Knowledge of curriculum embedded mathematics: exploring a critical domain of teaching

Abstract

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term knowledge of curriculum embedded mathematics (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and representations in mathematics curriculum materials. The KCEM framework is situated within existing research on content-specific teacher knowledge. Through analysis of elementary mathematics teacher's guides from the USA, we identified elements of curriculum resources teachers interact with when using them to plan instruction. These findings were complemented by interviews of teachers using curriculum guides to plan lessons, uncovering how they interacted with different elements of their guides. From this analysis, we propose four overlapping dimensions of KCEM: foundational mathematical ideas, representations and connections among these ideas, problem complexity, and mathematical learning pathways. Using an excerpt from one elementary curriculum guide and one of the teacher interviews on using this guide to plan a lesson, we illustrate how these dimensions might be activated as teachers read and use their guides.

Teacher–Textbook Relationships in Mathematics in Contexts of Limited Resources

“…For example, Leshota and Adler (2018) show that teachers omitting critical elements of the object of learning affects the teacher-textbook relationship adversely. Furthermore, research suggests that steering instruction towards the mathematical point is crucial to the teacher-textbook relationship, especially with innovative resources (Remillard & Kim, 2017;Sleep, 2012). Effective mobilisation of textbook affordances by the teacher presupposes alignment of the affordances with various teacher features, specifically, their beliefs, knowledge, orientation and goals (Brown, 2009;Pepin et al, 2017;Remillard, 2005).…”

Unpacking the Processes of Materials Use: An Interdisciplinary Perspective of Language Teachers’ Use of Materials in China

“…In other words, materials should be developed as intellectually engaging and meaningful to their users. The pedagogical representation embedded in the materials could be more direct, explicit, and concrete to cater to teachers' various needs (Remillard & Kim, 2017). Educative materials to advocate innovative pedagogy with teachers as the audience could also be developed (Davis et al, 2017) because materials as artifacts have the agency to change and modify human cognition through multilayered affordances (Radford, 2012).…”

“…Scholars in language education have long recognized teachers' expertise in using materials (e.g., Grossman, 1990;Richards, 2010;Tomlinson, 2012). However, the "funds of knowledge" (Seargeant & Erling, 2011) that teachers deployed to enact curriculum is recently identified in four domains, namely, the curriculum materials (Remillard & Kim, 2017), disciplines (Brown, 2009;Remillard, 2018), students (Gueudet & Trouche, 2012), and contexts (Choppin, 2009). Based on Shulman's (1986) categorization of teacher knowledge, Remillard and Kim (2017) termed knowledge of curriculum embedded mathematics to define what mathematics teachers need to activate to design instruction through the use of curriculum materials.…”

Mensagens Da Prática Pedagógica Em Textos De Materiais Curriculares Educativos: Uma Análise a Partir Da Dimensão Interacional

“…Educational Curriculum Materials (ECM 3 ) have become an emerging field and referenced in international literature as a possibility to support teacher learning (BEYER; DAVIS, 2009; REMILLARD; HERBEL-EISENMANN; LLOYD, 2009; REMILLARD; KIM, 2017). According to Remillard (2018), the materials must "talk to" teachers about the ideas intrinsic to mathematical assignments and not just "guide" their actions.…”

“…ECM are resources historically used to support the learning of teachers and students, as pointed out by Remillard and Kim (2017) and Remillard (2018), which consist of any physical or digital material -such as textbooks, handouts or activity books produced by the Municipal and State Educational Departments. This support may be given by the constituent elements of ECM, such as: guidance on student questions, student answers commented, videos of a class (NIE et al, 2013;OLIVEIRA, , 2017.…”