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Research has identified a number of problems limiting the implementation of content standards in the classroom. Curriculum materials may be among the most important influences on teachers’ instruction. As new standards roll out, there is skepticism about the alignment of “Common Core-aligned” curriculum materials to the standards. This analysis is the first to investigate claims of alignment in the context of fourth-grade mathematics using the only widely used alignment tool capable of estimating the alignment of curriculum materials with the standards. The results indicate substantial areas of misalignment; in particular, the textbooks studied systematically overemphasize procedures and memorization relative to the standards, among other weaknesses. The findings challenge publishers’ alignment claims and motivate further research on curriculum alignment.

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... Bu araştırmanının yürütülmüş olmasındaki bir diğer gerekçe, matematik eğitimi alan yazınında program uyumluluğuyla ilgili oldukça az sayıda çalışmanın yer almasıdır (Kara, Karakoç, Yıldırım ve Bay, 2017;Leung, Leung ve Zuo, 2014;Osta, 2007;Polikoff, 2015;Polikoff, Zhou ve Campbell, 2015;Seitz, 2017). Bununla birlikte, var olan çalışmaların çoğunluğu belgesel (doküman) araştırma niteliğindedir (Leung, Leung ve Zuo, 2014;Osta, 2007;Polikoff, 2015;Polikoff ve diğerleri, 2015). ...

... Bu araştırmanının yürütülmüş olmasındaki bir diğer gerekçe, matematik eğitimi alan yazınında program uyumluluğuyla ilgili oldukça az sayıda çalışmanın yer almasıdır (Kara, Karakoç, Yıldırım ve Bay, 2017;Leung, Leung ve Zuo, 2014;Osta, 2007;Polikoff, 2015;Polikoff, Zhou ve Campbell, 2015;Seitz, 2017). Bununla birlikte, var olan çalışmaların çoğunluğu belgesel (doküman) araştırma niteliğindedir (Leung, Leung ve Zuo, 2014;Osta, 2007;Polikoff, 2015;Polikoff ve diğerleri, 2015). Belgesel araştırmalarda genellikle şu konular üzerine odaklanılmıştır: matematik ders kitaplarının içeriğiyle ortak çekirdek standartlar (common core standards) arasındaki uyum (Polikoff, 2015;Polikoff ve diğerleri, 2015); öğretim programı kazanımları ve ulusal merkezi sınav sorularıyla genel süreç becerileri arasındaki uyum (Leung ve diğerleri, 2014) ve öğretim programı kazanımlarıyla ulusal merkezi sınav soruları arasındaki uyum (Osta, 2007). ...

... Bununla birlikte, var olan çalışmaların çoğunluğu belgesel (doküman) araştırma niteliğindedir (Leung, Leung ve Zuo, 2014;Osta, 2007;Polikoff, 2015;Polikoff ve diğerleri, 2015). Belgesel araştırmalarda genellikle şu konular üzerine odaklanılmıştır: matematik ders kitaplarının içeriğiyle ortak çekirdek standartlar (common core standards) arasındaki uyum (Polikoff, 2015;Polikoff ve diğerleri, 2015); öğretim programı kazanımları ve ulusal merkezi sınav sorularıyla genel süreç becerileri arasındaki uyum (Leung ve diğerleri, 2014) ve öğretim programı kazanımlarıyla ulusal merkezi sınav soruları arasındaki uyum (Osta, 2007). Öte yandan, program uyumluluğuyla ilgili ampirik (görgül) araştırmalar belgesel araştırmalara kıyasla oldukça az sayıdadır (Kara ve diğerleri, 2017;Seitz, 2017). ...

Uyumluluk; kazanımlar, öğretim ve değerlendirme arasındaki örtüşmenin derecesine karşılık gelmektedir. Program uyumluluğu öğrenci başarısını artıran en önemli etkenlerden biri olmasına rağmen alan yazında bu kavramla ilgili az sayıda çalışma yer almaktadır. Bu boşluktan yola çıkarak bu çalışmada ortaokul matematik öğretmenlerinin çözümlü örneklerinin ve yazılı sınav sorularının öğretim programında yer alan kazanımlarla uyum düzeyini belirlemek amaçlanmıştır. Araştırmada iç içe geçmiş çoklu durum deseni kullanılmıştır ve katılımcılar maksimum çeşitlilik örneklemesi kullanılarak belirlenmiştir. Bu çalışmanın verileri 2009 yılında yayımlanan ilköğretim matematik dersi 1-5 sınıflar öğretim programı, 6-8. sınıflar öğretim programı ve kılavuzu, birinci araştırmacı tarafından bir dönem boyunca kayıt altına alınan sınıf içi gözlemler ve öğretmenlerin yazılı sınav kâğıtları yardımıyla toplanmıştır. Veriler, karşılaştırmalı durum sentezi tekniği kullanılarak analiz edilmiştir. Araştırmanın bulguları, öğretmenlerin çözümlü örneklerinin ve yazılı sınav sorularının öğretim programında yer alan kazanımlarla uyumunun sayılar öğrenme alanı için yeterli düzeyde olduğunu göstermiştir. Öte yandan, öğretmenler; cebir, olasılık ve istatistik ve geometri öğrenme alanlarında ciddi uyumsuzluklar sergilemişlerdir. Bulgulardan yola çıkılarak, öğretmenlerin program uyumluluğu ile ilgili yeterliklerinin geliştirilmesini sağlayacak önerilerde bulunulmuştur. Anahtar Kelimeler: Uyumluluk kavramı, öğretim programı kazanımları, çözümlü örnekler, yazılı sınav soruları, ortaokul matematik öğretmenleri, 7. sınıf öğrencileri ABSTRACT Alignment refers to the degree of correspondence among the objectives, instruction, and assessment. Although curriculum alignment is one of the most important factors increasing student achievement, there exist few studies about this concept in the educational literature. Based on this gap, in the current study, it was aimed to explore the alignment of mathematics teachers' worked examples and written exam tasks to the learning objectives of the middle school mathematics curriculum. Multiple-case design with multiple units of analysis was used in the study and maximum variation sampling was used in the selection of the participants. The main data sources of this study were the elementary (grades 1-4) and middle school mathematics curriculum (grades 5-8) released in 2009, lesson observations conducted in the 7th grade classrooms in the first semester of the educational year 2013-2014, and written exam tasks prepared by the teachers for assessing students' learning of the topics covered in this semester. Data were analyzed via the technique of cross-case synthesis. The findings showed that the level of alignment between teachers' worked examples, written exam tasks, and the curriculum objectives was satisfactory for the numbers learning domain. However, the teachers demonstrated severe misalignments in the algebra, probability and statistics, and geometry learning domains. Recommendations on how to improve teachers' curriculum alignment competencies were provided based on the findings.

