Trickle Across Theory: Student Flow

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Trickle Across Theory: Student Flow Into and Away from the California Community Colleges Mei Cooc & Willard Hom Chancellor s Office, CCC 1

Session Objectives Release and discuss the results of a swirl analysis for each district and for the system. Collect input from IR staff, et al, about future efforts in this area 2

Three Issues 1. Losing residents and gaining nonresidents (headcounts) can be political concerns. 2. Swirl can affect instit l funding (change to units and FTES), in some budget situations. 3. Swirl can affect performance indicators (change to completion/award rates). 3

Student Swirl A Narrowed Concept Defined here as exclusive enrollment of individuals in a community college district other than the community college district of their official residence 4

Movers Imports Exports Stayers Terms 5

Data Source District boundary zip codes GIS Collaborative Student level data First time Fall 2007 Cohort First time the student was reported in the MIS with a headcount status not equal to X (differ from enrollment status from Data Mart) First time across all districts SSN Enrollment in single district only Data as of October 2011 6

Overview Statewide movers and stayers Headcount Units Credit awards Top importing and exporting districts Headcount Units Districts with Least Imports and Exports by Headcount 7

The State at a Glance Headcount 80.7% stayers The other 19.3% 12.6% movers 6.6% zip code mismatched Unknown residential zip code (i.e., XXXXX) Residential zip code not mapped to any district Will exclude the 6.6% with zip code mismatch 8

The State at a Glance Headcount Enrollment Headcount Movers 13.5% Stayers 86.5% 9

The State at a Glance Headcount Age Group Enrollment Total <=19 20-24 25-29 30-34 35-39 40-49 50+ Unknown Movers 12.1% 12.2% 18.1% 18.9% 18.7% 16.9% 12.8% 13.1% 13.5% Stayers 87.9% 87.8% 81.9% 81.1% 81.3% 83.1% 87.2% 86.9% 86.5% 10

The State at a Glance Headcount Age Group Enrollment Total <=19 20-24 25-29 30-34 35-39 40-49 50+ Unknown Movers 12.1% 12.2% 18.1% 18.9% 18.7% 16.9% 12.8% 13.1% 13.5% Stayers 87.9% 87.8% 81.9% 81.1% 81.3% 83.1% 87.2% 86.9% 86.5% Students between ages of 25 to 49 tend to move more than other age groups. 11

The State at a Glance Headcount Race/Ethnicity Enrollment Asian Black or African American Hispanic/ Latino American Indian or Alaska Native Native Hawaiian or Other Pacific Islander Two or More Races White Unknown/ Non- Respondent Movers 14.4% 14.9% 13.8% 11.9% 12.5% 7.4% 12.8% 13.8% Stayers 85.6% 85.1% 86.2% 88.1% 87.5% 92.6% 87.2% 86.2% Total 13.5 % 86.5 % 12

The State at a Glance Headcount Race/Ethnicity Enrollment Asian Black or African American Hispanic/ Latino American Indian or Alaska Native Native Hawaiian or Other Pacific Islander Two or More Races White Unknown/ Non- Respondent Total Movers 14.4% 14.9% 13.8% 11.9% 12.5% 7.4% 12.8% 13.8% 13.5% Stayers 85.6% 85.1% 86.2% 88.1% 87.5% 92.6% 87.2% 86.2% 86.5% More movers in Asian, African American, and Hispanic (and Unknown/NR) groups 13

The State at a Glance Headcount Gender Enrollment Female Male Unknown Total Movers 11.6% 15.6% 11.8% 13.5% Stayers 88.4% 84.4% 88.2% 86.5% 14

The State at a Glance Headcount Gender Enrollment Female Male Unknown Total Movers 11.6% 15.6% 11.8% 13.5% Stayers 88.4% 84.4% 88.2% 86.5% Males are more likely to move than females. 15

The State at a Glance Units Earned Credit units earned only Units per headcount Includes an adjusted measure due to 21.5% of students who earned zero credit units Non credit students Attempted but did not earn credit units 16

Credit Units per Headcount Fall 07 Cohort Units/Headcount Adj. Units/Headcount Movers 21.5 26.2 Stayers 23.3 29.9 Stayers earned more units than movers. 17

