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This study explores STEM identity among Underrepresented and Underserved Racially and Ethnically Minoritized (UUREM) middle school girls within informal learning settings. Focusing on micro-level interactions, we explored a single-gendered STEM summer camp where UUREM middle school girls comprised 81% of the participants (N=59). Guided by ecological systems theory as a methodological approach to developing well-designed informal STEM activities, we sought to positively shape UUREM middle school girls’ STEM identity. STEM identity is complex, multi-layered, and inseparable from the intersectionality of their racial and gender identities. This approach is particularly salient in affective factors such as self-efficacy, ability-belief, and a sense of belonging during their pivotal middle school years. Critical implications include (a) single-gender spaces, like STEM camps, provide affirming, safe environments for authentic discussion and belonging in STEM, and (b) role models of similar racial and gender backgrounds support positive STEM identity formation for UUREM middle school girls. 

This case study explores how middle-grade learners use a game-based app for math learning at an informal site, the Nature Center. We apply distributed and self-directed learning theories, emphasizing learning in specific contexts, social settings, and through tools like an iPad app. We employ the embodied action conversation framework to analyze critical interactions. Two cases emerged: (1) learners followed MathExplorer app rules, and (2) learners went on personal excursions, creating their own rules to improve their MathExplorer rankings. We discuss implications for designing technologies for informal math learning. 

Background This comparative case study examined the use of math walks with middle grade youths and adult facilitators in an informal STEM learning space. Math walks are place-based walking tours where youths and facilitators critically examine and ask math-related questions about their environment. Method Drawing on situated theories of learning and frameworks for understanding group participation, we examined how facilitators constrained or supported youths’ mathematical thinking as they participated in math walks at the local zoo. Results Using interaction and stance analysis, we identified, analyzed, and compared three contrasting cases: In the first case, the facilitator may have overly constrained youths’ mathematical thinking by asking leading questions and not providing time for youths to discuss their personal interests. In the second case, the facilitator may have underly constrained youths’ mathematical thinking by allowing youths to ask too many new questions without refining or developing any one specific question. In the third case, the facilitator supported mathematical thinking by praising youths’ work, layering on mathematical terminology, and providing clear and actionable instructions for how youths could refine their mathematical questions. Conclusions Findings support efforts to understand how adult facilitators can support youths in seeing mathematics within and asking mathematical questions about the world around them. 

Informal science education researchers have become increasingly interested in how out-of-school spaces that offer STEM (science, technology, engineering, and math) programs inform learners’ STEM achievement, interests, and affective outcomes. Studies have found that these spaces can offer critical learning and developmental opportunities for underrepresented racially minoritized (URM) students (Black, Latinx, low socioeconomic status) in STEM subjects. Shifting away from the leaky STEM pipeline analogy, researchers have posited contemporary understandings to explain why the minoritization of URM girls persists. Informal learning environments such as STEM summer camps are being studied to assess how URM girls experience and interact with STEM in novel ways. These environments can inform the research field about how URM girls’ perceptions of their STEM identities, abilities, efficacy, and belonging in STEM develop as they engage in those spaces. This mixed-method study used a multiple-case-study approach to examine how aspects of URM middle school girls’ STEM identities positively changed after participating in a one-week, sleep-away, single-gender STEM summer camp held at a university in the Southwestern U.S. Drawing on intersectionality and STEM identity, we used ecological systems theory to design our research study, examining how URM middle school girls narrate their STEM identities in this informal learning environment. Using quantitative analyses and deductive coding methods, we explored how elements of girls’ STEM identities were shaped during and after their participation in the STEM summer camp. Findings from our study highlight (1) quantitative changes in girl participants’ STEM identities, sense of belonging in STEM, and perceived STEM ability belief, (2) qualitative results supporting our quantitative findings, and (3) how the intersectionality of participants’ race and gender played a role in their STEM identities. This study points to the potential of STEM informal learning camps as a way of developing and fostering URM girls’ STEM identities. 

