Teacher Implemented Communal Learning in Math: Boosting Learning with African American Elementary Students

Abstract

The current study examined lasting learning effects of communal contexts for 124 African American third and fourth-grade students using a mathematics fractions unit with students’ regularly assigned teachers. Teachers in two experimental conditions received training on implementing communally or individually structured fractions curricula, and a naturalistic control was included whose participants did not receive the intervention. Findings revealed that students in the communal condition outperformed those who learned individually, and students in both intervention conditions outperformed those in the naturalistic control group. Survey of communal home-socialization obtained a relationship with identifying fractions performance. Implications for facilitative effects of culturally informed learning environments and teacher training toward enhanced academic achievement are discussed.

Keywords

best practices social diversity culture subjects culturally relevant pedagogy academic achievement urban education African American Students teacher development asset-base mathematics identity achievement gap

Background

The academic performance of American students continues to be of widespread concern and debate. African American and other students consistently achieve lower scores than their European American counterparts in reading and mathematics at all testing ages (U.S. Department of Education, NCES, 2020). For example, compared to European Americans (89%), in 2019 only 65% of African American, 4th grade students achieved scores at or above basic math competence on the National Assessment of Educational Progress (NAEP), and their scores have not changed meaningfully in more than a decade. These issues are even more pronounces among African American students from urban and low-income backgrounds. Current scholarship appropriately reframes these differences as symptomatic of the range of educational debts owed to these children (Milner, 2012). Among the more promising prescriptions for repaying these debts is the incorporation of fundamental cultural themes into academic learning environments (Boykin & Noguera, 2011; Coleman et al., 2017; Gay, 2000; Ladson-Billings, 2014). This contention suggests that learning environments that reflect and engage with students’ culture of socialization provide better developmental scaffolding (Brown et al., 1991; Howard & Rodriguez-Minkoff, 2017) and so have value for improving minoritized students’ experiences, attitudes, engagement, and other precursors of high achievement (Ladson-Billings, 1995; Whaley & Noël, 2012). From this viewpoint, academic achievement is inclusive of both social and cognitive processes and outcomes; and repaying the debt involves closing the opportunity gap impacting these academic experiences for all students (Milner, 2012). As educators are responsible for providing optimal learning opportunities (Milner, 2012), it becomes necessary to build educators’ capacity for shaping culturally informed learning environments as a pathway to closing the opportunity gap and repaying the multi-facited education debt (Bottiani et al., 2018; Campbell & Rowan, 1997; Cochran-Smith et al., 2011).

Conceptual Framework

In this and related work, fundamental culture is defined as a collection of themes that represent values and orientations that embraced by members and which facilitate ways of understanding and being (Markus & Kitayama, 2010; National Academies of Sciences, Engineering, and Medicine [NASEM], 2018; Stevens et al., 2014). Further, fundamental culture frames socialization themes that in turn serve as guiding standards for the thoughts, behaviors and actions of members (Bailey & Boykin, 2001). To that end, cultural transmission occurs at the beginning of a child’s life through tacit and explicit teaching and learning, from both family and community members (Boykin, 1986).

Communalism is one of nine dimensions of fundamental culture that are well documented in the socialization experiences of many African American children (Boykin, 1986; Boykin & Noguera, 2011; Coleman, 2013; Dill & Boykin, 2000;) ¹. Related to collectivism and other similar constructs (Triandis, 2001; Vargas & Kemmelmeier, 2013), Communalism, denotes an awareness of and paramount commitment to the fundamental interdependence among people and to social bonds and relationships. This work therefore asserts that integrating communal themes into academic learning environments can allow its behavioral and psychological manifestations, such as sharing and support for others to be promoted and leveraged as learning capital (NASEM, 2018; Siddel-Walker, 2012) rather than punished or discouraged as violating norms and expectations of typical individualistic classrooms.

Literature Review

By now, it is well documented in qualitative and quantitative research that use of cultural resources can facilitate academic achievement for students of color (Boykin & Noguera, 2011; Dixon & Ladson-Billings, 2017). Qualitative research has demonstrated that the use of cultural assets affords elaboration of the social and symbolic capital, positive emotional energy, shared goals, self-definition, and engagement potential that many racially minoritized students bring to the classroom (e.g., Seiler & Elmesky, 2007; Tatum & Gue, 2012; Wortham & Contreras, 2002; and see Howard & Terry, 2011, for a review of earlier work). This work has also suggested that using cultural assets is related to other academic and psychosocial benefits among such students, such as reduced disruptiveness and truancy. As culturally sensitive learning environments suggests that pedagogical approaches are attentive to the larger context of the learning setting and climate, largely facilitated by teacher-student interaction (Boykin & Noguera, 2011; Coleman & Davis, 2020; Tyler et al., 2018), quantitative work has found benefits of these environments for targeted grade school students consistently across a variety of subject areas and outcomes (Coleman et al., 2017; Cunningham et al., 2017; and see Boykin & Noguera, 2011, for a review of earlier research), and even across ages ranging from preschool to college (Sankofa et al., 2019).

Some cultural asset work focuses on the utility of integrating specific fundamental cultural resources common among African Americans into classroom practice. For example, some studies have examined the value of communally structured learning. Tyler et al. (2008) found that African American parents reported encouraging their children toward communal over individualistic or competitive learning and work habits. Classroom studies have found that African American middle and high schoolers show preference for peers who achieve via communal attitudes and behaviors for social (Marryshow et al., 2005) and academic (Tyler et al., 2006) interactions.

Beyond cultural preference, studies have also found that many African American students perform better on skills learned in contexts designed to engage and build upon their communal orientations than in other modes of learning (Coleman et al., 2017; Dill & Boykin, 2000; Hurley et al., 2005, 2009). For example, Hurley et al. (2005) reported that, on average, fifth grade African American students perform better on a math estimation task after learning in communal than in individualistic learning environments. More compelling, Hurley et al. (2009) found that, on average, African American children exhibited better performance after learning in communally structured learning environments than even in other forms of group work identified in the cooperative learning literature. In that study, fourth and fifth grade African American and European American students studied math estimation in communal, group competitive, in or group interpersonally competitive contexts. In contrast to the African American participants, European American students’ best average performance was in the group interpersonally competitive context.

These and related works serve as important demonstrations of the potential of cultural asset-based education, but most are limited in having employed a narrow range of tasks, single group research designs with a maximum of four students per session. Coleman et al. (2017) extended this line of research by exploring the facilitative effects of communally structured learning in simulated classroom environments. The study operationalized the teaching of several lessons and learning objectives over a 3-week math fractions unit. As in earlier studies, students in the communal context outperformed students who learned in the individualized context, and the same trend was found for the identifying, adding, and subtracting fractions learning objectives separately. That study advanced communalism research by evaluating communal pedagogy in settings very similar to real classrooms, but still employed specially trained researchers to implement specialized curricula and assessments. Still missing is work testing the utility of communal learning environments when used by students’ regular teachers as part of the regular curriculum.

The prospect of doing so necessarily raises questions about implementation training and calls for some examination of larger trends in professional development. Here again, the qualitative literature is rich with compelling descriptions of individual teachers’ personal journeys and transformations into shapers of culturally informed classrooms (Milner, 2011). Such work is invaluable for inspiring and guiding other educators seeking their own way forward, but necessarily leaves some kinds of issues unaddressed. For example, such analyses need to more often be paired with reliable evidence of concrete benefit to student academic outcomes. Unfortunately, there is too little work demonstrating whether and how teachers can become equipped to do this important work effectively enough for it to be reflected in student academic outcomes, and virtually no work looking systematically at whether this can be managed at any kind of scale.