Units/Headcount by Age Group Units/Headcount by Age Group Fall 07 Cohort Overall <=19 20-24 25-29 30-34 35-39 40-49 50+ Unknown Movers 10.7 37.2 15.5 12.5 8.8 7.9 6.7 0.8 21.5 Stayers 11.6 36.7 16.9 13.9 11.8 11.2 7.7 1.0 23.3 Students between the ages of 20-24 earned more credit units than other age groups Stayers typically earned more units than movers in most age groups, except in the 20-24 age group. 18

Adjusted Unit/Headcount by Age Group Fall 07 Cohort Adjusted Unit/Headcount by Age Group <=19 20-24 25-29 30-34 35-39 40-49 50+ Unknown Overall Movers 14.4 41.7 18.9 15.5 11.3 10.2 8.9 11.8 26.2 Stayers 15.7 41.5 23.2 20.2 18.4 16.8 13.6 12.6 29.9 Students between the ages of 20-24 earned more credit units than other age groups Stayers typically earned more units than movers in most age groups, except in the 20-24 age group. 19

Units/Headcount by Race/Ethnicity Units/Headcount by Race/Ethnicity Fall 07 Cohort Asian Black or African American Hispanic / Latino American Indian or Alaska Native Native Hawaiian or Other Pacific Islander Two or More Races White Unknown/ Non- Respondent Overall Movers 27.9 15.4 20.8 16.6 18.6 31.5 21.7 19.0 21.5 Stayers 27.9 15.6 23.6 18.9 22.3 31.0 24.0 19.5 23.3 With the exception of Two or more races, Asians earned more units than other race/ethnic groups Stayers earned more units than movers in all race/ethnic groups except Asian and Two or More races a movement trade-off? 20

Adjusted Unit/Headcount by Race/Ethnicity Adjusted Unit/Headcount by Race/Ethnicity Fall 07 Cohort Asian Black or African American Hispanic / Latino American Indian or Alaska Native Native Hawaiian or Other Pacific Islander Two or More Races White Unknown/ Non- Respondent Overall Movers 33.3 21.4 25.3 21.4 23.9 34.1 25.9 23.5 26.2 Stayers 35.2 22.4 30.7 25.0 28.3 33.9 29.4 27.4 29.9 Asians earned more units than other race/ethnic groups Stayers earned more units than movers in all race/ethnic groups except Two or More Races group. 21

Units/Headcount by Gender Units/Headcount by Gender Fall 07 Cohort Total Female Male Unknown Movers 24.3 19.2 17.4 21.5 Stayers 23.7 23.1 16.8 23.3 Females averaged more units than males. Female movers averaged slightly more units than female stayers 22

Adjusted Unit/Headcount by Gender Adjusted Unit/Headcount by Gender Fall 07 Cohort Total Female Male Unknown Movers 29.9 23.3 22.1 26.2 Stayers 30.4 29.5 23.8 29.9 Females averaged more units than males. Stayers of both gender averaged more units than movers. 23

The State at a Glance Awards Credit awards only Associate of Arts/Science Certificates requiring at least 6 units Other credit awards under 6 semester units. 24

Percent of Students Receiving Awards Fall 07 Cohort No Award Award Total Movers 91.4% 8.6% 100% Stayers 91.1% 8.9% 100% Distribution of students receiving awards is about the same for movers and stayers. 25

Percent of Awards Given Fall 07 Cohort Headcount Awards Movers 13.5% 16.6% Stayers 86.5% 83.4% 83.4% of the awards were earned by stayers. Movers accounted for 13.5% of the cohort headcount, but earned 16.6% of credit awards. *Headcount is unduplicated, but a student could have earned multiple awards. 26

Awards Given by Age Group Fall 07 Cohort Awards by Age Group <=19 20-24 25-29 30-34 35-39 40-49 50+ Total Movers 15.1% 16.3% 18.4% 11.8% 17.5% 17.2% 19.0% 16.6% Stayers 84.9% 83.7% 81.6% 88.2% 82.5% 82.8% 81.0% 83.4% Movers in the highlighted age groups earned a bigger share than the other age groups. *Headcount is unduplicated, but a student could have earned multiple awards. 27

