5.2338.067.2715.3940%6020.41%0%3% 0.5.45-.54 4,8247%82%4.6632.787.0416.4550%6016.984%0%7% 0.6.55-.64 3,9475%86%6.7850.837.530.660%6013.2914%1%18% 0.7.65-.74 4,8507%87%6.8951.317.4435.8870%6011.5321%1%25% 0.8.75-.84 5,7428%88%7.0451.747.3541.3280%6010.2226%2%30% 0.9.85-.94 5,2847%91%8.0962.397.7256.2190%608.6346%3%44% 1.95-1.0 25,58335%73%2.7716.385.916.2299%6010.264%1%9% Grand Total 72,299 100 %80%3.9927.456.8819.3671%6012.367%9%12%

10. Achievement of Completely Successful Students by Units-Per-Term Interval Units Per Term IntervalN % of Total Persist ence TermsUnits Units per Term Units Passed Passed % Units Needed Terms Needed Predicted Achieve ment Contri bution to Total Actual Achieve ment 0 0-2.53,68514%0%1.832.271.242.27100%6048.40% 4 2.6-6.514,25456%75%2.418.493.528.46100%6017.091%0%1% 8 6.6-10.54,19616%81%3.9931.37.8530.9399%607.7420%3%20% 12 10.6-14.52,78511%85%4.1447.511.4846.9499%605.2942%5%40% 16 14.6 -18.56513%67%2.1432.815.2932.5199%603.9521%1%22% Grand Total 25,583100%73%2.7716.45.916.2299%6010.264%9%

11. And the Equation for 60 unit Completion? 1 20 A = ∑ ∑ (p ij (t/u ij s ij ) )(n ij /n) i=0 j = 0 Where i refers to passing rate and j refers to units per term

12. English Transfer Course Completion by Starting Level English Students Starting 2003-2006 Levels Below Transfer N Persist ence TermsUnits Units per Term Units Passed Passed % Units Needed Terms Needed Predicted Achieve ment Actual Achieve- ment English 904 1,88966%3.239.793.035.6257%158.623%19% English 923 1,14171%3.259.7635.9761%126.5411%30% English 932 2,83066%2.477.4135.169%94.3616%38% English 961 2,21060%2.026.0633.8764%63.1320%52%

13. Observed Versus Predicted Achievement in the English Sequence 2003-2006 starters followed through fall 2010 with a single summation overall passing rate. Levels Below Transfer Transfer Course completion LevelActualPredicted 90419% 92330% 93238% 96152%53%

14. Mathematics Students Starting Fall 2004 – Spring 2006 Followed to Spring 2011 Math CourseNTermsUnits Units Per Term Units Passed Passing Rate Persistence Units Needed Terms Needed Predicte d Achieve ment Actual Achieve ment E3- Arithmetic 1021 2.68 8.40 3.13 4.10 49%65%13 8.51 3%6% 840 - Elementary Algebra 1481 2.51 8.50 3.38 4.72 56%67%10 5.33 12%17% 860 - Intermediate Algebra 1035 2.58 9.92 3.84 5.53 56%73%7 3.27 35%40%

15. Observed Versus Predicted Achievement in the Math Sequence 2003- 2006 starters followed through fall 2010 with a single summation overall passing rate. Levels Below Transfer Math Course Transfer Course completion ActualPredicted 3E36%7% 284017%19% 186040%43%

16. Completion of 60 Units New Students at CCSF By Academic Year tracked to fall 2011 Starting Year of Credit CCSF Students Data198719901993199720002003 N 16,901 16,423 12,292 15,922 17,17915337 Terms 4.27 4.36 4.64 4.20 4.00 3.89 Units 27.44 29.29 33.14 28.35 26.89 28.20 Units Passed 18.29 19.80 23.12 19.68 18.97 19.78 UnitsPerTerm 6.43 6.72 7.14 6.75 6.73 7.24 Passing %67%68%70%69%71%70% Terms to 60 13.99 13.20 12.04 12.80 12.64 11.81 Persistence81% 82%81%80% Predicted to605%7%9%6% 7% Actual to 6011%13%15%12%

17. Predicted Achievement with changes in Persistence - a = p (t/us) Total UnitsPersistenceUnits per Term Units Passed Percent Terms Needed Predicted Achievement 60100%1070%8.57100% 6090%1070%8.5741% 6080%1070%8.5715% 6070%1070%8.575% 6060%1070%8.571% 6050%1070%8.570% 6040%1070%8.570% 6030%1070%8.570% 6020%1070%8.570% 6010%1070%8.570%

18. Predicted Achievement for All Factors Together

19. The Timeframe Issue a = p t/us Log a = log p t/us Log a = (t/us) log p Log a/ log p = t/us What’s log a / log p ?

20. Log a / Log p Terms Needed = Log a / Log p IMPLICATION: You can figure out the terms you have available in order to obtain a desired level of achievement by ONLY KNOWING the Persistence! The educational goal (Phd, 6 unit certificate, remedial sequence completion), terms, and passing rate are not factors.

