What Happens to Underprepared First-Time-in-College Students When Developmental Education is Optional? The Case of Developmental Math and Intermediate Algebra in the First Semester

Figures & data

Table 1. Sample characteristics by level of preparation.

	(0)	(1)	(2)	(3)	(4)	(5)	(6)
	Non-PERT Students	Study Sample	Severely Underprepared	Moderately Underprepared	Slightly Underprepared	College-Ready	Ordered Logistic Regression
			(Math PERT 50–95)	(Math PERT 96–106)	(Math PERT 107–113)	(Math PERT ≥ 114)	OR	SE	Sig.
Student Background Characteristics (S)
White	37.55%	38.10%	30.60%	38.20%	41.50%	42.50%	1.391	0.036	***
Black	20.73%***	23.00%	31.80%	23.00%	20.20%	16.50%	0.569	0.017	***
Hispanic	35.86%***	33.60%	33.80%	33.80%	32.90%	33.80%	0.994	0.026
Other Race	5.85%*	5.30%	3.80%	4.90%	5.50%	7.10%	1.522	0.085
Female	51.09%***	53.40%	57.50%	53.20%	54.40%	48.90%	0.818	0.021	***
Free/Reduced-Price Lunch	49.32%***	53.30%	57.60%	53.60%	51.80%	49.90%	0.817	0.021	***
High School Academic Preparation (HS)
Algebra 2	83.34%***	74.40%	52.30%	70.00%	85.30%	92.90%	4.604	0.141	***
Trigonometry	6.01%***	3.90%	1.00%	2.50%	5.70%	7.00%	3.031	0.197	***
Other Advanced Math	25.05%***	14.70%	4.10%	8.90%	16.30%	30.60%	4.443	0.168	***
Honors English	58.7%***	46.70%	26.20%	43.90%	55.50%	63.30%	2.764	0.072	***
AP English	14.46%***	9.50%	3.20%	7.30%	11.80%	16.30%	2.802	0.122	***
N	25,539	20,591	5,065	6,308	3,930	5,288	20,591

* p < .05. ** p < .01. *** p < .001.

Note. PERT = Postsecondary Educational Readiness Test; AP = Advanced Placement. Column 0 contains descriptive information on the 25,539 first-time-in-college (FTIC) students without a valid PERT score who were excluded from the study; the stars in Column 0 indicate the statistical significance from a series of bivariate t tests that compared these 25,539 FTIC students to the 20,591 FTIC students with a valid PERT score who were used in the analysis, along the characteristics in S and HS. Columns 2 to 5 disaggregate the study sample into the four levels of preparedness. Column 6 contains the odds ratios, standard errors, and significance levels from an ordered logistic regression model that regressed the four levels of preparation on the vectors S and HS.

Table 2. Enrollment patterns by level of preparation.

	No Math		DE Math		Gateway Math		DE and Gateway Math
	Number	Percent	Number	Percent	Number	Percent	Number	Percent	Total
Severely Underprepared	1,952	38.5%	2,289	45.2%	773	15.3%	51	1.0%	5,065
Moderately Underprepared	2,096	33.2%	2,180	34.6%	1,775	28.1%	277	4.4%	6,308
Slightly Underprepared	1,187	30.2%	868	22.1%	1,689	43.0%	186	4.7%	3,930
Total	5,235	34.2%	5,337	34.9%	4,237	27.7%	514	3.4%	15,303

Note. DE = developmental education. Slightly underprepared first-time-in-college (FTIC) students scored 50 to 95 on the Postsecondary Educational Readiness Test (PERT); moderately underprepared FTIC students scored 96 to 106 on the PERT; and slightly underprepared FTIC students scored 107 to 113 on the PERT.

Table 3. Multinomial logistic regression relative risk ratios.