Indeed, one major reason that the immense potential of culturally responsive pedagogy, in particular, is underrealized nationally is related to issues with scaling up (Sleeter, 2012; Dixon & Ladson-Billings, 2017). Despite a growing recognition of the need for cultural responsiveness training for preservice teachers, implementation in certification programs nationally have been described as largely inconsistent and inadequate (Allen et al., 2017). This issue is at least in part due to faulty and oversimplified conceptions of what it is, too little research clarifying how it works to scaffold student achievement and too few concrete examples of what it looks like in effective practice (Sleeter, 2012). There appears to be an even greater shortage of quality in-service professional development opportunities related to culturally informed pedagogy (Smith & Bahr, 2014) with few, if any, whose effectiveness is empirically validated in research rigorous enough to satisfy What Works Clearinghouse standards of evidence (Bottiani et al., 2018). Accordingly, despite that some 90 percent of teachers complete some in-service learning annually, only a small percentage of teachers who teach in diverse classrooms have undergone substantial professional preparation for teaching students with diverse backgrounds (Yuan, 2017).

We view calls for more research as well justified. In order for the use of culturally informed learning environments to become a normative standard in education, a number of questions must still be addressed. The work reviewed so far approaches from one end, seeking to document that culturally informed learning environments, in particular themes like communalism, can be reliably leveraged to benefit student social and academic outcomes. Missing from these are evidence that they can be meaningfully integrated with the range of factors that influence what happens every day in real classrooms. The qualitative literature has largely approached from another route, that of teachers documenting their journeys of transforming ideologies, viewpoints, and practice on an individual scale. Largely missing from those are assessment and identification of the key process element that are shared among such accounts and direct linkages to student outcomes (Sleeter, 2012).

Work bridging that gap between them, by documenting that communal learning can be effectively implemented by classroom teachers who have undergone appropriate in-service professional development stands to open up the way to bringing it to classrooms more systematically than has been done before. Such work, in enabling wider use of culture and the classroom, promises to improve the educational outlooks of large numbers of African American and other marginalizable children who are persistently underserved in US schools. It should also help to identify the kinds of challenges that will be involved in the necessary scaling-up work.

Work integrating communal learning with other best practices in mathematics education stands to affirm the relevance of culturally informed learning environments to real academic settings. The mathematics education research field recommends multiple support mechanisms concerning best practices in math education such as what to teach in mathematics, how to teach, and teacher preparation on both (Davis et al., 2018; Ferrini-Mundy et al., 2007; National Council of Teachers of Mathematics [NCTM], 2012; National Mathematics Advisory Panel [NMAP], 2008; Wright et al., 2017). Further, the literature suggests that students should learn conceptual and skills-based mathematics, with the use of a problem-centered teaching approach; and constructivist tasks, for example, using manipulatives, may further promote this conceptual learning within problem-centered structures (Fantuzzo et al., 2012; Ferrini-Mundy et al., 2007; Gillies, 2011; Morin & Samelson, 2015; NMAP, 2008; Seriki, 2018; Trafton & Midgett, 2001; Trafton et al., 2001). Pedagogy that incorporates peer assistance may effectively facilitate conceptual learning; and through sharing ideas, as students realize that there are multiple ways to approach a problem. Additionally, collaborative work allows opportunities for students to reflect on, communicate, and compare various ideas about given problems (Gillies, 2011).

Teacher professional development becomes quite necessary to successfully implement a curriculum with demands of higher order objectives for students (NASEM, 2018; Polly et al., 2014; Saxe et al., 2001; Supovitz et al., 2013). In this context, professional development should cover pedagogical mathematics content knowledge, as children as learners within particular mathematics content (Aguirre et al., 2013; NASEM, 2018; NMAP, 2008; Polly et al., 2014; Supovitz, et al., 2013). The communalism cultural dimension, serving as a culturally sensitive learning environment, aligns well with best practices in mathematics education. Researchers support the notion that African Americans participate in activities whereby they learn and identify with mathematic goals, skills, and competencies outside of formal schooling. As such, culture informs the transmission of such mathematic skills and competencies. Thus, cultural activities should inform mathematic pedagogy (Bonner & Adams, 2012; Nasir, 2012; Nasir & de Royston, 2013); and these students may better absorb mathematic concepts, as various cultural themes support the mathematic academic setting (Bonner, 2014; Davis & Farran, 2018; Ladson-Billings, 1997; Leonard & Guha, 2002; Nasir & Vakil, 2017).

While the use of culture in the classroom also shows promise for enhancing academic success among African American students, systematically defining and operationalizing culture through ways that would be useful in the day-to-day operation of classrooms over the long term has presented a challenge. The purpose of this research was to take an important next step by examining the effectiveness of communal learning as implemented by students’ regular teachers, in whole classrooms and over the course of an entire math unit. Here, we use an experimental approach to demonstrate the facilitative and enhancing effects of communal learning on elementary school-age African American students’ fractions learning. This approach considers the nuances of daily teaching over an extended period of time. These include climate shaping related to classroom management, individual social-emotional and academic student supports, time management, planning, informal and formal assessment, and facilitating student-student and teacher-student relationships. To do this, we compared the learning outcomes of African American third and fourth grade students who learned fractions in either communally or individually structured classrooms from teachers who received PD training. Students in the two experimental conditions completed a measure of communal socialization. We also included a naturalistic control condition comprised of one third and one fourth grade class whose teachers and students did not participate in any training, intervention, or complete any measures of personal attitudes. Teachers in the control condition did cover the same material, and their students did complete the same pre and post fractions assessments at the same intervals employed in the two experimental conditions.

Methods

Participants

Participants attended public schools in low-income communities of the Mid-Atlantic region of the United States. The schools were categorizable somewhere between urban intensive and urban emergent in Milner’s typology (2012). The schools comprised of ~94% African American, and schoolwide average scores on state mathematics assessments remained among the lowest in the state at less than 20% proficiency. Participants were from low-income socio-economic backgrounds as determined by their participation in the school’s free and reduced lunch program.

Students in the two experimental conditions were from two third and two fourth grade classes, totaling 86 female (44) and male (42) African American students. One class at each grade level was randomly assigned to the communal (42) and individual (44) learning conditions. The third, naturalistic control condition comprised of 38 third and fourth grade female (20) and male (18) African American students.

Parents/guardians and their students received informed consent/assent letters to sign before participating in the study. Students were also informed orally that they had the right to withdraw at any time.

Teachers

Teachers were third (3) and fourth (3) grade instructors recruited during an information session arranged by administrators at their schools. After the information sessions, in which a broad overview of the study highlighting evidence-based practices in math fractions education was provided, teachers had the opportunity to volunteer. No compensation was offered for participation in the study although the 6-hour training did count toward in-service PD requirements.

All six teachers earned state certification via a traditional university preservice education program and each held a bachelor’s degree in education or a related field. All had 3 to 5 years teaching experience overall and each had taught their respective grade continuously since they started teaching. None of the teachers had any experience or training with the fractions curriculum employed, using culturally sensitive learning environments in general or communal learning specifically.

