**2.3 Current state of college calculus education**

For the past decade, I have been a part of a large research team studying college calculus. This research team has been led by David Bressoud, run under the auspices of the Mathematical Association of America, and funded by the National Science Foundation. Our research has come from two projects, the first begun in 2009 and focused on mainstream college differential calculus programs (typically called Calculus I) in all institution types, called *Characteristics of College Calculus (CSPCC);* the second begun in 2014 and focused on precalculus, differential and integral calculus programs at Masters and PhD-granting institutions, called *Progress through Calculus (PtC).* Our work has been generally focused on identifying aspects of college calculus programs that are more successful or innovative than comparative institutions, and supporting more mathematics departments to improve their programs based on these findings. For our purposes, success in college calculus is primarily marked by a large percentage of the students who plan to complete

both differential and integral calculus (typically called Calculus I and Calculus II; requirements of most STEM-degrees) reporting that their confidence, interest, and enjoyment of mathematics did not decrease after the first course in calculus, and that these students primarily planned to continue studying calculus (and thus continue studying STEM) after taking the first course1 .

Overall, based on these measures, we did not see great evidence of success in college calculus across the country. Among the students surveyed, we saw significant decreases in confidence, enjoyment, and interest in continuing to study mathematics [8], and we found that nearly 18% switched out of the calculus sequence after taking differential calculus [12]. The main reasons for switching out of the calculus sequence given by students were changing their majors and no longer needing to finish the sequence, not having the time and effort to put into calculus to do well, and having a negative experience in differential calculus. Women students switched out at significantly higher rates than men, and disproportionately credited a lack of confidence in their mathematical abilities as the reason why [12].

From the 213 schools that participated in the CSPCC survey, we identified 18 schools that showed promise, including community colleges, Bachelor's-granting, Master's-granting, and PhD-granting schools. We conducted case studies at these sites, and based off of these case-studies have identified a number of components of calculus programs potentially related to student success. A collection of these findings can be found on our project website, www.maa.org/cspcc. For this paper, I focus on the findings that have had the most direct impact on the follow up study, PtC. From the five doctoral-granting departments we visited, we identified seven features that were common and that we believed were related to their success [13]. These features are: a coordinated calculus program, collection and use of local data to inform changes to the calculus program, rich and engaging curriculum, support of active learning, teaching preparation of the graduate students involved in the program, tutoring centers and other supports available for students, and adaptive placement systems into the calculus program. Since publishing those findings, we have seen a number of calculus programs across the country use these findings to guide improvements to their own programs, showing the impact that such studies can have on shifting the national landscape of calculus education.

I am confident these features provide concrete aspects of calculus programs that departments can focus their improvement efforts on, and that these are likely to lead to some improvements. However, I have recently argued [14] that it is also likely that focusing on these aspects alone can lead to programs making improvements that better serve the populations of students already being supported through calculus programs. In **Table 1**, I provide demographic data of the students earning Bachelor's degrees in any major, and specifically in STEM, from each school near the time of our data collection in 2010 from the five universities visited.

**Table 1** highlights the low population of students of color at the institutions visited, and the lack of STEM degrees earned by women of all ethno racial backgrounds and students of color of both sexes. The percentage of students who switched out of the calculus sequence at these institutions varied drastically by institution, from as low as 2% at one technical institutions to 30% at one large, public. However, the trends of women students switching at higher percentages than men and low enrollment by students of color are common across each of these sites. A deficit-oriented interpretation of this data would argue that these differences in interest, success, and persistence by different student populations are due to internal deficiencies of some populations of students, playing into common

**141**

*Towards a Forward-Thinking College Calculus Program DOI: http://dx.doi.org/10.5772/intechopen.87940*

Asian and Native Hawaiian/ other pacific Islander

Percent American Indian/

Alaska Native

*2009 in parenthesis).1*

*1*

*2*

**Table 1.**

STEM as white, Asian, and male students [15].