Awards Given by Ethnicity Race/Ethnicity Fall 07 Cohort Asian Black or African American Hispanic /Latino American Indian or Alaska Native Native Hawaiian or Other Pacific Islander Two or More Races White Unknown/ Non- Respondent Total Movers 18.1% 13.6% 14.8% 5.3% 0.0% 5.0% 18.0% 16.3% 16.6% Stayers 81.9% 86.4% 85.2% 94.7% 100.0% 95.0% 82.0% 83.7% 83.4% Asian and White movers earned a bigger share than the other race/ethnic groups. *Headcount is unduplicated, but a student could have earned multiple awards. 28

Awards Given by Gender Fall 07 Cohort Gender Female Male Total Movers 14.3% 19.4% 16.6% Stayers 85.7% 80.6% 83.4% Male movers earned a bigger share than female movers. *Headcount is unduplicated, but a student could have earned multiple awards. 29

Importing and Exporting Districts 30

Top Importing Districts by Headcounts District of Enrollment Imports Stayers West Kern 76.3% 23.7% Santa Monica 67.8% 32.2% Foothill De Anza 44.0% 56.0% Rio Hondo 39.7% 60.3% Citrus 39.6% 60.4% Palo Verde 34.4% 65.6% Pasadena Area 33.9% 66.1% Rancho Santiago 32.1% 67.9% Coast 31.1% 68.9% Feather River 30.9% 69.1% Cerritos 30.1% 69.9% West Valley Mission 26.3% 73.8% Santa Barbara 26.0% 74.0% Mt. San Antonio 24.9% 75.1% Glendale 21.5% 78.5% 31

Top Importing Districts by Headcounts District of Enrollment Imports Stayers 67.2% from Kern CCD West Kern 76.3% 23.7% Santa Monica 67.8% 32.2% Foothill De Anza 44.0% 56.0% Rio Hondo 39.7% 60.3% 46.6% from LA CCD Citrus 39.6% 60.4% Palo Verde 34.4% 65.6% Pasadena Area 33.9% 66.1% Rancho Santiago 32.1% 67.9% Coast 31.1% 68.9% Feather River 30.9% 69.1% Cerritos 30.1% 69.9% West Valley Mission 26.3% 73.8% Santa Barbara 26.0% 74.0% Mt. San Antonio 24.9% 75.1% Glendale 21.5% 78.5% 32

Top Exporting Districts by Headcounts District of Residence Exports Stayers Rio Hondo 84.9% 15.1% San Jose Evergreen 30.0% 70.0% Kern 29.6% 70.4% Los Angeles 21.2% 78.8% LA, Pasadena, Mt. SAC, North Orange, etc. 33

Districts Importing More Units/Headcount District of Enrollment Unit/Headcount Imports Stayers Difference Copper Mountain 34.0 18.0 16.0 San Luis Obispo 38.7 23.8 14.9 Santa Barbara 29.4 19.0 10.4 Mendocino-Lake 23.4 14.2 9.2 West Valley-Mission 22.7 14.3 8.4 Butte-Glenn 33.6 26.7 6.9 Mt. San Jacinto 29.7 24.7 5.1 Shasta-Tehama-Trinity 26.8 21.9 4.9 Pasadena Area 35.7 32.0 3.7 Santa Monica 27.8 24.4 3.4 Citrus 35.6 32.8 2.8 Imports from 25 of the 72 districts earned more units/headcount than stayers. Copper Mountain s imports earned far more units than its stayers. 34

Districts Importing More Units/Headcount District Headcount Unit/Headcount Imports Stayers Imports Stayers Difference Copper Mountain 0.3% 99.7% 34.0 18.0 16.0 San Luis Obispo 7.9% 92.1% 38.7 23.8 14.9 Santa Barbara 26.0% 74.0% 29.4 19.0 10.4 Mendocino-Lake 3.9% 96.1% 23.4 14.2 9.2 West Valley-Mission 26.3% 73.8% 22.7 14.3 8.4 Butte-Glenn 8.1% 91.9% 33.6 26.7 6.9 Mt. San Jacinto 2.0% 98.0% 29.7 24.7 5.1 Shasta-Tehama-Trinity 2.0% 98.0% 26.8 21.9 4.9 Pasadena Area 33.9% 66.1% 35.7 32.0 3.7 Santa Monica 67.8% 32.2% 27.8 24.4 3.4 Citrus 39.6% 60.4% 35.6 32.8 2.8 Copper Mountain s imports earned far more units than its stayers, but Copper Mountain s imports only account for 0.3% of the cohort enrollment. 35

