Keywords

1 Introduction

Despite the increasing importance of mathematics in the world today, we continue to face issues of declining motivation in school mathematics and underrepresentation of racial and ethnic minority students in advanced mathematics courses. A range of countries including Germany, Australia, and the United States have attempted to address such issues by working to enhance students’ perceptions of usefulness, which can improve academic performance, course enrollment, and interest (e.g. Harackiewicz, Rozek, Hulleman, & Hyde, 2012; Hulleman, Godes, Hendricks, & Harackiewicz, 2010). While potential benefits of perceived usefulness have been illustrated, little research has examined the relationship between students’ perceptions of usefulness and their own goals and identity, which Eccles and Wigfield (2002) highlight as a direct influence on perceived utility. In this research, I take a sociocultural approach to consider the relationship between students’ perceptions of usefulness and one aspect of identity, students’ personal values, or “those beliefs held by individuals to which they attach special priority or worth, and by which they tend to order their lives” (Hill, 1991, p. 4). In particular, this work focuses on independent versus interdependent values, which are especially important to explore given current emphases in the literature. While existing research on utility value has typically emphasized independent conceptions of usefulness, or ways in which school content can be applied to accomplish individual tasks or to perform well personally, research on models of the self has illustrated that working-class contexts in the United States tend to promote interdependence, or connectedness and the needs of others, rather than independence (Grossmann & Varnum, 2011; Stephens, Markus, & Townsend, 2007). These different perspectives highlight a potential point of mismatch between existing conceptions of usefulness and the values of students in working-class communities.

This research explores the question, What is the relationship between students’ personal values and their ideas about the usefulness of mathematics? In particular, this work explores potential connections between perspectives on usefulness and interdependent values among a group of predominantly LatinxFootnote 1 middle school students in a working-class community. In discussing the implications of this work, I also consider how classroom instruction might draw on students’ personal values to enhance their perceptions of the usefulness of mathematics.

2 Conceptual Framework

Literature in three primary areas informs this research—the expectancy-value model, sociocultural theories, and models of the self. I will describe key findings and constructs from each of these bodies of research below.

2.1 Expectancy-Value Model

In order to understand how students’ values and beliefs influence their achievement-related choices and performance, Eccles and colleagues amended and expanded Atkinson’s (1964) expectancy-value model (Eccles & Wigfield, 2002; Eccles (Parsons) et al., 1983; Wigfield & Eccles, 1992). In the updated expectancy-value model, there are a multitude of direct and indirect influences on one’s achievement-related choices and academic performance (Eccles & Wigfield, 2002). Some indirect influences are personal beliefs, such as one’s own self-concept or one’s perceptions of others’ expectations, while others are features of one’s environment, such as family demographics and existing cultural stereotypes. All of these beliefs and features of the environment influence the two factors that directly affect achievement-related choices and performance: expectations of success and beliefs about the value of a task. While both of these factors are certainly important, in this paper I focus on one particular component of one’s beliefs about the value of a task—utility value.

2.1.1 Utility Value

Utility value, or the relevance of a task for one’s current/future goals or other aspects of one’s life, is one of four components of task value in the expectancy-value model (Eccles & Wigfield, 2002; Eccles (Parsons) et al. 1983; Wigfield & Eccles, 1992). As the model highlights, utility value can directly impact one’s achievement-related choices and performance. In particular, research has highlighted the relationship between high perceptions of usefulness and improved academic performance (Bong, 2001; Durik, Vida, & Eccles, 2005; Hulleman, Durik, Schweigert, & Harackiewicz, 2008; Mac Iver, 1991; Simons, Dewitte, & Lens, 2004), greater enrollment in mathematics courses (Durik et al., 2005; Updegraff, Eccles, Barber, & O’brien, 1996), and enhanced interest (Harackiewicz, Durik, Barron, Linnenbrink-Garcia, & Tauer, 2008; Hulleman et al., 2008). Several studies have also illustrated the ability to manipulate students’ perceived utility value and for enhanced perceptions of utility to increase interest and course performance (Canning & Harackiewicz, 2015; Harackiewicz et al., 2012; Hulleman & Harackiewicz, 2009; Hulleman et al., 2010). Furthermore, some of these studies have found that enhanced perceptions of utility are particularly advantageous for low performers in mathematics (Hulleman & Harackiewicz, 2009; Hulleman et al., 2010). However, very few studies have examined the role of utility value, or even task values more broadly, among early adolescents from racial or ethnic minority groups (e.g. Safavian & Conley, 2016). Given the potential benefits of utility beliefs for academic performance, persistence, and interest, it is crucial that we explore strategies for improving perceptions of utility in the mathematics classroom for youth from diverse racial/ethnic backgrounds.