21. Log a ÷ Log p Persistence a/p 10.90.80.70.60.50.40.30.20.1 Log0-0.05-0.10-0.15-0.22-0.30-0.40-0.52-0.70 Achievement 10.00 0.9-0.05 1.00 0.8-0.10 2.12 1.00 0.7-0.15 3.39 1.60 1.00 0.6-0.22 4.85 2.29 1.43 1.00 0.5-0.30 6.58 3.11 1.94 1.36 1.00 0.4-0.40 8.70 4.11 2.57 1.79 1.32 1.00 0.3-0.52 11.43 5.40 3.38 2.36 1.74 1.31 1.00 0.2-0.70 15.28 7.21 4.51 3.15 2.32 1.76 1.34 1.00 0.1 21.85 10.32 6.46 4.51 3.32 2.51 1.91 1.43 1.00 a=p (t/us)

22. The Pipeline Problem – Total Population as a Multiple of the New Student Population TermNewTotal New Student Multiple Fall 2008 10,333 36,360 3.52 Spring 2009 7,677 37,813 4.93 Fall 2009 9,824 36,756 3.74 Spring 2010 6,290 36,974 5.88 Fall 2010 8,005 34,855 4.35 Spring 2011 6,931 37,568 5.42 Total 49,060 220,326 4.49

23. Enrollment Metric Total Enrollment = new students + Remaining students who had one prior term + Remaining students who had two prior terms + Remaining students who had three prior terms + …. = a 0 p 0 0 + a 1 p 1 1 + a 2 p 2 2 + … + a k p k k where a = new student enrollment p = persistence rate.

24. Simplifying Assumptions Assume: a 0 = a 1 = a 2 = … = a p 0 = p 1 = p 2 = … = p The new student enrollment number and the persistence rate are the same across groups. k Total enrollment=a ∑ p i i=0

25. The relationship between Persistence and Total Enrollment Persistence Rates Terms before60%70%80%90% 01.00 10.600.700.800.90 20.360.490.640.81 30.220.340.510.73 40.130.240.410.66 50.080.170.330.59 60.050.120.260.53 70.030.080.210.48 80.020.060.170.43 90.010.040.130.39 100.010.030.110.35 110.000.020.090.31 120.000.010.070.28 Sum2.503.304.737.46

26. Enrollment and Persistence Total enrollment=a ∑ p i i=0 36,000 = (8,000)(4.50) at a persistence rate of 80%. If the persistence rate were 90% then the multiple would be 7.50 and 60,000 = (8,000)(7.50) And 60,000/36,000 = 1.67 AN ENROLLMENT INCREASE OF 67%! From a persistence increase of 10%!

27. And if Enrollment cannot be increased? Total enrollment=a ∑ p i i=0 Total Enrollment = (4.5/7.5)a ∑ p i ( 7.5/4.5) 36,000 = (4.5/7.5)(8,000)(4.5)(7.50/4.5) 36,000 = (4,800)(7.50) A reduction in access of 1- 4,800/8,000 = 40% And a = access through new students served ∑ p i = achievement (through persistence) INCREASED ACCESS AND ACHIEVEMENT ARE INCOMPATIBLE GOALS IN A FIXED ENROLLMENT ENVIRONMENT!

28. A mathematical Simplification P =((n 1 /n 1 )(n 2 /n 1 )(n 3 /n 2 )(n 4 /n 3 )…(n k /n k-1 )) (1/k) P = (n k / n 1 ) (1/k) a = p t/us t/us = k a = ((n k / n 1 ) (1/k) ) (k) a = n k / n 1 ACHIEVEMENT IS THE NUMBER OF STUDENTS REMAINING AT THE COMPLETION TERM AS A FRACTION OF THOSE WHO STARTED! Occam’s Razor!!!

