A Culturally Responsive Math Program: A Case Study in a Rural Tribal College in the United States

Abstract

For many Native American students, the thirty-seven existing tribal colleges improve their access to post-secondary education, especially for those living in reservation communities and surrounding rural areas. They also support tribal nations’ goals of offering accredited degree programs, as well honoring Indigenous knowledge. This is important for students enrolled in STEM courses since Native Americans are under-represented in these fields. In the early 2000s, Chief Dull Knife College (CDKC), the tribal college of the Northern Cheyenne Nation, was supported by National Science Foundation funding in developing a new math program to meet the unique cultural and instructional needs of its students. In this case study of a culturally responsive math program, we hypothesize that students participating in the new developmental math program attempt and earn more credits compared to cohorts participating in previous math programs and take less time on average to reach college-level math. We present information on the math outcomes of the participants in two variations of the math program reforms that have addressed the obstacles to student retention and achievement. The panel data available include students’ demographic characteristics, placement test scores, and math course grades and the credits for all students enrolled from 2006 to 2019. While the number of credits attempted or earned did not differ statistically across the cohorts, the qualitative data further show that the students appreciate the culturally responsive aspects of the program. Ultimately, we have found that these aspects resulted in increased confidence of the students in their academic skills, stronger Native identities and engagement as students, as well as an improved sense of belonging in this higher education environment, all of which were important goals of the developmental math program.

1. Introduction

For many Native American students, tribal colleges have an important role in higher education. Thirty-seven tribal colleges improve the access to post-secondary education for Native students, especially those living in reservation communities and rural areas (Bryan, 2019; Cole, 2006). These colleges, created by US legislative acts in the 1970s, expanded the control of Native American tribal nations over their education, resulting in the establishment of tribal colleges and universities (TCUs), which numbered 35 by the early 2000s (Cole, 2006). Today, most TCUs, which are chartered by tribal nations and located on reservation lands, receive federal funding to support their operations and student assistance needs (Cole, 2006).

Tribal colleges support the goals of tribal nations by offering their communities opportunities to learn about Native knowledge and practices. These include studying subjects such as Native languages, history, culture, and art. Additionally, tribal colleges honor the cultural knowledge and perspectives that students bring to learning STEM—science, technology, engineering, and math—in which Native Americans are one of several under- represented minorities (Ward et al., 2020). Most importantly, more than half (57%) of employed Native Americans with science and engineering degrees in 2019 had attended a community college (National Science Foundation, 2021a), which suggests that community and tribal colleges have an important role in minority STEM education. In this paper, we present a case study of the effects of a culturally responsive math program developed for a tribal college population which was specifically intended to provide culturally relevant instructions and support for student achievement in a STEM field.

Although the overall college enrollment of minority students has increased in the United States, college enrollment rates vary considerably by race and ethnicity, increasing for some groups but lagging for others. For example, the enrollment rate of 18- to 24-year-old American Indian1 and Alaskan Natives in 2000 did not differ substantially from that in 1990 (16% vs. 19%) (Musu-Gillette et al., 2017). However, while there was a substantial increase in enrollment in 2010 (41%), this rate had declined by almost half by 2020 (U.S. Department of Commerce, 2021). By comparison, college enrollment rates have increased each decade for young Hispanic adults to more than 35% in 2020. Not surprisingly, college graduation rates also vary by race and ethnicity. Among 25- to 29-year-olds in 2022, 56% of white and 78% of Asian young adults had completed an associate’s degree or higher, while 29% of American Indian and Alaska Native, 36% of Black, and 34% of Hispanic youth had completed an associate’s degrees or higher (U.S. Department of Commerce, 2022).

Disparities by race and ethnicity in STEM degree attainment also persist. According to the National Science Foundation (NSF), the under-representation of American Indian and Alaskan Native science degree earners has not changed significantly over the past two decades (National Science Foundation, 2017, 2021b). Additionally, the results from the Survey of American Freshmen in 2014 indicate that about 30% of American Indian and Alaskan Native freshmen enrolled in four-year colleges reported the intention to major in science and engineering, compared to 45% of Latino, 40% of African American, 54% of Asian, and 40% of white freshmen (National Science Foundation, 2017). Notably, two-year colleges play a significant role in Native American student enrollment and degree completion (Trahant, 2015). In 2018, American Indian and Alaskan Native college students were the most likely minority group to be enrolled full time in two-year institutions (National Science Foundation, 2021b).

Tribal college students often begin their enrollment in college with poor preparation in math (Guillory, 2009; Postsecondary National Policy Institute, 2018). At Chief Dull Knife College (CDKC), the two-year tribal college of the Northern Cheyenne Nation in rural Montana, placement tests indicate that over the past 15 years, more than 90% of students have been placed in pre-college math courses when they have first enrolled. As a result, most CDKC students take developmental math skill courses to work toward meeting the college-level math course requirements. This extends the time it takes for students to complete their degrees. For example, only 34% of the 2011–2012 cohort graduated within 200% of the expected time frame.

In the early 2000s, CDKC math instructors used funding from a National Science Foundation (NSF)-funded project to develop solutions for the math instructional needs of their students. This included implementing curriculum reforms to support increased mastery of math skills in students and progress toward meeting the math requirements for degree attainment, as well as enhancing student interest and participation in innovative science research programs at the college. This paper presents an instrumental case study (Creswell, 2007; Lune & Berg, 2017) focusing on a culturally responsive math program designed to address the instructional needs of students in the context of the Northern Cheyenne tribal college and community. Culturally responsive instruction includes attention to and support for students’ cultural identities and brings relevant social and cultural approaches and methods into the classroom as tools for effective instruction and learning (cf. Castagno & Brayboy, 2008; Ladson-Billings, 1995).