2.1.2 Utility Value Interventions

In existing research, two main types of interventions have been conducted to enhance perceptions of usefulness: directly communicated utility value interventions and self-generated utility value interventions. In interventions involving directly communicated utility value, participants are told about the ways in which the techniques they are learning or courses they are taking can be useful (Durik, Shechter, Noh, Rozek, & Harackiewicz, 2014; Harackiewicz et al., 2012). For example, in Durik and Harackiewicz’s (2007) research, college students were taught how to use a particular technique for solving two-digit multiplication problems. In one condition, participants also received information about the utility of the technique for “everyday situations that would be relevant to college students” (p. 603). They were provided examples such as “doing personal banking, tallying grocery bills, and taking notes during math lectures” (p. 603), as well as calculating restaurant tips and store discounts. In contrast, interventions that involve the use of self-generated utility value statements ask participants to make their own connections between the material they are learning and its usefulness in other contexts (Hulleman & Harackiewicz, 2009). For example, Hulleman et al. (2010) introduced college participants to the aforementioned two-digit multiplication technique; however, rather than being told how the technique could be useful, participants were asked to write a short essay “describing the potential relevance of this technique to your own life, or to the lives of college students in general” (p. 22). Similarly, Harackiewicz, Canning, Tibbetts, Priniski, and Hyde (2016) implemented a written utility-value intervention with the goal of enhancing perceptions of utility among first-generation and underrepresented minority college students in introductory biology courses.

Recently, Canning and Harackiewicz (2015) compared the effectiveness of interventions involving the use of directly communicated utility value versus self-generated utility value. Their findings illustrate that direct communication of utility value undermines the interest and performance of students with low perceptions of competence, while self-generated utility value interventions are beneficial to that same subset of students. However, they found that effects were most powerful for college students with low perceptions of competence when both direct communication and self-generation techniques were used. In other words, students who were told about the value of a technique and also asked to write about how it might apply to their lives reaped the greatest benefit from the intervention. Similarly, Gaspard et al. (2015) successfully implemented an intervention involving both techniques with ninth-grade students, who read quotations from young adults about the usefulness of mathematics and then evaluated the personal relevance of those statements. Including both directly communicated and self-generated utility value statements was more effective at enhancing students’ perceptions of usefulness than employing self-generated utility value statements alone.

Additionally, Canning and Harackiewicz (2015) included a manipulation to examine the impact of focusing on utility for everyday activities versus utility for school or career. Through this manipulation, the authors found that directly communicated utility value was effective for participants with low confidence only when examples of utility for everyday activities were provided. They hypothesized that everyday examples are more accessible and less threatening to individuals with low perceived competence in school and that future interventions involving direct communication should tailor information “to the characteristics and needs of the individual” (p. 65).

The current study aims to contribute to such efforts by digging more deeply into the characteristics and needs of middle school learners. While the expectancy-value model highlights that one’s own goals and self-schemata are direct influences on an individual’s perceived utility value (Eccles & Wigfield, 2002), little research has explored the ways in which one’s goals and values might influence perceptions of usefulness. Thus, in this study, I apply a sociocultural lens to consider one component of students’ values and explore the ways in which those values might be related to students’ ideas about the usefulness of mathematics.

2.2 Sociocultural Perspectives in Education

Applying a sociocultural lens (e.g. Lave & Wenger, 1991; Rogoff, 2003) to study perceived utility in mathematics necessitates building on the knowledge that social and cultural processes mediate thought and activity. Thus, in order to understand one’s learning or thinking in a given moment we must consider the influence of prior experiences and interactions over time. As such, it is important to examine not solely the individual but the individual in interaction with the environment.

In mathematics education research, such approaches have highlighted that children and adolescents develop mathematical understandings through participation in out-of-school activities that often go unnoticed in the classroom (Brenner, 1998; Nasir, 2000; Taylor, 2009). For example, Saxe (1988) illustrated the power of drawing on everyday understandings in his study of Brazilian child candy sellers. He found that the children used complex mathematics to solve problems related to candy selling and explored the degree to which that knowledge might influence their performance on school problem-solving tasks. While sellers and non-sellers performed comparably on certain traditional tasks, Saxe found that sellers were able to apply their candy selling strategies to solve school mathematics problems that were closely linked to the selling practice. In particular, candy sellers outperformed non-sellers on tasks that required them to do arithmetic calculations with bills and to compare two pricing ratios. This finding, as well as the results of other studies such as Taylor and Dobie’s (2013, 2016) examination of mathematical understandings learned through the practice of tithing (giving 10% of one’s earnings to the church), highlights achievement-related benefits of creating tasks and assessments that draw on and are aligned with students’ own experiences and cultural practices.