This qualitative case study examines the learning that occurred when a small group of middle grade youths embarked upon a personal excursion during a game-based math walk. Math walks are an informal learning activity where learners and facilitators explore mathematical concepts embedded in everyday spaces. The MathExplorer app is a location-based mobile game designed to enhance and gamify math walks. In our broader research, we investigated a group of 18 middle grade learners who used MathExplorer to engage in math walks at a local nature preserve. While most youths in this study used the game as planned by the researchers, one group deviated from the plan and devised new ways of playing the game and participating in the math walks. We see this deviation, or personal excursion, as a source of insight for research on game-based math walks. To understand the learning that took place during this personal excursion, we draw upon sociocultural and self-directed theories of learning. Using methods of interaction analysis and embodied action conversation framework, we analyzed the small groups’ discussion, movement, and game-use to understand: (1) the point at which the students departed from the planned use of MathExplorer; and (2) the learning that took place after this departure. The findings include how the youth explicitly incorporate mathematics into game play through an activity-as-planned, and how the youth embark on a personal excursion relating to game mechanics and gamification, with an implicit focus on mathematics. We discuss the importance of personal excursions for designing informal mathematics learning experiences. 

Informal mathematics learning has been far less studied than informal science learning – but youth can experience and learn about mathematics in their homes and communities. “Math walks” where students learn about how mathematics appears in the world around them, and have the opportunity to create their own math walk stops in their communities, can be a particularly powerful approach to informal mathematics learning. This study implemented an explanatory sequential mixed-method research design to investigate the impact of problem-posing activities in the math walks program on high school students' mathematical outcomes. The program was implemented during the pandemic and was modified to an online program where students met with instructors via online meetings. The researchers analyzed students' problem-posing work, surveyed students' interest in mathematics before and after the program, and compared the complexity of self-generated problems in pre- and post-assessments and different learning activities in the program. The results of the study suggest that students posed more complex problems in free problem-posing activities than in semi-structured problem-posing. Students also posed more complex problems in the post-survey than in the pre-survey. Students' mathematical dispositions did not significantly change from the pre-survey to post-survey, but the qualitative analysis showed that they began thinking more deeply, asking questions, and connecting school content to real-world scenarios. This study provides evidence that the math walks program is an effective approach to informal mathematics learning. The program was successful in helping students develop problem-posing skills and connect mathematical concepts to the world around them. Overall, “math walks” provide a powerful opportunity for informal mathematics learning. 

Mathematics is an important tool in engineering practice, as mathematical rules govern many designed systems (e.g., Nathan et al., 2013; Nathan et al., 2017). Investigations of structural engineers suggest that mathematical modelling is ubiquitous in their work, but the nature of the tasks they confront is not well-represented in the K-12 classroom (e.g., Gainsburg, 2006). This follows a larger literature base suggesting that school mathematics is often inauthentic and does represent how mathematics is used in practice. At the same time, algebra is a persistent gatekeeper to careers in engineering (e.g., Harackiewicz et al., 2012; Olson & Riordan, 2012). In the present study, we interviewed 12 engineers, asking them a series of questions about how they use specific kinds of algebraic function (e.g., linear, exponential, quadratic) in their work. The purpose of these interviews was to use the responses to create mathematical scenarios for College Algebra activities that would be personalized to community college students’ career interests. This curriculum would represent how algebra is used in practice by STEM professionals. However, our results were not what we expected. In this paper, we discuss three major themes that arose from qualitative analyses of the interviews. First, we found that engineers resoundingly endorsed the importance of College Algebra concepts for their day-to-day work, and uniformly stated that math was vital to engineering. However, the second theme was that the engineers struggled to describe how they used functions more complex than linear (i.e., y=mx+b) in their work. Students typically learn about linear functions prior to College Algebra, and in College Algebra explore more complex functions like polynomial, logarithmic, and exponential. Third, we found that engineers rarely use the explicit algebraic form of an algebraic function (e.g., y=3x+5), and instead rely on tables, graphs, informal arithmetic, and computerized computation systems where the equation is invisible. This was surprising, given that the bulk of the College Algebra course involves learning how to use and manipulate these formal expressions, learning skills like factoring, simplifying, solving, and interpreting parameters. We also found that these trends for engineers followed trends we saw in our larger sample where we interviewed professionals from across STEM fields. This study calls into question the gatekeeping role of formal algebraic courses like College Algebra for STEM careers. If engineers don’t actually use 75% of the content in these courses, why are they required? One reason might be that the courses are simply outdated, or arguments might be made that learning mathematics builds more general modelling and problem-solving skills. However, research from educational psychology on the difficulty of transfer would strongly refute this point – people tend to learn things that are very specific. Another reason to consider is that formal mathematics courses like advanced algebra have emerged as a very convenient mechanism to filter people by race, gender, and socioeconomic background, and to promote the maintenance of the “status quo” inequality in STEM fields. This is a critical issue to investigate for the future of the field of engineering as a whole.