Our research questions concern how effectively the reforms of the new developmental math program have supported student performance at CDKC. We present information on the key math outcomes for students who have experienced variations of the math program reforms developed by the faculty at CDKC to address some of the key obstacles to student retention and achievement. Qualitative research published previously (Ward et al., 2014b) on the early program reforms indicated that participants in the math program reforms at CDKC reported increased engagement in math, confidence in their math and science skills, and more positive student identities. However, we can now quantitatively examine the academic performance outcomes of CDKC students in relation to these math program reforms. Additional qualitative elements of the case study data contextualize and support the outcome analyses by providing updated student assessments of the recent forms to the math program. This research sheds light not only on the obstacles faced by Native American students but also on several promising solutions that instructors developed from student feedback, assessment data, and their own observations. Given the focus on minority student math achievement, this study’s findings are relevant to other tribal colleges where students face similar challenges concerning retention and academic progress in math, as well as to other minority-serving institutions, community colleges, and open-enrollment universities.

2. The Relevant Literature

Native American students are the racial and ethnic group tracked in post-secondary American education most likely to be affected by poverty and limited access to educational opportunities. Mosholder and Goslin (2013) identified five factors that can mitigate the effects of poverty and limited access to educational opportunities and improve college persistence: skill development, family and peer support, appropriate role models, the awareness and use of financial aid, and a culturally sensitive school environment. These factors closely align with the Family Education Model (HeavyRunner & DeCelles, 2002) for Native American college student retention and success, according to which other important factors include better academic advising; goal setting, including progress monitoring and regular feedback; faculty support, tutoring, and mentoring; culturally and socially relevant instruction; and family and community support. The authors identified these contextual factors as pivotal—an especially important element for minority students that some researchers (e.g., Ovink & Veazey, 2011) say previous college retention models have neglected.

Other research has identified strategies to help eliminate obstacles that are specific to math achievement among minority students, such as poor preparation in high school (Guillory, 2009). Strategies for overcoming such obstacles include increased student control over their learning activities and mastery-based instruction (Boggs et al., 2004), as well as reduced math anxiety (Clute, 1984; Collins, 1996). In a recent review of the research on culturally responsive math instruction, Abdulrahim and Orosco (2020) identified several critical factors that support minority students’ math achievement. Among these are creating learning environments, including teaching and learning practices, that provide an interface between students’ lived experiences and math activities which, in turn, promotes comprehension and math identity. Additionally, culturally responsive teaching incorporates interaction styles that support students’ cultural identities and promote math learning. Importantly, the culturally responsive learning context created by teachers engages students by responding to their socio-emotional and cognitive needs, challenges them, and maintains high expectations (pp. 12–18). Kolovou’s (2023) review of the related literature indicates that a combination of subject content knowledge, pedagogical content, and cultural knowledge is important for effective mathematics instruction for minoritized students (p. 155). Abrams et al. (2013) have also asserted the importance of educating all STEM teachers to be culturally responsive and the need to address the implicit power narrative in the ways STEM subjects are taught and learned (pp. 10–11). These contributions to the literature point to the central values that Kirkness and Barnhardt (1991) call “the four Rs” of higher education for Native students: relevance, respect, reciprocity, and responsibility. Two additions, representation and relationship, were supported in related research by Tsosie et al. (2022).

Within the context of tribal schools and communities, an important influence on student retention and performance is the perception of the relevance of skills and knowledge, including math and science obtained in higher education, to students and their communities (Ward et al., 2014a, 2014b). Nam et al. (2013) add that relevant and meaningful instruction and attention to place as a context for learning are important elements in effective STEM instruction for Indigenous students. Likewise, when the knowledge and perspectives that students bring to their college learning are respected and faculty and staff engage in reciprocal relationships with students and take responsibility for supporting their success, student performance and retention are positively affected (Kirkness & Barnhardt, 1991). Joseph and Windchief (2015) posit that Native American college student success is the result of student empowerment founded in both their home communities and their new communities of higher education. In these contexts, the key elements for success are the relationships, cultural resources, and identities that provide support as students navigate their higher education journey.

The model developed by Joseph and Windchief (2015) builds on others offered by Native scholars that have focused on the special significance of cultural and social elements for Native American students in an academic environment. Most Native American students attend public schools, which often fail to provide the supportive environment needed by minority students to succeed (Clarren, 2017; Postsecondary National Policy Institute, 2018). In fact, Native American students enrolled in majority white higher education institutions often report experiences with isolation, stereotype threat, bullying, and discrimination (Postsecondary National Policy Institute, 2018).

In contrast, tribal college missions include incorporating social services and student support, as well as culturally responsive teaching methods and cultural activities, which provide linkages between the college and the tribal community (Stein, 1999; Cole, 2006). While Native American faculty and staff can positively affect Native students, research on Native American schooling indicates that non-Native instructors who are sensitive to the needs of Native students can also provide effective instruction and mentoring (Hermes, 2005; Brayboy et al., 2014; Ward et al., 2014a). These instructors create a pedagogical space that engages both Western (i.e., non-Indigenous) and Native perspectives in teaching and learning (Abrams et al., 2013; Davidson et al., 2018).

Thus, central to the possibility of supporting Native American students in tribal colleges is the notion of culturally responsive pedagogy (Ladson-Billings, 1995). Gloria Ladson-Billings founded culturally responsive pedagogy on three main principles: teachers’ “conceptions of self and others”, “the manner in which social relations are structured” by teachers, and teachers’ “conceptions of knowledge” (p. 478). A key element of culturally responsive pedagogy is that it addresses the local cultural context, which means that work must be carried out to carefully understand how these principles apply in any given setting. Thus, extensive research has been undertaken to understand how and in what ways culturally responsive pedagogy might apply to Native American students (Castagno & Brayboy, 2008). We briefly review some of this literature and describe how its findings relate to these foundational principles of culturally responsive pedagogy.

Related to the first principle of culturally responsive pedagogy, teachers’ conceptions of self and others, tribal college instructors often use instructional and mentoring strategies to eliminate the obstacles to school engagement and performance that result from poor academic preparation in math and science or from limited access to secondary-level STEM courses (Ward et al., 2014a, 2020; Adelman et al., 2013). These strategies are tailored to particular tribal contexts. Some strategies included active experimentation, apprenticeships, internships, and methods that highlight learning, cooperation, and visual–spatial and interactive learning (More, 1989; Wilson, 1998; Swisher & Deyhle, 1989; Van Hamme, 1995; Ward et al., 2022). Particularly valuable on this front are mentoring relationships that mirror traditional relations with elders (e.g., Lipka et al., 2005).

