# Re-Examining the Public–Catholic School Gap in STEM Opportunity to Learn: New Evidence from HSLS

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background Literatures

#### 2.1. High School STEM Learning: An Opportunity to Learn Perspective

#### 2.2. Curricular Differentiation, and OTL across Countries

#### 2.3. Course-Taking, School Sector Gaps, and Standards-Based Reform

## 3. Methodology

#### 3.1. Data

#### 3.2. Dependent Variables

#### 3.3. Analytic Strategy

^{T}is the transpose matrix of X. As King and Nielsen (2019) argued, multivariate distance matching is more efficient, has less model dependence, and can improve balance relative to traditional covariate adjustment or propensity score matching. To find potential matches based on multivariate distance and determine the matching weights, we use a Kernel matching algorithm, which provides a non-parametric estimation of outcomes using Kernel weights. The Kernel weight is defined as (Frölich 2004),

## 4. Results

#### 4.1. Descriptive Statistics

#### 4.2. Using Matching to Address Selection into Public and Catholic Schools

#### 4.3. Effect of Catholic School Attendance on Course-Taking Outcomes

#### 4.4. Adjacent Categories Model for Tracking

## 5. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Coding Process for Mathematic Course Sequence (MCS) Codes

Individual Math Code | Description |
---|---|

1 | less than Algebra 1 |

2 | Algebra 1 |

3 | Geometry |

4 | Transition |

5 | Algebra 2 |

6 | Applied math elective |

7 | Algebra 3 and equal |

8 | Trigonometry and equal |

9 | Calculus and equal |

10 | Higher than “Calculus” |

**Table A2.**Complete individual mathematic course codes (Frequency out of 21,860 students in transcript data).

Course Name | SCED Code | Code | Freq | Course Name | SCED Code | Code | Freq |
---|---|---|---|---|---|---|---|

Informal Mathematics | 02001 | 1 | 292 | Mathematic Analysis/Analytic Geometry ^{1} | 02108 | 8 | 87 |

General Mathematics | 02002 | 1 | 576 | Elementary Functions ^{2} | 02109 | 8 | 341 |

Particular Topics in Foundation Mathematics | 02003 | 1 | 97 | Pre-Calculus | 02110 | 8 | 7062 |

Mathematics (early childhood education) | 02028 | no obs ^{3} | 0 | Linear Algebra ^{4} | 02111 | 9 | 41 |

Mathematics (pre-kindergarten) | 02029 | no obs | 0 | Linear Programming ^{5} | 02112 | 9 | 40 |

Mathematics (kindergarten) | 02030 | no obs | 0 | Abstract Algebra ^{6} | 02113 | 9 | 87 |

Mathematics (grade 1) | 02031 | no obs | 0 | Calculus | 02121 | 9 | 1250 |

Mathematics (grade 2) | 02032 | no obs | 0 | Multivariate Calculus ^{7} | 02122 | 10 | 39 |

Mathematics (grade 3) | 02033 | no obs | 0 | Differential Calculus ^{8} | 02123 | 10 | 28 |

Mathematics (grade 4) | 02034 | no obs | 0 | AP Calculus AB ^{9} | 02124 | 9 | 2070 |

Mathematics (grade 5) | 02035 | no obs | 0 | AP Calculus BC ^{10} | 02125 | 10 | 673 |

Mathematics (grade 6) | 02036 | no obs | 0 | Particular Topics in Calculus ^{11} | 02126 | 9 | 97 |

Mathematics (grade 7) | 02037 | no obs | 0 | IB Mathematical Studies^{12} | 02131 | 8 | 95 |

Mathematics (grade 8) | 02038 | no obs | 0 | IB Mathematics ^{13} | 02132 | 8 | 79 |

Mathematics—General | 02039 | no obs | 0 | IB Further Mathematics—HL ^{14} | 02134 | 8 | 122 |

Foundation Mathematics—Independent Study | 02047 | 1 | 5 | IB Mathematics, Middle Years Program ^{15} | 02135 | 7 | 40 |

Foundation Mathematics—Other | 02049 | 1 | 187 | Finite Mathematics | 02136 | no obs | 0 |

Pre-Algebra | 02051 | 1 | 1143 | Mathematical Modeling | 02137 | no obs | 0 |

Algebra I | 02052 | 2 | 15022 | College Mathematics Preparation | 02138 | no obs | 0 |

Algebra I—Part 1 | 02053 | 2 | 1641 | Particular Topics in Analytic Mathematics | 02141 | 7 | 79 |

Algebra I—Part 2 | 02054 | 2 | 1472 | Analytic Mathematics—Other | 02149 | 7 | 284 |

Transition Algebra ^{16} | 02055 | 4 | 615 | General Applied Mathematics ^{17} | 02151 | 4 | 544 |

Algebra II | 02056 | 5 | 13570 | Occupationally Applied Mathematics ^{18} | 02152 | 4 | 91 |

Algebra III | 02057 | 7 | 818 | Technical Mathematics ^{19} | 02153 | 6 | 278 |

Particular Topics in Algebra ^{20} | 02058 | 4 | 348 | Business Mathematics ^{21} | 02154 | 6 | 407 |

Integrated Mathematics I | 02062 | no obs | 0 | Business Mathematics with Algebra ^{22} | 02155 | 6 | 151 |