*IPEDS data retrieved from: https://nces.ed.gov/ipeds/datacenter/Data.aspx*

*university; PTU, public technical university; PTI, private technical institute.*

stereotypes of women and students of color not being as good at or as interested in

*Percentage of bachelor's degrees earned in 2009 (percentage of bachelor's degrees earned in STEM fields in* 

*University pseudonyms follow those given in [8]: LPU1 and LPU2, large public universities; LPrU, large private* 

Total 620 (542) 6473 (1822) 5323 (2004) 1073 (816) 6864 (1350) Woman 26.1 (23.7) 51.2 (29.9) 52.5 (43) 21.7 (15.2) 50.9 (23.7) White, non-Hispanic/Latinx 79 (80.1) 67.4 (62.7) 31 (26) 87.2 (88.4) 87.3 (87.2) Hispanic/Latinx 3.4 (3) 4.6 (2.5) 10.9 (8.1) 1.6 (1.5) 3.2 (2.1) African American and Black 1.8 (1.7) 5.7 (3.8) 1.6 (1.0) 1.5 (1.2) 0.5 (0.4)

**PTI2 LPU1 LPU2 PTU LPrU**

6.9 (6.8) 12.3 (17.0) 43.2 (52.2) 1.1 (1.2) 3.3 (3.8)

0.5 (0.4) 0.9 (0.5) 0.5 (0.5) 0.7 (0.5) 0.8 (1.0)

An anti-deficit interpretation rejects this assumption and rather assumes (1) that women and students of color can thrive in STEM, (2) that the disproportionate enrollment of white and Asian students, and disproportionate persistence of men indicate a failure of the system and not of the students, and (3) we can learn how to better support women and students of color to thrive in STEM by studying the

The enrollment and persistence data indicates that the five schools we visited, and that we based our "features of successful calculus programs" (which have come to shape improvements to calculus programs across the country) were based on programs serving a predominantly white and Asian, male student population. That is, the demographics of the students in these calculus programs were predominantly white and Asian men and women students, and the students persisting through the sequence were disproportionately men of all races and ethnicities. Knowing this information and coming from an anti-deficit perspective, I argue that the seven features can only offer possible improvements for calculus programs when considered in conjunction with diversity, equity, and inclusion practices. Diversity practices refer to actions done within the calculus program and mathematics department that attract and retain a diverse population of students. Equity practices refer to actions that (1) acknowledge the multiple ways in which some people face barriers (both visible and invisible) to their success, and (2) work to dismantle these barriers [17, 18]. Inclusion practices refer to actions that support the full participation of a diverse student population within the classroom community and within the broader departmental and institutional communities. By focusing on the original seven characteristics alone, departments may foster inequities by further supporting the populations of students who are already successful in calculus. Instead, departments should explicitly implement diversity, equity, and inclusion practices while also

women and students of color who are already thriving in STEM [16].

improving their programs through focus on the seven characteristics.

As a follow-up project to CSPCC, the PtC project has identified 12 research-oriented mathematics departments implementing a combination of the seven features in the Precalculus and calculus programs. For the PtC project, we used IPEDS data to very purposefully consider the demographics of the students enrolled at the schools, and the demographics of the students graduating with STEM degrees,

<sup>1</sup> The surveys used can be found at [11].

*Towards a Forward-Thinking College Calculus Program DOI: http://dx.doi.org/10.5772/intechopen.87940*


*1 IPEDS data retrieved from: https://nces.ed.gov/ipeds/datacenter/Data.aspx*

*2 University pseudonyms follow those given in [8]: LPU1 and LPU2, large public universities; LPrU, large private university; PTU, public technical university; PTI, private technical institute.*

#### **Table 1.**

*Theorizing STEM Education in the 21st Century*

continue studying STEM) after taking the first course1

confidence in their mathematical abilities as the reason why [12].

can have on shifting the national landscape of calculus education.

I am confident these features provide concrete aspects of calculus programs that departments can focus their improvement efforts on, and that these are likely to lead to some improvements. However, I have recently argued [14] that it is also likely that focusing on these aspects alone can lead to programs making improvements that better serve the populations of students already being supported through calculus programs. In **Table 1**, I provide demographic data of the students earning Bachelor's degrees in any major, and specifically in STEM, from each school

near the time of our data collection in 2010 from the five universities visited. **Table 1** highlights the low population of students of color at the institutions visited, and the lack of STEM degrees earned by women of all ethno racial backgrounds and students of color of both sexes. The percentage of students who switched out of the calculus sequence at these institutions varied drastically by institution, from as low as 2% at one technical institutions to 30% at one large, public. However, the trends of women students switching at higher percentages than men and low enrollment by students of color are common across each of these sites. A deficit-oriented interpretation of this data would argue that these differences in interest, success, and persistence by different student populations are due to internal deficiencies of some populations of students, playing into common

both differential and integral calculus (typically called Calculus I and Calculus II; requirements of most STEM-degrees) reporting that their confidence, interest, and enjoyment of mathematics did not decrease after the first course in calculus, and that these students primarily planned to continue studying calculus (and thus

