Three Strategies for Opening Curriculum Spaces

Abstract

Make these small adjustments to your syllabus and watch spaces open to connect to children's multiple mathematical knowledge bases.

Teacher Agency and Resilience in the Age of Neoliberalism

“…Work in elementary mathematics teacher preparation on “curriculum spaces,” for example, supports teachers in noticing and leveraging the opportunities for using and adapting curriculum materials in ways that connect to both children’s mathematical thinking and children’s community and cultural funds of knowledge (Drake et al, 2015; Land et al, 2019). Teachers might, for example, enact agency, based on knowledge of their students’ community and cultural funds of knowledge, gleaned through social networks consisting of teachers, students, and students’ families and communities, and critically examine the real-world contexts presented in curriculum materials, modifying them to make more authentic connections with students’ mathematical practices inside and outside of school.…”

Teacher Orchestrations of Transitions Within and Beyond Fractions Virtual Manipulatives

“…Janice chose to use the MLC Fractions app because it allowed students to create multiple wholes—a necessary feature when representing fractions greater than 1. Frameworks and other guidance already exist to support teachers in selecting and implementing high-quality tasks (e.g.Drake et al, 2015 ; Smith & Stein, 1998 ; Sullivan et al, 2015 ), but less attention has been giving to developing teacher learning experiences for selecting tools that could support students in engaging in tasks at a high level—for example, by ensuring they have opportunities to transition among multiple representations. The need for such experiences is likely to become more pressing as more and more digital tools become available to teachers.…”

“…Generalized frameworks and other guidance already exist to support teachers in using task choice and questioning techniques to orchestrate opportunities for engage in high-level mathematical thinking, including tasks and questions related to making transitions between representations (e.g.Drake et al, 2015 ; Smith & Stein, 1998 ; Sullivan et al, 2015 ). Although the frameworks do not relate specifically to using VMs or other technology tools in instruction, some of the guidance could be applied to selecting tasks or asking questions that facilitate students making transitions within or beyond representations in VMs.…”

“…For example, the math task framework (Smith & Stein, 1998 ) highlights opportunities to make connections among representations as a characteristic of tasks with higher-level cognitive demand. Drake and colleagues’ (Drake et al, 2015 ) strategies for opening curriculum spaces include suggestions for teachers to cut lesson components that tell, direct, or show students how to approach problems and instead focus on using prompts that allow for multiple solution strategies shown with multiple representations. To date, little research has focused on connecting these frameworks for supporting implementation of high-level tasks to teachers’ use of technology tools.…”

DisCrit noticing: Theorizing at the intersections of race and ability in mathematics education

“…Through readings and activities authored by ambitious and responsive mathematics teaching research community (Carpenter et al, 2014; Empson & Levi, 2011; Yeh et al, 2017), TeachMath Project (Bartell et al, 2017; Drake, Aguirre, et al, 2015), alongside other texts (e.g., books, blog posts, and current events) authored by disability studies (Collins, 2013; Lambert, 2020, Tan, 2017; Tan et al, 2019; Yeh, 2021; Yeh, Ellis, et al, 2020; Waitoller & Thorius, 2016; Yeh, Sugita, et al, 2020) and disability justice activists (Annamma & Morrison, 2018; CAST, 2018; Lewis, 2020; Sins Invalid, 2019) for PSTs to engage in reflection and redesign of mathematics learning spaces. During the first 5 weeks of the course, PSTs interviewed students, caregivers, and school and community members and visited school and community locations to deepen their knowledge about the students and the local communities that the school serves and document the community‐based resources and past and current historical context that can be used for lesson planning purposes (Drake, Land, et al, 2015). Then, PSTs began implementing their lessons in Week 6 providing weekly opportunities to examine their own mathematics teaching practices and to work collectively to inquire into and identify ways ableism and racism pervade traditional mathematics routines to design alternative, more humanizing classroom spaces.…”