Integrated Mathematics II | 02063 | no obs | 0 | Computer Mathematics with Algebra ^{23} | 02156 | 4 | 34 |

Integrated Mathematics III | 02064 | no obs | 0 | Consumer Mathematics ^{24} | 02157 | 1 | 577 |

Integrated Mathematics IV | 02065 | no obs | 0 | Probability and Statistics | 02201 | 7 | 1425 |

Algebra—Other ^{25} | 02069 | Dep. | 1193 | Inferential Probability and Statistics | 02202 | 7 | 175 |

Informal Geometry | 02071 | 1 | 594 | AP Statistics | 02203 | 9 | 1197 |

Geometry | 02072 | 3 | 16903 | Particular Topics in Probability and Statistics ^{26} | 02204 | 6 | 58 |

Analytic Geometry ^{27} | 02073 | 6 | 96 | Statistics | 02205 | no obs | 0 |

Principles of Algebra and Geometry ^{28} | 02074 | 6 | 704 | Probability and Statistics—Independent Study | 02207 | no obs | 0 |

Particular Topics in Geometry ^{29} | 02075 | 3 | 340 | Probability and Statistics—Other ^{30} | 02209 | Dep. | 62 |

Geometry—Other ^{31} | 02079 | 3 | 231 | History of Mathematics | 02991 | 1 | 32 |

Number Theory ^{32} | 02101 | 7 | 4 | Mathematics—Test Preparation ^{33} | 02993 | 6 | 549 |

Discrete Mathematics ^{34} | 02102 | 9 | 413 | Mathematics Proficiency Development ^{35} | 02994 | Dep. | 514 |

Trigonometry | 02103 | 8 | 1043 | Mathematics—Aide ^{36} | 02995 | Dep. | 20 |

Mathematic Analysis | 02104 | 8 | 513 | Mathematics—Supplemental ^{37} | 02996 | Dep. | 454 |

Trigonometry/Mathematic Analysis | 02105 | 8 | 278 | Mathematics—Independent Study ^{38} | 02997 | 6 | 64 |

Trigonometry/Algebra | 02106 | 8 | 2577 | Mathematics—Workplace Experience ^{39} | 02998 | 5 | 12 |

Trigonometry/Analytic Geometry | 02107 | 7 | 203 | Mathematics—Other | 02999 | Dep. | 2308 |

Undefined | 02061 | Dep. | 1828 |

^{1}Mathematic Analysis/Analytic Geometry prepares students eventually qualified in Calculus courses.

^{2}Elementary Functions prepares students eventually qualified in Calculus courses.

^{3}There is no observation on HSLS Transcript Students Course File.

^{4,5}Linear algebra and linear programming require students to finish pre-calculus or equal courses.

^{6}Abstract Algebra requires students to finish pre-calculus or equal courses.

^{7,8}Multivariate Calculus and Differential Calculus include topics that are based on calculus. In the meanwhile, to justify this coding level, I examined typical trajectories of students who took these two courses and found that students usually took Calculus and/or AP Calculus AB before these two courses if Multivariate Calculus or Differential Calculus was not the only calculus course they had ever taken.

^{9}Students usually took AP Calculus AB after Calculus if AP Calculus AB was not the only calculus course they had ever taken. However, according to course descriptions, AP Calculus AB shared the similar topics as Calculus including derivatives, differentiation, integration, the definite and indefinite integral, and applications of calculus.

^{10}Students usually took AP Calculus BC after Calculus and/or AP Calculus AB. In the meanwhile, in addition to topics covered by AP Calculus AB, AP Calculus BC covers parametric, polar, and vector functions; applications of integrals; and polynomial approximations and series, including series of constants and Taylor series.

^{11}To identify this coding level, I examined typical trajectory of students who took this course and found that students usually took Particular Topics in Calculus independently (i.e., Particular Topics in Calculus was usually the only calculus course students took if they chose to take Particular Topics in Calculus). I coded this course as equal as Calculus because, in some scenarios, Particular Topics in Calculus is the replacement course for Calculus.

^{12,13}These two IB courses prepare students to take IB math studies at standard level. Courses includes topics from algebra III, number theories, and trigonometry, but only introductory level calculus.

^{14}This IB course prepare students to take IB math studies at higher level. Course topics include Calculus and other high-level topics.

^{15}Instead of preparing student to take IB exam, IB Mathematics, Middle Years Program is built on a framework of five branches of mathematics: number, algebra, geometry and trigonometry, statistics and probability, and discrete mathematics. The program encourages students to develop an understanding of mathematical reasoning and processes, the ability to apply mathematics. Students usually took this course on 9th grade and 10th grade (84.7% of students took Middle Year Program on 9th grade and/or 10th grade). As a contrast, students usually took IB Mathematics or IB Mathematics studies on 11th or 12th grade (78.4% and 89.3% of students took these two IB courses on 11th and/or 12th grade, respectively). Therefore, I coded Middle Year Program one level lower than IB Mathematics or IB Mathematics.