The next principle of culturally responsive pedagogy involves structuring social relations in a supportive way. For learning math, group instruction and peer mentoring have shown promising results (Hooker, 2010; Larimore & McClellan, 2005; Lundberg, 2007; Schmidtke, 2010). What is more, recent efforts by community colleges typically serving students with academic needs find that restructuring the instructional time or the math curriculum itself can support student performance and persistence (Community College Research Center, n.d.). Thus, the structure of social relations changes at the level of individual interaction (groups, etc.) and also at the level of the curriculum. Notable among these higher-level changes are modularizing the instructional units, self-paced computerized instruction, math course “pathways” tailored to students’ academic goals, and accelerating the developmental course sequence (Rutschow et al., 2019; Moussa & Bickerstaff, 2019; Bickerstaff et al., 2016). Additionally, culturally based instruction and problem-solving facilitate and strengthen learning (Rutschow et al., 2019; Larimore & McClellan, 2005; Huffman, 2001). This indicates that culturally relevant support to Native students (Kirkness & Barnhardt, 1991) requires both positive relationships and the redistribution of resources (Harris & Wasilewski, 2004).

Finally, related to the principle of teachers’ conceptions of knowledge, the existent research highlights the importance of tribal sovereignty. This is consistent with Tribal Critical Race Theory (Brayboy, 2005), which focuses attention on several elements of school dynamics, especially the central role of student experiences, tribal cultural knowledge, and perspectives in the development of relevant solutions to higher education issues. Research involving Native students also indicates a unique phenomenon related to knowledge: instead of wanting to obtain a degree and leave their rural communities to pursue work opportunities, Native students often express an interest in returning to their communities to use their skills and knowledge after they complete their degrees (Brayboy, 2005; Guillory, 2009; Huffman, 2011; Ward et al., 2014a). Therefore, improving the retention and graduation of Native college students has important implications for students wanting to bring valuable skills to their tribal nations and communities (Brayboy et al., 2014). Thus, programs are more culturally responsive when they take community needs into account and focus on knowledge that is useful to the community rather than solely in the service of mastering an academic subject or even individual career advancement.

Overall then, culturally responsive programs for Native American students seem to change teachers’ conceptions of self and others by reimagining their relationships, especially their mentoring relationships. These approaches restructure social relations at the individual and curricular levels to support new relationships and ensure access to resources. And, finally, they have a primary aim of connecting knowledge to community goals and cultural values. With this in mind, we turn toward describing our research context.

3. The Research Context

The case study presented in this paper examines the effects of culturally responsive math program reforms on the progress toward meeting the associate degree requirements among students attending Chief Dull Knife College. Because about 90% of CDKC students are Native American and most are first-generation college students from low-income families, this tribal college has a unique opportunity to avoid the types of social and cultural barriers typical of the experiences of Native American students attending majority white higher education institutions (Guillory, 2009). Additionally, it can proactively address students’ academic needs. Since about half of the students enrolled at CDKC tested below (and many tested well below) the college level in their math skills, the majority of those tested were placed in pre-college math courses (e.g., an average of 90% between 2014 and 2019) (Chief Dull Knife College (CDKC), 2019). CDKC’s student enrollment averages from 200 to 300 full- and part-time students each semester, at least half of whom are full-time students, and the majority are female. The characteristics of CDKC’s students did not change substantially over the 15-year period relevant to this study. In addition, about 30 Associate of Arts and Science degrees are awarded annually. While most students report that they plan to graduate from CDKC, about 50% also intend to transfer to four-year degree programs following graduation.2

Math Retention and Completion Issues and Solutions

The experiences of CDKC students related to math performance are reflected in course data from the last 20 years. To illustrate the need for math reform, data for the early 2000s showed that an average of 50% of CDKC’s students withdrew from or failed their math courses and that repeating courses hindered the students’ progress toward completing their degree requirements. To address this, an NSF-funded project was designed to strengthen the math curriculum and address issues such as the inadequate preparation of new students, poor student placement in math courses, instructional inconsistency, culturally incompatible instruction, inadequate out-of-class support, and inconsistent skill levels.

A major task of the project included creating a series of developmental skill classes that utilized a new instructional approach—a self-paced, interactive, computer-based program for students placed at four different math skill levels (Adult Basic Education, Basic Math, Introduction to Algebra, and Intermediate Algebra). Other new key features of the program included a new math placement test and academic advising designed to improve their math course placement. The goal was for the students to demonstrate proficiency at each level to continue through the sequence of pre-college courses until they were eligible to enroll in a college-level math course. Additional elements designed to provide support to the math students included additional math instructors, tutors, and a Math Learning Center available to students to work on math at any time during the school day. The initial curriculum developed between 2000 and 2005 improved the consistency of instruction and course expectations, course content, and instructor feedback and provided ongoing support for student performance.

Additional reforms between 2006 and 2012 included flexible credits which allowed students to complete one credit and then enroll in the next credit at no cost during the same semester, better use of the computerized math program (e.g., tutorials), and regular instructor feedback to students. Additionally, the faculty became more proactive in helping students set goals and timelines for completing their math course credit requirements, monitoring their progress, and recognizing students’ achievements. A critical challenge that continued during this period, however, was that the number of math instructors varied, and for several years, only two full-time math faculty members were available. This made fully staffing the Math Learning Center difficult.

During the final period of program development (2013 to 2019), the program’s key features were stabilized. Importantly, the addition of a third full-time math instructor increased the math faculty’s time in the Math Learning Center and the opportunities for mentoring and the use of culturally relevant learning activities. Other central features of the program included improved math skill testing, course placement, monitoring of student progress by faculty, and weekly feedback to the students, which addressed the kinds of curriculum-level restrictions to social relations mentioned above. Additionally, the faculty and advisors helped students to identify and plan for their enrollment in math courses needed for their transfer to four-year programs. The other improvements finalized during this period provided for additional instruction in number theory, graphing, and linear systems and the instructors’ use of relevant math and science problems, emphasizing how these concepts related to tribal and community issues. Central to the goals of the developmental math program remained improving students’ math performance and experiences with math, including increased engagement and improved attitudes towards math.