... As we describe below, most California districts indeed adopt textbooks approved by the state as being aligned with the CCSS. While adoption by the state of California presumably signals some degree of alignment and quality, we know that textbooks often vary in their content (Polikoff, 2015). Thus, we wondered whether the problems highlighted in Williams-systematic variation in student opportunity to learn-remain issues in present-day California. ...

... We apply the SEC framework to the textbooks in our sample following the methods described in detail, with a worked example, in Polikoff (2015). The first step is "chunking" the textbooks, by which we mean breaking each textbook down into its finest-grained level of detail. ...

... These alignment values are somewhat lower than those found for third-grade mathematics textbooks (0.28 to 0.40 for Alignment Index 1, 0.64 to 0.80 for Alignment Index 2) in the one prior published study of mathematics textbook alignment to standards using the SEC (Polikoff, 2015). Prior research on alignment indices cautions against direct comparisons of alignment indices outside the confines of a single study, however, because features of the alignment process such as the number of cells in the coding framework can affect the expected magnitude of alignment indices (Polikoff & Fulmer, 2013). ...

Low-income students and students of color are faced with pervasively lower levels of opportunity to learn compared with their peers, creating unequal opportunities for educational success. Textbooks, which serve as the backbone of the curriculum in most mathematics classrooms, present a potentially powerful tool to help mitigate unequal opportunity to learn across students. Using the Surveys of Enacted Curriculum framework, we investigate the content of commonly used eighth-grade math textbooks in California and the extent to which they align with the Common Core State Standards. We also explore the relationship between the variation in content coverage and alignment and student characteristics. We find poor alignment between the textbooks in our sample and the Common Core State Standards and low overall levels of cognitive demand, but only limited evidence of systematic differences in alignment or cognitive demand coverage associated with student characteristics at the school or district level.

... Therefore, many teachers rely heavily on textbooks to support their day-to-day teaching and allows textbooks to significantly influence students learning experience. This is possible for what is presented in them will likely affect what teachers teach, and, eventually, what students learn (Polikoff, 2015;Ur, 2015). ...

... Textbooks represent the curriculum at classroom level (Russell & Airasian, 2012;Byrd & Schuemann, 2014;Smart & Jagannathan, 2018). It can be said that textbooks represent the taught curriculum; i.e. all the teaching and learning activities teachers attempt to create in the classroom with a view to facilitating students in achieving the learning outcomes specified in the intended curriculum (Byrd & Schuemann, 2014;Oates, 2014;Polikoff, 2015;Ur, 2015). ...

... Such situation is prevalent in countries with English as a foreign language (EFL) context. Textbooks are developed to provide models of how the new curriculum should be translated into classroom instructions so that the desired change occurs in the classrooms (Hutchinson & Torres, 1994;Oates, 2014;Polikoff, 2015;Ur, 2015;Smart & Jagannathan, 2018). Guilloteaux (2013) asserts that 'A quality textbook should be a model of good teaching and should facilitate students' language learning'. ...

... This study is grounded in the intended curriculum of English language arts (ELA) and math standards, the written curriculum adopted to align with the intended curriculum, and its influence on teachers' enacted curriculum. Many scholars agree that high-quality curriculum materials aligned to the standards can help translate standards to practice (Polikoff, 2015, Smith & O'Day, 1991 by focusing teacher practice on standards-based content and strategies. ...

... We focus on educational leaders (e.g., district administrators, principals) as they are among those who can strategically mobilize people, resources, policies, and procedures in support of a wellmanaged vision for instructional change (DeMatthews 2014; Leithwood et al., 2004;Ylimaki, 2012). Yet educational leaders are largely invisible from the curriculum literature, which has focused on (a) teachers' enactment of the curriculum (e.g., Ball & Cohen, 1996;Ogawa et al., 2003;Remillard, 2005), (b) the quality of the materials and their effects on student achievement (Bhatt et al., 2013;Polikoff, 2015), and (c) professional development (PD) to support teacher learning and implementation of curriculum (Anglum et al., 2020;Crowley, 2017;Desimone & Hill, 2017;Penuel et al., 2011). ...

... Common Core State Standards demanded instructional shifts that emphasized the conceptual over the procedural, disciplinary content expertise, and the comprehension of complex texts (Floden et al., 2017). While traditional textbook companies started producing curricular materials that were purportedly aligned to the standards, early analyses suggested these alignment claims were overstated (see Polikoff, 2015). ...

The ambitious goals of standards-based reform call for both technical and adaptive leadership to address problems of practice involving the technical and adaptive alignment of teachers’ instruction to the standards. Thus, standards-aligned curriculum implementation necessitates both types of strategies; otherwise, adaptive challenges will persist. In this study, we analyze case studies of four districts where new English Language Arts and math curricula were recently adopted to help align teachers’ practice with their state’s English Language Arts and math standards. We draw from interviews with district leaders, principals, instructional coaches, and teachers to illustrate how mostly technical strategies for curriculum implementation do little to address the adaptive challenges that prevent teachers from fundamentally shifting their practice to be more aligned to the standards and to meet the needs of all learners. We conclude with a set of insights and implications for educational leaders approaching curriculum implementation in both technical and adaptive ways.