Additionally, research on funds of knowledge has illustrated that the knowledge developed within families and communities can serve as a rich resource in the classroom (e.g. Moll, Amanti, Neff, & Gonzalez, 1992). Drawing on funds of knowledge in the school setting has the potential to improve students’ participation and interest in mathematics (Civil, 2002, 2007). For example, Civil (2007) analyzed second grade students’ experiences participating in a series of lessons in which they created garden enclosures and explored the sizes of their gardens. She found that as students participated in the lessons, they drew on everyday experiences, engaged with challenging mathematics, and exhibited personal interest while working on tasks.

Across this body of work—as well as research on culturally relevant pedagogy (Ladson-Billings, 1995) and teaching mathematics for social justice (Gutstein, 2006)—researchers have highlighted the importance of grounding instruction in students’ own daily practices and lived experiences to enact pedagogy that is socially and culturally relevant to students. This practice of building bridges between school mathematics and everyday cultural practices can be especially powerful in working towards achieving equity in mathematics education (Tate, 1994, 1995). In the current study, applying a sociocultural lens means considering the culturally based knowledge and practices that students bring to discussions of utility, focusing especially on students’ values, prior experiences, and relationships with others. In this work, I examine those themes and then use that knowledge to explore the possibility of drawing on students’ values and everyday experiences to improve their perceptions of the usefulness of mathematics.

2.3 Models of the Self

Given the sociocultural focus of this work, it is important to consider the culturally based knowledge and values that influence the ways in which students view and interact with the world. In particular, I draw on research on cultural models of the self, or views about one’s relation to other people and to the world. Research has illustrated that while U.S. middle-class contexts typically promote independent models of the self, or a focus on personal motives and distinctiveness from others, U.S. working-class contexts typically promote interdependence, or connectedness and the needs of others (Grossmann & Varnum, 2011; Stephens et al., 2007). One’s model of the self can in turn influence a variety of outcomes, including one’s academic experiences.

Stephens, Fryberg, and Markus (2012a) and Stephens, Fryberg, Markus, Johnson, and Covarrubias (2012b) examined the relationship between educational context and one’s view of the self in a study of students who attend American colleges. The researchers discovered a mismatch between American colleges, which typically promote norms of independence, and students from working-class backgrounds, who most often identified with interdependent norms. The latter group experienced greater difficulty on academic tasks and lower grades in college when the culture of the university was described in terms of independent norms, such as exploring one’s own personal interests, expressing one’s opinions, participating in independent research, and developing one’s own intellectual journey. However, when the university culture was presented as promoting interdependence—characterized by being part of a community, connecting with other students and faculty members, working together, and taking part in collaborative research—students from working-class backgrounds performed equivalently to students from middle-class backgrounds. In other words, students’ academic success increased and experience of difficulty decreased when college was framed in a way that aligned with their interdependent values.

Similarly, researchers have highlighted an emphasis on interdependent motives in particular ethnic communities. For example, Gay (2002) notes that “many students of color grow up in cultural environments where the welfare of the group takes precedence over the individual” (p. 110). In particular, familism—or having a strong identification with and loyalty to one’s family—is a central value among Latinxs (Esparza & Sanchez, 2008; Sabogal, Marín, Otero-Sabogal, Marín, & Perez-Stable, 1987), and Mexican and Mexican-American communities often exhibit strong family values (Valdés, 1996). Given that students in the current study identify primarily as Mexican, Mexican-American, and Chicanx, considering the possible role of students’ models of the self in their views about the usefulness of mathematics seems especially important.

Additionally, applying this lens of models of the self to research on utility value reveals that conceptions of utility in existing research tend to focus on independent goals and usefulness for the individual (e.g. for getting accepted into college or performing a job), rather than interdependent goals. For students who live in communities that promote interdependence over independence, seeing the usefulness of mathematics for achieving interdependent goals might be especially motivating. For example, in Gutstein’s (2006) work on social justice mathematics, using mathematics for interdependent purposes—such as to liberate one’s community—had the potential to improve students’ attitudes towards mathematics and ability to use mathematics to better understand the world. Similarly, Moses’ work on the Algebra Project (Moses & Cobb, 2001; Moses, Kamii, Swap, & Howard, 1989) connects mathematics literacy with economic access in Black urban and rural communities, highlighting implications of learning algebra for equality and citizenship. By emphasising the social and political implications of being mathematically literate, Moses encouraged students to pursue mathematics as a tool to liberate their communities. In existing research on utility value, while interdependence has not generally been explicitly promoted, Harackiewicz et al. (2016) found that underrepresented minority and first-generation college students emphasized social relationships—and family, in particular—in their essays about the relevance of mathematics for their own lives. This focus aligned with the students’ expressed emphasis on helping their families and communities, which was a primary motive for attending college. The current research builds on such work by examining students’ values and prior experiences and then considering how we can align discussions and interventions related to the utility of mathematics with those values.