One important contextual feature of this phase of finalizing the current math program is the extensive experience of the CDKC faculty in teaching math at the secondary and post-secondary levels in local K-12 and tribally controlled schools. Another is the contribution of the relevant research on math instruction, culturally relevant pedagogy, and learning among tribal college students which informed the CDKC faculty’s work on the math program reforms (e.g., Hooker, 2010; Topham, 2022). Specifically, the faculty’s experiences with the instruction of Native American K-12 and undergraduate students informed the development of the proactive mentoring approach, which was amplified in the newest version of the math program (2013–2019). This approach is consistent with the traditional role of Cheyenne elders in the instruction of youth through mentoring and learning by doing (Weist, 1997; Ward, 2005). Additionally, independent evaluation research funded by the college’s NSF-funded project provided program assessment data for use by the project staff and faculty. This included de-identified qualitative interview and survey responses included in the annual assessments available to the researchers. The evaluation team utilized the Indigenous Evaluation Framework (LaFrance & Nichols, 2009), which was developed with National Science Foundation support to the American Indian Higher Education Consortium (AIHEC). This approach focuses on telling “the story” of a project as it unfolds and using both qualitative and quantitative data appropriate for representing the perspectives of all stakeholders and participants. Of particular importance is the use of these evaluation data to provide feedback on the progress of the project in meeting its goal of improving the experiences of tribal college students with learning math.

4. Research Questions

The primary research questions for this study are as follows: (1) How do the effects of the new culturally responsive math program on the number of math credits attempted and earned compare for two cohorts of CDKC math program participants? (2) How do the effects of the new culturally responsive math program on reducing the amount of time it takes students to reach college-level math compare for two cohorts of CDKC math program participants? (3) To what features of the program do students attribute positive program experiences and/or other benefits? We hypothesize that students participating in the final developmental math program attempt and earn more credits compared to student cohorts participating in the previous math program at the college and take less time on average to reach college-level math.

5. Materials and Methods

The instrumental case study presented focuses on a culturally responsive math program for a specific population of tribal college students who have experienced a range of obstacles to math learning and the math program reforms designed to address these issues. Case study research designs are especially useful for the purpose of gaining detailed, contextualized data related to a specific purpose, such as program evaluation (Creswell, 2007; Lofland et al., 2006; Patton, 2015; Lune & Berg, 2017). The panel data available from CDKC for the analyses included students’ demographic characteristics, placement test scores, and math course grades and the credits for all students enrolled in the academic year from 2006 to 2019. These institutional data were provided by the CDKC Student Affairs Department as part of annual program evaluations of students’ progress in STEM courses.

The composition of the student body enrolled in math courses during this time period included degree-seeking college students and high school students preparing for college, as well as non-degree-seeking students. The academic year at CDKC comprises a short summer term and two regular semesters, fall and spring. The primary dependent variable is the completion of a college-level math course. The primary independent variable is the math program that the two cohorts of students experienced: Cohort 1, the first revised developmental math skill program implemented in 2006–2012, and Cohort 2, the final stable version of the math skill program implemented in 2013–2019. The cohort was determined by the year and semester/term in which a student first enrolled in a math course and when their last recorded enrollment occurred within the time period and the data available for the analysis. To compare the effects of participation in the two math programs, students who took courses in both programs were excluded from the analyses.

Other independent variables included the students’ initial math placement scores, the number of semesters/terms in which math credits were taken, continuous or non-continuous enrollment, and students’ self-reported gender, ethnicity, and age, all of which were obtained from college records. Two variables, the number of developmental math credits attempted and the number of credits earned, are important independent variables as well. They represent the extent to which the math program reforms promote increased student enrollment in and completion of math credits. As such, these variables also indicate a preliminary effect of the math program reforms related to math course behaviors. These measures are particularly relevant given the history of CDKC students’ struggles with the completion of math course credits, as discussed above.

Due to the panel nature of the data, the age of each respondent was calculated based on their first year of developmental math enrollment minus their birth year. Continuous enrollment is treated as an indicator variable, with continuous enrollment being 1 and non-continuous enrollment being 0; non-continuous enrollment indicates that the student was not enrolled in each consecutive term since their initial enrollment during 2006–2019. The number of math credits attempted was determined from the number of credits in which a student enrolled during each semester/term, and the math credits earned were then determined from the number of credits a student passed in each semester/term within the time period and the data available for the analyses. College math attainment is an indicator variable, with 1 indicating that the student reached college-level math during 2006–2019 and 0 indicating that they did not. Students were attributed a 1 or a 0 depending only on whether they had enrolled in a college-level math course at any point in their enrollment within the time period for the analyses. The number of semesters/terms of math enrollment was determined from the number of semesters/terms for which a student was enrolled in at least 1 credit until they reached college-level math or had no other enrollments during this time period for the analyses. Both gender and ethnicity were constructed as indicator variables, with female and Native American as 1 and everything else as 0.

6. Analytic Strategies

6.1. The Quantitative Analytic Strategy

Our first two research questions rely on quantitative data to investigate the differences between Cohorts 1 and 2 for students in the developmental math program and include students initially placed into a college-level math course through the placement exams. Students enrolled in both Cohorts 1 and 2 were excluded from the analyses. In addition, the students included in the sample had been enrolled during the years 2006–2019 and had no missing data. This resulted in a sample size of 815 students. As the residuals of the data did not meet the assumption of normality required for an ANOVA and we were comparing two groups, we utilized the Mann–Whitney U nonparametric test. To complement the Mann–Whitney U tests, chi-square tests were utilized for the analysis of the categorical variables.

