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# The Math Major—What Size?: Accessing Data on Your Program

Communicated by *Notices* Associate Editor William McCallum

## Introduction

What enrollment do we expect for an effective mathematics or statistics major program? Are mathematics major enrollments in national decline? Are STEM majors increasing? What programs graduate large numbers of mathematics and statistics majors? Are we making progress on representation numbers for women and underrepresented minorities? Do non-tenure-track faculty provide the majority of instruction in freshmen and sophomore mathematics and statistics courses? What are your campus’ majors in size order?

Our present goal is to encourage and energize leaders, departments, and policy advocates to examine available data to analyze their programs. Comparisons can be made to peer departments and to disciplines (such as economics, chemistry, biology …) on one’s own campus. Detailed data can be examined on feeder schools. Demographic statistics can be analyzed over time. Data can be used to assess recruitment and retention efforts. Data can be used to advocate for resources. Data can be used to identify mathematics course audiences on individual campuses.

Many questions are facing the academic mathematics community. Where can we find answers? It is not our purpose to comprehensively analyze matters. Instead, our purpose is to energize the reader to access and examine their own data. A wide range of data is readily available. We direct the reader to the Transforming Post-Secondary Education in Mathematics (TPSE Math) presentation of Nimmi Kannankutty, National Science Foundation (NSF) senior advisor. Kannankutty describes and demonstrates the many publicly available national education data tools. The March 3, 2022 presentation video and slides with links to sources is available at Events | TPSE Math. Data on AP exams, dual enrollment, enrollments, transfer success, program completion, and postgraduate earnings is available from Community College Research Center | Tableau Public, Teacher’s College, Columbia University. The Western Interstate Commission for Higher Education (WICHE) publishes *Knocking at the College Door*: *Projections of High School Graduates. *The report provides detailed data and projections more than 15 years forward on high school graduate populations for all 50 states, the District of Columbia and selected US territories and outlying areas, including detail about the race/ethnicity of public/private school graduates. Projections of WICHE and Nathan Grawe, Professor of Economics at Carleton College, predict large regional enrollment variations in the coming years—see *Knocking* 10th Data and Forecasting Growth in College-Going Students, 2012--2029. Also see the Mathematical Association of America (MAA) Launchings Columns, especially David Bressoud’s October 1, 2023 article on Trends in Math Degrees. Also valuable are the American Mathematical Society (AMS) Annual Survey and working with one’s campus institutional research data resources. In the final section of this note we give beginning instructions and tips for using the National Center for Science and Engineering Statistics (NCSES) Completion and Enrollment websites and discuss identified limitations of the data.

For relative simplicity, we focus on the Integrated Postsecondary Education Data System (IPEDS) system enrollment and completions data. Universities and colleges receiving any form of Federal funding are required to report statistics on their programs. IPEDS is a system of surveys conducted by the National Center for Education Statistics. Data on completions (degrees awarded), enrollments, demographics, and research and development (R&D) resources is publicly available at Data Tools Home | NCSES | NSF. Of special interest are the Fall Enrollment Surveys and the Completions Surveys. Fall Enrollments has an information page IPEDS Enrollments information and a data search page Enrollment Table Builder | NCSES, while Completions has an information page IPEDS Completion information and a data search page Completion Table Builder | NCSES. The Enrollment Survey collects detailed information for 2002 to 2020 on the breakdowns of enrollment by area of study, institution, institution type, public vs. private, geographic location, Carnegie classification, undergraduate vs. graduate and by student demographics. The Completions Survey collects information on the number and types of degrees (associate’s, bachelor’s, master’s and PhD) awarded. Counts of degrees by level, by major, and by institution for 1997 to 2021 are publicly available. The data is broken down by institution, institution type, geographic location, public vs. private, Carnegie classification, and by student demographics. Data is reported by each campus’ institutional research office following specifications of NCES, in particular following the Classification of Instructional Programs (CIP) Codes. On the two websites, student counts are *by first listed major only*, and so typically are less than local department tallies. On the two websites searches restricted to specific majors are straightforward. On the alternative IPEDS site NCES Custom Tables searches are generally only campus wide but major tallies include first and second degrees completed, admissions data, student-to-faculty ratios, and graduation rates. There is some complexity of the data on the Custom Tables site. We use only the simpler Enrollment and Completion sites.