... While history suggests that revising textbooks to meet ambitious goals is insufficient to change teacher practice without a level of support that is often lacking in the U.S. (Schoenfeld, 2004;Willoughby, 2000), studies also show that without rigorous textbooks, teachers are unlikely to increase rigor and conceptual understanding on their own (Stein et al., 2000. As such, there have been calls for research on textbooks as a critical measure for understanding the influence of the CCSSM on U.S. mathematics education (Heck et al., 2011;Polikoff, 2015). ...

... States (Ball & Cohen, 1996;Houang & Schmidt, 2008;Polikoff, 2015;Remillard, 2005;Stein et al., 2007;Valverde et al., 2002). Because of this critical role in interpreting and enacting the standards, research on textbooks provides valuable insights for understanding the influence of the CCSSM on mathematics education in the United ...

... States (Heck et al., 2011;Polikoff, 2015). ...

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.

... Porter y Smithson (2001) y Webb (1997;1999) fueron los pioneros en estudiar la relación entre la evaluación, el contenido y los procesos cognitivos expresados en los estándares estatales. También se encuentran estudios de la alineación entre los libros de texto con el currículo Polikoff, 2015),con el propósito de determinar la coherencia que existe entre los materiales curriculares y los estándares. En Honduras, se ha estudiado la alineación o coherencia, a nivel de demanda cognitiva, entre los estándares académicos y las tareas o actividades que se proponen en los libros de texto de matemáticas en la educación secundaria (Ramos y Casas, 2016). ...

... Los libros de texto también han sido objeto de estudio desde el punto de vista de la alineación. Por ejemplo, Polikoff (2015) realizó una investigación en los Estados Unidos en la que se identifican una serie de problemas que limitan la implementación de estándares de contenido en el aula, dado que, en los libros de texto estudiados, los resultados indican áreas sustanciales de desalineación; entre otras debilidades, enfatizan en exceso los procedimientos y la memorización en relación con los estándares. Para analizar este tipo de alineación, los autores utilizaron el modelo Surveys of the Enacted Curriculum Alignment Model (SEC). ...

En este artículo estudiamos en qué medida los planes de área de matemáticas de la educación media colombiana se alinean con los estándares básicos de competencia en matemáticas (Ministerio de Educación Nacional, 2006). Se describe qué significado daremos al término alineación de un plan de área con los estándares y se explica cómo se aplica esta idea a cada plan de área. Bajo un planteamiento cuantitativo, se calculó la alineación de 206 planes de área, estratificados por área geográfica, tipo de institución y modalidad académica. Mediante técnicas de estimación y contraste de hipótesis se establece la alineación de los planes de área colombianos con los estándares. Encontramos que esta alineación es reducida con una dispersión importante, y que no hay diferencias significativas en la alineación de los planes de área de los diferentes tipos de colegios.

... Of these companies, only McGraw-Hill and Harcourt appeared to publish elementary and middle school health textbooks at the time this research was initiated. Following precedent from other textbook analyzes (Polikoff, 2015;Sleeter and Grant, 1991), a representative sample of texts was selected from a range of elementary and middle school grades from each publisher, which publishers provided based on the research team's location in New York State. Publishers did not share specific information with us on the adoption of these textbooks across districts. ...

... Determining interrater reliability. As an expected practice with content analyses (Gabriel and Lester, 2013;Polikoff, 2015) and given the fraught nature of coding images based on visual cues, authors engaged in norming sessions, wherein members of the research team individually coded and debated the coding of various images, until an agreement was reached. Subsequently, members of the research team all coded HAR2. ...

Purpose: In light of the systemic and pervasive nature of ableism and how ableist ideology structures-or limits-educational opportunities, this paper aims to contribute to the ongoing conversation within the field of multicultural education regarding how to meaningfully include dis/ability in K-12 curricula.
Design/methodology/approach: This paper explores how elementary and middle school health textbooks from two prominent publishers in the USA portray dis/ability through quantitative and qualitative content analysis methods of 1,468 images across texts.
Findings: Findings indicate that the majority of the textbook portrayals of dis/ability tacitly forward assimilationist ideals. Specifically, the textbooks assume and speak to a normatively-abled reader, pointing out those with dis/abilities as different from the reader. Additionally, mainstream or normative markers are provided as evidence of success and those with dis/abilities who have been successful as such are positioned as overcoming their limitations. Practical implications-Such portrayals stifle the possibility of social transformation by reinforcing and privileging dominant, ableist views. Therefore, teachers are recommended to take steps that might counter such messages in curricular materials and teacher educators are called on to support these efforts.
Originality/value: This paper extends the tradition of curricular analysis as one of the first studies to examine the portrayals of dis/ability in US health textbooks and offer practical implications for educators.

... In contrast, mathematical understanding refers to the problem solving strategies and complex thinking of NGP which is constituted in the process of generalising number patterns using algebraic and geometric reasoning (Blanton & Kaput, 2005). Various studies have employed the SEC to investigate alignment between content standards, assessment and learning materials in terms of the alignment indices (Ndlovu & Mji, 2012;Polikoff, 2015). Ndlovu and Mji (2012) describe the SEC as the most effective and simplest procedure for evaluating alignment. ...

... The computed Porter's alignment index of 0.73 of the current study signals that 27% of the content and cognitive levels were misaligned. Porter (2002) made assertions that the alignment indices, as tools of measuring A handful of studies (Ndlovu & Mji, 2012;Polikoff, 2015;Polikoff & Porter, 2014) have used the alignment index to evaluate alignment between content and assessment. ...

Improving the strength of alignment between educational components is essential for quality assurance and to achieve learning goals. The purpose of the study was to investigate the strength of alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns. The study contributes to strengthening the intended curriculum and the workbook activities, since workbooks are widely used in South African public schools. The study employed the concurrent triangulation research design. The theoretical framework comprised Webb’s alignment model and the Surveys of Enacted Curriculum. The Senior Phase mathematics content standards and Department of Basic Education workbooks were selected for content analysis. The findings showed that the alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns was significantly acceptable with misaligned content and representations that require urgent attention. We recommend reconfiguration of both the workbook activities on numeric and geometric patterns and Senior Phase mathematics content standards to align content, cognitive levels, representations and assessment. Further studies on teaching and learning that are aided by the workbook activities should be mandated.