6.2. The Qualitative Analytic Strategy

To answer our third research question, we drew on qualitative interviews with students carried out during the later years of the program. These interviews were available for the years 2016 through 2019 and 2021 through 2024. Interview data were not available for 2020 due to the pandemic (see Ward et al., 2018, 2021, 2022, 2024; Ward & Solomon, 2024). The initial analyses used inductive coding to identify emergent themes related to students’ experiences based on the approaches to analyzing case-based evaluation data recommended by the Indigenous Evaluation Framework (LaFrance & Nichols, 2009; Patton, 2015; Braun & Clarke, 2022; Lofland et al., 2006). This framework advocates for incorporating data from all groups with a vested interest in a program. It emphasizes the importance of using various types and sources of data to present the program’s story in a way that accurately reflects the interests, values, and perspectives of the community. This approach aligns with grounded theory methods, utilization-focused evaluation, Garroutte’s (2003) work on Native identities, and Brayboy’s (2005) focus on sovereignty and culture. In the final stages of the analysis, coders used a priori codes developed from the principles of culturally responsive pedagogy and their knowledge of the math program to connect the emergent themes with the aims of this paper.

7. Results

7.1. Descriptive Statistics

Our analyses compare two student cohorts to show the effects of the initial revised math program (Cohort 1: 2006–2012) and the final stable version of the program (Cohort 2: 2013–2019). These cohorts represent developmental math programs that included different reforms. Therefore, comparing the outcomes for students who are similar in their key background characteristics but who differ in the math program that they experienced should indicate which program is more effective for supporting developmental math credit completion.

Table 1. Descriptive statistics of sample.

	Cohort 1 (N = 370)			Cohort 2 (N = 445)
	Mean	%	SD	Mean	%	SD
Credits Attempted	4.73		4.30	5.28		5.22
Credits Earned	3.11		3.60	3.29		4.39
College-Level Math Attainment
Attained		22.43%			19.33%
Not Attained		77.57%			80.67%
Terms Taken to Reach College Math	7.33		4.26	6.45		4.45
Terms Taken and Has Not Reached College Math	14.24		15.48	6.56		6.72
Age	27.21		10.14	25.65		10.66
Ethnicity
African American		0.27%			0.45%
Caucasian		5.14%			4.94%
Hispanic		0.27%			0.22%
Native American		94.32%			94.38%
Gender
Female		59.46%			53.48%
Male		40.54%			46.52%
Math Placement Scores
Adult Basic Education		8.11%			4.27%
Basic Math		43.78%			49.44%
Intro to Algebra		29.73%			22.02%
Intermediate Algebra		18.38%			24.27%
Continuous Enrollment
Continuous		73.51%			76.40%
Non-Continuous		26.49%			23.60%

Note. Percentages reported for categorical variables.

provides the descriptive statistics for each variable included in our analysis as they relate to the two cohorts of students enrolled in the developmental math program.

The descriptive information for the central dependent variable for these analyses shows the percentages of students who reached college-level math for each cohort. These numbers suggest that a slightly greater proportion of the students in Cohort 1 attained college-level math. Other descriptive statistics on relevant variables include the number of math credits attempted and earned and the average number of semesters/terms in which students were enrolled before they reached a college-level math class. These numbers suggest that the Cohort 2 students had a higher average of math credits attempted and earned compared to these values for Cohort 1. Importantly, these numbers show that the average number of semesters/terms taken to reach a college-level math class was larger for Cohort 1 (7.33) than that for Cohort 2 (6.45), descriptively suggesting that the students in the prior program took a longer period of time to reach the college-level math requirements. This descriptive information also suggests that for students who had not reached college-level math by the time that they stopped enrolling in math courses during 2006–2019, the average number of semesters/terms in which students were enrolled was again greater for Cohort 1 (14.24) than that for Cohort 2 (6.56).

The information in Table 1 further shows that descriptively speaking, the gender composition was similar for both cohorts, with most of the students being female. The descriptive information suggests that most of the students within each cohort were Native American, while the average age varied somewhat, with Cohort 1 being slightly older, with an average age of 27.21 compared to 25.65 for Cohort 2. Descriptively speaking, the math placement scores indicate that the average placements were similar for the two cohorts: the average placement was at the basic math level, with more students in Cohort 2 placing in the basic math level.

Additionally, the descriptive information presented in Table 1 shows that for most students, their credits were “continuous”, indicating that they took credits each semester/term after they had enrolled in a degree program at CDKC between 2006 and 2019. Specifically, 73.51% of Cohort 1 and 76.40% of Cohort 2 were continuously enrolled. However, the descriptive statistics also show that most of the students within this sample had not reached college-level math (77.57% of Cohort 1 and 80.87% of Cohort 2), prompting further investigation of the potential effects of the new math program.

7.2. Quantitative Findings

The analyses below compare the students’ math performance in the two cohorts of students who experienced successive models of the developmental math program that included different reforms. The main outcome of interest, whether or not the students attained college-level math, is important because it indicates the extent to which the math program reforms facilitate a greater number of students reaching college-level math. Because our statistical analysis used a bidirectional two-cohort approach, we applied Bonferroni correction to adjust the significance threshold. As a result, the Bonferroni-corrected p-value was set at 0.025 (0.05 divided by 2) to determine statistical significance.

Comparisons of the Math Outcomes by Cohort and Student Characteristics

Table 2. Significance tests by college math attainment.

	Cohort 1		Cohort 2
	Mean	p	Mean	N
Credits Attempted	9.627	0.281	10.988	169
Credits Earned	6.566	0.094	8.291	169
Terms Taken to Reach College Math	7.325	0.095	6.453	169
Age	26.917	0.203	25.477	169
Native American	0.880	0.933	0.884	169
Female	0.735	0.007	0.535	169
Math Placement Scores
Adult Basic Education/Basic Math	0.289	0.755	0.267	169
Intro to Algebra and Intermediate Algebra	0.711	0.754	0.733	169
Continuous Enrollment
Continuous	0.627	0.985	0.628	169
Non-Continuous	0.373	0.985	0.372	169

Note. Mann–Whitney U tests performed for continuous variables; chi-square tests performed for categorical variables. Cohort 1: N = 83; Cohort 2: N = 86.

shows the analyses of the college math attainment for the student characteristics by cohort. The coefficients shown are the means for each group. Since the distribution of the data on college math attainment was highly skewed and we were comparing two categorical groups, we chose to use a Mann–Whitney U test of the significance in place of a one-way ANOVA test. The null hypothesis was that the means of the two cohorts were equal.