3 Methods

In this section I describe the methods and forms of analysis that were used to explore the aforementioned questions, drawing on a subset of data collected for a study of perceptions of usefulness in mathematics (Dobie, 2016). I first describe the focal participants and then discuss the three forms of data collection—student surveys, student interviews, and ethnographic classroom observations—that were used in this research. Finally, I highlight the qualitative and quantitative methods that were used to analyze this data. Rather than seeking to make causal claims, this work aims to uncover information about students’ values and experiences with mathematics that can inform research and design moving forward.

3.1 Participants

Participants in this study were four classes of seventh-grade students (n = 84, mean age = 12.7 years) at Legacy Middle School,Footnote 2 which is located in the suburbs of a large city in the United States. When asked to describe their race or ethnicity using as many identifications as appropriate, students reported the following: 76% identified as Mexican, Mexican-American, or Chicanx; 18% identified as Puerto Rican; 18% identified as White/European-American; and 10% identified as African American. Of the 83 students who completed a question about gender identification, 47 identified as male, and 36 identified as female. Students were also asked to report the languages they felt most comfortable speaking. Eighty of 83 students selected English, and 32 selected Spanish; only two students listed both English and a language other than Spanish. According to data gathered by the state, approximately 68% of students in the school come from low-income families.

3.2 Student Surveys

Student surveys were one form of data collection used to explore students’ values and views of usefulness in mathematics. All 84 students completed a survey, which examined conceptions and perceptions of usefulness, attitudes towards mathematics, feelings of competence in mathematics, and personal values. In this paper, findings focus on two survey questions. First, to gain insight into students’ values, students were asked about the importance of various reasons for wanting to do well in school, based on the Motives for Attending College scale items used by Stephens et al. (2012a, 2012b). Ten of the twelve scale items from the original scale were used, and one new item was added (“Gain respect from my friends”). The two items selected for removal focused on motives that were not relevant to middle school students. Language was also changed to make items more understandable to and relevant for middle school students.

The second survey question discussed in this paper was created to examine students’ values specific to their mathematics learning. In particular, students were asked to use a scale of 1–5 (1 = Strongly Disagree, 5 = Strongly Agree) to rate their agreement with the statement, “It is important to me that the math I’m learning…” Six different sentence completers were provided for rating—“is fun,” “is useful,” “is easy,” “challenges me,” “relates to my everyday life,” and “reflects my culture.”

3.3 Ethnographic Classroom Observations

Ethnographic observations of three of the four classes were conducted 1–3 times per week for five months. The classes were selected both to include variation in level/track and to comply with their teacher’s observation preferences. One of the classes was labeled an “honors” mathematics class, and the other two were considered “regular” mathematics classes. In total, 60 classroom observations were conducted across the three classes between January and May of 2015 to explore discussions of usefulness, student values, student interactions, and references to everyday experiences with mathematics. Jottings were taken during all class sessions, and fieldnotes were written up after each observation.

3.4 Student Interviews

Student interviews were also conducted with 12 students across the three observed classes to delve into students’ survey responses. Students were selected across the three classes to maximize diversity in achievement level, gender, and attitudes towards mathematics. Each interview lasted between 16 and 34 minutes, with the mean interview length being approximately 26 minutes. Interviews were structured around four main themes: definitions of and attitudes towards mathematics, ideas about the usefulness of mathematics, experiences in mathematics class during the current academic year, and mathematics in one’s daily life.

Responses to several questions in particular are drawn upon for analyses. First, one item asked students to elaborate on their survey ratings  specifying whether it is important that the mathematics they learn is useful. Additionally, students were asked to report where they currently use mathematics and how they expect mathematics to benefit them—if at all—in the future. Students were also asked to consider where—if anywhere—they might use six specific mathematics topics in the future. Finally, students were asked questions about their current mathematics class, including what topics they found to be useful and not useful and how they would describe their own participation in math class.

3.5 Data Analysis

In study analyses, triangulation of the three data sources was used to increase the robustness of findings and examine both the breadth and depth of various themes using a combination of quantitative and qualitative analyses. Means and standard deviations of individual items were calculated for survey responses, and paired t-tests were used to examine differences in students’ responses. A coding scheme was also developed to analyze observation and interview data. The coding scheme focused on student interactions, orientations, and perceptions with particular attention to dimensions that align with themes of interdependence. Coding categories drawn on for the current analyses include conceptions of utility in mathematics (e.g. utility for a job, utility for daily activities), connections between mathematics and students’ out-of-school lives (e.g. connections to activities involving money, connections to family), and orientation towards collaboration (e.g. valuing collaboration, opposing collaboration). Two coders applied the coding scheme to several sets of fieldnotes, comparing their coding and then refining the coding scheme as needed throughout. Two new sets of fieldnotes, which constituted approximately 10% of the data, were then selected for interrater reliability coding, which occurred in two rounds. After each round of coding, Cohen’s Kappa was calculated, and a strong level of agreement was achieved in both instances (Cohen’s Kappa = 0.76, 0.85). Any segments that were coded differently were discussed by the coders, and a single code was agreed upon for each excerpt. Both coders then shared the responsibility of coding the remainder of the data.