... Textbooks play an irreplaceable role in promoting students' mastery of scientific knowledge and organization of learning activities. Besides, textbooks are the factor affecting students' academic performance (Aldahmash et al., 2016;Andersen, 2020;Polikoff, 2015), and the guarantee for teachers to implement curriculum standards (Hill, 2001), so it is necessary to examine the textbooks (Vojíř & Rusek, 2021). Under the standards-based reform, standards become the important basis of measurement, guide the curriculum development and classroom teaching, and put forward clear goals and expectations for teachers to improve teaching quality and students to improve their academic performance (Troia et al., 2018). ...

... Qhibi et al. (2020) conducted a study on alignment between content standard and practice materials in high school mathematics and concluded that the results were acceptable but needed further adjustment. Polikoff et al. (2015) tested the alignment of primary school mathematics textbooks and curriculum standards and found that the alignment index was not high. It can be found that in the existing studies, there is insufficient research on the alignment of teaching materials with curriculum standards, and the research subjects mostly focus on mathematics. ...

This study applied the Porter’s alignment model to construct a localized two-dimensional framework based on Anderson's taxonomy. The research chose the third-grade primary school science textbooks from two representative presses in China and Japan, coded the textbooks and curriculum standards, calculated the alignment level between the textbooks of the two presses and their corresponding curriculum standards, and discussed the alignment level from the topic, cognitive demand, and emphasis. The results show that the B version in Japan is significantly aligned with the Japanese curriculum standard, but the A version in China does not have significant alignment with the Chinese curriculum standard. Besides, a common problem is that the ratios of life science in sample science textbooks both exceed the requirements of the curriculum standards, and the problems of exceeding the standard in cognitive demand and not highlighting the key points also need to be concerned. This study provides ideas and references for countries with similar educational situations to study the compilation of science textbooks and fills up the deficiency of the international comparison of the alignment between primary school science textbooks and curriculum standards by using the alignment model. Keywords: alignment evaluation, content analysis, curriculum standards, primary school, science textbooks

... Within the existing textbook analysis research, most studies were interested in examining if reform-based textbooks effectively translated and incorporated the new standards under the mathematical reform (e.g., Hong et al., 2018;Jitendra et al., 2005;Polikoff, 2015). The results of the textbook analyses indicated that the answer was not always "Yes". ...

... Although both textbook series are referred to as reform-based textbooks, they are somewhat different. Go-Math is identified as reform-based but with a more traditional orientation because it stresses fluency, procedures, and memorization; whereas, Investigations is identified as reform-based but with a more progressive orientation because it places more emphasis on mathematical thinking and opportunities for students to create strategies and make mathematical connections (Hong et al., 2018;Polikoff, 2015;Remillard et al., 2014). The data used for this study come from the first-grade lesson books on whole number addition and subtraction problems that contained at least one word problem. ...

One of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform‐based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized in the Essential Understanding Series (EU) presented by NCTM against the backdrop of mathematics education reform. In particular, we analyzed the features of the lessons for teaching addition and subtraction word problem solving. In some aspects, the results indicated that in terms of teaching problem comprehension and algebra readiness, the two textbook series showed improvement compared to formerly used textbooks. However, both textbook series may fall short of reflecting some important EU big ideas (e.g., teaching the underlying structure and part‐part‐whole relation of addition and subtraction word problems; providing students with chances to deal with exhaustive problem types and situations). In particular, our findings highlight the need for teaching word problem solving through building abstract level conceptual understanding. Implications for future textbook developing and limits are discussed.

... Examinations of content standards often focus on alignment between standards and related curriculum and assessments [12,13]. Less common are crosswalks between two or more sets of K-12 content standards; among those types of studies, international comparisons have provided insight regarding how cultural and political views reflect in educational standards [14]. ...

... Missouri presents K-5 PEs across 31 pages in six columns: sections of rows are demarked by DCIs and columns represent grades. Wisconsin similarly presents PEs in columnar format but instead of specifying grade-specific standards, their standards indicate the PEs are to be addressed by grade bands (K-2, 3-5, 6-8, [9][10][11][12]. Some states, in addition to their discrete or rolling layouts, provide learning progression charts that resemble the Missouri and Wisconsin columnar designs. ...

Science standards across 44 states in the United States are often assumed to be equivalent because they are all based on the National Research Council’s (NRC) Framework for K-12 Science Education. Twenty of those states adopted the Next Generation Science Standards (NGSS), which is based on the NRC Framework, and the 24 other states developed their own NRC Framework-based science standards. In this article, two related studies are described that focused on assessing this homogeneity assumption. In the first study, a comparative document analysis categorized the variety of ways performance expectations are presented. Analysis also focused on relative placement of information related to performance expectations and components of three-dimensional learning. To assess how variations affect teacher noticing, in the second study nearly 300 elementary school teachers viewed, in random order, seemingly similar fourth-grade standards from three states. Comparisons focused on teachers’ noticing of student objectives, elements that stood out, and teachers’ rationales regarding their noticing. Though both studies underscored that all NRC Framework-based science standards do integrate NRC Framework tenets, findings counter the assumption that NRC Framework-based science standards are necessarily equivalent to each other or to NGSS.

... For example, work on the Common Core has included the development of cross-state assessment consortia (e.g., PARCC, Smarter Balanced) and many organizations are engaged in developing curricula and professional development aligned to the standards and used across districts and states (Hodge, Salloum, & Benko, 2016). Thus, one crucial test of the implementation of the Common Core lies in evaluating the extent of vertical and horizontal alignment between the standards and the curriculum, assessments, incentives, and learning opportunities for educators and students in different communities (Polikoff, 2015;Porter et al., 2011). By contrast, coherence reflects the sense that individuals and groups make of particular aspects of their experience and the extent to which they perceive those aspects as consistent and understandable. ...

... • The magnitude of the CCSS and teacher evaluation components may mean that even "aligned" materials end up addressing and emphasizing different aspect of the standards for students and teachers (Polikoff, 2015;Stosich, 2018). ...

