How well aligned are common core textbooks to students’ development in area measurement?

Abstract

Among dozens of factors that influence mathematics teaching in the elementary classroom, textbooks endure as a significant contributor to the conversation. While teachers have many considerations while lesson planning, the textbook often forms an important launch point in determining what to include in lessons and how to do so. It follows that discrepancies between textbooks and research-recommended pathways for learning may lead to concerns or issues with pacing in the classroom. To explore this idea further, this study examined the alignment between three popular Common Core-aligned textbooks series and learning trajectories with respect to the topic of area measurement. Our findings indicated key differences in the ways textbooks presented area lessons and research-recommended ways of learning area topics, including a lack of appropriate area topic coverage in early grades and a mismatch of timing of concepts in later grades. The results indicated that the standards-based textbooks examined may lack attention to important topics in the pacing of area instruction, and suggest the need to inform both preservice and inservice teachers about the gap between textbook lessons and area learning trajectories so that development steps in area learning trajectory can be included in lesson plans. K E Y W O R D Scurriculum, curriculum standards, geometry, math/math education, textbooks

The challenges of alignment for the Next Generation Science Standards

“…LPs have shown an increased visibility in the field, including being an essential element in the NRC's () Framework document as well as informing the NGSS itself. However, just like Hong et al () found for mathematics and learning trajectories, misinterpretation or inattention could result in disordered sequence of content and practices that is inconsistent with the proposed trajectories. Yet for science, despite the widespread discussion about LPs, they are recognized as tentative, hypothetical, and requiring ongoing empirical validation.…”

“…Should we compare everything directly to NGSS, to an alternative framework derived directly from the NRC Framework , or to some other framework such as PISA, TIMSS, or the NAEP documents? Comparison frameworks could be made on an ad hoc basis using established content and cognitive distinctions (Liu & Fulmer, ), generated by analysis of alternative frameworks with international visibility (Alonzo, ; Khaliqi, ), produced with input from experts in policy and research (Porter et al, ), or developed by reinterpreting standards to emphasize other characteristics (Hong et al, , Troia et al, ). Even if a researcher opts to compare against NGSS directly, should they compare with respect to PEs, the three dimensions associated with the PEs, or some combination of dimensions?…”

“…This highlights how it is possible to compare a wide variety of source documents against each other with methods that are relatively transparent and reproducible. However, work on alignment to CCSS has just scratched the surface in trying to define and operationalize focus (Cobb & Jackson, ; Porter, McMaken, Hwang, & Yang, ) or multi‐year coherence with respect to mathematical learning trajectories or other notions of successive learning expectations (Confrey, Maloney, & Nguyen, ; Hong, Choi, Bhansali, Hwang, & Runnalls, ; Troia et al, ). Studied curriculum materials have inconsistent alignment with CCSS, without clear match to the hypothetical learning trajectories that inform CCSS‐M.…”

Comparing the frequency and variation of additive word problems in United States first‐grade textbooks in the 1980s and the Common Core era

“…Hong et al. (2019) examined math textbooks identified as being aligned with the CCSSM in comparison to the research literature for a particular topic, area measurement. They reported substantial misalignments, especially in the early grades.…”

“…(1986) seems to imply that many U.S. students are now expected to solve a wider variety of problem types than they were when Stigler et al performed their analysis of first‐grade textbooks. Although curriculum standards influence the textbooks and other instructional resources, and scholars agree that textbooks continue to play an important role in determining the enacted curriculum, the degree of alignment between the official curriculum and the instructional materials and other components of the enacted curriculum can vary (Hong et al., 2019; Polikoff, 2015; Remillard et al., 2014; Remillard & Heck, 2014; Tran, 2016). Comparing contemporary science textbooks with those of the 1980s, for example, Groves (2016) found that little had changed.…”