Steven Spurling City College of San Francisco [email protected]
ftp://advancement.ccsf.edu/general/ModelingAchievement.ppt Modeling
Educational Achievement
Slide 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
Slide 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 Occams 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 Platos cave The ARCC report asks the wrong questions.
Its the educational winter, not educational summer. The water is
overflowing the river banks.
Slide 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.
Slide 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%
Slide 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
Whats 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.
Slide 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%
Slide 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%
Slide 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
Slide 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%
Slide 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%
Slide 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%
Slide 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%
Slide 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%
Slide 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%
Slide 18
Predicted Achievement for All Factors Together
Slide 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 Whats log a / log p ?
Slide 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.
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
Slide 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.
Slide 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
Slide 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
Slide 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%!
Slide 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!
Slide 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! Occams Razor!!!
Slide 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
Slide 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.
Slide 31
Scheduling for Achievement If increased achievement requires
more educational resources i.e. course sections, what happens if
you dont increase sections? The Consequences of Impaction -
Slide 32
Achievement of the SPAR Cohorts (2001-2006) by Impaction
Level
Slide 33
Number of SPAR Cohort Students at Each Impaction Level
Slide 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%
Slide 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 rivers 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?
Slide 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%
Slide 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%
Slide 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%
Slide 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 dont need more students,
we dont need more persistence (and consequent achievement) and we
dont 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.
Slide 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 states 4-year
sector relative to its college-age population. The more important
determinant of B.A. attainment is 4-year enrollment capacity.
Slide 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