Materials and Measures

Curriculum

Experimental classrooms were instructed using the Problem Solving with Fractions curriculum unit (PSF). The PSF was designed according to NCTM (2012) Standards for use with third through six grade students and covers three instructional domains (identifying, adding, and subtracting fractions). Each of those domains is covered in three 1-day lessons, and each lesson includes periods of direct instruction, practice items, and review for a subset of the practice items. The curriculum is designed around employing fractions manipulatives to develop students’ conceptual and practical understanding in each domain (NMAP, 2008). The manipulatives consist of a standard set of plastic pattern blocks in shapes that link together, and twelve circles each divided evenly into fractional proportions.

The PSF includes summative pre and post-tests assessing students’ understanding of all three fractions domains, and three interim tests for assessing students’ mastery of the three domains. The summative assessments include two equivalent 15-item four-option multiple-choice forms, A and B, which were rotated as the pre and post-tests. Each interim assessment is also a 15-item four-option multiple-choice test. The PSF does not include homework, and no supplementary math homework was assigned in the two conditions that used it.

Professional development sessions

Teachers in the experimental conditions participated in three, 2-hour in-service professional development sessions that took place in the 2 weeks before they began teaching the PSF lessons. The PD sessions were designed and facilitated by the first author who, among other qualifications, holds a Ph.D. in psychology, M.A. in curriculum and instruction with experience in curriculum development, and was previously a certified preK-8 teacher and a district-level instructor for new teacher professional development. The sessions used a learning community framework emphasizing a shared sense of purpose, collective focus on student learning, collaboration, de-privatization of practices and reflective dialogue (Ferrini-Mundy et al., 2007; Gabriel et al., 2012; Polly et al., 2014; Turner et al., 2018). Teachers implementing the communal and individual conditions were trained separately, and although the curriculum (agenda, material, etc.) was the same across condition groups, their sessions were designed to differ in how the development of skills would be supported among students.

To begin their first session, respectively, teachers were given a general overview of the training and allowed to ask questions. Next, teachers were walked through the curriculum lessons, assessments, and manipulatives. During this walkthrough, teachers were given instructions for the daily structuring and facilitation of communal or individual learning in a math classroom and as related to the PSF curriculum. These included the physical configuration of the space and furnishings (sitting close together at shared desks versus spaced apart), daily administration of the communalism or individualistic prompt, distribution, and use of materials (shared vs. individual) and sharing and collaboration (group interactive work vs. individual work). Teachers were also coached on strategies for promoting communal attitudes, thinking, and behavior among students for the communal condition and reminded of the individual structure with independent working environment for the individualistic condition. Once introduced, these procedures and principles were reinforced in the second and third sessions and raised in relation with other topics and discussions about the PSF curriculum. Logistics concerning collecting and data processing students’ work and assessments were also covered in the first session. Teachers were able to pose questions about the curriculum and procedures throughout all sessions.

The second session featured a more focused examination of the PSF curriculum. To set the stage for the session, procedures for facilitating communal or individualistic learning were briefly reviewed. Teachers then engaged in learning community discussion about students’ typical understanding of mathematics fractions as described in the NCTM standards, their prior experience in teaching fractions, and whether and how their district standards were aligned with those standards. Teachers reviewed and discussed alignment between the PSF and NCTM learning objectives for third, fourth, and fifth grade fractions.

In session three, the teachers studied the approaches and techniques employed in each PSF lesson for developing students’ conceptual and applied understanding of fractions. This began with their completing a sample of each curriculum lesson(s) using the curriculum-based manipulatives. While completing the lessons, teachers were encouraged to further discuss the curriculum’s conceptual and skill-based tactics, how to integrate those with the communal or individualistic learning context they would be facilitating, and to anticipate students’ questions about the lessons and manipulatives.

PD session notes

During the information sessions and in conversations leading into the training, we learned that the teachers were not optimistic about their students’ preparation for advanced math content and that they believed that because its abstract nature fractions would be especially challenging. They also described not feeling especially confident about teaching fractions themselves. None had been trained to use fractions-specific manipulatives, and instead used base-ten counting blocks to illustrate fractions concepts. They mentioned finding this choice better than not using manipulatives at all, but frustrating and of debatable value. We also learned that aside from strategies like think-pair-share none of the teachers used cooperative learning regularly in their teaching.

By the conclusion of PD sessions, teachers expressed enthusiastic buy-in overall, they expressed feeling better prepared to teach fractions and having more optimistic expectations for their students. They were a bit skeptical about a few issues. For example, teachers from both conditions were eager to use the fractions-specific manipulatives but believed the two sets called for in the PSF would be too many small objects and would cause behavioral management issues with their students. Teachers in the individual condition expressed this as doubt about students’ ability to “manage themselves’ while using the manipulatives. Those in the communal condition seemed certain that students sharing the manipulatives would “create problems.” Finally, the communal condition teachers expressed some doubt about facilitating the communal condition—in particular, they thought the communal prompt was “corny” and doubted that students would respond well to it.

Home communal measure (HCM)

Students in the two intervention conditions completed the HCM, a self-report measure of communal activities and attitudes in respondents’ home environments. The twenty-item HCM assessed the interdependence, group duty, sharing, and group-identity dimensions of communalism. Items include “People in my house often ask each other to do things together” and “Whenever I have something I am expected to share it with other family members and when they have things, they usually share with me.” Items are rated on a four-point Likert-type scale anchored with the descriptors not at all (1) and very much (4). The HCM has yielded an alpha reliability coefficient of .91 in previous work (Bailey & Boykin, 2001).

Procedures

The study lasted for approximately 2 weeks, and each PSF lesson occurred during students’ regularly scheduled mathematics class, one per day. There were eleven class sessions that included an introductory class, nine learning classes, and one post-class.

During the introductory class, the pretest and HCM were administered. Before the pretest, teachers gave students an opportunity to familiarize themselves with the manipulatives via 5 minutes of free exploration with each type. After this unstructured time, teachers introduced the pattern blocks and fractions circles by naming each shape in the set provided. Next, teachers read the instructions aloud and allotted students 15 minutes to complete the pretests. Students worked individually on the pretest, and the A and B versions were counterbalanced so that students sitting adjacent to one another had a different retest version. The HCM was administered after the pretest.

In the first lesson, the teacher introduced the goals and format of the fractions unit and gave the first oral presentation of the appropriate condition prompt. For those in the communal condition, teachers arranged students into their assigned groups and explained that they would work with the same group members for the duration of the curriculum unit. Students in the individualistic learning condition were given the individualism prompt while sitting at their pre-assigned individual desks which were theirs for the duration of the study.

Teachers then began the lesson with 10 minutes of direct instruction, followed by 15 minutes during which students worked (communally or individually depending on condition) to complete a fractions assignment based on that day’s lesson. Finally, teachers conducted a review session that lasted approximately 5 minutes. Subsequent lessons followed the same format, starting with the appropriate condition prompt, direct instruction, completion of an assignment, and a brief review. Domain assessments followed review sections on the last day of each domain or section such that students completed the assessment for identifying fractions at the end of the third lesson, for adding fractions at the end of the sixth lesson and for subtracting fractions at the end of the ninth lesson. Domain assessments also lasted 15 minutes, and students in both conditions completed them independently.

Students completed the posttest during the concluding session on the final day of the overall study procedure, and teachers did not conduct a math lesson. Posttest procedures were identical to those for the pretest, and those who received test A for the pre-test completed test B as the posttest, and vice-versa. Students were allotted 15 minutes to complete the posttest.