... Analysis of how content is treated in textbooks is also studied (Lui & Leung, 2012;Park & Leung, 2006;Seah & Bishop, 2000), including cognitive aspects of mathematics textbooks. For example, Polikoff (2015) analyzes the alignment of three US textbooks to curriculum standards. He finds that textbooks systematically overemphasize procedures and memorization, underemphasizing higher cognitive skills. ...

... Research has shown that there is a need for both more and more detailed information on curriculum quality (Chingos & Whitehurst, 2012;Polikoff, 2015); this study attends to this need. ...

... The CCSS were intended to offer educators a more ambitious and coherent vision for teaching and learning (Swars & Chestnutt, 2016). However, in practice, educators often experience multiple and conflicting demands related to these standards, emanating both from the compliance-oriented way many states and districts implement the CCSS (Akiba & Wilkinson, 2016;Durand, Lawson, et al., 2016) as well as from the various nonsystem actors in the education field that provide textbooks, curricula, technology, and assessments that are all said to align with the standards (Burch, LaFave, & Good, 2015;Polikoff, 2015). The messages educators receive from these various sources often relate to surfacelevel aspects of practice rather than the underlying principles related to teaching and learning (McDuffie, Drake, et al., 2015;Porter, Fusarelli, & Fusarelli, FIGURE 4 Changing coupling patterns in schools, from ceremonial rules to technical ceremonies Early eras through the 1980s ...

After decades of accountability and market-based reforms in education, school systems are now organizing more around improving teaching and learning. Yet these efforts frequently yield unintended, superficial, or even counterproductive changes at the school level. In this article, Maxwell Yurkofsky develops the concept of technical ceremonies as a way of theorizing this emerging pattern of school organizations. Technical ceremonies involve educators changing their practice to align with new reforms in a way that privileges what is visible and measurable as a way of appeasing external stakeholders over more substantive improvements to practice. He argues that technical ceremonies arise as principals navigate a multitude of surface-level demands from the environment and the uncertainties that pervade efforts to transform teaching and learning.

... Research on mathematics textbooks generally focuses on content analysis-comparing the content in different contexts (e.g., Charalambous, Delaney, Hsu, & Mesa, 2010), comparing content against a prescribed curriculum (e.g., Polikoff, 2015;Sidenvall, Lithner, & Jäder, 2015), or evaluating the depth or level of content on a particular focus area (e.g., Davis & Fonger, 2015). There are also discourse analyses that, for example, identify gender constructions (e.g., Hottinger, 2010), and features of grammar that illuminate aspects of mathematics and mathematics education discourse (e.g., O'Keeffe & O'Donoghue, 2015;Herbel-Eisenmann & Wagner, 2007;Wagner, 2012). ...

... In the SEC, there are also two areas of measuring alignment ─ content and cognitive levels (Polikoff, 2015;Polikoff et al., 2011). The cognitive levels are a revised version of Bloom's taxonomy of Memorize, Perform Procedures, Demonstrate Understanding, Conjecture, Generalize, Prove and Solve non-routine problems, and Make connections. ...

... Despite theories that the classroom environment may be associated with CCR mathematics teaching and learning, this relationship has not been examined empirically. Extant research on CCR-aligned mathematics teaching and learning focuses instead on standards (Cobb & Jackson, 2011;Dingman et al., 2013;Porter et al., 2011), curriculum and assessment (Polikoff, 2015;Schoenfeld, 2015), improving teacher content knowledge (Bausmith & Barry, 2011), and implementation and accountability efforts (Coburn et al., 2016;Roth McDuffie et al., 2017). While these each represent important elements of the shift to CCR standards, they do little to illuminate the characteristics of classroom environments where students do and do not engage in standardsaligned mathematics practices. ...

Research focused on emotionally supportive teaching has typically run in parallel to the study of rigorous, standards-aligned mathematics teaching. However, recent work theorizes that positive and warm classroom environments may be necessary to help students meet the ambitious goals outlined in newer mathematics standards. We analyze the relationship between facets of classroom environments and the prevalence of standards-aligned mathematics instruction across more than 400 mathematics lessons in Washington, D.C., classrooms. We find no evidence of consistent standards-aligned mathematical engagement absent an engaging, emotionally supportive learning environment. These findings suggest that efforts to help teachers make the instructional shifts outlined in college and career ready standards might also need to support the provision of productive, warm, and nurturing learning environments.

... Lack of examination of new support tools for writing, such as VR, may be in part because there is an assumption that the textbook has primacy and by far is the most commonly used support tool in the classroom (Polikoff 2015). Researchers examining K-20 science classrooms illustrate the point that the textbook is the most predominant support tool for delivering content to students and is often the tool most referred to for development of arguments and summaries (Robinson et al. 2014). ...

The purpose of this study was to investigate the role textbooks can play on writing complexity and lexical density as a proxy for critical thinking and ultimately learning, in relation to argumentative and summative writing when integrated with a virtual reality experience. In this study, differences in writing complexity and lexical density scores were measured across four different pedagogical modalities: VR alone, VR followed by textbook readings, textbook readings followed by VR, and textbook readings alone. Adult students, recruited from non-science-based higher education programs, responded to two prompts related to content found in the VR environments and discussed in the textbooks. The authors hypothesized that exposure to a virtual marine environment prior to responding to the writing prompts would enhance both argumentative and summative writing products, when compared to participants who only had access to the textbook experiences. Participants who were exposed to the VR environment then a textbook demonstrated significantly greater writing complexity and lexical density scores than those who had access to VR alone, or access to the text alone.

... This research is timely, given recent attention on curricula as a focus of education policies and advocacy. As the Common Core and similar standards spread across states, educators and researchers noted considerable shortcomings in existing curricula intended to help students meet new standards (Heitin, 2015;Herold and Molnar, 2014;Polikoff, 2015). In response, states and organizations began developing tools so that school administrators, teachers, and other stakeholders could assess the alignment of their materials with new standards. ...