## General Distributions

Course enrollment counts, instructor data, DWF rates, full major counts are best obtained from one’s campus institutional research office. NCSES data can be most useful for comparisons. As much as possible we use the NCSES categories and labels in the following. Here is the recent national tally of all degree levels by math/stat pure/applied breakdown (using the 4-digit CIP codes). (All tables include the most recent available IPEDS data.)

Fiscal Year | 2021 | 2020 | 2019 | 2018 | 2017 |

27.01 - Mathematics. | 26,976 | 27,870 | 27,391 | 26,841 | 25,705 |

27.03 - Applied Mathematics. | 10,531 | 9,995 | 9,125 | 8,175 | 6,617 |

27.05 - Statistics. | 8,993 | 8,598 | 8,033 | 7,308 | 6,507 |

27.06 - Applied Statistics. | 463 | 183 | - | - | - |

(Apparently Applied Statistics is a new classification.)

Here is the national tally of math stat (2-digit CIP code 27) by degree type.

Fiscal Year | 2021 | 2020 | 2019 | 2018 | 2017 |

Associate’s degree | 4,842 | 4,848 | 4,631 | 4,135 | 3,454 |

Bachelor’s degree | 27,162 | 27,299 | 26,215 | 25,345 | 24,155 |

Master’s degree | 12,604 | 12,075 | 11,417 | 10,473 | 9,112 |

Doctor’s degree | 1,960 | 2,027 | 2,008 | 2,015 | 1,928 |

research/scholarship - |

Here is the 2021 national tally of math stat degrees by degree by underrepresented minority and by gender.

Degree | Associate’s | Bachelor’s | Master’s | Doctor’s |

-r/s | ||||

Hispanic or Latino | 1,688 | 2,855 | 572 | 71 |

American Indian or Alaska Native, | 15 | 39 | 6 | 1 |

non-Hispanic | ||||

Black or African American, | 131 | 1,064 | 253 | 25 |

non-Hispanic | ||||

Female | 1,615 | 11,414 | 5,216 | 546 |

Here is the national tally of first-time, full-time, first-year, degree-seeking students in engineering, mathematics and the physical sciences (2-digit CIP codes 14, 27, and 40) by year.

Fiscal Year | 2020 | 2018 | 2016 | 2014 | 2012 |

Engineering | 122,183 | 133,100 | 131,815 | 126,767 | 108,819 |

Mathematics | 13,469 | 15,194 | 14,434 | 13,394 | 13,149 |

Physical sciences | 26,268 | 30,957 | 30,977 | 31,607 | 29,920 |

Here is the national demographic tally of first-time, full-time, first-year, degree-seeking students in engineering, mathematics and physical sciences (2-digit CIP codes 14, 27, and 40) by year.

Fiscal Year | 2020 | 2018 | 2016 | 2014 | 2012 |

Hispanic or Latino | 25,935 | 26,450 | 24,461 | 21,882 | 17,774 |

American Indian or Alaska Native, | 521 | 585 | 630 | 638 | 624 |

non-Hispanic | |||||

Black or African American, | 10,525 | 11,360 | 11,414 | 10,726 | 10,001 |

non-Hispanic |

Here is the national demographic tally of full and part time fall enrollment, degree-seeking in math stat (2-digit CIP code 27).

Fiscal Year | 2020 | 2018 | 2016 | 2014 | 2012 |

Total | 13,930 | 15,584 | 14,704 | 13,657 | 13,358 |

Hispanic or Latino | 2,415 | 2,398 | 2,208 | 1,924 | 1,585 |

American Indian or Alaska Native, | 50 | 56 | 56 | 62 | 43 |

Hispanic non | |||||

Black or African American, | 891 | 1,025 | 1,002 | 1,116 | 1,224 |

Hispanic non |

## Math Stat Distributions

We present tables on the number of first major math stat bachelor’s degrees as percentages of all bachelor’s degrees. The data will be broken down by institution type and departments with highest percentages will be cited. We also cite departments with the highest numbers of master’s and PhD degrees. In addition, we present statistics on degrees for underrepresented minorities and females—and cite departments with the largest tallies.

We begin with the math stat first major bachelor’s as a percent of all bachelor’s degrees over 1353 US institutions granting math stat degrees. We use 4-digit CIP codes 27.01, 27.03, 27.05, and 27.06 and take the three-year 2019–2021 average to smooth the annual data. Excluding schools at 0% (which may be closed programs), the resulting distribution quartiles are .6%, 1.5% and 1.8% with one hundred and eight schools having three-year average values less than 0.1%. The histogram of values, excluding 0%, is given in Figure 1.