^{16}Transition Algebra courses review and extend algebra and geometry concepts for students who have already taken Algebra I and Geometry. Although, similar to Algebra II where students usually took it on 10th and/or 11th grade (77.8%), students usually took Transition Algebra after 9th grade (88.5%), Transition Algebra did not sufficiently apply knowledge harder than Algebra I series or Geometry. Therefore, I coded Transition Algebra as “4- transition”.

^{17,18}General Applied Mathematics and Occupationally Applied Mathematics applied knowledge from Algebra I and used these skills in specific fields. However, similar to Transition Algebra, these two courses did not apply knowledge and skills from Algebra II or equal courses. Therefore, these two courses should belong to 4.

^{19,21,22}Technical Mathematics, Business Mathematics, and Business Mathematics with Algebra sufficiently applied basic principles from Algebra I, Algebra II and Geometry. I code these three courses as “applied math elective” because, although they combine principles of Algebra and geometry, they do not adequately provide solid theoretical background as pre-calculus does.

^{20}Particular Topics in Algebra built upon topics from pre-Algebra and Algebra I and examine specific topics such as linear equations or rational numbers. More than half of students usually took this course before 10th grade (56.8%). Compare to Algebra II where only less than 10% of students took Algebra II before 10th grade (7.8%), I coded Particular Topics in Algebra as “4-between Algebra I and Algebra II”.

^{23}Intended for students who have attained the objectives of Algebra I, Computer Mathematics with Algebra courses include a study of computer systems and programming and use the computer to solve mathematics problems. However, this course did not applied knowledge higher than Algebra I.

^{24}Consumer Mathematics only applied knowledge from pre-Algebra such as arithmetic using rational numbers, measurement, ratio and proportion, and basic statistics to consumer problems and situations. Therefore, I coded this course as pre-Algebra.d.

^{25}The level of Algebra-other depended on individual courses that students had taken. For example, Algebra Lab for ninth graders, or College Algebra and Intermediate Algebra for 12th graders both belonged to Algebra-Other.

^{26}Particular Topics in P&S usually covered topics such as elementary statistic and general statistic topics. Therefore, I coded this course one level lower than Statistic.

^{27,28}These courses apply basic principles from algebra I, and algebra II into studying of geometry. I code these two courses as “applied math elective” because, although they combine principles of Algebra and geometry, they do not adequately provide solid theoretical background as pre-calculus does.

^{29}Out of 678 students who took Particular Topics in Geometry, 490 students (72.2%) took this course as the only geometry course along four-year high school as the replacement of general Geometry and/or advanced level geometry courses. Therefore, I coded this course as a transition level course (4).

^{30}The category of P&S-Other contained courses for different levels of students. For example, there were introductory statistic courses for 10th grade, and advanced statistic, college statistic, and advanced mathematical decision making for 12th grade.

^{31}Unlike Algebra-Other with diversified content for students in different grades, student usually took Geometry-Other before 11th grade (70.3%). As a contrast, 80.2% of students took Geometry before 11th grade. Out of 374 students who took Geometry-Other, 246 students (65.8%) took this course as the only geometry course along their four-year high school as the replacement of general Geometry and/or advanced level geometry courses. Therefore, I coded this course as a transition level course (4).

^{32}This course reviews the properties and uses of integers and prime numbers which prepare students with higher level course, Discrete Mathematics. Part of theories in this course may be covered in Algebra III.

^{33}This course prepares students with test skills in PSAT, SAT and ACT. Topics include knowledge in algebra I and II and geometry.

^{34}Discrete Mathematics is built upon Algebra III and Number theory which is a higher-level course.

^{35–37}The level of these three courses are hard to be decided because the content of these courses depends on grade level.

^{38}Students usually took this independent study (70.1%) after 10th grade. The goal of this course was to expand their expertise in a particular application, to explore a topic in greater detail, or to develop more advanced skills based on courses they had taken on first two years. However, this independent study was not necessarily the subsequent course of Algebra III and other higher-level courses. Therefore, I coded this course as an elective math course.

^{39}Mathematics—Workplace Experience was not usually part of math sequence (i.e., students might take calculus at 11th grade and then take Mathematics—Workplace Experience at 12th grade for other reasons). Therefore, although more than 60% of students took Mathematics—Workplace Experience after 10th grade, it is hard to decide the level of Mathematics—Workplace Experience based on trajectories. According to course description, there was not a solid math inquiry associated with this course, Mathematics—Workplace Experience set cooperatively by the student, teacher, and employer. Therefore, I coded this course as a transition level course.

## Appendix B. Coding Process for Science Course Sequence (SCS) Codes

Code 1 | |
---|---|

Science course category code | Description |

1 | Biology Category |

2 | Chemistry Category |

3 | Physics Category |

4 | Other Category, any combination course |

Code 2 | |

Science course difficulty level code | Description |

1 | Course provides basic concepts on specific field |

2 | Course is based on level 1 course, providing a more detailed understanding on specific field, or introduction to a sub-field |

3 | Course provides an in-depth study on a specific sub-filed |

4 | Course provides a higher-level comprehensive study of specific field |

5 | In addition to level 4, course requires higher-level interdisciplinary knowledge to finish |