Districts Importing More Units/Headcount Headcount Unit/Headcount District Imports Stayers Imports Stayers Difference Copper Mountain 0.3% 99.7% 34.0 18.0 16.0 San Luis Obispo 7.9% 92.1% 38.7 23.8 14.9 Santa Barbara 26.0% 74.0% 29.4 19.0 10.4 Mendocino-Lake 3.9% 96.1% 23.4 14.2 9.2 West Valley-Mission 26.3% 73.8% 22.7 14.3 8.4 Butte-Glenn 8.1% 91.9% 33.6 26.7 6.9 Mt. San Jacinto 2.0% 98.0% 29.7 24.7 5.1 Shasta-Tehama-Trinity 2.0% 98.0% 26.8 21.9 4.9 Pasadena Area 33.9% 66.1% 35.7 32.0 3.7 Santa Monica 67.8% 32.2% 27.8 24.4 3.4 Citrus 39.6% 60.4% 35.6 32.8 2.8 The highlighted districts imports earned more units than the stayers, and imports account for more than a quarter of these districts cohort headcounts. 36

Districts Importing More Units/Headcount Headcount Unit/Headcount District Imports Stayers Imports Stayers Difference Copper Mountain 0.3% 99.7% 34.0 18.0 16.0 San Luis Obispo 7.9% 92.1% 38.7 23.8 14.9 Santa Barbara 26.0% 74.0% 29.4 19.0 10.4 Mendocino-Lake 3.9% 96.1% 23.4 14.2 9.2 West Valley-Mission 26.3% 73.8% 22.7 14.3 8.4 Butte-Glenn 8.1% 91.9% 33.6 26.7 6.9 Mt. San Jacinto 2.0% 98.0% 29.7 24.7 5.1 Shasta-Tehama-Trinity 2.0% 98.0% 26.8 21.9 4.9 Pasadena Area 33.9% 66.1% 35.7 32.0 3.7 Santa Monica 67.8% 32.2% 27.8 24.4 3.4 Citrus 39.6% 60.4% 35.6 32.8 2.8 Santa Monica is serving more imports than its residents, in headcount and units. 37

Districts Where Stayers Earned More Units/Headcount District of Enrollment Unit/Headcount Imports Stayers Difference Hartnell 3.1 24.4-21.4 Kern 10.7 22.8-12.1 Gavilan 13.4 24.7-11.3 Desert 15.6 26.6-11.0 Yuba 9.3 19.0-9.7 Rio Hondo 1.4 10.7-9.3 Siskiyou Joint 8.0 16.6-8.7 San Bernardino 14.6 23.2-8.6 Lake Tahoe 19.4 28.0-8.6 Sequoias 16.3 24.9-8.6 San Jose-Evergreen 17.7 25.7-8.0 Chabot-Las Positas 22.2 30.0-7.8 Palo Verde 3.3 11.1-7.7 Barstow 5.9 13.5-7.6 West Kern 1.5 8.9-7.5 Chaffey 20.5 27.5-7.0 Stayers from 47 of the 72 districts averaged more units than their imports. 38

Districts Where Stayers Earned More Units/Headcount District of Enrollment Headcount Unit/Headcount Imports Stayers Imports Stayers Difference Hartnell 16.9% 83.1% 3.1 24.4-21.4 Kern 2.3% 97.7% 10.7 22.8-12.1 Gavilan 2.9% 97.1% 13.4 24.7-11.3 Desert 1.8% 98.2% 15.6 26.6-11.0 Yuba 3.6% 96.4% 9.3 19.0-9.7 Rio Hondo 39.7% 60.3% 1.4 10.7-9.3 Siskiyou Joint 3.6% 96.4% 8.0 16.6-8.7 San Bernardino 6.4% 93.6% 14.6 23.2-8.6 Lake Tahoe 10.3% 89.7% 19.4 28.0-8.6 Sequoias 2.8% 97.2% 16.3 24.9-8.6 San Jose-Evergreen 8.6% 91.4% 17.7 25.7-8.0 Chabot-Las Positas 12.8% 87.2% 22.2 30.0-7.8 Palo Verde 34.4% 65.6% 3.3 11.1-7.7 Barstow 18.8% 81.2% 5.9 13.5-7.6 West Kern 76.3% 23.7% 1.5 8.9-7.5 Chaffey 7.9% 92.1% 20.5 27.5-7.0 With the exception of West Kern, these districts primarily served their residents. 39