Experimental learning conditions

One class of students at each grade level was randomly assigned to one of the two learning conditions. The communal and individualistic conditions were designed to differ in the modes of thinking and learning behavior encouraged among students. To accomplish this, the physical configuration of the classroom space and policies on movement (sitting close together versus spaced apart), distribution of materials (shared or individual), the learning structure (group work vs. individual work), and the scripted motivational prompts differed between conditions.

In the communal learning condition, students were divided into groups of four students who sat together and shared materials during the direct instruction, practice exercises, and review activities. In the communal condition, the teacher sat with students and asked group members to hold hands with their neighbors before each learning session while he or she delivered the communal prompt. The communal prompt (Dill & Boykin, 2000) is a scripted statement designed to emphasize the interdependent attitudes, thinking, and behavior encouraged during the lessons. This oral prompt reminded students of their shared school and community ties and encouraged them to do their best and to help and support each other in learning the material. In emphasizing seating proximity, social contact, and sharing, the communal learning context is intended to stimulate students’ expression of existing communal attitudes and behaviors.

Students in the individualistic classrooms each sat at separate desks, and each received their own set of materials. Teachers encouraged students in the individualism condition to complete their assignments independently and did not permit interaction with other students. Before each learning session in the individualism condition, the teacher stood in front of the separated desks to deliver the individualism prompt. The individualism prompt, similar in structure and length and tone to the communal prompt, is designed to emphasize individual effort and to encourage participants to do their best. In emphasizing physical and social separation, individual effort, and autonomy, the individualistic learning context is intended to stimulate the expression of individualistic attitudes and behaviors.

Naturalistic control condition

Although we believed that our implementation of the individualistic condition reflects the well documented individualistic contexts in which math is taught in most US classrooms, given that teachers in the individualism condition of this study received training for the PSF curriculum, we also included a naturalistic control condition. One class at each grade-level was observed for this purpose. Teachers and students in this condition experienced no additional intervention and were allowed to proceed with the unit on fractions per usual. The unit was covered in the same number of days and with the same number of lessons as in both experimental conditions.

Fractions lessons in the control condition lasted for approximately 55 minutes and regularly included a brief warm-up period, teacher-guided practice, independent student practice, and assessment. Teachers used skill-based textbooks to instruct students in identifying, adding, and subtracting fractions. Teachers used their discretion in assisting students at any stage of the lessons. Both teachers assigned fractions homework during the 2-weeks study. Two potentially meaningful differences between the control classes were observed. First, although both control classes sat in their regular seats, the fourth grade students’ desks were organized into table groups of four, while the third graders were seated separately. Students in both classes were assigned individual materials and did not share. Secondly, the fourth-grade teacher conducted a cumulative fraction review immediately prior to the posttest.

Students in the control classes completed the same pre and posttest as students in the experimental conditions. A graduate research assistant administered the assessments at the same interval as in the experimental conditions. As in the other conditions, students were read the instructions and allowed 15 minutes to complete the tests. Students worked individually, and the A and B versions were counterbalanced so that students sitting adjacent to one another had different versions.

Intervention notes

A researcher attended the fractions lessons in all participating classrooms on most days of the study. These visits, which lasted between 10 and 20 minutes, allowed for informal observations of implementation and of how things seemed to be progressing. The following are some observations that came out of those.

The first theme to emerge was that, despite their doubts, all of the teachers employed all elements of the curriculum for their condition right from the start and persisted in doing so throughout the 2-week curriculum unit. The teachers also appeared to become at ease with the lessons and quickly seemed “in control” of their classes. Secondly, there appeared to be minimal classroom management issues, and students remained consistently engaged with the material.

Observers noted that students in the individualized condition generally engaged positively with the fractions manipulatives, seemed attentive to their assignments, and they tended to do so quietly. Students in the communal condition appeared to engage with the manipulatives and one another, discussing lessons, problem solving according to instructions supporting peers who seemed to have difficulty.

Post intervention interview notes

During the debriefing interview, teachers were invited to share their impressions of how things had gone. At that time, they did not know how their students had performed on any of the assessments, so their impressions were drawn from their own in-class observations. All four of the intervention teachers expressed being glad they had participated. All also mentioned feeling they learned a lot about how to teach fractions, how to use the “new” manipulatives, and that their students enjoyed the lessons too (stayed engaged and on task).

Both communal condition teachers described being pleased to see how supportive students were to one another and surprised that students did not fight/fuss/argue over access to the materials. One communal teacher mentioned being able to tell that students were “getting it” and that their talk was mostly about the lessons and did not often need to be redirected. A communal teacher mentioned feeling better about using the communal prompt and support methods once they saw that it was “working” and “serving students well.”

Teachers in the individualized classrooms also enjoyed implementing what they learned during the professional development but mostly commented on the usefulness of the PSF curriculum and manipulatives. For example, one expressed surprise that her students seemed to handle the manipulatives “without getting distracted” and that after all, it “did not seem like there were too many manipulatives or too much stimulation in general,” as she had originally worried.

Finally, more than one teacher mentioned that being in the study helped open their eyes to what their students are capable of with the right support, and one extended this comment to include having gained insight into what she and her colleges are themselves capable of with support.

Results

Scoring and Psychometrics

Scores on the home communalism measure were computed as the simple mean of relevant items after omitting filler items and conducting reverse coding as appropriate. Cronbach’s alpha analyses indicated an internal reliability coefficient of .82 for the experimental groups. The mean HCM score for the sample was 3.23 (SD = 0.43), out of 4, indicating that most students perceived substantial communal socialization in their home environments. Means on the HCM were similar across conditions at 3.13 (SD = 0.37), and 3.33 (SD = 0.46), for students in the communal and individual classrooms, respectively, F(1, 84) = 1.81, p = .18.

The 15-item pre, post, and interim domain assessments were scored as a simple sum of correct items, yielding a range of 0 to 15. Scores were also calculated separately for the identifying, adding, and subtracting items of the pre and posttests, each of which had a range of 0 to 5.

Performance

Interim assessments

A 2 × 2 × 2 Analysis of Covariance (ANCOVA) was conducted to tests for effects of gender, grade level, and learning context on performance on the identifying fractions interim assessment. Students’ scores on the adding fractions section of the pretest were included as a covariate. There were no main or interaction effects of gender or grade level. Figure 1 displays the main effect of learning context, F(1, 76) = 6.34, p < .01 on identifying fractions performance. Means were 9.90 (SD = 2.24) or 66% correct, and 8.69 (SD = 2.19) or 58% correct, for the communal and individualistic classes respectively, indicating that on average, students who learned in the communal context performed significantly better on the identifying fractions interim assessment than students who learned in the individualistic context. The effect size (d = 0.26) suggests that the difference between them is of large practical significance (Kraft, 2020).

Figure 1.

Identifying fractions interim assessment: Main effect of learning context, F (1,76) = 6.34, p < .01.

A 2 × 2 × 2 ANCOVA was also conducted to tests for effects of gender, grade level, and learning context on performance on the adding fractions interim assessment. Pretest scores on the adding fractions items were included as a covariate. There were no main interaction effects of gender or grade level on performance. Figure 2 displays the main effect of learning context, F(1, 77) = 6.15, p < .02. The means for the communal and individualistic learning contexts were 12.64 (SD = 2.85) or 84% correct, and 11.12 (SD = 2.78) or 74% correct, respectively, indicating that, on average, students who learned in the communal context performed significantly better on the adding fractions interim assessment than students who learned in the individualistic context. Additionally, the effect size (d = 0.26) suggests that the difference between conditions is of also large practical significance (Kraft, 2020).