**Table A4.**Complete individual science course codes (Frequency out of 21,777 students in transcript data).

Course Name | SCED Code | Code 1 | Code 2 | Freq. |
---|---|---|---|---|

Earth Science | 03001 | 4 | 1 | 4012 |

Geology ^{1} | 03002 | 4 | 2 | 209 |

Environmental Science | 03003 | 4 | 1 | 2778 |

Astronomy | 03004 | 4 | 1 | 559 |

Marine Science | 03005 | 4 | 1 | 933 |

Meteorology | 03006 | 4 | 1 | 80 |

Physical Geography ^{2} | 03007 | 4 | 2 | 69 |

Earth and Space Science | 03008 | 4 | 1 | 1024 |

Particular Topics in Earth Science | 03009 | 4 | 1 | 72 |

Earth/Space Science (prior-to-secondary) | 03010 | 4 | 1 | 0 |

Physical Science (prior-to-secondary) | 03011 | 4 | 1 | 0 |

Energy and the Environment | 03012 | 4 | 1 | 0 |

Earth Science—Independent Study | 03047 | 4 | 1 | 25 |

Earth Science—Workplace Experience | 03048 | 4 | 1 | 2 |

Earth Science—Other | 03049 | 4 | 1 | 316 |

Biology | 03051 | 1 | 1 | 19,332 |

Biology—Advanced Studies ^{3} | 03052 | 1 | 2 | 969 |

Anatomy and Physiology ^{4} | 03053 | 1 | 2 | 3507 |

Anatomy ^{5} | 03054 | 1 | 3 | 301 |

Physiology | 03055 | 1 | 3 | 184 |

AP Biology ^{6} | 03056 | 1 | 4 | 1551 |

IB Biology ^{7} | 03057 | 1 | 4 | 157 |

Botany ^{8} | 03058 | 1 | 2 | 170 |

Genetics ^{9} | 03059 | 1 | 2 | 163 |

Microbiology ^{10} | 03060 | 1 | 2 | 86 |

Zoology ^{11} | 03061 | 1 | 2 | 468 |

Conceptual Biology | 03062 | 1 | 1 | 484 |

Particular Topics in Biology | 03063 | 1 | 1 | 509 |

Regional Biology | 03064 | 1 | 1 | 0 |

IB Sports, Exercise, and Health Science ^{12} | 03065 | 1 | 2 | 0 |

PLTW Principles of Biomedical Science ^{13} | 03066 | 1 | 3 | 0 |

PLTW Human Body Systems ^{14} | 03067 | 1 | 3 | 0 |

PLTW Medical Interventions ^{15} | 03068 | 1 | 3 | 0 |

Nutrition Science | 03069 | 1 | 2 | 0 |

PLTW Biomedical Innovation | 03070 | 1 | 3 | 0 |

Biology—Independent Study | 03097 | 1 | 1 | 2 |

Biology—Workplace Experience | 03098 | 1 | 1 | 1 |

Biology—Other | 03099 | 1 | 1 | 330 |

Chemistry | 03101 | 2 | 1 | 14,276 |

Chemistry—Advanced Studies ^{16} | 03102 | 2 | 2 | 652 |

Organic Chemistry ^{17} | 03103 | 2 | 3 | 87 |

Physical Chemistry ^{18} | 03104 | 2 | 5 | 50 |

Conceptual Chemistry | 03105 | 2 | 1 | 266 |

AP Chemistry ^{19} | 03106 | 2 | 4 | 1039 |

IB Chemistry ^{20} | 03107 | 2 | 4 | 95 |

Particular Topics in Chemistry | 03108 | 2 | 1 | 87 |

Chemistry—Independent Study | 03147 | 2 | 1 | 10 |

Chemistry—Workplace Experience | 03148 | 2 | 1 | 5 |

Chemistry—Other | 03149 | 2 | 1 | 153 |

Physics | 03151 | 3 | 1 | 6813 |

Physics—Advanced Studies | 03152 | 3 | 2 | 249 |

Principles of Technology | 03153 | 3 | 2 | 155 |

AP Physics C ^{21} | 03156 | 3 | 5 | 149 |

IB Physics ^{22} | 03157 | 3 | 5 | 81 |

Life Science | 03158 | 1 | 1 | 1 |

Physical Science | 03159 | 3 | 1 | 7107 |

Conceptual Physics | 03161 | 3 | 1 | 477 |

Particular Topics in Physics | 03162 | 3 | 1 | 83 |

AP Physics C: Electricity and Magnetism ^{23} | 03163 | 3 | 5 | 58 |

AP Physics C: Mechanics ^{24} | 03164 | 3 | 5 | 89 |

AP Physics 1 ^{25} | 03165 | 3 | 4 | 37 |

AP Physics 2 ^{26} | 03166 | 3 | 4 | 3 |

Physics—Independent Study | 03197 | 3 | 1 | 7 |

Physics—Workplace Experience | 03198 | 3 | 1 | 0 |

Physics—Other | 03199 | 3 | 1 | 94 |

Integrated Science | 03201 | 4 | 1 | 2894 |

Unified Science | 03202 | 4 | 1 | 574 |

Applied Biology/Chemistry | 03203 | 4 | 1 | 103 |

Technological Inquiry | 03204 | 4 | 1 | 4 |

Origins of Science | 03205 | 4 | 1 | 24 |

IB Design Technology ^{27} | 03206 | 4 | 3 | 1 |

AP Environmental Science ^{28} | 03207 | 4 | 3 | 816 |

IB Environmental Systems and Societies ^{29} | 03208 | 4 | 3 | 35 |

Aerospace | 03209 | 4 | 2 | 46 |

Science, Technology and Society | 03210 | 4 | 1 | 51 |

Technical Science | 03211 | 4 | 1 | 58 |

Scientific Research and Design | 03212 | 4 | 1 | 154 |

IB Sciences, Middle Years Program | 03213 | 4 | 1 | 42 |

Forensic Laboratory Science | 03214 | no obs | 0 | |

Science (early childhood education) | 03228 | no obs | 0 | |

Science (pre-kindergarten) | 03229 | no obs | 0 | |

Science (kindergarten) | 03230 | no obs | 0 | |

Science (grade 1) | 03231 | no obs | 0 | |

Science (grade 2) | 03232 | no obs | 0 | |

Science (grade 3) | 03233 | no obs | 0 | |

Science (grade 4) | 03234 | no obs | 0 | |

Science (grade 5) | 03235 | no obs | 0 | |

Science (grade 6) | 03236 | no obs | 0 | |