29. 1 18 a = ∑ ∑ (p ij (t/u ij s ij ) )(n ij /n 1 ) i=0 j=1 1 18 a = ∑ ∑ (n kij / n 1ij )( n1ij /n 1 ) i=0 j=1 1 18 a = ∑ ∑ (n kij /n 1 ) i=0 j=1 a = (n k11+ n k12+...+ n k21 + n k22+...+ n kij )/n 1

30. In Sum Achievement can be modeled with an exponential equation. Persistence is the most important variable because achievement changes most rapidly with changes to it. Without increases to persistence the timeframe for achievement is so narrow that no meaningful improvement can be made. Increases to persistence either overwhelm scarce resources, or squeeze out the access of new students.

31. Scheduling for Achievement If increased achievement requires more educational resources i.e. course sections, what happens if you don’t increase sections? The Consequences of Impaction -

32. Achievement of the SPAR Cohorts (2001-2006) by Impaction Level

33. Number of SPAR Cohort Students at Each Impaction Level

34. Enrollments in Courses as a Percent of Registration Attempts - Most Impacted Subject Codes Subject200720082009201020112012Grand Total PHYS40% 41%34%35%34%37% BOT54%51%33%34%35%44%40% ANAT44%41%35%41%39%46%41% ERT45%42%41%38%41%46%42% ZOOL50%51%38%39%36%47%43% PALE56%49%40%38%43%38%43% CHEM51%49%42%46%43%44%46% BIO57% 50%48%42%46%50% P SC54%56%38%46%53%54%50% GAME 66%52%42%51%50% M B55%52%50%54%42%54%51% SPCH62%53%52%51%49% 53% PHOT65%60%52%49%44%51%53% ECOL 50% 57%53% MMSP 61%50% 55%54% GEN64%58%55%49% 57%55% WOMN69%70%63%58%49%48%56% ASIA62%57%56%53%52%62%57% GRPH65%61%58%54%49%57% MATH63%61%59%56%53%55%58% ENGL70%67%65%64%59%63%64% Grand Total72%70%65%64%60%63%65% ESL74%72% 70%72%

35. The Educational River Analogy In the summer: River capacity exceeds the flow of water. The questions are: How do we increase water flow into the reservoir? Where can we access more water? How can we reduce leakage? In the Winter: Torrential rains and engorged tributaries cause water to overflow the river banks. The flow of water exceeds the river’s capacity. The questions become: How do we limit access of water to the river? Where can we build up river sections and levies to contain the water flow? Can we widen the mouth of the river to contain all of the water coming into the river from either its head, or its many tributaries?

36. In the winter, the mouth of the river should be much bigger than the head. Mathematics Sequence Registration Demand and Course Supply 2011-12 Registration DemandSection Supply CourseNumberPercentNumberPercent Arithmetic5036100%67100% Elementary Algebra6457128%76113% Intermediate Algebra6937138%71106% Transfer Level Course9422187%104155%

37. Demand and Supply in English 2011-12 Registration DemandSection Supply NumberPercentNumberPercent 90/913371100%46100% 92249474%56122% 93/94/956353188%130283% 966641197%139302% 1A7903234%145315%

38. Completion of a Transfer Level Course Over Time Percent of Remedial Students Completing a Transfer Level Class within Four Years Subject 2001-02 2003-04 2005-06 2007-08 2008-09 2009-10 English27%31%32%37%39%37% Math23%22% 23%21%

39. We have been in Educational Winter for at least four years. We are graduating and transferring as many students as we possibly can given the structure we currently have. We don’t need more students, we don’t need more persistence (and consequent achievement) and we don’t need longer sequences or more units to students’ educational goal. We need to: limit access or filter the population to reduce its size or Shift educational resources to higher level courses from lower level courses thereby reducing access and increasing achievement or Reduce the units to the education goal to reduce the demand on educational resources and increase achievement or Convince the legislature to dramatically increase funding for higher education.

40. Beyond the Master Plan: The Case for Restructuring Baccalaureate Education in California Saul Geiser and Richard C. Atkinson The present study confirms that structural differences among state postsecondary systems are strongly related to differences in college-completion rates. … however, what matters most is not the proportion of enrollments in 2-year institutions, but 4-year enrollment capacity, that is, the size of a state’s 4-year sector relative to its college-age population. … The more important determinant of B.A. attainment is 4-year enrollment capacity.

41. The fiscal wind - The pessimist complains about the wind. The optimist expects it to change. The realist adjusts the sails. William Arthur Ward We need to adjust the sails. ftp://advancement.ccsf.edu/general/modelingeducationalachievement.docx