... The evidence to date is mixed. A recent study (Polikoff, 2015) used a prominent alignment methodology, the Surveys of Enacted Curriculum (SEC), to examine the content and standards alignment of several pre-and post-CCSS mathematics textbooks, all of which show up in our sample. That study found moderate overall levels of alignment of textbooks to state standards or to the CCSS. ...

Can a school or district improve student achievement simply by switching to a higher‐quality textbook or curriculum? We conducted the first multi‐textbook, multi‐state effort to estimate textbook efficacy following widespread adoption of the Common Core State Standards (CCSS) and associated changes in the textbook market. Pooling textbook adoption and student test score data across six geographically and demographically diverse U.S. states, we found little evidence of differences in average achievement gains for schools using different math textbooks. We found some evidence of greater variation in achievement gains among schools using pre‐CCSS editions, which may have been more varied in their content than post‐CCSS editions because they were written for a broader set of standards. We also found greater variation among schools that had more exposure to a given text. However, these differences were small. Despite considerable interest and attention to textbooks as a low‐cost, “silver bullet” intervention for improving student outcomes, we conclude that the adoption of a new textbook or set of curriculum materials, on its own, is unlikely to achieve this goal.

... Comparison of the CCSSM with the findings of Stigler et al. (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 firstgrade 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 & Heck, 2014;Tran, 2016). Comparing contemporary science textbooks with those of the 1980s, for example, Groves (2016) found that little had changed. ...

Decades of research conducted worldwide has resulted in a taxonomy for word problems involving additive situations. Research published in the 1980s found that U.S. curricula only exposed first‐grade students to a small subset of the easiest types of word problems. Widely adopted curriculum standards in the United States call for first‐grade students to be exposed to the full set of 11 types of problems in the taxonomy, but research shows that substantive changes to the content of instructional materials can be elusive. We asked whether the U.S. curricula continue to expose students to the same small subset of problems. We coded four widely used first‐grade textbooks from the Common Core era. Comparing our findings with those from the 1980s, we found many more word problems, a wider variety of word problems, and a consistent pattern in relative emphasis of various problems in the current textbooks. These results clearly show that U.S. students’ exposure to word problems through curriculum materials has changed. This finding lays the groundwork for further research to determine whether such changes in exposure to different types of word problems have resulted in changes to relative problem difficulty.

... Books are generally seen as the main curriculum source in the classroom. Many studies discuss the importance of textbooks, Rezat (2012); Shield and Dole (2013); Polikoff (2015); Remillard, Harris, and Agodini (2014) mentioned in their researches that textbooks are important artifacts and the main source of providing educational opportunities. This textbook is an important teaching resource and appeals to many stakeholders, such as lecturers, teachers, students, students and parents. ...

The purpose of this study is to look for the validity of badminton textbooks for Physical Education and Recreational Education students. This type of research is research and development research. The study procedure uses development procedures according to Borg and Gall, namely: "(1) Research and information collecting, (2) planning, (3) developing preliminary forms of product, (4) preliminary field testing, (5) main product revision, (6) main field testing, operational product revision, (8) operational field testing, (9) final product revision, (10) dissemination and distribution. "In developing the research, it does not use entirely but only with 7 steps, namely 1) needs analysis, 2) makes products consisting of preparation of material preparation, instructional, books, and evaluation tools, 3) product validation consisting of media experts, learning experts, 4) small group trials using subjects 6-12 people, interview data, observations, and questionnaires are collected and analyzed, 5) revises phase I products, 6) large group trials using subjects 30-100. 7) phase II product revision. This textbook research used a questionnaire, namely (1) needs analysis questionnaire, (2) expert trials, (3) small groups, and (4) large groups. The conclusion of this study is that the validity score of this textbook is very high and this badminton textbook is very feasible to use because it has been validated by the material expert and instructor media.

... When textbooks are analyzed, the frequency or the number of times a particular topic appears on textbook pages are often computed. These frequencies are usually weighted equally (Ding, 2016;Polikoff, 2015;Smith et al., 2016) because it is too challenging to decide which items would give more meaningful OTL to students. Next, we needed to decide on the unit of analysis. ...

... While some states are considering further changes, the increased demands of these new standards compared with previous state standards, require a corresponding increase in the rigor and content of instructional materials that teachers use in their classrooms (Porter et al., 2011). Recent studies suggest that some of the most widely used instructional materials are not well aligned with CCSS and CCR standards, despite claims to the contrary by many publishers and sources of online materials (Polikoff, 2015;Heitin, 2015;Herold and Molnar, 2014). Many state education agencies and school districts are struggling to fill the void in standards-aligned curricula and instructional materials to help students meet their state standards (Rentner, 2013;Rentner and Kober, 2014). ...

... The results seem to reflect the current set up of Philippine mathematics classrooms where students get to know mathematics by memorizing rules and do mathematics by following them. This runs parallel to Polikoff's (2015) investigation of the alignment of fourth-grade mathematics textbooks in Florida to the common core standards that saw strong emphasis on procedures and memorization. Nevertheless, situational problems and application tasks can contribute to the development of learners' higher order thinking. ...

As major sources of information, curriculum materials (CMs) have generally served teachers and students by providing instructional and learning support. The impact of CMs on teachers’ pedagogical practice and learners’ engagement and success had been fairly documented. However, just as the use of CMs is influenced by teachers’ orientations and learners’ identity with the subject matter, the same can be said for textbook writers who attend, interpret and respond to curriculum content and standards. Guided by Dietiker, Males, Amador and Earnest (2018)’s curriculum noticing construct, this study examined the epistemological features of Philippine secondary school mathematics textbooks of the Department of Education. Four textbooks, one from each grade level, were analyzed via a directed qualitative content analysis. Following the inductive approach, significant statements from the texts were culled and organized through coding, categorizing and abstraction using a repertory grid. Member checking was done to validate the findings of the study. Interestingly, the study afforded the development of the Onion Model of Curricular Noticing Dynamics in Mathematics Textbooks. The model reveals how CM writers frame the mathematics curriculum in the design and development of textbooks. Specifically, the encountering frame lays emphasis on their interaction with the mandated curriculum through an examination of curricular elements. In the sense-making frame, writers reflect on four curricular questions leading to an understanding of the curriculum and the context in which it operates. Finally, the operationalizing frame captures the unique moves observed by textbook writers in developing the materials. The emerged model can serve as a valuable means in achieving heightened consciousness among textbook writers as they develop materials that promote teacher learning and respond to learners’ needs, interests and orientations.