Figure 2.

Adding fractions interim assessment: Main effect of learning context, F(1,77) = 6.15, p < .02.

A 2 × 2 × 2 ANCOVA was conducted to tests for effects of gender, grade level, and learning context on subtracting fractions interim assessment performance. Scores on the subtracting fractions pretest items were included as a covariate. As with the other interim assessments, the mean difference between the communal 9.92 (SD = 2.78) and individual contexts 8.97 (SD = 3.34) was in the predicted direction, though less pronounced F(1, 77) = 2.70, p = .10. Post hoc comparisons indicated a greater difference between the communal, 11.94 (SD = 3.68) or 80% correct, and individual 9.91 (SD = 3.61) or 66% correct, conditions for 4^th, F(1, 40) = 2.99, p = .09, than for third graders F(1, 40) = .252, p = .62. Figure 3 displays the means. The effect size (d = 0.27) suggests that the difference for 4th graders is of large practical significance (Kraft, 2020).

Figure 3.

Subtracting fractions interim assessment: Interaction of grade and learning context. NS.

Pre and Posttests

The mean pre and posttest scores for the sample were 6.21 (SD = 3.21) and 10.76 (SD = 2.85), respectively. We ran a preliminary 3 × 2 × 2 × 2 ANOVA on pretest scores to test for differences due to condition, gender, grade level, and test-form order. No significant effects emerged.

Next, a 3 × 2 × 2 ANCOVA was computed to test for effects of learning context, grade level, and gender on posttest performance. Pretest scores were included as a covariate. A main effect emerged for learning context, F(1, 114) = 14.49, p < .01. The means were 11.98 (SD = 1.93), for the communal context, 10.83 (SD = 2.80), for the individualistic context and 9.20 (SD = 3.15), for the naturalistic control condition. Figure 4 displays the pattern of posttest performances in percentage of correct responses. Post hoc analysis indicated that all three posttest means were significantly different. The effect sizes suggest high practical significance (d = 0.31) for the better performance by students who studied communally over those who studied individually, high practical significance for the difference between the individualistic and control conditions (d = 0.25) and very high practical significance between the communal and control conditions (d = 0.52). Figure 5 displays the percentage of correct responses for the identifying, adding, and subtracting subsections of the posttest. The patterns closely mirror those for the interim assessments.

Figure 4.

Posttest. Percent correct in each learning context. F (1, 114) = 14.49, p < .01.

Figure 5.

Posttest subsections: Percent correct in each learning context.

Correlation

Correlational analyses were conducted to examine relationship between scores on the HCM and students’ performances in the two experimental conditions.² Predictably, there was no overall relationship between HCM scores and performance assessment scores for the whole sample. There was also no relationship between HCM scores and post-test performance for students who studied in either communal or individualistic classrooms separately, r(42) = .03; r(44) = −.13. However, among students who studied in communal classrooms, there was a moderately strong positive correlation between HCM scores and their performance on the identifying fractions interim assessment, r(42) = .45, p < .001. The same relationship emerged on the identifying fractions subsection of the posttest in that, for those in the communal classrooms, there was a marginally significant positive correlation r(42) = .202, p = .09, while among students who studied in the individualistic classrooms there was a significantly negative correlation, r(44) = −.279 p = .03, between HCM scores and identifying fractions performance. See Table 1 for summary of findings.

Table 1.

Summary of Findings.

Measure	Finding	Practical significance of observed differences
		Effect Size
Fractions performance:	Learning context:
Pretest	Communal = Individual = Naturalistic control	No difference
Interim assessments
Identifying	Communal > Individual	Large
Adding	Communal > Individual	Large
Subtracting
3rd	Communal = Individual	No difference
4th	Communal > Individual	Large
Posttest	Communal > Individual > Naturalistic Control	Large
Correlations:
Among students who learned in the communal classrooms only:
	HCM scores were positively correlated with performance on the identifying fractions interim assessment.
	HCM scores were positively correlated with performance on the identifying fractions section of the posttest.
Among students who learned in the individualistic classrooms only:
	HCM scores were negatively correlated with performance on the identifying fractions section of the posttest.

HCM = home communal measure.

Discussion

A range of previous studies have found that African American students assigned to learn in communally structured environments, on average, outperform their counterparts who study in environments structured to promote and reward individualism. We set out to determine whether these benefits could be duplicated among students in actual classrooms, as they are tasked with learning a standard curriculum unit, evaluated on standard assessments and, importantly, taught by their own regular classroom teachers. We were especially interested in examining the feasibility of preparing in-service teachers to effectively structure communal math learning. To do this, we compared the fractions performance of students whose teachers had been trained to implement a fractions curriculum either communally or individualistically, with that of students whose teachers covered the same content without new training.

Student Performance

Communal learning

This study’s findings are consistent with the outcomes of other studies, in particular Coleman et al.’s (2017) finding that communal learning can benefit students throughout multiple sessions and learning objectives of a math fractions unit—thus, encompassing multiple dynamics of daily classroom environments. The PSF curriculum was designed to prepare students for relevant district and NCES requirements and standards. In the current study, its implementation served as the fractions unit in the classrooms that employed it, and its tests serve as actual graded assessments. As in Coleman et al. (2017), our students who learned in the communal simulated classrooms, on average, outperformed those who learned in the individualistically structured simulated classrooms. In fact, students who learned in the communal context achieved better learning outcomes on two of the three sub-skills and overall, compared to those who studied the same skills in the individual and naturalistic control conditions. This finding takes this line of work an important step forward in that the communal learning context was implemented by regular teachers for their full complement of students and in the presence of all the dynamics of real teaching and learning. It demonstrates that culturally informed learning environments, communalism in particular, can be effectively implemented in “real” classrooms over extended periods. It also affirms our prediction that teachers’ capacity for shaping culturally informed learning environments can be improved via appropriate professional development.

Professional development

Students in both intervention conditions outperformed students in the naturalistic control condition, suggesting that training teachers to use the PSF curriculum had a positive impact on fractions instruction and students’ learning. That in-service training can improve teaching practices is not an especially new finding but affirms the value of continued professional development for in-service teachers (Turner et al., 2018). That finding is also interesting, because related previous investigations have described/cast the individualistic learning condition as the de facto control, standing in for “what would otherwise be happening in classrooms,” but in fact employed specific curricula delivered by specially trained researchers (Coleman et al., 2017; Hurley et al., 2005). Our choice to include a naturalistic control condition in this study has, therefore, been illuminating. As it happens, our individualistic condition was more effective than “what was otherwise happening,” but still statistically and practically less effective than the communally structured learning context. This may suggest that previous work has actually underestimated the potential benefits of communal learning over standard classroom practices.

Communal socialization

The theoretical work underlying the use of culturally informed learning environments, such as communalism, holds that the patterns of thinking and behavior common in many students’ home and community culture are assets that can be engaged to scaffold cognitive and skill development (Brown et al., 1991; Howard & Rodriguez-Minkoff, 2017; Hurley et al., 2019; Whaley & Noël, 2012). An important implication of this line of reasoning is that communal learning (communalism), an Afro-cultural dimension, can function by allowing communally oriented students to draw upon existing competencies (assets) in the service of attaining new ones. Our finding that, for African American students’ who learned in the communal classrooms, there was a positive relationship between communal socialization and performance outcomes lends some support for that contention. That relationship seems especially noteworthy given the foundational and highly conceptual nature of the identifying compared to adding and subtracting fractions (Fennell & Karp, 2017). The complementary negative correlation between communal socialization and identifying fractions performance among students in the individualistic classrooms speaks fairly directly to the lost opportunities and scaffolding failures that are all too common in the educational experiences of African American students.