	No Math	Gateway Math	DE and Gateway Math
Level of Preparedness
Moderately Underprepared	1.067	1.890***	4.991***
	[0.048]	[0.103]	[0.786]
Slightly Underprepared	1.454***	3.776***	7.625***
	[0.083]	[0.235]	[1.278]
Student Background Characteristics (S)
Black	0.975	0.835**	1.321
	[0.051]	[0.050]	[0.196]
Hispanic	0.958	0.993	2.632***
	[0.048]	[0.054]	[0.326]
Other Race	1.045	1.138	1.074
	[0.102]	[0.120]	[0.307]
Female	0.878**	0.902*	1.097
	[0.035]	[0.040]	[0.106]
Free/Reduced-Price Lunch	0.893**	0.947	1.097
	[0.038]	[0.044]	[0.113]
High School Academic Preparation (HS)
Algebra 2	1.058	2.171***	2.332***
	[0.046]	[0.117]	[0.311]
Trigonometry	1.281	1.256	0.274**
	[0.171]	[0.165]	[0.127]
Other Advanced Math	1.210*	1.730***	1.305
	[0.100]	[0.135]	[0.199]
Honors English	1.126**	1.485***	1.460***
	[0.050]	[0.070]	[0.146]
Advanced Placement English	1.133	1.288**	0.849
	[0.102]	[0.113]	[0.164]
Constant	0.935	0.211***	0.006***
	[0.048]	[0.014]	[0.001]
chi2	1964.289
N	15,303

* p < .05. ** p < .01. *** p < .001.

Note. DE = developmental education. Included in this multinomial logistic regression model are the 15,303 first-time-in-college (FTIC) students in the sample identified as severely underprepared; severely underprepared is the reference group. Slightly underprepared FTIC students scored 50 to 95 on the Postsecondary Educational Readiness Test (PERT); moderately underprepared FTIC students scored 96 to 106 on the PERT; and slightly underprepared FTIC students scored 107 to 113 on the PERT. Estimates displayed are relative risk ratios; standard errors are in brackets.

Table 4. Predicted probabilities of enrollment pathways.

	No Math			DE Math			Gateway Math			DE and Gateway Math
	Low	Est.	High	Low	Est.	High	Low	Est.	High	Low	Est.	High
Severely Underprepared	37.8%	39.2%	40.5%	44.3%	45.7%	47.1%	13.4%	14.3%	15.3%	0.6%	0.8%	1.1%
Moderately Underprepared	32.8%	34.0%	35.2%	33.8%	35.0%	36.2%	26.1%	27.3%	28.3%	3.3%	3.8%	4.3%
Slightly Underprepared	29.3%	30.7%	32.2%	20.7%	22.0%	23.3%	41.5%	43.1%	44.7%	3.5%	4.2%	4.8%

Note. DE = developmental education. Slightly underprepared first-time-in-college (FTIC) students scored 50 to 95 on the Postsecondary Educational Readiness Test (PERT); moderately underprepared FTIC students scored 96 to 106 on the PERT; and slightly underprepared FTIC students scored 107 to 113 on the PERT. The “Est.” column lists the estimated predicted probability while the “Low” and “High” columns list the lower bound and upper bound, respectively, of a 95% confidence interval around the estimated predicted probability.

Table 5. Gateway completion for underprepared students.

Levels of Preparedness
Moderately Underprepared	1.866***
	[0.179]
Slightly Underprepared	3.174***
	[0.310]
Enrollment Pathway
Corequisite	1.380*
	[0.219]
Compressed	1.575***
	[0.189]
Student Background Characteristics (S)
Black	0.898
	[0.080]
Hispanic	1.251**
	[0.096]
Other Race	0.972
	[0.143]
Female	1.384***
	[0.087]
Free/Reduced-Price Lunch	0.867*
	[0.058]
High School Academic Preparation (HS)
Algebra 2	1.607***
	[0.148]
Trigonometry	2.589***
	[0.432]
Other Advanced Math	1.654***
	[0.146]
Honors English	0.966
	[0.064]
Advanced Placement English	1.246*
	[0.129]
Constant	0.170***
	[0.021]
chi2	426.766
N	4,731
+ p < .10. * p < .05. ** p < .01, *** p < .001.

Note. Included in this logistic regression model are the 4,731 first-time-in-college (FTIC) students in the sample who took Intermediate Algebra and were identified as severely underprepared; severely underprepared is the reference group. Slightly underprepared FTIC students scored 50 to 95 on the Postsecondary Educational Readiness Test (PERT); moderately underprepared FTIC students scored 96 to 106 on the PERT; and slightly underprepared FTIC students scored 107– to 13 on the PERT. Estimates displayed are odds ratios; standard errors are in brackets.

Table 6. Predicted probability of passing gateway math by gateway pathway.

	Pass Gateway Math
	Low	Est.	High
Gateway Alone	39.2%	40.8%	42.3%
Gateway + Corequisite DE	40.7%	48.2%	55.8%
Gateway + Compressed DE	48.0%	53.5%	59.0%

DE = developmental education.