The overall median of 1.5% is in line with the rule of thumb that a math program might be expected to have between 1% and 2% of campus degrees. The current median is deflated because of only counting first majors and is inflated because of including statistics. The schools Carnegie Mellon University, Harvard University, University of Chicago, and Amherst College are above 10% math stat degrees.

**Associate’s degree in math stat**. The five community colleges San Jacinto Community College, Pasadena City College, College of the Canyons, El Camino Community College District, and Irvine Valley College averaged over one hundred Associate’s for 2019–2021.

**Master’s and PhDs in math stat**. The tally of math stat (CIP code 27) Master’s and PhDs is given above. In 2021, the three schools Columbia University, University of Chicago, and New York University each awarded over 450 math stat master’s, and the six schools North Carolina State University, Stanford University, Texas A&M University, University of California–Berkeley, Florida State University, and University of Wisconsin each awarded over 37 math stat PhDs. Of the 153 schools granting pure math PhDs, 15 schools granted over one quarter of the degrees. Of the 66 schools granting applied math PhDs, 6 schools granted over one quarter of the degrees.

**Females in math stat**. In 2021, the female tallies of math stat (CIP code 27) were bachelor’s 11,414, master’s 5,216 and PhDs research/scholarship 546. The four University of California schools Berkeley, Los Angeles, Santa Barbara, and San Diego each awarded over 150 Bachelor’s. The four schools Columbia University, University of Chicago, New York University, and Harrisburg University of Science and Technology each awarded over 150 master’s. The ten schools North Carolina State University, University of Wisconsin, University of Illinois Urbana-Champaign, University of Michigan, University of Texas at Dallas, University of Minnesota, Stanford University, Texas A & M University, Virginia Polytechnic Institute, and Iowa State University, each awarded ten or more PhDs.

**Hispanics or Latinos in math stat**. The tally of math stat (CIP code 27) Bachelor’s, Master’s and PhDs is generally described above. In 2021, the five schools University of California—Riverside, University of California—Santa Barbara, California State Polytechnic University—Pomona, University of Texas Rio Grande Valley, and University of Houston each awarded over 50 Bachelor’s. The five schools University of Houston, University of Miami, University of Chicago, University of California—Irvine, and Southern Methodist University each awarded at least 14 Master’s. The four schools University of Illinois Urbana-Champaign, University of California—Irvine, University of Washington, and University of Notre Dame each awarded at least three PhDs.

**African Americans in math stat**. The tally of math stat (CIP code 27) bachelor’s, master’s and PhDs is generally described above. In 2021, the five schools Southern New Hampshire University, Georgia State University, Spelman College, Texas Tech University, and University of Maryland—Baltimore County each awarded at least 14 Bachelor’s. The six schools University of Chicago, National University, Vanderbilt University, DePaul University, Elizabeth City State University, and CUNY Baruch College each awarded at least five master’s. The four schools Morgan State University, Middle Tennessee State University, Georgia State University, and North Dakota State University each awarded at least two PhDs.

**Distribution quartiles for percent of math stat Bachelor’s for institution categories in the Carnegie Classification 2021**. We take the rosters of institutions from within the Completion Table—exporting the rosters within Dimensions:Institution, Names:Carnegie Classification 2021. We omit institutions not reporting or consistently reporting zero math stat Bachelor’s degrees. The data is pulled from the above 2019–2021 averages table for the 4-digit CIP codes 27.01, 27.03, 27.05 and 27.06. The Excel function XLOOKUP is well suited for the pulling data task.

**The Carnegie quartiles**. The quartiles for Doctoral Universities: Very High Research activity are 1.0%, 1.5% and 3.1%. The quartiles for Doctoral Universities: High Research Activity are 0.6%, 0.8%, and 1.3% respectively. The quartiles for the combined Master’s Colleges & Universities: Small, Medium, and Larger Programs are 0.6%, 0.9%, and 1.5% respectively. The quartiles for Baccalaureate Colleges: Arts & Sciences Focus are 1.4%, 2.3%, and 3.4% respectively. The quartiles for historically Black colleges and universities (HBCUs) are 0.5%, 0.8%, and 1.4% respectively. The quartiles for Association of American Universities (AAU) are 2.0%, 3.0%, and 5.1%.

## Finding Distributions

*Here is how to get started viewing data on* Completion Table Builder | NCSES. The Enrollment Table Builder functions similarly.