Science (grade 7) | 03237 | no obs | 0 | |

Science (grade 8) | 03238 | no obs | 0 | |

Science—General | 03239 | no obs | 0 | |

Life and Physical Sciences—Proficiency Development | 03994 | 4 | 1 | 33 |

Life and Physical Sciences—Aide | 03995 | 4 | 1 | 29 |

Life and Physical Sciences—Supplemental | 03996 | 4 | 1 | 13 |

Life and Physical Sciences—Independent Study | 03997 | 4 | 1 | 33 |

Life and Physical Sciences—Workplace Experience | 03998 | 4 | 1 | 10 |

Life and Physical Sciences—Other | 03999 | 4 | 1 | 1006 |

^{1}Geology courses provide an in-depth study of the forces that formed and continue to affect the earth’s surface.

^{2}Knowledge for Physical Geography is based on Earth science and Marine science that examine the physical environment place on human development.

^{3}This course usually taken after a comprehensive initial study of biology, Biology—Advanced Studies courses cover biological systems in more detail.

^{4}This course usually taken after a comprehensive initial study of biology, Anatomy and Physiology courses present the human body and biological systems in more detail.

^{5}Anatomy courses present an in-depth study of the human body and biological system. Students usually took this course after anatomy and physiology.

^{6}Adhering to the curricula recommended by the College Board and designed to parallel college-level introductory biology courses, AP Biology courses emphasize four general concepts: evolution; cellular processes (energy and communication); genetics and information transfer; and interactions of biological systems.

^{7}IB Biology courses prepare students to take the International Baccalaureate Biology exams at either the standard or higher level.

^{8,9,10,11}These four courses provide students with a understanding of general concepts of specific sub-field.

^{12}Although this is an IB course, this course provides students with standard level of understanding of this sub-field.

^{13,14,15}These three PLTW courses provide students with in-depth understanding of specific sub-field based on the knowledge from physiology and genetics.

^{16}This course usually taken after a comprehensive initial study of chemistry, Chemistry—Advanced Studies courses cover chemical properties and interactions in more detail.

^{17}Organic Chemistry courses involve the study of organic molecules and functional groups. Usually taken after advanced studies.

^{18}This is an interdisciplinary course. Usually taken after completing a calculus course, Physical Chemistry courses cover chemical kinetics, quantum mechanics, molecular structure, molecular spectroscopy, and statistical mechanics.

^{19}This AP course requires high school chemistry and algebra II.

^{20}This IB course provides students with higher level of understanding in Chemistry.

^{21}AP Physics C in a combination course of Physics C: Electricity and Magnetism and Physics C: Mechanics and requires calculus to resolve problems.

^{22}IB Physics requires calculus.

^{23.24}. See note 21.

^{25,26}Unlike AP C, these two AP courses are algebra-based physics, can’t be coded as higher-level interdisciplinary course.

^{27,28,29}Although these three AP/IB courses provide comprehensive study of specific field, they don’t provide a higher-level understanding of sub-field as AP chemistry or physics does.

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Mathematic Course Sequence (MCS) | Content |
---|---|

1 | Less than Algebra I |

2 | Algebra I or Geometry, but not both |

3 | Algebra I and Geometry |

4 | Algebra I or Geometry, with at least one transition course |

5 | Algebra II |

6 | Algebra II with at least one math elective course |

7 | Algebra III or Trigonometry, but not both |

8 | Algebra III and Trigonometry |

9 | Calculus or higher |

Science Course Sequence (SCS) | Content |
---|---|

1 | No big-three course (Physics, Chemistry, Biology) |

2 | One big-three course |

3 | Two big-threes without higher-level course |

4 | Three big-three without higher-level course |

5 | Two or three big-threes with at least one higher-level course |

Sector Means (SE) | |||
---|---|---|---|

Student-Level Covariates | Catholic (n = 1851) | Public (n = 12,671) | Raw Difference |

Took Algebra I before 9th grade (1 for yes) | 0.30 (0.011) | 0.27 (0.0038) | 0.033 (0.011) ** |

Math Std. score at the start of 9th grade | 54.71 (0.20) | 50.67 (0.087) | 4.04 (0.24) *** |