A descriptive comparison of the credits attempted and earned by the students in both cohorts who achieved college-level math reveals that Cohort 2 had a higher mean number of both attempted and earned credits than that in Cohort 1. However, the Mann–Whitney U test indicates no significant differences in either the credits attempted or those earned between the cohorts. This suggests that the students in Cohort 2 who reached college-level math were attempting and earning credits at a rate similar to that of their peers in Cohort 1. Furthermore, we found no significant difference in the number of semesters/terms taken by each cohort to reach college-level math.

Comparing the college math attainment by cohort for the math placement levels reveals (Table 2) that while the means between Cohorts 1 and 2 differed, the Mann–Whitney U test shows that there was no significant difference between the math placement levels for the students who attained college math in either cohort. Furthermore, we find no significant difference between continuous and non-continuous enrollment in Cohorts 1 and 2 for students who reached college-level math. We likewise find no significant difference based on the mean ages and those who identified as Native American in Cohorts 1 and 2. However, we do find a significant difference between the means of the female students in Cohorts 1 and 2, indicating that there were slightly more female students enrolled in Cohort 1 than there were in Cohort 2. The lack of a significant difference shown between the rest of the demographic characteristics of the two cohorts further indicates that any differences between the academic characteristics of the sample are due to the program changes between cohorts.

We next compared the differences between Cohorts 1 and 2 for students who did not attain college-level math before ceasing to take math courses at CDKC, as shown in

Table 3. Significance tests by no college math attainment.

	Cohort 1		Cohort 2
	Mean	p	Mean	N
Credits Attempted	3.310	0.151	3.911	646
Credits Earned	2.115	0.429	2.086	646
Terms Taken and Has Not Reached College Math	14.240	0.000	6.557	646
Age	27.289	0.000	25.691	646
Native American	0.962	0.824	0.958	646
Female	0.554	0.627	0.535	646
Math Placement Scores
Adult Basic Education/Basic Math	0.585	0.675	0.602	646
Intro to Algebra and Intermediate Algebra	0.415	0.675	0.398	646
Continuous Enrollment
Continuous	0.767	0.357	0.797	646
Non-Continuous	0.233	0.357	0.203	646

Note. Mann–Whitney U tests performed for continuous variables; chi-square tests performed for categorical variables. Cohort 1: N = 287; Cohort 2: N = 359.

. We again used the Mann–Whitney U test to test for significant differences between the means of the two cohorts. We found the difference between the number of developmental math credits attempted and earned in Cohorts 1 and 2 for students who did not reach college-level math during the time frame of the analysis to be statistically insignificant. We additionally found that the students in Cohort 2 took fewer semesters/terms compared to this number in their peers in Cohort 1. We found that the mean age of the students in Cohort 2 was younger than that of the students in Cohort 1, although the difference between the means was relatively small. We found no significant differences between the means of Cohorts 1 and 2 for ethnicity, gender, and continuous or non-continuous enrollment. This again shows that any differences between the means for the two cohorts can be attributed to program differences rather than sample characteristics.

7.3. Qualitative Findings

In this section, we provide the qualitative findings from the student interviews and surveys regarding their experiences with and views of the developmental math skill program. Similar to the student feedback on the math program reforms reported in the early years of the program (e.g., Ward et al., 2014a), the qualitative student assessments during both the Cohort 2 period (2013–2019) and in more recent years (2018, 2021, 2022, 2023, and 2024) have continued to be positive. Specifically, student feedback in these years indicates their appreciation of the mentoring and caring support received from the math seminar faculty and the accessibility of the math program format, frequently citing these aspects as integral to their increased academic achievement. These program features are culturally relevant responses designed to meet the needs of the tribal college students. In the years prior to 2020, a central theme from students’ comments represented their appreciation of these program elements, and the comments displayed their sense of belonging in the math program and the higher education environment, in addition to their increased confidence in their math skills:

“This is kinda like home; you can always come back. I mean, if I wasn’t even a student here and I came back and I asked [faculty member], “Can you help me with this math problem,” he would…. And you even make friendships with the teachers and with just the staff in general. They care about you. You’re not just a number.”

(2017)

“I’ve always known how much I like math, but it proved it at Dull Knife. Having great teachers like [the math instructor]-it’s not so bleak.”

(2018)

“Yeah, …I’ve always kind of had a hard time with math, but then [the math instructors] helped me understand it better. They all have their own formulas and they kind of make it fun, and it’s fun once you understand it.”

(2018)

In more recent years, the student feedback addressed the quality of the math instruction, which supported increased student engagement in math and their progress in completing both developmental skill and college-level math courses. These responses again reflect their strengthened confidence in their academic abilities, both within math and in continuing on to other subjects:

“[The instructor] made it really understandable, like the concepts and stuff. I was able to get through it and finish Stats. …Like I kind of want to get into college chemistry this year so I’m trying to get my pre-calc done.”

(2022)

“I love the 3 instructors, all very helpful & I’ve learned to like math because of them all.”

(2024)

Additional emergent themes indicated the student satisfaction with the format, learning environment, and accessibility of the self-paced program:

“Yeah, I like how you are supposed to be going at your pace, learn in your own way… it was user-friendly.”

(2021)

“I just love that the math lab is quiet and focused on math.”

(2024)

These findings relate to the deeper, more curricular transformation of social relations inherent in the new format of the math program, connecting again with the transformation of social relations in culturally responsive pedagogy. Similarly, in recent years, another important emergent theme reflected the students’ experiences with overcoming the challenge of being underprepared for college-level math, demonstrating the successful patterns of the program format in helping students succeed in their math coursework. Compared to past decades before the developmental program where math course failures were prevalent, this theme also speaks to a marked change in the students’ math outcomes:

“I’m sure if [the developmental skills program] wasn’t there, especially with math, I probably wouldn’t have even taken math, or I probably would have failed out of it. It’s nice to be able to, to go somewhere, where there’s always an instructor there to be able to help you.”