4 Findings

Three main themes will be examined in this section—students’ emphasis on learning mathematics that is useful, students’ focus on interdependence, and connections between students’ interdependent values and ideas about the usefulness of mathematics.

4.1 Emphasis on Usefulness in Mathematics

Before exploring potential influences on students’ ideas about the usefulness of mathematics,  we should first examine the importance that students place on usefulness. On a survey question about values in mathematics, students reported finding it very important that they learn mathematics that is useful (see Table 4.1). The statement “It is important to me that the math I’m learning is useful” received the highest mean rating of agreement with the smallest standard deviation (M = 4.35, SD = 0.692), illustrating that students have a strong desire to learn mathematics they perceive as useful. In fact, only two of the eighty-two students disagreed with the statement, and four were neutral; all other students either agreed or strongly agreed that it is important for the mathematics they learn to be useful.

Table 4.1 Mean student ratings of important features of mathematics (1 = Strongly disagree, 5 = Strongly agree)
Full size table

While we might entertain the fact that students’ calls for usefulness are actually expressions of boredom or frustration with the difficulty of mathematics, these results suggest otherwise. Paired samples t-tests were conducted to compare students’ ratings of the importance of mathematics being useful to their ratings of the importance of mathematics being fun or easy. There were significant differences in students’ ratings of the importance of mathematics being useful and the importance of mathematics being fun, t(81) = 5.58, p = 0.000, as well as between ratings of usefulness and easiness, t(81) = 11.019, p = 0.000. Furthermore, the item with the second highest mean was “It is important to me that the math I’m learning challenges me” (M = 4.10, SD = 0.951). Ratings of the importance of challenge were also statistically significantly higher than ratings of the importance of mathematics being easy, t(81) = 6.816, p = 0.000, or fun, t(81) = 2.323, p = 0.023. Thus, it is unlikely that students primarily emphasize usefulness because they find mathematics too challenging or boring.

To explore students’ emphasis on usefulness in greater depth, interview participants were asked to explain why they either agreed or strongly agreed that it is important for the mathematics they learn to be useful. Of the twelve interviewees, six expressed that they do not see a purpose in learning mathematics that is not useful when they could instead be learning mathematics that they will use in the future. For example, Rachelle explained that she will be happier in the future if she learns useful mathematics now, rather than being taught concepts that she has no reason to learn: “If I learn math that’s not useful, then it will be kind of like pointless to learn it, but if I learn math that is useful, then I can use it and it can be like very helpful for whatever I do and I’ll be really glad that I knew it.” Omar similarly echoed that he doesn’t see a purpose in learning mathematics that is not useful since there are many types of mathematics he believes he needs to use in his life: “Math is in effect our everyday lives… So I feel like… if we don’t learn math that is useful… why learn it at all?”

Meanwhile, five students focused on the fact that it is important to them that mathematics is useful specifically because of its applicability to future jobs or careers. While two students mentioned the importance of learning mathematics that will be needed “to get a better job” or for a career broadly speaking, three students mentioned specific careers. For example, Victoria stated that she wants to be an engineer, so learning useful mathematics “will help me do better in my job and like help me get hired.”

One student blended together these two types of explanations, stating that it is important to learn mathematics that will be needed in the future and that careers are one place where mathematics might be needed. This student, Carrie, also connected her perceptions of usefulness to her motivation in mathematics:

If I’m learning things that I’m actually not going to use later on in my life, you know, I’m not going to know the things that I do need to know, for like careers and stuff, but if I learn things that are useful to me, I feel like—I mean, I pay attention in class but it would make me a little bit more you know, I’m going—you need this, so I better pay attention.

In this quote, Carrie not only emphasized the importance of learning things that she will need to know in the future but also explained that learning useful material will increase her focus. Thus, in addition to reporting an emphasis on learning mathematics that is useful, students also offered particular ideas about why learning useful mathematics is beneficial to them.

4.2 Emphasis on Interdependence

Since one influence on perceptions of usefulness is students’ own goals and values, we can explore these goals and values as a means of understanding the factors that affect students’ experiences of the usefulness of mathematics. In this section, I examine one value in particular—interdependence. Students’ survey and interview responses, as well as classroom comments, highlight a strong focus on interdependence. On the survey, students were asked to rate the importance of different reasons for wanting to do well in school on a scale of 1–5, where 1 = Not at all important and 5 = Extremely important. Students’ mean ratings can be viewed in Table 4.2. Of eleven survey items, the three that related to family received the highest mean ratings of importance: “Make my family proud” received the highest rating (4.55/5.00, SD = 0.848); “Provide a better life for my own children” received the second highest rating (4.43/5.00, SD = 0.926); and “Help my family out after I graduate” received the third highest rating (4.34/5.00, SD = 0.887). These responses demonstrate not only a significant emphasis on interdependent reasons for success but also strong family values in particular.

