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ALGEBRA FOR 8 TH GRADERS: EVIDENCE ON ITS EFFECTS FROM 10 NORTH CAROLINA DISTRICTS Charles T. Clotfelter Helen F. Ladd Jacob L. Vigdor

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October 2010

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North Carolina’s 10 Largest Districts

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Largest City, Enrollment, and EOC Passing Rates, Ten N.C. Districts School DistrictsLargest City District Enrollment Pass Algebra I Pass Geometry Pass Algebra II by 12th Grade by 10th Grade by 11th Grade WakeRaleigh141,19493.184.584.0 CMSCharlotte134,12157.135.141.3 GuilfordGreensboro71,07973.248.355.0 CumberlandFayetteville53,26466.044.047.4 Forsyth Winston 51,52674.957.459.8 Salem UnionMonroe39,20093.680.980.1 JohnstonSmithfield32,06370.939.342.5 Durham 31,86756.333.546.7 GastonGastonia32,16986.460.660.7 CabarrusConcord28,12797.693.190.4

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Chi-squared Tests for Variation in Risk for Algebra I Bottom Decile Decile 2Decile 3Decile 4Decile 5Decile 6Decile 7Decile 8Decile 9 Top Decile Wake0.3390.5470.8570.1540.0480.1410.7880.0440.0170.000 CMS0.0280.000 0.744 Guilford0.000 Cumberland0.2610.000 0.0010.000 Forsyth0.6340.0040.0000.0570.7270.0300.0630.000 UnionN/A 0.4650.6830.0240.1580.0030.0060.0030.000 JohnstonN/A0.0700.0390.0070.3080.0030.2810.0040.0690.148 Durham0.000 0.0190.000 Gaston0.5650.6640.4870.0450.0500.0250.0670.2490.0000.002 CabarrusN/A 0.6400.7550.4240.0030.0000.035

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F-tests for Unexplained Variation in Risk for Algebra I Bottom Decile Decile 2Decile 3Decile 4Decile 5Decile 6Decile 7Decile 8Decile 9 Top Decile Wake0.0010.000 0.0010.000 CMS0.000 0.0010.000 0.0840.0780.000 Guilford0.000 Cumberland0.000 0.0010.4490.0000.0040.0030.000 Forsyth0.000 Union0.3140.0010.000 0.1160.0000.2420.000 Johnston0.000 0.0010.000 Durham0.000 0.1750.000 Gaston0.000 0.6340.0000.0040.0000.0040.000 Cabarrus0.000 0.2990.000

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Decile-district Subsamples Excluded Bottom Decile Decile 2Decile 3Decile 4Decile 5Decile 6Decile 7Decile 8Decile 9 Top Decile Wake XXXX XX CMS XX X Guilford Cumberland X X Forsyth X XX X Union XXXX X X Johnston XX X X XX Durham X Gaston XXXX XX Cabarrus XXXXXXX

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OLS: Coefficients on Algebra I by 8 th Grade (other correlates: cohort, district, test decile) Independent variable Algebra I Test Scores Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade Enrolled in Algebra I by 8 th Grade -0.0850*** (0.021) 0.137*** (0.012) 0.0519*** (0.006) 0.0866*** (0.006)

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Instrumental Variable Estimates of the Impact of Acceleration into Algebra I in 8 th Grade Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade Independent variable IVQR w/imputatio n 2SLSBP2SLSBP2SLSBP Enrolled in Algebra I by 8 th Grade -0.374***0.091***0.400***-0.066***-0.152**-0.026*-0.038 (0.006)(0.021)(0.086)(0.014)(0.056)(0.012)(0.046) Adjusted R 2 0.484 0.564 0.436

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Quintile Interaction Effects of the Impact of Acceleration into Algebra I in 8 th Grade Independent variable: Quintile X student * enrolled in Algebra I by 8th grade Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade QuintileOLS QR w/imputati on OLS 5 -0.183***0.028***0.192***0.0202*0.0935*** 0.0350.0020.0180.0090.008 4 -0.197***-0.156***0.140***0.0160.089*** 0.0360.0010.0140.0110.015 3 -0.185***-0.160***0.091***0.02490.108*** 0.0310.0010.0120.0150.013 2 -0.098**-0.046***0.075***0.0767***0.0903*** 0.030.0010.0060.0070.009 1 0.0580.136***0.130***0.0736***0.0721*** 0.0370.0010.0270.0070.006 Adjusted R 2 0.7210.3760.4250.5720.443

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Instrumented Quintile Interaction Effects of the Impact of Acceleration into Algebra I in 8 th Grade Independent variable: Quintile X student * enrolled in Algebra I by 8th grade Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade Quintile2SLS RFQR w/imputa- tion 2SLS 5 -0.479***-0.240***0.221***-0.108***-0.0627 0.080.0150.0370.0310.048 4 -0.456***-0.397***0.0921***-0.081***-0.0401* 0.0340.0060.0220.0120.016 3 -0.429***-0.398***0.0356*-0.085***-0.0174 0.0340.0060.0150.0180.02 2 -0.324***-0.260***0.0462**-0.0129-0.015 0.0480.0060.0140.0180.017 1 -0.306***-0.140***0.096***0.0687**0.011 0.0920.010.0220.0260.023 Adjusted R 2 0.7120.3760.4240.5680.436

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Instrumented Gender Interaction Effects of the Impact of Acceleration into Algebra I in 8 th Grade Independent variable Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade 2SLS RFQR w/imputa- tion 2SLS Enrolled in Algebra I by 8 th Grade -0.416***-0.398***0.0695**-0.0678***-0.0447*** 0.0280.0110.0220.0140.013 Male -0.064***-0.118***-0.051***-0.0159***-0.068*** 0.0090.0050.0060.0040.007 Enrolled in Algebra I by 8 th Grade 0.0140.070***0.045***0.00420.0379*** * Male0.0210.0080.0070.0060.011 Adjusted R 2 0.710.3770.4850.5640.439

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Instrumented Free/Reduced Lunch Interaction Effects of the Impact of Acceleration into Algebra I in 8 th Grade Independent variable Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade 2SLS RFQR w/imputa- tion 2SLS Enrolled in Algebra I by 8 th Grade -0.330***-0.315***0.0467*-0.0765***-0.0534*** 0.0340.0120.0190.0180.015 On Free/Reduced Lunch -0.0752***-0.141***-0.0835***-0.0831***-0.103*** 0.0110.0060.0070.01 Enrolled in Algebra I by 8 th Grade -0.124***-0.039***0.0884***0.0308*0.0621*** * On Free/Reduced Lunch 0.020.01 0.0140.013 Adjusted R 2 0.7140.3780.4850.5670.439

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Instrumented Parent Education Interaction Effects of the Impact of Acceleration into Algebra I in 8 th Grade Independent variable Algebra I Test Score Pass Algebra I by 10 th grade Pass Geometry by 11 th grade Pass Algebra II by 12 th grade 2SLS RFQR w/imputa- tion 2SLS Enrolled in Algebra I by 8 th Grade -0.547***-0.358***0.128***-0.0955***-0.0375* 0.030.010.0220.0140.016 Parent with College Degree or More 0.021*0.159***0.077***0.0534***0.0869*** 0.0090.0040.0060.0080.009 Enrolled in Algebra I by 8 th Grade 0.202***0.028**-0.0512***0.0456***0.02 * Parent with College Degree or More 0.0240.0080.01.0120.015 Adjusted R 2 0.7120.3780.4870.5670.441

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Taking Calculus: Algebra by 8th versus Algebra after 8th

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Repeating Algebra I: Algebra by 8th, Algebra in 9th, and Algebra After 9th

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