Special Course Effect? Are West Kern and Rio Hondo drawing students for single courses? 40

Districts Exporting More Units/Headcount District Units/Headcount Exports Stayers Difference Feather River 40.9 14.8 26.1 Siskiyou Joint 39.4 16.6 22.8 Rio Hondo 29.1 10.7 18.4 Rancho Santiago 28.4 15.8 12.6 West Valley-Mission 26.8 14.3 12.6 Gavilan 36.1 24.7 11.4 Peralta 20.0 12.2 7.9 Los Angeles 27.1 19.8 7.3 Cerritos 24.4 17.1 7.2 San Francisco 20.2 13.5 6.7 Allan Hancock 26.0 19.8 6.2 Monterey Peninsula 20.5 14.6 5.9 Marin 19.5 15.2 4.3 Yuba 23.0 19.0 4.0 San Diego 22.4 18.8 3.6 Sierra Joint 18.5 16.5 2.0 San Jose-Evergreen 27.2 25.7 1.4 Exports from 23 of the 72 districts averaged more units than stayers. Feather River s exports averaged far more units than its stayers. 41

Districts Exporting More Units/Headcount District Headcount Units/Headcount Exports Stayers Exports Stayers Difference Feather River 2.6% 97.4% 40.9 14.8 26.1 Siskiyou Joint 2.0% 98.0% 39.4 16.6 22.8 Rio Hondo 84.9% 15.1% 29.1 10.7 18.4 Rancho Santiago 4.4% 95.6% 28.4 15.8 12.6 West Valley-Mission 11.2% 88.8% 26.8 14.3 12.6 Gavilan 0.8% 99.2% 36.1 24.7 11.4 Peralta 6.6% 93.4% 20.0 12.2 7.9 Los Angeles 21.2% 78.8% 27.1 19.8 7.3 Cerritos 3.7% 96.3% 24.4 17.1 7.2 San Francisco 5.7% 94.3% 20.2 13.5 6.7 Allan Hancock 5.5% 94.5% 26.0 19.8 6.2 Monterey Peninsula 1.1% 98.9% 20.5 14.6 5.9 Marin 18.2% 81.8% 19.5 15.2 4.3 Yuba 5.0% 95.0% 23.0 19.0 4.0 San Diego 7.3% 92.7% 22.4 18.8 3.6 Sierra Joint 4.7% 95.3% 18.5 16.5 2.0 San Jose-Evergreen 30.0% 70.0% 27.2 25.7 1.4 Feather River s exports averaged far more units than its stayers, but only accounted for 2.6% of its residents in the cohort. 42

Districts Exported More Units/Headcount District Headcount Units/Headcount Exports Stayers Exports Stayers Difference Feather River 2.6% 97.4% 40.9 14.8 26.1 Siskiyou Joint 2.0% 98.0% 39.4 16.6 22.8 Rio Hondo 84.9% 15.1% 29.1 10.7 18.4 Rancho Santiago 4.4% 95.6% 28.4 15.8 12.6 West Valley-Mission 11.2% 88.8% 26.8 14.3 12.6 Gavilan 0.8% 99.2% 36.1 24.7 11.4 Peralta 6.6% 93.4% 20.0 12.2 7.9 Los Angeles 21.2% 78.8% 27.1 19.8 7.3 Cerritos 3.7% 96.3% 24.4 17.1 7.2 San Francisco 5.7% 94.3% 20.2 13.5 6.7 Allan Hancock 5.5% 94.5% 26.0 19.8 6.2 Monterey Peninsula 1.1% 98.9% 20.5 14.6 5.9 Marin 18.2% 81.8% 19.5 15.2 4.3 Yuba 5.0% 95.0% 23.0 19.0 4.0 San Diego 7.3% 92.7% 22.4 18.8 3.6 Sierra Joint 4.7% 95.3% 18.5 16.5 2.0 San Jose-Evergreen 30.0% 70.0% 27.2 25.7 1.4 The highlighted districts exports earned more units than the stayers, and exports accounted for more than 18% of the district residents in the cohort. 43