(2021)

“That program was, actually, really helpful. It’s all remedial stuff, but it also helps you, catches [you] up really fast … I forgot a lot of stuff, but that program really helped me like catch back up.”

(2021)

This final emergent theme does not connect as clearly to the three main principles of culturally sustaining pedagogy, except in the sense that it reveals the students’ sense of success in overcoming the extra barriers that they faced. Notable here is the fact that the students framed their experiences as primarily individual experiences.

Additional student interview and survey data, however, provide insights into the ways that the CDKC students find deeper cultural meanings in their increased success in math and science, which supported their engagement with STEM courses. When students succeed in math skills, their individual achievement is particularly meaningful because many students reported being told that “the Northern Cheyenne do not do math or science.” However, in Northern Cheyenne culture and society, while individual achievement is celebrated, its meaning involves additional cultural and social dimensions. Specifically, student accomplishments are perceived to be closely connected to family and the community, i.e., academic accomplishments reinforce successful student identities as well as Northern Cheyenne tribal identity. This is related to the importance of individual success to the extended family and has potential significance for the community’s sustainability. Preliminary research on the CDKC’s math program reforms included the family and community benefits students perceived in the early years of the program (Ward et al., 2014a). These strong linkages between individuals and their cultural community are distinctive in Northern Cheyenne society but are also found in other Native American reservation and community contexts, as discussed in the relevant literature.

Students’ success in math has prepared them for college-level courses in math and other STEM fields, as well internships in health, Cheyenne language, environmental studies, and natural resource research. Success in math expands students’ access to fields in higher education that most have previously perceived as closed to them. Importantly, many Northern Cheyenne tribal college student interviewees expressed the strong cultural goal of acquiring further education which they could bring back to the community when they returned to their reservation home. Their interests included advanced study in fields relevant to the rural Northern Cheyenne community context, such as environmental studies, healthcare, education, ranching, and agriculture. They also identified skills (e.g., the use of remote sensing technology) that they could use locally to identify sacred historical and cultural sites in their home community.

In other interview questions, the students were asked about their future education and work plans and how they may use their college experiences and degrees. Quotes from the student interviews represent how recent CDKC students perceived using the math and science skills acquired through classes and internships to give back to their community. Several quotes related to this theme are from students from Cohort 2 included in the analyses presented above, while other quotes represent recent students who also indicated their goals of using their new knowledge and skills to benefit their community.

The first set of quotes below represents the students’ interests and goals related to combining local ethnobotany knowledge with academic knowledge to improve local food systems and local water quality.

“So, if I could lead the way on bringing self-sustainability and edible food that we can grow ourselves, pesticide-free and stuff, then that’s a start for me. That’s where I want to lead.”

(2018)

“I really love ethnobotany. I want to understand wildflowers and raspberries, cranberries, all that wild stuff. Really interested in that. …. So, I want to learn from them on how to garden the right way, the smartest way.”

(2018)

“Testing the water on the reservation is really something to do because we have all of these surrounding springs. Some of them are good and some of them are bad. So that would be something to do.…. Probably would have to go look at natural resources or something.”

(2018)

The quotes in this section reflect the students’ interests in contributing to local education and local economic activities such as ranching and agriculture.

“I’m gonna be a math teacher. … I mean, that’s what I want to do.”

(2022)

“Computer mathematics. … I wanted to kind of combine business with it.”

(2022)

“I think I want to be a teacher…Maybe PE and history…Either that or an agriculture teacher.”

(2022)

“I either narrowed it down to ranching systems or animal science. I’m not too sure yet.”

(2022)

“Yeah, I’ve talked to them about planning to come back and help the reservation. I’m going into political science so I’m going to be learning more about the government and try to, like, come and help. Maybe talk to kids when I come back and tell them how things kind of shaped up the way they did since from how we were in the 1800s.”

(2023)

This final quote represents a student’s interest in using remote sensing technology to explore and document Northern Cheyenne cultural and historical sites for the tribe.

“So then we can scan over a large area and then detect… one sample of grass that looks pretty good. And then put that on a scale and then whatever is dead or way more flourishing, we could look at that. And then hopefully see if there’s like buffalo or dead buffalo there, or if it was a butchering site.”

(2024)

Overall, the students’ responses inform our final research question by indicating that the culturally responsive math program features were especially appreciated and have successfully helped the students prepare for college-level courses, specifically through caring faculty relationships, effective mentoring, and the accessibility of the program. Indeed, these themes suggest that the students largely attribute their success in math courses to the culturally responsive aspects of the math program. We find that these aspects resulted in increased student confidence in their academic skills and engagement, as well as an improved sense of belonging in this higher education environment, all of which were important goals of the developmental math program. Additional qualitative data indicate that some of the key themes related to the students’ interest in and goal of using their academic skills and higher education degrees in ways that would contribute to and support the cultural and social sustainability of the Northern Cheyenne Nation community.

8. Discussion and Conclusions

The analyses presented here reveal meaningful differences among the students participating in two successive models of the math developmental skills program at CDKC between 2006 and 2019. Although the characteristics of the students participating in each version of the math program were similar, their academic outcomes differed. Regarding our first research question, we found no statistical evidence of differences in the number of credits attempted or earned between the two cohorts, either for students who had attained college-level math or those who had not. Regarding research question 2, the effects of the new culturally responsive math program on reducing the time taken to reach college-level math show mixed results. For students who attained college-level math, there was no statistical difference in the time it took them. However, the students in the culturally responsive program completed significantly fewer semesters of developmental math compared to that completed by their peers in the earlier program. This is an important finding showing new more successful patterns of math credit completion in the students and is an important departure from the decades of student experiences with math failure at CDKC. While the number of credits attempted or earned did not differ statistically across the cohorts, Rossi et al. (2018) suggest that statistical significance is only one measure indicating important program effects. Another measure is the practical importance of the findings, which in this context indicates that the culturally responsive math program is making a difference to students’ math attainment. From the perspective of the Indigenous Evaluation Framework (LaFrance & Nichols, 2009), the exploratory goals of this evaluation research and the context are particularly important to keep in mind. In fact, qualitative data are especially useful for understanding student experiences, the meanings they give to their achievement, and the implications for their identities as Northern Cheyenne students and community members.

