This study explores how to support Turkish–American secondary school students to co-develop covariational reasoning (CR) and representational fluency (RF) in solving contextually based quadratic function tasks in an after-school community center learning setting. We conducted a teaching experiment (n = 8) at a community center. Ongoing and retrospective analyses of classroom interaction and video transcripts revealed a culturally inclusive mathematics learning environment framework with several intertwined components: co-developing CR and RF and community-based practices. This study provides evidence that students coordinate symbolic, tabular, and graphical representations, which not only deepen their understanding of how quantities change in relation to one another but also enable them to interpret and construct representations in increasingly flexible ways. This reciprocal process of co-developing CR and RF allowed students to recognize and express quantitative relationships as meaningful functional relationships, demonstrating a dynamic interplay between reasoning about change and fluency across representations. This study situates learning within culturally inclusive learning environments and acknowledges the reflexive positionality of the teacher–researcher in relation to students. We highlight how shared community-based practices can enhance mathematics teaching and learning.

Graphs are productive tools for communication and sensemaking in STEM, making graphical interpretation a crucial skill for STEM learning and professional work. However, during interpretation, novice students draw on a myriad of cognitive resources - past experiences, knowledge, and strategies - some of which may not be relevant to the context or may be based on intuitive ideas or heuristics. This study explores the research question: how may intuitive or learned resources have helped or hindered one student interpret a covarying graph within introductory chemistry? Of 16 student participants in a task-based, semi-structured interview, Aubrey (pseudonym) was the only student who fluidly activated knowledge from biology, mathematics, and chemistry as she made sense of strong acid-strong base titration curve. We showcase how Aubrey visually chunked the graph, associating intuitive and learned ideas with each chunk, and explore how those ideas may have helped and/or hindered her chemical interpretation of the graph as well as her ability to make sense of change along the curve. Aubrey demonstrates that students’ resources for graphical interpretation are an amalgam of what they see and experience across an interdisciplinary landscape. This raises questions about how different instructional approaches foreground or obscure particular features of graphs and how we might better support students in coordinating insights from multiple domains to reason about covarying quantities. Using Aubrey, we argue that it may be valuable to engage students with graphs in introductory science courses from a more mathematical perspective.

This study explores the impact of gender, engineering experiences, and role models on high school students’ overall STEM interests and perceptions of engineering. A survey with Likert-scale and open-ended questions was given to 96 high school students (51 female, 45 male; 83% African American, 8% white, and 8% other races) in grades 9–12. We developed a scale measuring STEM interest, mathematical problem-solving confidence, misconceptions about engineering, perceptions of STEM, and self-efficacy. The STEM Dimension Survey (SDS) has a strong Cronbach alpha (= 0.96) and inter-coder agreement (Cohen’s Kappa = 0.77). ANOVA analysis on open response categories and the survey indicates that gender had a relatively small but statistically significant effect on STEM interest, with female students reporting slightly lower interest levels than male students. Students with prior engineering-related experiences demonstrated significantly higher STEM interest and more positive perceptions of engineering, but did not differ in self-efficacy or misconceptions. Notably, 63% of students reported no role model in STEM, and these students consistently reported lower interest, confidence, and self-efficacy. In contrast, those who identified role models reported significantly more positive STEM outcomes across all dimensions. The findings highlight the importance of recognizing students’ lived experiences and their definitions of engineering rather than relying solely on adult-defined narratives. Engineering-related experiences and role model presence are strongly linked to students’ interest and confidence in STEM.