Teachers Experiences and Impressions

Our informal observations and conversations with teachers were encouragingly consistent with our theory- based expectations. Teachers of the intervention classrooms were unanimous in their feeling better equipped to teach fractions, they would continue to use the PSF fractions unit, and they wished their district would provide more professional development of the type received as part of our investigation. Communal condition teachers indicated they would continue to use the communal learning strategies they learned, including affirmations similar to the communal prompt, and would work toward integrating communal learning into other curriculum areas. In addition, it was reported to us that participating teachers were later recruited to train their colleagues on how to structure and implement communal learning context.

Implications

Culture in the classroom

Together these observations are significant in helping to address pressing questions about the use of culturally informed learning environments. For example, they help to answer questions about what culturally informed learning environments are (Sleeter, 2012), and continues to include communal learning environments as an option within this construct. In demonstrating that it is possible to disconnect academic success from common presumptions about a single best way to teach and learn, this work contributes to the general argument that culturally informed learning environments, are an effective teaching approach, building upon students own assets, including their cultural assets, to scaffold their acquisition of new knowledge. It helps make the point that it is the responsibility of educators to become prepared for the fact that such assets will vary systematically among students of different cultural backgrounds.

In demonstrating that communally structured learning can be effective in real classrooms and that, with appropriate training, communal learning can be effectively implemented by in-service teachers, this work contributes a concrete example of what communalism as a pedagogical tool can actually look like in effective classroom practice. It also contributes a concrete example of what it might look like to leverage existing infrastructures for in-service professional development toward wider implementation of culture in the classroom (Smith & Bahr, 2014; Yuan, 2017). In finding a relationship between communally structured learning and students’ self-reports of communal emphases in their home and community socialization, this work affirms our and others’ assertion that how culturally informed learning works is by affirming and leveraging students’ existing cultural assets, in this case communalism, to scaffold new learning, in this case math fractions (Howard & Rodriguez-Minkoff, 2017).

Practical implications

In addition to the effect sizes, each of which exceeded the criteria for large and practically significant effects according to the benchmarks for assessing educational intervention established by Kraft (2020), our use of a graded assessments allows us to discuss issues of practical significance in a fairly more direct way than is typically feasible in similar research studies. Based on the most commonly used grading scales, on average, students in our communal classrooms achieved “B” grades on the final assessment, students in the individualistic context achieved “C” grades while students in the naturalistic control classrooms earned “D” grades. Plotting those against per pupil expenditure that was well below the $500 boundary for “low cost” (Kraft, 2020), suggests such an intervention is likely to also be highly cost effective.³ These outcomes do something beyond further demonstrating the classroom potential of asset-based pedagogies; they underscore the ethical imperative of efforts to capture it while casting a negative light on the reluctance to systematically direct resources toward large-scale efforts.

Implications for teacher education and related policy

The implications of this body of research, as extended in this study, are fairly straightforward. The questions above are those offered as reasons that culturally informed learning environments has not been and cannot be more widely implemented in real school settings. If this work has helped to answer those questions, and if our use of graded assignments amplifies the ethical imperative on educators to capitalize on asset-based education, those reasons are now decidedly less reasonable.

For example, now that we know it can be done, and even if the positive effects were known to be limited to improving only fractions learning among only urban African American, low-income, grade-school students, that would still be a win worthy of pursuing with significant investments of policy, financial, and human resources. Even that would represent a meaningful installment on the debt owed to millions of students. Given the likelihood, and mounting evidence that the use of culture in the classroom is relevant to many more academic and psychosocial outcomes and to students of a range of racial/ethnic identities,⁴ ages, and socioeconomic positions, continued reluctance to direct resources and take action may be most intelligible as negligence.

One way forward that we can imagine is top down. For example, with policy support, states, districts, and schools could begin to demand, via hiring and advancement preference and criteria, teachers with substantial training in the employ of cultural asset-based pedagogies. To meet that demand, teacher education programs, both pre and in-service, would be pressured to offer courses and structure curricula that center cultural asset-based education rather than continue to treat it as an add on. Districts might respond with hiring preference and incentives for persons qualified to design the desired curricula and pursue the scholarship in needed directions. Such action could, over a few years, create significant expansion momentum for and enable continued articulation and refinement for the use of culture. And, this effort may yield a climate denoting the importance for cultural assets and teachers’ embrace over simply following a script. Of course, there are other viable levers and paths forward as well, and we do not mean to suggest no significant efforts have taken place. There are. The social justice program at UCLA school of education is a noteworthy example (Quartz, 2009), however, the questions of scale and momentum have remained. This article was written in the hope that in demonstrating that some of the main scaling-up issues can be solved, we might help to shift the conversation and momentum for the use of culturally informed learning environments to reach a forward tipping point. It is not intended as a technical manual for implementation; however, we have not excluded the possibility of producing something more concretely prescriptive as a follow-up.

Limitations and Recommendations

This study reveals a few limitations. We are not in a good position to interpret the poorer performances on identifying fractions assessments across all three conditions, other than by noting its more conceptual (and so presumably difficult) nature compared to the other two domains. The fact that students in the communal condition did “better,” especially if they were higher in communalism, is intriguing. For example, it may allude to variation in the kinds of skills that can benefit most from communally structured learning. It seems intuitively sensible that the interactive nature of communal learning would be especially beneficial for the acquisition of foundational concepts compared to learning to execute algorithms and procedures. Systematic study of such issues seems in order for theoretical and practical purposes.

Another shortcoming is the limited number of classrooms sampled. Although the unit of analysis was intentionally at the student level, given our interest in growing the capacities of in-service teachers, there is a pressing need for research like this to be executed on a scale large enough to begin to unpack how variation in teachers’ own cultural and ethnic backgrounds, prior experience, education, and professional mindsets would interact with PD of the type employed in this work. Future studies should seek larger samples at the classroom level. Nested designs would enable useful analyses at the teacher, classroom, and student levels. Beyond that, there is need for work examining how the use of cultural assets and related PD will interact with a variety of other forces, including campus, district, state, and national requirements that influence what happens in classrooms.

Communalism is but one in an array of cultural themes that will have relevance for classroom practice (Bailey & Boykin, 2001), and urban low-income African Americans are not the only population of students who promise to gain from our advancing understanding of and intentional attention to these issues. For example, themes related to communalism are well documented in LatinX, Southern Asian and other non-White cultures. These are some of the same populations who are also systematically underserved in US schools, and there is also some evidence that such children may also benefit from communally structured learning (Sankofa et al., 2019; Wortham & Contreras, 2002) and who will certainly benefit from learning contexts designed to leverage their unique cultural assets toward their learning and achievement.

