Rethinking Standards-Textbook Alignment: How Elementary Math Textbooks Are Interpreting And Enacting The Common Core State Standards

The Common Core State Standards for Mathematics (CCSSM) set ambitious goals for conceptual understanding through the content standards and developing mathematical habits of mind through the performance standards. Textbooks often serve as a mediator between standards and classroom instruction, as they expand a few short statements into a year of lessons, tasks, and educative supports that teachers use as a primary resource for both making sense of the standards and bringing them to life with students. Because of this critical role, understanding how curriculum developers have interpreted standards contextually and enacted those interpretations through developing textbook structures and content. I explore the concept of alignment between standards and textbooks and argue that many approaches to evaluating alignment are not sufficiently nuanced. Instead, I advocate for an approach that attends to both the holistic intentions and the details of the standards. My intention is to shift alignment conversations from asking if or how much a textbook is aligned to asking how and in what ways it is aligned. I analyzed how the CCSSM content and practice standards were interpreted and enacted in multiplication lessons across eight curriculum programs for grades 3-5. In each analysis, I addressed both structural features of the standards and structural features of the textbooks that seemed to support or inhibit full enactment of the standards. I identified several structural features of standards that seemed to impact both the depth and frequency at which they were addressed across the curriculum programs. Addressing textbooks, I found that the content standards have largely been successful in designating the topics covered and increasing conceptual understanding, which is an important achievement for mathematics education in the United States. However, I also found that only four of the eight programs meaningfully addressed the practice standards and more rigorous application of the content standards due to several structural features of lesson design. Based on these findings and additional research, I identify three instructional models that have emerged in textbooks in response to the CCSSM

Examining Elementary Teachers’ Use of Digital Instructional Resources : A Cross-Cultural Study

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A cross-cultural study of curriculum systems : mathematics curriculum reform in the U.S., Finland, Sweden, and Flanders

This paper relates to the mathematics curriculum systems of the United States, Finland, Sweden, and Flanders (Belgium). These four regions are in the midst of curriculum reform, which provides interesting grounds for cross-cultural comparison. Our analysis builds on a framework that focuseson curriculum policy, design and enactment in each of these regions and draws on interview data with teachers in all four regions, sample cases of curriculum use, context descriptions, and available descriptions of mathematics education in these four regions. This leads to a more nuanced understanding of the particular curriculum systems through which reform manifests, and sheds light on a challenging balance concerning a curriculum reform that is both coherent across a region and supported by teachers.Peer reviewe

Mathematics curriculum reform in the U.S., Finland, Sweden and Flanders : region-wide coherence versus teacher involvement?

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A Cross-Cultural Study on Teachers’ Use of Print and Digital Resources in Sweden, Finland, the USA, and Flanders : Some Methodological Challenges

Cross-cultural studies have inherent challenges as researchers from different cultural backgrounds attempt to make sense of similar-seeming material in unfamiliar contexts and communicate seemingly-obvious aspects of their own culture to outsiders (Clarke, 2013; Osborn, 2004). This contribution explores some of the methodological challenges in a cross-cultural study on teachers’ use of print and digital resources in four regions: Sweden, Finland, the USA, and Flanders (Belgium). All but one of the seven team members are insiders to one of the four contexts and to different extents outsiders to the other contexts. In order to benefit from insider-outsider perspectives, we designed five tools to develop alignment of insider and outsider lenses. We describe these tools in this contribution.Peer reviewe

Elementary teachers’ reflections on their use of digital instructional resources in four educational contexts : Belgium, Finland, Sweden, and US

We examine teachers' reflections on incorporating digital instructional resources (DIRs) into their mathematics teaching. We analyze qualitative interviews with 39 elementary school teachers from four educational contexts: Belgium, Finland, Sweden, and the U.S., using a framework proposed by Pepin et al. (Int J Math Educ 46: 645-661, 2017) to consider opportunities for DIRs to shift elements of teaching and learning in potentially transformative ways. Teachers described three major domains of teaching practice where they used DIRs: (a) class instruction, (b) student practice, and (c) professional participation. We found that teachers readily used DIRs during class instruction and to support student practice, guided by their existing instructional goals, which were shaped in part by education structures in the context. Few teachers incorporated DIRs in ways that transformed typical learning spaces. We also found that DIRs impacted several aspects of teachers' professional practices, including professional learning and collaboration. In particular, participation in social media and resource sharing altered the nature of and ways teachers participated in their own professional learning. We assert that efforts to use DIRs to stimulate change need to begin with an understanding of teachers' current practices and use our findings to identify three potential levers that might support movement toward change.Peer reviewe

Rethinking Standards-Textbook Alignment: How Elementary Math Textbooks Are Interpreting and Enacting the Common Core State Standards

The Common Core State Standards for Mathematics (CCSSM) set ambitious goals for conceptual understanding through the content standards and developing mathematical habits of mind through the performance standards. Textbooks often serve as a mediator between standards and classroom instruction, as they expand a few short statements into a year of lessons, tasks, and educative supports that teachers use as a primary resource for both making sense of the standards and bringing them to life with students. Because of this critical role, understanding how curriculum developers have interpreted standards contextually and enacted those interpretations through developing textbook structures and content. I explore the concept of alignment between standards and textbooks and argue that many approaches to evaluating alignment are not sufficiently nuanced. Instead, I advocate for an approach that attends to both the holistic intentions and the details of the standards. My intention is to shift alignment conversations from asking if or how much a textbook is aligned to asking how and in what ways it is aligned. I analyzed how the CCSSM content and practice standards were interpreted and enacted in multiplication lessons across eight curriculum programs for grades 3-5. In each analysis, I addressed both structural features of the standards and structural features of the textbooks that seemed to support or inhibit full enactment of the standards. I identified several structural features of standards that seemed to impact both the depth and frequency at which they were addressed across the curriculum programs. Addressing textbooks, I found that the content standards have largely been successful in designating the topics covered and increasing conceptual understanding, which is an important achievement for mathematics education in the United States. However, I also found that only four of the eight programs meaningfully addressed the practice standards and more rigorous application of the content standards due to several structural features of lesson design. Based on these findings and additional research, I identify three instructional models that have emerged in textbooks in response to the CCSSM

Emergency remote teaching as a window into elementary teachers’ mathematics instructional systems in Finland and the U.S.

This cross-cultural study examines how elementary mathematics teachers in Finland and the United States shifted their instructional systems during the period of Emergency Remote Teaching (ERT) in the spring of 2020. Using Ruthven's (2009) framework of Structural Features of Classroom Practice, researchers analysed 15 teachers’ descriptions of their mathematics teaching during ERT in contrast to their typical practice. Exploring how teachers in both contexts navigated challenges of ERT through a cross-cultural lens allowed researchers to identify similarities and differences in teaching practices and use of activity formats, synthesized in composite models of teachers’ instructional systems. The differences in the systems can be traced to underlying cultural assumptions about the nature of elementary mathematics education and the roles of teachers, students, and curriculum resources within each system.Peer reviewe