Overall, based on these measures, we did not see great evidence of success in college calculus across the country. Among the students surveyed, we saw significant decreases in confidence, enjoyment, and interest in continuing to study mathematics [8], and we found that nearly 18% switched out of the calculus sequence after taking differential calculus [12]. The main reasons for switching out of the calculus sequence given by students were changing their majors and no longer needing to finish the sequence, not having the time and effort to put into calculus to do well, and having a negative experience in differential calculus. Women students switched out at significantly higher rates than men, and disproportionately credited a lack of

From the 213 schools that participated in the CSPCC survey, we identified 18 schools that showed promise, including community colleges, Bachelor's-granting, Master's-granting, and PhD-granting schools. We conducted case studies at these sites, and based off of these case-studies have identified a number of components of calculus programs potentially related to student success. A collection of these findings can be found on our project website, www.maa.org/cspcc. For this paper, I focus on the findings that have had the most direct impact on the follow up study, PtC. From the five doctoral-granting departments we visited, we identified seven features that were common and that we believed were related to their success [13]. These features are: a coordinated calculus program, collection and use of local data to inform changes to the calculus program, rich and engaging curriculum, support of active learning, teaching preparation of the graduate students involved in the program, tutoring centers and other supports available for students, and adaptive placement systems into the calculus program. Since publishing those findings, we have seen a number of calculus programs across the country use these findings to guide improvements to their own programs, showing the impact that such studies

.

**140**

<sup>1</sup> The surveys used can be found at [11].

*Percentage of bachelor's degrees earned in 2009 (percentage of bachelor's degrees earned in STEM fields in 2009 in parenthesis).1*

stereotypes of women and students of color not being as good at or as interested in STEM as white, Asian, and male students [15].

An anti-deficit interpretation rejects this assumption and rather assumes (1) that women and students of color can thrive in STEM, (2) that the disproportionate enrollment of white and Asian students, and disproportionate persistence of men indicate a failure of the system and not of the students, and (3) we can learn how to better support women and students of color to thrive in STEM by studying the women and students of color who are already thriving in STEM [16].

The enrollment and persistence data indicates that the five schools we visited, and that we based our "features of successful calculus programs" (which have come to shape improvements to calculus programs across the country) were based on programs serving a predominantly white and Asian, male student population. That is, the demographics of the students in these calculus programs were predominantly white and Asian men and women students, and the students persisting through the sequence were disproportionately men of all races and ethnicities. Knowing this information and coming from an anti-deficit perspective, I argue that the seven features can only offer possible improvements for calculus programs when considered in conjunction with diversity, equity, and inclusion practices. Diversity practices refer to actions done within the calculus program and mathematics department that attract and retain a diverse population of students. Equity practices refer to actions that (1) acknowledge the multiple ways in which some people face barriers (both visible and invisible) to their success, and (2) work to dismantle these barriers [17, 18]. Inclusion practices refer to actions that support the full participation of a diverse student population within the classroom community and within the broader departmental and institutional communities. By focusing on the original seven characteristics alone, departments may foster inequities by further supporting the populations of students who are already successful in calculus. Instead, departments should explicitly implement diversity, equity, and inclusion practices while also improving their programs through focus on the seven characteristics.

As a follow-up project to CSPCC, the PtC project has identified 12 research-oriented mathematics departments implementing a combination of the seven features in the Precalculus and calculus programs. For the PtC project, we used IPEDS data to very purposefully consider the demographics of the students enrolled at the schools, and the demographics of the students graduating with STEM degrees,

when selecting the 12 institutions involved in our study. This resulted in a number of institutions serving a more racially and ethnically diverse student population, and with a few of those institutions implementing programs specifically designed to support women and/or students of color and/or first-generation students to be successful in STEM. This work is ongoing, and we are in the process of learning more about these programs so that we can share more about them with others schools. One disappointing finding in our recent work has been the general lack of programs geared to increasing the diversity in STEM among research-oriented math departments across the country; while there were programs at the university and college level developed to foster diversity, equity, and inclusion in STEM, there were very few programs at the department level [19].