Family SES | 0.55 (0.017) | −0.045 (0.0064) | 0.60 (0.018) *** |

Middle school sector (1 for Private) | 0.75 (0.0010) | 0.022 (0.0012) | 0.073 (0.005) *** |

Frequency of reading science book before HS | 2.22 (0.036) | 2.19 (0.013) | 0.030 (0.038) |

Hispanic | 0.15 (0.0083) | 0.17 (0.0032) | −016 (0.009) ^{~} |

Gender (1 for male) | 0.50 (0.012) | 0.49 (0.0043) | 0.016 (0.012) |

Black | 0.11 (0.014) | 0.058 (0.0085) | 0.053 (0.023) * |

Asian | 0.095 (0.014) | 0.016 (0.0083) | 0.079 (0.23) *** |

Frequency of taking other courses with mother before HS | 0.42 (0.036) | 0.19 (0.016) | 0.23 (0.046) *** |

Frequency of participating math/science activity before HS | 0.64 (0.026) | 0.72 (0.011) | −0.082 (0.031) ** |

8th grade most advanced science course | 2.35 (0.030) | 2.07 (0.015) | 0.28 (0.040) *** |

8th grade most advanced math course | 3.34 (0.032) | 2.91 (0.017) | 0.43 (0.046) *** |

Frequency of using computer for learning before HS | 2.23 (0.038) | 2.16 (0.015) | 0.069 (0.042) ^{~} |

Frequency of taking math courses with mother before HS | 0.21 (0.041) | 0.031 (0.017) | 0.18 (0.048) *** |

Frequency of taking science courses with mother before HS | 0.43 (0.035) | 0.24 (0.015) | 0.19 (0.041) *** |

^{~}p < 0.10. * p < 0.05. ** p < 0.01. *** p < 0.001.

Sector Means (SE) | |||
---|---|---|---|

Public (n = 12,671) ^{a} | Catholic (n = 1851) | Raw Difference | |

Require high-level Science courses ^{b} | 0.091 (0.0025) | 0.47 (0.012) | 0.38 (0.0079) *** |

Full-time teacher ratio | 0.96 (0.00058) | 0.88 (0.0032) | −0.081 (0.0020) *** |

Mean math achievement | 50.56 (0.040) | 54.75 (0.096) | 4.19 (0.11) *** |

Mean SES | −0.050 (0.0031) | 0.55 (0.067) | 0.60 (0.0087) *** |

Require high-level Math courses ^{b} | 0.11 (0.0027) | 0.51 (0.012) | 0.40 (0.0084) *** |

Offer advanced Physics courses ^{b} | 0.44 (0.0043) | 0.53 (0.012) | 0.090 (0.012) *** |

Offer advanced Chemistry courses ^{b} | 0.59 (0.0043) | 0.66 (0.011) | 0.065 (0.012) *** |

% of Hispanic students | 13.90 (0.18) | 9.69 (0.33) | −4.20 (0.49) *** |

Offer Calculus courses ^{b} | 0.74 (0.0038) | 0.85 (0.0082) | 0.11 (0.011) *** |

Offer advanced Biology courses ^{b} | 0.65 (0.0041) | 0.70 (0.011) | 0.043 (0.012) *** |

% of Black students | 13.23 (0.16) | 8.92 (0.30) | −4.31 (0.43) *** |

% of Asian students | 3.23 (0.061) | 4.93 (0.25) | 1.70 (0.19) *** |

% free lunch students | 38.15 (0.20) | 5.29 (0.34) | −32.86 (0.55) *** |

Urbanicity | |||

Suburb | 0.36 (0.0042) | 30 (0.011) | −0.57 (0.012) *** |

Town | 0.13 (0.0029) | 0.14 (0.0081) | 0.014 (0.0083) ^{~} |

Rural | 0.28 (0.0039) | 0.019 (0.0031) | −0.26 (0.010) *** |

Block schedule | 0.45 (0.0043) | 0.19 (0.0091) | −0.26 (0.012) *** |

Region | |||

Midwest | 0.24 (0.0037) | 0.31 (0.011) | 0.068 (0.011) *** |

South | 0.41 (0.0043) | 0.33 (0.011) | −0.082 (0.012) *** |

West | 0.20 (0.0034) | 0.091 (0.0066) | 0.10 (0.0095) *** |

^{a}Stand errors are in parenthesis.

^{b}1 for offering or requiring corresponding courses.

^{~}p < 0.10. * p < 0.05. ** p < 0.01. *** p < 0.001.

**Table 5.**Constructing measures of course taking using information from the cumulative sequence of courses taken.

Math Course Sequence Level | Collapsed Level of Course Sequence ^{b} | Science Course Sequence Level | Collapsed Level of Course Sequence | ||
---|---|---|---|---|---|

1 | Less than Algebra I | Low | 1 | No big-three ^{a} course | Low |

2 | Algebra I or Geometry, but not both | 2 | One big-three course | ||

3 | Algebra I and Geometry | 3 | Two big-threes without higher-level course | Middle | |

4 | Algebra I or Geometry, with at least one transition course | 4 | Three big-three without higher-level course | ||

5 | Algebra II | Middle | 5 | Two or three big-threes with at least one higher-level course | High |

6 | Algebra II with at least one math elective course | ||||

7 | Algebra III or Trigonometry, but not both | High | |||

8 | Algebra III and Trigonometry | ||||

9 | Calculus or higher |

^{a}Big-three includes biology, chemistry, and physics.

