Evaluating and Revising Algebra Tasks: Culturally Responsive Mathematics in the Making

• In Event: Black People Are Not a Monolith: Designing and Nuancing Culturally Responsive Mathematics

Abstract

This study explores the process we devised for evaluating and revising algebra tasks to make them culturally responsive for Black students. Given the importance of creating culturally responsive instruction in mathematics classrooms, more research on culturally responsive mathematics tasks is needed (Gallivan, 2017). In creating a rubric for evaluating and revising existing algebra tasks to become culturally responsive algebra tasks, we used the following theoretical perspectives: funds of knowledge (González et al., 2005; Moll et al., 1992), teaching mathematics for social justice (Gutstein, 2003), representations of marginalized groups (Peoples et al., 2021) and cognitive demand of mathematical tasks (Smith et al., 2004). Our rubric accordingly includes descriptors for each of the four domains: (a) cultural competency, (b) social justice, (c) representation, and (d) high academic expectation.

Using the rubric, we evaluated and revised 14 lessons (each lesson contains three to four mathematical tasks) from a free online algebra curriculum that is currently used by our participating district. To establish the inter-rater reliability, two authors individually analyzed the five original tasks and five revised tasks using the four domains. Before discussing any disagreement, the inter-rater reliability of codes from each domain was shown in Table 1. After reaching a consensus on coding, both authors individually analyzed the rest of the tasks and met to resolve further discrepancies. See Table 1 for the final results of the evaluation of the tasks. The number in each column represents a score for each mathematical content (e.g., Linear Models and Correlation Coefficient) which includes four or five lessons.

The results show our efforts to revise mathematical tasks to leverage students’ funds of knowledge and understanding of social justice while ensuring a high cognitive demand for each task. As shown in Table 1, revised lessons show an increased score for each of the four domains. We provide a sample of an original task and revised task in Figure 1 to show the nature of the tasks. While both tasks affirm a practice across student lives and connect it to mathematical content and practices, the revised task provides an opportunity for implicit and explicit connections to these practices as inherently cultural with explicit connections to mathematics (cultural competency). The original task does not contain a social justice context, whereas the revised task incorporates a story that centers on a problem to be solved in the context of justice (social justice). In terms of Domain 3, the original task includes a name (Priya) assumed to imply a representation of a historically marginalized group, while the revised task reflects not only names but also experiences of marginalized groups of students (representation). Both tasks offer several elements of high expectations, including using multiple representations in sensemaking and mathematical justification (high expectation). This study highlights the need for revision of curricular tasks to include culturally sustaining practices and shows collaborative efforts in improving learning conditions for students. In our session, we will present the rubric descriptors and the specific process of using the rubric to refine algebra lessons.

Authors

• Hyunyi Jung, University of Florida
  Presenting Author

• John Grab
  Presenting Author