Districts Exported More Units/Headcount District Headcount Units/Headcount Exports Stayers Exports Stayers Difference Feather River 2.6% 97.4% 40.9 14.8 26.1 Siskiyou Joint 2.0% 98.0% 39.4 16.6 22.8 Rio Hondo 84.9% 15.1% 29.1 10.7 18.4 Rancho Santiago 4.4% 95.6% 28.4 15.8 12.6 West Valley-Mission 11.2% 88.8% 26.8 14.3 12.6 Gavilan 0.8% 99.2% 36.1 24.7 11.4 Peralta 6.6% 93.4% 20.0 12.2 7.9 Los Angeles 21.2% 78.8% 27.1 19.8 7.3 Cerritos 3.7% 96.3% 24.4 17.1 7.2 San Francisco 5.7% 94.3% 20.2 13.5 6.7 Allan Hancock 5.5% 94.5% 26.0 19.8 6.2 Monterey Peninsula 1.1% 98.9% 20.5 14.6 5.9 Marin 18.2% 81.8% 19.5 15.2 4.3 Yuba 5.0% 95.0% 23.0 19.0 4.0 San Diego 7.3% 92.7% 22.4 18.8 3.6 Sierra Joint 4.7% 95.3% 18.5 16.5 2.0 San Jose-Evergreen 30.0% 70.0% 27.2 25.7 1.4 Most of the residents of Rio Hondo are taking a lot of units in other districts. 44

Some Hypotheses Exported student residence in proximity to importing district (travel factor) Exported student worksite in proximity to importing district (travel factor) Perceived advantage of institutional qualities (aside from travel factor) at importing district 45

Districts Where Stayers Earned More Units/Headcount District Headcount Units/Headcount Exports Stayers Exports Stayers Difference Imperial 8.3% 91.7% 9.5 42.9-33.4 Lake Tahoe 0.0% 100.0% 0.0 28.0-28.0 Santa Clarita 2.7% 97.3% 9.9 33.8-23.9 Kern 29.6% 70.4% 3.2 22.8-19.6 Copper Mountain 0.0% 100.0% 0.0 18.0-18.0 Ventura County 4.5% 95.5% 12.8 29.0-16.1 Foothill-De Anza 3.5% 96.5% 13.7 29.8-16.1 Pasadena Area 5.2% 94.8% 16.8 32.0-15.2 Coast 4.9% 95.1% 15.2 29.7-14.5 Stayers from 48 of the 72 districts averaged more units than their exports. 46

Districts with Least Imports and Exports by Headcount 47

Districts with Least Imports Headcount District of Enrollment Imports Stayers Copper Mountain 0.3% 99.7% Imperial 0.5% 99.5% State Center 1.2% 98.8% Victor Valley 1.3% 98.7% Desert 1.8% 98.2% Solano 1.8% 98.2% Redwoods 1.9% 98.1% Shasta-Tehama-Trinity 2.0% 98.0% Mt. San Jacinto 2.0% 98.0% 38 of the 72 districts enrolled less than 10% imports (i.e., at least 90% of students are residents). 48

Districts with Least Exports District of Residence Headcount Exports Stayers Lake Tahoe 0.0% 100.0% Copper Mountain 0.0% 100.0% Palo Verde 0.0% 100.0% West Kern 0.0% 100.0% Barstow 0.2% 99.8% Santa Monica 0.5% 99.5% Lassen 0.5% 99.5% West Hills 0.6% 99.4% Santa Barbara 0.6% 99.4% Napa Valley 0.7% 99.3% Gavilan 0.8% 99.2% Butte-Glenn 0.9% 99.1% 58 of the 72 districts have less than 10% exports (i.e., these districts served at least 90% of their residents in cohort). 49

Conclusion This type of swirl can distinguish districts. District specific reports will become available as resources permit. Additional analyses are planned. 50

References Adelman, C. (2005). Moving into town and moving on: The community college in the lives of traditional age students. Washington, D.C.: U.S. Department of Education. Willett, T. & Hom, W. (2007). Student Flow Analysis for a Community College. Journal of Applied Research in the Community College.15 (1): 17 27. 51

Contact Information Mei Cooc, Specialist Research, Analysis, and Accountability Unit, CCCCO Willard C. Hom, Director Research, Analysis, and Accountability Unit, CCCCO mcooc@cccco.edu or (916) 327 5883 52

Thank you for your participation. Mei & Willard 53