Table 4.2 Importance of reasons for wanting to do well in school
Full size table

During classroom observations and student interviews, this theme of interdependence arose, as well—albeit in different forms. While connections to family emerged as significant for some students during interviews, students’ value of family infrequently surfaced in classroom observations. Rather, students were observed emphasising the importance of working collaboratively with their peers.

After analysing classroom observation fieldnotes coded for themes of collaboration and independence, a focus emerged on students valuing collaboration over independent work. Across all sets of fieldnotes, students were captured opposing collaboration or requesting independent work on only six occasions. Furthermore, in some of those instances students were not opposing collaboration at large but rather collaboration with particular classmates. In contrast, 16 requests for collaboration were captured, as well as seven comments that expressed opposition to independent work. Requests for collaboration included questions such as “Can we work with our tables?” and “Can we work with partners?” Meanwhile, opposition to independent work occurred when students either commented that they did not want to work independently or questioned why they had to work independently, as in the following example: “Upon hearing the noise, Ms. Sanchez comes over and tells them to work independently. ‘My god, why we always gotta work independently?’ the boy asks.” (February 26, 2015)

In addition to students’ requests for collaboration and opposition to independent work, on three occasions students were captured stating the importance of collaboration. For example, on January 23, 2015, Carrie was working with her group when some members started to get sidetracked. After about a minute, Carrie loudly and sternly announced to her classmates that they all needed to “focus and pay attention and help each other out… because some of us don’t get it.” Similarly, on January 27, 2015, a different student was captured telling his tablemates, “We need to work together if we’re going to get through this.”

Finally, some students commented on the authenticity of different forms of engagement in the mathematics classroom. Related to interacting with others in particular, one student compared the way activity is arranged in the mathematics classroom to the way activity is arranged in everyday life. After Ms. Sanchez asked the class to work independently, the boy highlighted the disconnect between working independently in mathematics class and regularly engaging with others in everyday life: “‘Why does everything have to be independent?’ a boy sitting near me asks. ‘Life is not independent. You have a partner!’ A few seconds later he adds more quietly, ‘And then you have kids.’” (April 17, 2015) This comment illustrates the boy’s view of life not as an independent endeavour but as one that involves connections with other people. He saw a lack of authenticity in the way activity was organized in the mathematics classroom and felt that he was often asked to work independently even though “life is not independent.” As this comment came from only one student, I do not attempt to claim that it illustrates a theme across the entire sample of students. Rather, I propose that the comment suggests a possible relationship between students’ requests to work collaboratively in the classroom and students’ value of family and working together in their everyday lives. One potential reason why students might oppose independent work and prefer collaboration is because working independently does not align with the forms of engagement they see and experience in their everyday lives, an idea that will be further considered in the discussion.

4.3 Connections Between Usefulness and Interdependence

One place where explicit connections emerged between students’ emphasis on usefulness and their value of interdependence was during student interviews and observations. In this section, I provide brief case studies of two students, Liliana and Ethan, who discussed ways of using mathematics to achieve interdependent goals.

Liliana is a 13-year-old girl who attends seventh grade at Legacy Middle School and who identifies as Mexican/Mexican-American/Chicana. She considers herself to be “not the best student in math,” though she sees herself as “improving.” Liliana reported that she views mathematics as a very useful subject and believes that she will use mathematics in the future because of the many examples that her parents and teachers have provided to her.

On two occasions during her interview, Liliana mentioned interdependent uses of mathematics as she discussed ways in which mathematics will benefit her in the future. First, while responding to a question about what things she expects mathematics will help her with, Liliana mentioned her career, purchasing goods, and “even just teaching other people what it is.” When asked to elaborate on the latter comment, Liliana clarified that she was thinking in particular about helping her brother with mathematics. Similarly, as Liliana recalled particular mathematics topics from the current year that she found to be useful, she explained that those concepts helped her in several family-related situations: “When we were doing things like when my mom would need, like, help with something—like anything like when we go out, I would immediately know what to do, you know? Um, and helping my cousins or my brother with homework.” Again, Liliana focused on the usefulness of mathematics for helping others—and this time not only her brother, but also her mother and her cousins.