Finally, in this work, we chose to center student rather than teacher outcomes. We feel this was a necessary and appropriate step toward demonstrating the potential scalability of communal learning environments and other culturally informed dimensions more generally. On the other hand, our approach and findings raise many questions related to PD and teacher education more generally. Although we believe the kinds of value-added teaching outcomes that our teachers evinced and identified are the mechanisms of communalism as a culturally informed pathway, we did not assess them systematically. Follow-up work doing so could shed light on precisely what our participating teachers gained from the PD that lead to children’s improved performance. It could be fruitful, for example, to mount a replication including observations of a larger number of teachers before and after the intervention in order to clarify what and how much actually changes in participants’ classroom practices. Systematic observations of these types would make it possible to assess whether and how individual elements of the PD training impacted teachers’ practice, and their orientation toward practice, would allow such PD to be refined and improved for broader use, including but not limiting to other math and other content in general. A number of tools are available for assessing value-added via classroom observations. Among them, those made using the ICOR-Math, because it aims to asses both content specific practices and practices directed toward the broader goals of shaping students toward resilience, and persistence (Nava et al., 2019) might be suitable.

Footnotes

Acknowledgements

The authors would like to acknowledge the valuable assistance of Daniel Park, Pomona College Class of 2019 in the preparation of this manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Sean T. Coleman

Eric A. Hurley

Notes

Author Biographies

Sean T. Coleman, PhD, is an associate professor in the Department of Educational Studies and Leadership at Bowie State University, Bowie, MD.

Eric A. Hurley, PhD, is a professor in the Department of Psychology & Africana Studies, at Pomona College, Claremont, CA.

A. Wade Boykin, PhD, is a professor and director of the Graduate Program in the Department of Psychology at Howard University. He also serves as the Executive Director of Capstone Institute at Howard University, Washington, DC.

References

Aguirre

Martin

Mayfield-Ingram

(2013). The Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices National Council of Teachers of Mathematics.

Allen

Hancock

S. D.

Starker-Glass

Lewis

C. W.

(2017). Mapping culturally relevant pedagogy into teacher education programs: A critical framework. Teachers College Record, 119(1), 1–26.

Bailey

C. T.

Boykin

A. W.

(2001). The role of task variability and home contextual factors in the academic performance and task motivation of African-American elementary school children. The Journal of Negro Education, 70, 84–95.

Bonner

(2014). Investigating practices of highly successful mathematics teachers of traditionally underserved students. Education Studies of Mathematics, 86(3), 377–399.

Bonner

Adams

(2012). Culturally responsive teaching in the context of mathematics: A grounded theory case study. Journal of Mathematics Teacher Education, 15, 25–38.

Bottiani

J. H.

Larson

K. E.

Debnam

K. J.

Bischoff

C. M.

Bradshaw

C. P.

(2018). Promoting educators’ use of culturally responsive practices: a systematic review of inservice interventions. Journal of Teacher Education, 69(4), 367–385.

Boykin

A. W.

(1986). The triple quandary and the schooling of Afro-American children. In Neisser

(Ed.), The school achievement of minority children: New perspectives (pp. 57–91). Lawrence Erlbaum.

Boykin

A. W.

Noguera

(2011). Creating the Opportunity to Learn: Moving from research to practice to close the achievement gap. ASCD.

Brown

J. S.

Collins

Duguid

(1991). Situated cognition and the culture of learning. In Yazdani

Lawler

R. W.

(Eds.), Artificial intelligence and education, Vol. 2. (pp. 245–268). Ablex Publishing.

10.

Campbell

P. F.

White

D. Y.

(1997). Project IMPACT: Influencing and supporting teacher change in predominantly minority schools. In Fennema

Nelson

B. S.

(Eds.), Mathematics teachers in transition (pp. 309–355). Lawrence Erlbaum.

11.

Cochran-Smith

Cannady

Mceachern

K. P.

Piazza

Power

Ryan

(2011). Teachers’ education, teaching practice, and retention: A cross-genre review of recent research. Journal of Education, 191, 19–31.

12.

Coleman

S.T.

(2013). Transforming communalism from a cultural dimension to a learning context for African American learners. African American Learners, 2(2), 1–14.

13.

Coleman

S.T.

White

Bruce

Boykin

A.W.

Tyler

K.M.

(2017). Communalism versus individualistic learning contexts as they relate to mathematical task performance under simulated classroom conditions. Journal of Black Psychology, 43, 6.

14.

Coleman

S.T.

Davis

(2020). Using asset-based pedagogy to facilitate STEM learning, engagement, and motivation for African American middle school boys. Journal of African American Male Learners, 11(2), 76–94.

15.

Cunningham

R. T.

Boykin

A. W.

Allen

B. A.

(2017). Facilitating diverse learning contexts and content on children’s (school-relevant) cognitive performance: Effects of music and movement expression. Journal of Cognition and Culture, 17(3–4), 232–252.

16.

Davis

D. B.

Farran

D. C.

(2018). Positive early math experiences for African American boys: Nurturing the next generation of STEM majors. Young Children, 73(2), 44–51.

17.

Davis

Goings

Allen

(2018). Developing pre-service mathematics teachers to meet the needs of Black male students in teacher education programs. In Prime

G. M.

(Ed), Centering race in the STEM education of African American K–12 learners (pp. 129–150). Peter Lang.

18.

Dill

Boykin

A. W.

(2000). The comparative influence of individual, peer tutoring, and communal learning contexts on the text-recall of African-American children. Journal of Black Psychology, 26(1), 65–78.

19.

Dixon

A. D.

Ladson-Billings

(2017). Harambee: Pulling it all together. Teachers College Record, 119(1), 1–6.

20.

Fantuzzo

LeBoeuf

Rouse

Chen

(2012) Academic achievement of African American boys: A city-wide, community-based investigation of risk and resilience. Journal of School Psychology, 50(5), 559–579.

21.

Fennell

Karp

(2017). Fraction sense: Foundational understandings. Journal of Learning Disabilities, 50(6), 648–650.

22.

Ferrini-Mundy

Burrill

Schmidt

W. H.

(2007). Building teacher capacity for implementing curricular coherence: Mathematics teacher professional development tasks. Journal of Mathematics Teacher Education, 10, 311–324.

23.

Gabriel

Coché

Szucs

Carette

Rey

Content

(2012). Developing children’s understanding of fractions: An intervention study. Mind, Brain, and Education, 6(3), 137–146.

24.

Gay

(2000). Culturally responsive teaching-theory, practice and pedagogy. New York Teachers College Press.

25.

Gillies

(2011). Promoting thinking, problem-solving and reasoning during smallgroup discussions. Teachers and Teaching, 17(1), 73–89.

26.

Howard

Terry

C. L.

Sr . (2011). Culturally responsive pedagogy for african american students: promising programs and practices for enhanced academic performance. Teaching Education, 22(4), 345–362.

27.

Howard

T. C.

Rodriguez-Scheel

(2017). Culturally relevant pedagogy 20 years later: progress or pontificating? what have we learned, and where do we go? Teachers College Record, 119(1), 1–22.

28.

Hurley

E. A.

Boykin

A. W.

Allen

B. A.

(2005). Communal versus individual learning of a math-estimation task: African-American children and the culture of learning contexts. The Journal of Psychology, 139, 513–527.

29.

Hurley

E. A.

Allen

B. A.

Boykin

A. W.

(2009). Culture and the interaction of student ethnicity with reward structure in group learning. Cognition and Instruction, 27, 121–146.

30.

Hurley

E. A.

Leath

S. C.

Hurley

S. P.

Pauletto

(2019). Cultural group membership Vs. (self-reported) group orientation: Which predicts student performance in cooperative & competitive math learning? For whom? Urban Education. Advance online publication. https://doi.org/10.1177/0042085919838012

31.

Kraft

M. A.

(2020). Interpreting effect sizes of education interventions. Educational Researcher, 49(4), 241–253.