^{b}Collapsed qualitative categories are used in adjacent categories models.

**Table 6.**Baseline difference in mathematic course sequence (MCS) between different school sectors and Chi square test (n = 14,522).

Mathematic Course Sequence (MCS) | Public School | Catholic School | ||
---|---|---|---|---|

Frequency (Expected Frequency) ^{a} | Cumulative Frequency of a Given Level or Above | Frequency | Cumulative Frequency of a Given Level or Above | |

1 Less than Algebra I | 181 (164.0) | 12671 (100%) | 7 (24.0) | 1851 (100% |

2 Algebra I or Geometry, but not both | 1216 (1220.7) | 12490 (98.6%) | 183 (178.3) | 1844 (99.6%) |

3 Algebra I and Geometry | 966 (876.9) | 11274 (89.0%) | 39 (128.1) | 1661 (89.7%) |

4 Algebra I or Geometry, with at least one transition course | 460 (418.8) | 10308 (81.4%) | 20 (61.2) | 1622 (87.6%) |

5 Algebra II | 2627 (2474.5) | 9848 (77.7%) | 209 (361.5) | 1602 (86.5%) |

6 Algebra II with at least one math elective course | 990 (881.3) | 7221 (57.0%) | 20 (128.7) | 1393 (75.3%) |

7 Algebra III or Trigonometry, but not both | 812 (821.1) | 6231 (49.2%) | 129 (119.9) | 1373 (74.2%) |

8 Algebra III and Trigonometry | 2835 (3023.3) | 5419 (42.8%) | 630 (441.7) | 1244 (67.2%) |

9 Calculus or higher | 2854 (2790.4) | 2584 (20.4%) | 614 (407.6) | 614 (33.2%) |

Total | 12,671 | 1851 |

^{a}Expected frequency under mathematical model of independence (part of the Chi-Square calculation).

**Table 7.**Baseline difference in Science Course Sequence (SCS) between different school sectors and Chi square test (n = 14,522).

Mathematic Course Sequence (MCS) | Public School | Catholic School | ||
---|---|---|---|---|

Frequency (Expected Frequency) ^{a} | Cumulative Frequency of a Given Level or Above | Frequency | Cumulative Frequency of a Given Level or Above | |

1 No big-three course | 333 (306.9) | 12,671 (100%) | 18 (44.9) | 1851 (100%) |

2 One big-three course | 1954 (1782.0) | 12,338 (97.4%) | 82 (260.3) | 1833 (99.0%) |

3 Two big-threes without higher-level course | 4600 (4421.9) | 10,384 (82.0%) | 462 (645.9) | 1751 (94.6%) |

4 Three big-three without higher-level course | 4697 (5021.4) | 5784 (45.7%) | 1069 (733.6) | 1290 (69.7%) |

5 Two or three big-threes with at least one higher-level course | 1087 (1138.9) | 1087 (8.6%) | 220 (166.4) | 220 (11.9%) |

Total | 12,671 | 1851 |

^{a}Expected frequency under mathematical model of independence (part of the Chi-Square calculation).

Balance Check for Standardized Mean Difference | ||||||
---|---|---|---|---|---|---|

Matching Covariates | Raw Sample (n = 14,522) | Matched Sample (n = 8199) | ||||

Treated | Untreated | Std. DIff | Treated | Untreated | Std. Diff | |

Took Algebra I before 9th grade (1 for yes) | 0.30 | 0.27 | 0.065 | 0.25 | 0.25 | 0.00 |

Math Std. score at the start of 9th grade | 54.71 | 50.67 | 0.43 | 53.57 | 52.73 | 0.089 |

Family SES | 0.55 | −0.045 | 0.80 | 0.23 | 0.16 | 0.091 |

Middle school sector (1 for Private) | 0.75 | 0.022 | 2.27 | 0.12 | 0.12 | 0.00 |

Frequency of reading science book before HS | 2.22 | 2.19 | 0.023 | 2.25 | 2.27 | −0.081 |

Hispanic | 0.15 | 0.17 | −0.057 | 0.097 | 0.097 | 0.00 |

Gender (1 for male) | 1.50 | 1.49 | 0.026 | 1.50 | 1.50 | 0.00 |

Black | 0.11 | 0.058 | 0.066 | 0.091 | 0.091 | 0.00 |

Asian | 0.095 | 0.016 | 0.099 | 0.054 | 0.054 | 0.00 |

Frequency of taking other courses with mother before HS | 0.42 | 0.19 | 0.13 | 0.62 | 0.60 | 0.012 |

Frequency of participating math/science activity before HS | 0.64 | 0.72 | −0.070 | 0.89 | 0.87 | 0.012 |

8th grade most advanced science course | 2.35 | 2.07 | 0.19 | 2.23 | 2.24 | −0.0096 |

8th grade most advanced math course | 3.34 | 2.91 | 0.26 | 3.07 | 3.04 | 0.016 |

Frequency of using computer for learning before HS | 2.23 | 2.16 | 0.038 | 2.36 | 2.33 | 0.021 |