... We cross-referenced responses with materials that met expectations of college and career-ready standards adopted in most states, according to independent reviews of commonly used curricula conducted by EdReports.org. Teachers were categorized as using high-quality materials if they reported using at 1 Porter et al., 2011;Schmidt andHouang, 2012. 2 Opfer et al., 2018;Kaufman et al., 2018;Polikoff, 2015. 3 Steiner, 2017, provides a summary of some of the most prominent of those studies. ...

... Increasingly since the outset of Common Core State Standards in 2010, curricula are viewed as a potential lever to reform education through materials aligned with rigorous standards (Chingos & Whitehurst, 2012). Yet there are many challenges for districts and states in adopting new curricula because, even if an evidence-based curriculum is provided, it is hard to ensure teachers will have the time to permit high FOI (Polikoff, 2015). Moreover, teachers in the present studies did not always have clear guidance from school and district leaders about which curriculum materials were the "backbone" or mandate and which were optional resources (Polikoff, 2018). ...

Research Findings: This study used the Theoretical Domains Framework (TDF) to examine barriers to teachersâ€™ implementation of a supplemental academic language curricula. Despite high satisfaction with this scripted curriculum, three past studies indicated heterogeneity in teachersâ€™ fidelity of implementing the curriculum as well as difficulty going off script. Thus, our goal was to identify barriers to fidelity of implementation and map these onto possible behavior change techniques. Participants included 175 teachers from pre-kindergarten and kindergarten classrooms. We used mixed-method approaches that included surveys, focus groups, and interviews with teachers and their coaches. The most salient barriers to fidelitious implementation were: competing priorities for instructional time as well as limited teacher knowledge and skills. For some teachers, other barriers included difficulty changing habits, challenges with memory and attention processes, or lack of fit when the curriculum was used with populations beyond the designed scope. Practice or Policy: To understand why teachers may not consistently implement evidence-based curricula with fidelity, we explain steps other education researchers can use to apply the TDF and insights from the field of implementation sciences. We provide sample TDF survey questions and suggestions to help educators and researchers systematically revise the theory of change for curricular interventions.

... The recognition of technology support tools such as EVR may promote learning because of the multiple modes of presentation. By contrast in many classrooms, textbooks are used as support tools and as a potential way of developing prior knowledge for students to respond to writing prompts (Polikoff, 2015). In many cases, the textbook in the science classroom is the most predominant support tool for delivering content to students (Robinson, Fischer, Wiley, & Hilton III, 2014). ...

This study examines the role of virtual reality (VR) in the promotion of writing with greater complexity and lexical density. Using a combination of neuroimaging and traditional measures, the author characterizes differences in writing complexity and lexical density scores across four different pedagogical modalities: VR alone, VR followed by a textbook reading, textbook reading followed by VR, and textbook reading alone. Middle school students recruited from a rural middle school in the Mid-Atlantic Region of the United States responded to two prompts related to science content found in VR environments and a textbook. The authors hypothesized that exposure to a virtual environment prior to responding to the writing prompts would enhance both argumentative and summative writing products, when compared to participants who only had access to the textbook experiences. Participants who were exposed to the VR environment then had access to a textbook demonstrated significantly greater writing complexity and lexical density scores than those who had VR alone, or access to the text alone.

... Two components, in particular, mediate the relationship between the intended curriculum and implemented curriculum: the textbook curriculum and the assessed curriculum. Indeed, different textbooks can have varying content coverage, alignment, depth, and flow (Polikoff, 2015;Schmidt & McKnight, 2012), and evidence from mathematics education suggests that variation in the content of instruction affects student achievement (see Schmidt & Maier, 2009). ...

Well-informed decisions on curricular materials can be an efficient way to boost student achievement. Prior studies have employed experimental and quasi-experimental designs to investigate the effects of textbooks on mathematics achievement. This is the first study to consider textbook effects in social studies education. Within the context of a textbook adoption cycle in Texas, we use a difference-in-differences approach with district-level administrative data and estimate the effects of adopting a state-approved textbook on social studies achievement. We find no evidence of a practically meaningful adoption effect. We conclude by highlighting the need for further high-quality research in this often-overlooked school subject area.

... One important operationalization of alignment that was outside the scope of our study but hope to see in future work is the extent to which preschool curricula are actually aligned, in terms of content, with state early learning standards. Researchers have done this work in K-12 policy using content analyses of textbooks and the Common Core State Standards, finding only limited evidence of alignment ( Polikoff, 2015 ;Porter, Polikoff, Zeidner, & Smithson, 2008 ). A similar analysis of widely used ECE curricula and state standards would be an important extension of this work. ...

State governments are largely responsible for most early childhood education (ECE) policies (e.g., state pre-K, Child Care and Development Fund [CCDF]). However, multiple ECE funding streams and governing agencies within a state can lead to misaligned policies and incoherent systems. Thus, there exists great variability within and across states in ECE policy implementation. In our study we descriptively analyzed nationally, publicly available data to assess alignment within state policy systems on three policy levers often used in K-12 education research: state ECE standards, curricula, and assessment, the latter of which we operationalized as states’ quality rating and improvement systems. Additionally, we examined the extent to which the governance of our focal policy levers is dispersed across, or housed within, different state-level institutions or agencies (i.e., alignment via governance). Our descriptive analyses reveal little and limited alignment between a state's policy levers of standards, curriculum, and assessment, and between state preschool policies—state pre-K and CCDF—with respect to curricular guidance. We also find wide variation in the number of ECE governing agencies within a state. The findings indicate potential for confusion around policies for early learning providers and demonstrate largely misaligned or poorly specified policies that are dispersed at the state level. We hope that researchers will continue to refine this initial model of alignment in the context of a rapidly changing ECE policy field.