- •
On the left, under Measures select Degrees Awarded by Colleges and Universities. Select Awards/Degrees Conferred on the pop-out panel, click the box on the next pop-out panel, and select Add to Table. You are now looking at the national annual count of degrees at all levels.

- •
Now return to the far-left panel and under Dimensions select Degrees Awarded by Colleges and Universities. Select Award Level Code in the pop-out panel. In the Filter Dimension panel, select Bachelor’s, highlight, and then use the > arrow to move the entry to the right box. Select Column at the bottom (so Bachelor’s becomes a column header). You are now looking at the annual national tally of bachelor’s degrees. Multiple degree levels can be selected simultaneously.

- •
Now under Dimensions select Institution Name in the left panel. In the Filter Dimension panel you can either build a list (displayed in the bottom left box) by selecting properties in the upper part of the panel, or use the Search feature in the middle left to enter a name, for example California State University (CSU). Then in the box at the bottom appears the list of CSU campuses. To select Long Beach, put the highlight on this entry and then click the > arrow to add to the list on the right. Multiple schools can be selected before clicking the arrow. Then click Add to table as Row at the panel bottom. You are now looking at CSU-LB bachelor’s degrees by year. (Affiliated programs such as nursing could be included.)

- •
Next click Field of Study under Dimensions on the far left. Select CIP Code and Dimension (2-digit) on the panel. (You could select the 4 or 6-digit CIP Codes and you will get a finer breakdown within majors.) In the pop-out Filter Dimension use the Search and, for example, enter “math.” You will see “27-Mathematics and Statistics,” highlight and then use the > arrow to move the entry to the right box. At the panel bottom, select Add to Table as Row. You are now looking at the reported combined count of math and stat degrees by year. (If you use 4-digit CIP codes then there are five subdivisions within “math” and three within “stat.” If a subdivision is grayed out then data does not exist for that class.)

- •
At any point, you can start over by clicking Clear Table on the left or by reloading the web page.

*Here is how to use* Completion Table Builder | NCSES *to find schools for recruiting in your region. *

On the left under Measures under Degrees Awarded by Colleges and Universities select and click Degrees/Awards Conferred and Add to Table. Then under Dimensions, select Fields of Study and select CIP Code and Description (4-digit), enter *math* in the search box and highlight Mathematics and/or Applied Mathematics, use the > arrow and at the bottom Add to Table as a Column. Next click Degrees Awarded by Colleges and Universities under Dimensions. In the pop-out select Award Level Code, in the pop-out highlight Associate’s or Bachelor’s or Master’s depending on the desired recruiting, use the > arrow and at the bottom Add to Table as Column. Next, under Dimensions click Race and Ethnicity and select Race and Ethnicity in the pop-out, select any desired demographics and Add to Table as Column. Next, under Dimensions click Institution Name. In the pop-out Filter Dimension, choose from the submenus. One option is select State—highlight states of interest and select Apply to load the requisite list of schools in the lower left. Select Add All above the lower left panel and at the bottom Add to Table as Row. You are now looking at the list of schools in your region with their degree counts and graduates’ demographics. The list can be explored by downloading into Excel.

**Final tips**. Again, data is reported at the direction of your campus institutional research office and major counts are by first-listed major only. Remember that the default in the Completions data is for certificates and all degree levels. Note in the upper right the Drag and Drop Bubbles to Rearrange table organizer. Properties listed in the same column (or row) prescribe simultaneous conditions. Press the blue plus circles in the output panel to unpack properties to individual tallies. Use Export to download data into Excel and then use the Excel data tools (sort, graph, statistics, sumif, rank.eq). In examples, mathematics education is sometimes reported under math and sometimes under education with the Mathematics Teacher Education 6-digit CIP code 13.1311. Computer and Information Sciences and Support Services are listed under the 2-digit CIP codes 11. The interdisciplinary Mathematics and Computer Science is listed in the 6-digit CIP code 30.0801. You should examine your school’s data to determine the reporting.

## Acknowledgments

This exercise has benefited from the input of members of the community. Nimmi Kannankutty’s TPSE Math presentation provided the original impetus for examining the data. TPSE Math’s Math Advisory Groups provided guidance in the study first stages. The analysis of data was raised to a higher level by input and suggestions from Mitch Keller at the University of Wisconsin.

## Credits

Figure 1 and author photo are courtesy of Scott A. Wolpert.