Frequency of taking math courses with mother before HS | 0.21 | 0.031 | 0.098 | 0.52 | 0.49 | 0.017 |

Frequency of taking science courses with mother before HS | 0.43 | 0.24 | 0.12 | 0.60 | 0.58 | 0.015 |

Balance Check for Variance Ratio | ||||||

Matching Covariates | Raw Sample (n = 14,522) | Matched Sample (n = 8199) | ||||

Treated | Untreated | Var. Ratio | Treated | Untreated | Var. Ratio | |

Took Algebra I before 9th grade (1 for yes) | 0.21 | 0.20 | 1.06 | 0.19 | 0.19 | 1.00 |

Math Std. score at the start of 9th grade | 76.36 | 101.52 | 0.75 | 63.51 | 68.86 | 0.92 |

Family SES | 0.55 | 0.55 | 1.01 | 0.41 | 0.44 | 0.93 |

Middle school sector (1 for Private) | 0.19 | 0.022 | 8.55 | |||

Frequency of reading science book before HS | 2.46 | 2.31 | 1.06 | 0.85 | 0.87 | 0.97 |

Hispanic | 0.13 | 0.14 | 0.90 | 0.087 | 0.087 | 1.00 |

Gender (1 for male) | 0.25 | 0.25 | 1.00 | 0.25 | 0.25 | 1.00 |

Black | 0.39 | 0.96 | 0.41 | 0.11 | 0.10 | 1.00 |

Asian | 0.38 | 0.92 | 0.41 | 0.073 | 0.073 | 1.01 |

Frequency of taking other courses with mother before HS | 2.43 | 3.50 | 0.69 | 0.39 | 0.39 | 0.99 |

Frequency of participating math/science activity before HS | 1.30 | 1.61 | 0.81 | 0.23 | 0.24 | 0.95 |

8th grade most advanced science course | 1.75 | 2.78 | 0.63 | 0.42 | 0.43 | 0.98 |

8th grade most advanced math course | 1.81 | 3.54 | 0.51 | 1.19 | 1.28 | 0.93 |

Frequency of using computer for learning before HS | 2.78 | 2.80 | 0.99 | 1.03 | 1.05 | 0.98 |

Frequency of taking math courses with mother before HS | 3.13 | 3.79 | 0.83 | 0.38 | 0.38 | 1.00 |

Frequency of taking science courses with mother before HS | 2.19 | 2.78 | 0.79 | 0.35 | 0.36 | 0.99 |

Math Course Sequence | Science Course Sequence | Total Math Credits | Total Science Credits | |
---|---|---|---|---|

1 Unadjusted difference | 0.73 (0.11) *** | 0.71 (0.12) *** | 0.24 (0.035) *** | 0.49 (0.034) *** |

2 Regression adjusted difference | −0.20 (0.16) | −0.11 (0.21) | −0.0041 (0.092) | 0.020 (0.083) |

Matched Sample | ||||

3 Unadjusted difference (ATE) | 0.35 (0.081) *** | 0.13 (0.034) ** | 0.024 (0.076) | 0.17 (0.059) ** |

4 Regression adjusted: Matched sample | 0.11 (0.078) | 0.17 (0.08) * | 0.016 (0.057) | −0.0025 (0.054) |

Linear Model Calculation | ||||

5 Unadjusted difference | 0.97 (0.059) *** | 0.42 (0.022) *** | ||

6 Regression adjusted for family background | 0.31 (0.078) *** | 0.22 (0.032) *** | ||

7 Regression adjusted for family background and school-level covariates | 0.26 (0.089) ** | 0.098 (0.036) ** |

^{~}p < 0.10. * p < 0.05. ** p < 0.01. *** p < 0.001.

**Table 10.**Summary of the effect of Catholic schools on STEM course-taking outcomes within Adjacent track levels.

Adjusted Difference with Logit Multilevel Model | Adjusted Difference with Logit Regression on Matched Sample | |
---|---|---|

Math Course Sequence (Low vs. Middle) | −0.04 (0.028) | 0.14 (0.32) |

Math (Middle vs. High) | 0.77 (0.23) *** | 0.31 (0.14) * |

Science (Low vs. Middle) | 0.47 (0.26) ^{~} | 0.56 (0.24) * |

Science (Middle vs. High) | 0.036 (0.026) | 0.027 (0.15) |

^{~}p < 0.10. * p < 0.05. ** p < 0.01. *** p < 0.001.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Xu, S.; Kelly, S. Re-Examining the Public–Catholic School Gap in STEM Opportunity to Learn: New Evidence from HSLS. *Soc. Sci.* **2020**, *9*, 137.
https://doi.org/10.3390/socsci9080137

**AMA Style**

Xu S, Kelly S. Re-Examining the Public–Catholic School Gap in STEM Opportunity to Learn: New Evidence from HSLS. *Social Sciences*. 2020; 9(8):137.
https://doi.org/10.3390/socsci9080137

**Chicago/Turabian Style**

Xu, Shangmou, and Sean Kelly. 2020. "Re-Examining the Public–Catholic School Gap in STEM Opportunity to Learn: New Evidence from HSLS" *Social Sciences* 9, no. 8: 137.
https://doi.org/10.3390/socsci9080137