During her interview, Liliana also discussed how using mathematics with her family helped her in the mathematics classroom. While discussing her participation in mathematics class, Liliana recalled a period of time during which she felt very competent as a result of prior experiences working with her parents. She first commented, “There was like this one month that I got everything [my teacher] was telling me. So it was really, really exciting.” When asked about what she was studying that month, she identified the topic as “commission and markup” and then again emphasized that it was “really, really good.” She even added, “I was super, super happy I got it,” highlighting the strong positive emotions she experienced as a result of feeling competent. When prompted to talk about why that topic in particular made so much sense to her, she associated her success with her parents: “Just because both of my parents have—they work uh, dealing with money and everything. Um, and I’ve—well, not for my mom, but for my dad who owns a shop, I will help out and I guess that kind of reminded me of that.” In this exchange, Liliana identified her experience helping her parents as critical in her success with the commission and markup unit. Furthermore, she expressed repeated positive sentiments regarding her feelings of competence on those topics, which she attributes to the work she did in her father’s shop.

Another student, Ethan, also made connections between the mathematics he was learning and interdependent goals/activities. Like Liliana, Ethan is a 13-year-old student in seventh-grade at Legacy Middle School. He identifies as African American and views himself as very competent in mathematics. Ethan believes that mathematics is the most useful subject and expects to encounter problems that involve mathematics in the future.

During his interview, Ethan mentioned several ways in which he expects to use mathematics related to family. First, when discussing where he might use particular mathematics topics, he suggested that adding and multiplying fractions is useful to know “because if, say in the future, I decide to get married and have a family, I know that possibly my children will be using this.” As Ethan thought about potential uses of different mathematics topics, he reflected on the fact that some material might be useful to know so that he will have the knowledge to help out his own future children. During another part of the interview, Ethan reflected on how he uses mathematics now. He recalled, “I would use it when I’m getting a snack or something, how to like cut, split it between me and my brother, and my sister.” Again, though he was never prompted to think about family, Ethan made his own connections between the usefulness of mathematics and his family.

Finally, like Liliana, Ethan also gained experience from working with his family that helped him in mathematics class. During one classroom observation, Ms. Sanchez introduced her students to the concept of sales tax. (This was part of the same unit Liliana mentioned on commission and markup.) When the teacher asked if anyone knew what sales tax was, Ethan loudly and immediately replied, “I know what this is. I use sales tax when I help sell candy.” He then added, “My family owns a candy truck.” Following that commentary, Ethan contributed several thoughts related to sales tax, which he learned from selling sweets in his family’s candy truck. Thus, in addition to viewing mathematics as useful for helping his own family, Ethan also gained knowledge of important mathematics concepts through participation in out-of-school activities with his family.

5 Discussion

Findings from this research highlight three main themes. First, students emphasized the importance of mathematics being useful. Second, students in this study exhibited strong interdependent values, related to both family and collaboration with others. Third, some students made connections between their interdependent values and the usefulness of mathematics, highlighting ways they could use mathematics to help others. Below I discuss each of these themes in turn and then highlight implications of this work, as well as directions for future research.

5.1 Emphasis on Usefulness

One finding emerging from this work is the importance to students of learning mathematics that is useful. Although we might question whether students’ calls for usefulness symbolize some other frustration with or lack of interest in mathematics, two pieces of evidence suggest that is not the case. First, the students on average rated the importance on mathematics being useful as significantly higher than the importance of mathematics being fun or easy. This suggests that students’ calls for usefulness are distinct from their desire for enjoyment or simple success. Additionally, the students more strongly agreed that they want mathematics to be challenging than to be easy, again suggesting that they are not simply expressing frustration with the difficulty of mathematics through their calls for usefulness. Furthermore, these students had real reasons for wanting to learn mathematics that they perceived as useful. In particular, they expressed the importance of learning information that they could apply in the future and reported that they expect to need mathematics for their future careers.

5.2 Interdependent Values

A second finding emerging from this work is that the students in the study exhibited strong interdependent values. The top three reasons students reported for wanting to do well in school all related to family, which is consistent with existing research on familism in Latinx communities (Esparza & Sanchez, 2008; Sabogal et al., 1987) and helping motives among underrepresented minority college students (Harackiewicz et al., 2016; Stephens et al., 2012a, 2012b). Furthermore, Ms. Sanchez’s students regularly requested to collaborate with others in mathematics and tended to oppose independent work, which echoes prior research on interdependent motives in working-class communities (Grossmann & Varnum, 2011; Stephens et al., 2007) and concern for the group, rather than the individual, among students of color (Gay, 2002). The students’ requests for collaboration might be a product of the disconnect that some of them observed between ways of interacting in everyday life and ways of interacting in the mathematics classroom. As one student highlighted, life involves working with others; however, students are often asked to work independently in math class. It might be the case that students will see mathematics as more useful if the ways in which they are asked to participate and interact with others in the classroom more closely align with the ways in which they expect to participate and interact with others in their everyday lives.