The qualitative data show that students found the developmental math program to be “really helpful,” enabling them to “catch up” in their math skills to the college level. The students also reported being able to complete their math courses and move forward into more advanced studies. Our third research objective was to identify the program features that the students attributed to positive experiences and benefits. The qualitative data further show that the students specifically appreciated the culturally responsive aspects of the program, including caring, individual mentoring from the math faculty (Lipka et al., 2005), and the ability of the instructors to make the course content “fun” and “understandable” through culturally responsive instructional strategies. Additionally, the students appreciated how the larger curricular transformations in the program made the program more accessible, which is related to Ladson-Billings’ focus on the transformation of social relations. The students describe these culturally responsive aspects to have led to increased academic confidence, a strengthened sense of belonging in higher education, and higher engagement and progress in the math program, all which were integral goals of the developmental math program.

Thus, the important contribution of this research is the finding that the faculty’s efforts to develop a math program that meets the needs of a specific Indigenous population of students have supported the desired benefits of facilitating students’ progress toward meeting the college requirements. Statistical significance alone does not capture the full picture. The students’ experiences highlight how program improvements, driven by the faculty’s responsiveness to the students’ needs within this cultural context, have positively impacted their attitudes and performance. A key aspect of cultural responsiveness, in the context of the Northern Cheyenne, is the role of instructors as elders, guiding students individually and in small groups to develop new skills. Trust and respect between students and these elders are essential. The instructors offer feedback and constructive support as the students practice new skills and apply new concepts. This approach aligns with traditional Northern Cheyenne cultural methods of teaching the young. However, a few limitations warrant mention. First, due to the nature of our data, these results should not be generalized to other populations. In addition, our data cannot account for factors external to the study environment that may have affected the program outcomes, such as the amount of math completion before entrance to the CDKC math course program. Furthermore, due to the academic time frame included in the analyses, we cannot account for their progress in math before and after the study period.

Just two additional differences were found in the sample characteristics. Significant differences by cohort were found for gender among those students who reached college-level math and for mean age for students who did not reach college-level math. However, the differences between these respective means were small. This indicates that any differences in the academic outcomes found were most likely attributable to program differences rather than cohort differences.

In sum, these findings indicate some positive results of the curriculum reforms made by the CDKC faculty in the developmental math skill program, which serves the large majority of Native American CDKC college students who are placed in pre-college math courses. The final version of the math program comprises key features that are consistent with supportive teaching and learning environments and effective restructuring of developmental skill courses. These include a computer-based, modularized, interactive math program that is accessible to students who need to work on their math coursework outside of class, which has been shown to be an effective aspect of developmental math programs (Rutschow et al., 2019; Moussa & Bickerstaff, 2019; Bickerstaff et al., 2016) and was appreciated by CDKC’s students. Some other recent studies have produced results that question whether such courses are superior to traditional remedial courses (e.g., Weiss & Headlam, 2019), with one specifically questioning the modularized nature of the units (Boatman, 2021). While our results should definitely be interpreted in light of all of this different evidence, the particular implementation of these systems in a tribal college is unique, and the qualitative data suggest that the students deeply appreciated these features of the program.

Additionally, the math lab environment is conducive to students having access to math faculty members who provide consistent, appropriate assistance and feedback to them. Regular feedback was also identified as an important culturally responsive factor in past research (HeavyRunner & DeCelles, 2002). Other key culturally responsive features of the program include the traditional Native American mentoring approach and the use of hands-on activities and culturally relevant content. Because students become familiar with the math instructors through classes and the time they spend in the math lab, they develop trust, rapport, and relationships with the math faculty as both instructors and elders/mentors. The students at CDKC emphasized the impact that the instructors and their teaching methods had on their math experience. Previous research has likewise supported the importance of culturally relevant mentoring relationships and instructional methods and activities as a culturally responsive strategy in academia (HeavyRunner & DeCelles, 2002; Lipka et al., 2005; Ward et al., 2014a, 2020; Adelman et al., 2013). Furthermore, as a consequence of the environment fostered in the math program, students feel free to ask for support from both faculty and their peers, as needed (cf. Ward et al., 2020, 2021; Topham, 2022). Past research has also indicated group instruction and peer mentoring to be promising culturally responsive strategies (Hooker, 2010; Larimore & McClellan, 2005; Lundberg, 2007; Schmidtke, 2010). Other program features include flexible credits that allow students to complete one credit and continue to enroll in another until they reach the required level and encouragement by faculty and advisors to set goals and timelines for completing the development skill credits that students require. Advising assistance and the correct math course placement have also improved math retention, with recent students earning more math credits in a semester/term than they had previously (Ward et al., 2020).

These curricular reforms include many of the contextual elements suggested by research focused on Native American students: the Family Education Model (HeavyRunner & DeCelles, 2002), the model offered by Joseph and Windchief (2015), and the principles suggested by Kirkness and Barnhardt (1991). Although the tribal college math faculty are not Native American, they have decades of experience in teaching Native students and working in tribal colleges and local schools serving Native American communities. As a result, their reforms are based not only on their knowledge of effective math pedagogy but also on their experiences with effective teaching and learning among Native American students. Indeed, past research has likewise shown that non-Native instructors who are sensitive to the needs of Native students can provide effective instruction (Hermes, 2005; Brayboy et al., 2014; Ward et al., 2014a). The evidence presented in this paper indicates that these strategies, now central to the current developmental math skills program, not only support a positive, culturally responsive learning environment for tribal college students beginning at pre-college math levels but also benefit the math course achievement of these students. Importantly, the qualitative data also indicate the cultural meanings that students perceive of their success in math and science. These meanings reflect not only individual achievements but the importance of increased academic success providing these students with greater opportunities to contribute their new knowledge and skills to the Northern Cheyenne tribal community.