32.

Ladson-Billings

(1995). Toward a Theory of Culturally Relevant Pedagogy. American Educational Research Journal, 32, 465–91.

33.

Ladson-Billings

(2014). Culturally relevant pedagogy 2.0: a.k.a. the remix. Harvard Educational Review, 84(1), 74–84.

34.

Leonard

Guha

(2002). Creating cultural relevance in teaching and learning mathematics. Teaching Children Mathematics, 9(2), 114–120.

35.

Markus

H. R.

Kitayama

(2010). Cultures and selves: A cycle of mutual constitution. Perspectives on Psychological Science, 5, 420–430.

36.

Marryshow

Hurley

E. A.

Allen

B. A.

Tyler

K. M.

Boykin

A. W.

(2005). Impact of learning orientation on African-American children’s attitudes toward high-achieving peers. The American Journal of Psychology, 118, 603–618.

37.

Milner

(2011). Culturally relevant pedagogy in a diverse urban classroom. Urban Review, 43, 66–89.

38.

Milner

H. R.

IV . (2012). Beyond a test score: Explaining opportunity gaps in educational practice. Journal of Black Studies, 43(6), 693–718.

39.

Morin

Samelson

(2015). Count on it: Congruent manipulative displays. Teaching Children Mathematics, 21(6), 362–370.

40.

National Academies of Sciences, Engineering, and Medicine (NASEM) (2018). How people learn II: learners, contexts, and cultures. The National Academies Press.

41.

National Council of Teachers of Mathematics. (2012). Principles and standards for school mathematics: Math standards and expectations.

42.

National Mathematics Advisory Panel (NMAP). (2008). Foundations for success: The final report of the national mathematics advisory panel. U.S. Department of Education.

43.

Nasir

N. S.

(2012). Racialized identities: Race and achievement among African American youth. Stanford University Press.

44.

Nasir

Vakil

(2017). STEM-focused academies in urban schools: Tensions and possibilities. Journal of the Learning Sciences, 26(3), 376–406.

45.

Nasir

de Royston

(2013). Power, identity, and mathematical practices outside and inside school. Journal for Research in Mathematics Education, 44(1), 264–287.

46.

Nava

Park

Dockterman

Kawasaki

Schweig

Quartz

K. H.

Martinez

J. F.

(2019). Measuring teaching quality of secondary mathematics and science residents: A classroom observation framework. Journal of Teacher Education, 70(2), 139–154.

47.

Polly

Neale

Pugalee

(2014). How does ongoing task-focused mathematics professional development influence elementary school teachers’ knowledge, beliefs and enacted pedagogies? Early Childhood Education Journal, 42, 1–10.

48.

Quartz

K. H.

(2009). The careers of urban teachers: A synthesis of findings from UCLA’s longitudinal study of urban educators. In Bayer

Brinkkjaer

Plauborg

Rolls

(Eds.), Teachers’ career trajectories and work lives, (pp.143–158). Springer.

49.

Sankofa

Hurley

E.A.

Allen

Boykin

(2019). From oppositional culture to cultural integrity: African American students’ perception of the activity structure and physical ecology of classrooms. Urban Education. Advance online publication. https://doi.org/10.1177/0042085919850257

50.

Saxe

Gearhart

Nasir

(2001). Enhancing students’ understanding of mathematics: A study of three contrasting approaches to professional support. Journal of Mathematics Teacher Education, 4(1): 55–79.

51.

Seiler

Elmesky

(2007).The role of communal practices in the generation of capital and emotional energy among urban African American students in science classrooms. Teacher College Record, 109(2), 391–419.

52.

Seriki

(2018). Toward a framework for culturally relevant inquiry-based science pedagogy. In Prime

G. M.

(Ed.), Centering race in the STEM education of African American K–12 learners (pp. 151–170). Peter Lang.

53.

Siddle-Walker

(2012). Black segregated schooling in the south. In Banks

(Ed.), Encyclopedia of diversity in education (pp. 237–239). SAGE.

54.

Sleeter

C. E.

(2012). Confronting the marginalization of culturally responsive pedagogy. Urban Education, 47(3), 562–584.

55.

Smith

N. L.

Bahr

M. W.

(2014). Increasing cultural competence through needs assessment and professional development. Professional Development in Education, 40(1), 164–181.

56.

Stevens

Markus

Phillips

(2014). Social class culture cycles: How three gateway contexts shape selves and fuel inequality. Annual Review of Psychology, 65, 611-634.

57.

Supovitz

Ebby

Sirinides

(2013). Teacher analysis of student knowledge (TASK): A measure of learning trajectory-oriented formative assessment. Consortium for Policy Research in Education.

58.

Tatum

Gue

(2012) The sociocultural benefits of writing for African American adolescent males, Reading & Writing Quarterly, 28(2), 123–142.

59.

Trafton

Midgett

(2001). Learning through problems: A powerful approach to teaching mathematics. Teaching Children Mathematics, 7(9), 532–536.

60.

Trafton

Reys

Wasman

(2001). Standards-based mathematics curriculum materials: A phrase in search of a definition. Phi Delta Kappan, 83(3), 259–264.

61.

Triandis

H. C.

(2001). Individualism and collectivism: Past, present, and future. In Matsumoto

(Ed.), The handbook of culture and psychology (pp. 35–50). Oxford University Press.

62.

Turner

J. C.

Christensen

Kackar-Cam

H. Z.

Fulmer

S. M.

Trucano

(2018). The development of professional learning communities and their teacher leaders: An activity systems analysis. Journal of the Learning Sciences, 27(1), 49–88.

63.

Tyler

K. M.

Boykin

A. W.

Miller

Hurley

(2006). Cultural values in the home and school experiences of low-income African-American students. Social Psychology of Education, 9, 363–380.

64.

Tyler

Boykin

A. W.

Coleman

S.T.

Hurley

Scott

Dillihunt

Bolter

(2008). Examining cultural socialization within African American and European American households. Cultural Diversity and Ethnic Minority Psychology, 14(3), 201–204.

65.

Tyler

K.M.

Burris

Coleman

S. T.

(2018). Investigating the association between home-school dissonance and disruptive classroom behaviors for urban middle grade students. The Journal of Early Adolescence, 38, 4.

66.

U.S. Department of Education. (2020). Institute of Education Sciences, National Center for Education Statistics (NCES), National Assessment of Educational Progress (NAEP), various years, 1990–2019 Mathematics Assessments.

67.

Vargas

J. H.

Kemmelmeier

(2013). Ethnicity and contemporary American culture: A meta-analytic investigation of horizontal–vertical individualism–collectivism. Journal of Cross-Cultural Psychology, 44(2), 195–222.

68.

Whaley

A. L.

Noël

L. T.

(2012). Sociocultural theories, academic achievement, and African American adolescents in a multicultural context: A review of the cultural compatibility perspective. Journal of Negro Education, 81(1), 25–38.

69.

Wortham

Contreras

(2002). Struggling toward culturally relevant pedagogy in the Latino diaspora. Journal of Latinos and Education, 1(2).

70.

Wright

B. L.

Ford

D. Y.

Scott

M. T.

(2017). Multicultural pathways to STEM: Engaging young gifted Black boys using the color-coded Bloom-Banks matrix. Gifted Child Today, 40(4), 212–217.

71.

Yuan

(2017). Developing culturally responsive teachers: current issues and a proposal for change in teacher education programs. World Journal of Education, 7(5), 66–78.