5.3 Connections Between Usefulness and Interdependence

Third, some students made explicit connections between their interdependent values and ideas about the usefulness of mathematics. For example, Liliana and Ethan identified ways in which they both currently use mathematics to help their families and expect to use mathematics to help their families in the future. While little research has explicitly discussed the potential link between independent or interdependent values and ideas about usefulness (e.g. Harackiewicz et al., 2016), Eccles and Wigfield’s (2002) expectancy-value model illustrates the direct relationship between one’s own identity—which might include a focus on independent or interdependent values—and perceptions of usefulness. Thus, identifying students’ models of the self might be helpful in understanding the judgments they make about the usefulness of mathematics. In contrast to Liliana and Ethan, many students who expressed strong interdependent values did not explicitly make such connections. This absence does not necessarily signal that those connections do not exist. Rather, it might be the case that many students do not see the relationship between mathematics and achieving interdependent goals since independent goals tend to be emphasized in U.S. classrooms. While these independent goals might be connected to larger, interdependent goals, those latter goals are generally not discussed. For example, teachers often tell students about how mathematics will be useful for their future jobs or for doing taxes and budgeting. While earning a living and handling finances are activities that allow one to provide for and contribute to one’s family, that connection is typically not discussed. It might be the case that many students do not make such connections on their own, so drawing attention to how mathematics can be useful for providing for one’s family, for example, would be especially helpful for students with strong interdependent values.

5.4 Implications and Future Directions

There are several important implications of this research. First, this work highlights the need to attend to the connection between one’s personal values and perceptions of usefulness in both research and practice. For example, among students who express strong interdependent values, connections might be made to underscore the usefulness of content for helping or working with others, rather than solely for independent means. Building on prior research illustrating the effectiveness of interventions that combine directly communicated and self-generated utility value (Canning & Harackiewicz, 2015; Gaspard et al., 2015), students might be asked to reflect on statements or quotations that highlight the usefulness of mathematics for helping others. This focus on interdependent goals might be especially motivating for students who emphasize the role of family and their desire to provide for their families in the future. Similarly, teachers can also work to increase alignment with students’ values in the classroom. For students who emphasize collaboration with others—as the students in this study did – teachers might incorporate more collaboration into the classroom. While doing so, teachers might also highlight the usefulness of the practice of collaborating for students who do not see value in collaboration. For example, teachers might discuss with students the importance of collaborating in workplace interactions or when navigating personal relationships. Highlighting such connections might help students to see mathematics as more useful, as they will be able to identify how interactions in math class can have value in out-of-school contexts.

On a similar note, consistent with research on funds of knowledge (Civil, 2007; Moll et al., 1992), this study suggests that students have rich experiences with mathematics in their out-of-school lives that might be valuable to draw on in the classroom. Future research might explore such resources and also tap into students’ interdependent values by gathering examples of students using mathematics to help their families. These stories can then be used as the basis for designing problem-solving tasks that are grounded in students’ real world experiences and that students are likely to perceive as useful. To further incorporate students’ emphasis on interdependence, these tasks might be completed using collaborative participation structures to both mirror forms of interaction that students experience in their everyday lives and allow students to draw on the rich funds of knowledge of their classmates. Additionally, in the classroom, teachers might have students share their views about the usefulness of different mathematics topics with their classmates. Students have valuable stories and thoughts about how they use mathematics now and expect to use mathematics in the future. Thus, having peers share their personal experiences with each other rather than only framing usefulness from the teacher’s perspective might be especially effective at enhancing students’ perceptions of usefulness.

More broadly, findings from this research highlight the importance of applying a sociocultural lens to study utility value. Examining students’ own perspectives is crucial for developing equitable interventions that build on the views of diverse populations of students. Prior survey items and interventions have tended to focus on ways in which mathematics can be used for accomplishing independent goals (e.g. Anderman, Eccles, Yoon, Roeser, Wigfield, & Blumenfeld, 2001; Durik et al., 2005; Fennema & Sherman, 1976; George, 2006; Harackiewicz et al., 2012; Hulleman et al., 2010). However, in this study, students reported strong interdependent values and emphasized collaborative modes of learning, which aligns with research on models of the self (Stephens et al., 2007, 2012a, 2012b) and familism in Latinx communities (Esparza & Sanchez, 2008; Sabogal et al., 1987). Additionally, these perspectives echo work in the area of social justice mathematics that explores ways of using mathematics to work towards liberation and achieve social change (Gutstein, 2006). Despite these connections to interdependent values in other bodies of research, such themes have rarely been explored in utility value research. This study brought together both perspectives by including analytical tools that tapped into students’ own perspectives and focusing on the perceptions of usefulness of students whose voices are typically underrepresented in this research. Moving forward, I argue for the importance of carefully considering the theoretical and methodological approaches applied to this work to broaden existing utility value research and identify ways to create more equitable learning opportunities for students in mathematics moving forward.