... Although instruction is increasingly multimodal, textbooks nevertheless endure and even thrive as a core classroom resource (Polikoff, 2015). Thus, it is important to find ways to improve the design of textbooks to support learning. ...

In this study, we investigated the literacy practices of undergraduate calculus students and non-mathematics STEM faculty members as they read excerpts from a calculus textbook. We found several differences in their practices that appeared to be tied to the didactical nature of the excerpts and the participants’ identities and power relationships with the textbook. We use these differences to explore the concept of didactical disciplinary literacy to examine the ways readers approach the process of learning from a mathematics textbook and how their practices are related to their positionality with respect to the text. We also explore the development of the readers’ thinking about the mathematical concepts and suggest connections between this development and their literacy practices. The study results have implications for the ways that mathematics textbooks can be used as resources for learning the content and literacy practices of the field.

... Indeed, over the past decade, states have developed accountability systems that are better at assessing higher-order thinking skills and improvements to instructional practice (Dee et al., 2021;Doorey & Polikoff, 2016). However, because there has been less progress building social and political consensus around these standards and assessments (i.e., educators must still navigate a variety of values, expectations, and resources that conflict with this vision of teaching and learning), such advances in addressing representational uncertainty have nevertheless yielded many of the same implementation challenges as earlier accountability systems (e.g., Marsh et al., 2017;Polikoff, 2015). ...

School systems are increasingly working to foster more ambitious learning environments and disrupt institutionalized educational inequities. But such efforts are complicated by a number of uncertainties-about the aims of schooling and how they might be achieved or measured-that suffuse educational organizations. Although there is general agreement that uncertainty is both pervasive and consequential in educational settings, as a field we lack a more unified analytic framework for making sense of this uncertainty. In this essay, I seek to advance such a project by drawing on educational and organizational scholarship to identify three forms of uncertainty that pervade school systems. While two of these forms of uncertainty-environmental and technical-are well-established in organizational theory, I develop the concept of representational uncertainty as a third form of uncertainty that is particularly impactful in schools. I show how these three forms of uncertainty manifest across different contexts, aims, and levels of school systems, how they interrelate, and how they must be strategically mitigated or fostered in the service of educational improvement.

... Reinforcing this preoccupation, another perspective points that textbooks are of significative influence in students' learning experiences (Polikoff, 2015, Chingos & Whitehurst, 2012Tarr et al, 2006;Hadar & Ruby, 2019;Van den Han & Heinze, 2018;Valverde et al., 2002). To Chingos & Whitehurst (2012) the selection of teaching materials, textbooks among them, will greatly affect students' learning. ...

This paper describes a research aimed at problematizing cases of indication to the use of Base Ten Blocks (BTB) and Green Chips (GC) for the teaching and learning of the Arabic numeral system and of arithmetic operations. The cases analyzed are present in the five collections of Elementary School mathematics textbooks selected by the National Program of Textbook (PNLD), which were the most purchased by the Ministry of Education (MEC) in 2016, to supply the system of public education in Brazil during the triennium 2016-2018. The identified indications were classified in three types, and two of them were particularly problematized for presenting some type of limitation or confusion. Only one of the five collections studied did not present problems regarding manipulatives.

... initial review of seven English language arts (ELA) series were mixed but more positive-three were considered fully aligned to the CCSS, three partially aligned, and one fully unaligned (Heitin, 2016). These findings mirror the findings from Polikoff's (2015) analysis of the alignment of four popular textbooks to the CCSS for Grade 4 mathematics, which revealed areas of substantial misalignment and challenged the publishers' claims of alignment. ...

This study was designed to assess the effects of states’ adoption of more rigorous standards as part of the current wave of standards-based reform on student achievement using comparative interrupted time series analyses based on state-level NAEP data from 1990 to 2017. Results show that the effects of adopting more rigorous standards on students’ mathematics achievement were generally small and not significant. The effects on students’ reading achievement were also generally small, but negative and statistically significant for Grade 4. The study also revealed that the effects of states’ adoption of more rigorous standards varied across NAEP subscales and student subgroups.

... Despite this widespread availability, instructional materials are rife with issues, especially in how they are being implemented in the classroom. Some textbooks are still misaligned with CCSS, stressing memorization and procedural knowledge over higher cognitive skills (Polikoff, 2015). However, what may be more alarming is that, even when the materials themselves use the recommendations of PSSM and embed activities that emphasize the construction of knowledge by students, their enactment by teachers in the classroom often undercuts the cognitive demand of the tasks, typically because the teacher is unaware why the task was built the way that it was (Heck et al, 2012;McDuffie et al., 2018). ...

Background
To increase teachers’ capacity to implement high-quality instructional materials with fidelity in their classrooms through a video-based professional learning cycle, the Analyzing Instruction in Mathematics Using the Teaching for Robust Understanding framework (AIM–TRU) research–practice partnership was formed. Drawing upon the design-based research paradigm, AIM–TRU created the initial design for the professional learning cycle and wanted to engage in continued iterative redesign as the year progressed. This necessitated a method, common among those who adjust their designs when applying them in context, by which to document and justify changes made over time to our model. The research contained in this article used qualitative methods to articulate and test the design underlying our professional learning cycle by advancing conjecture mapping, a device by which the embodiments of the design are made transparent to be analyzed in practice.
Results
The initial design conjectures and activity structures teachers engaged in through our model of professional learning were refined to address three themes that emerged. Firstly, it was found that the ways participants engaged with the mathematics of the lesson were underwhelming, in large part, because our own definition of what rich talk around mathematics should entail was lacking in details such as the mathematical objects in the lesson, the presence of multiple solution pathways, or the various representations that students could use. Second, talk structures did not always allow for equitable exchanges among all teachers. Finally, activity structures did not encourage teachers to delve deeply into the mathematics so they could perceive the lesson as a coherent piece of their own classroom curriculum. Our design conjectures and activity structures were revised over the course of the year.
Conclusions
Our use of conjecture mapping allowed us to address the concern with research–practice partnerships that they should develop and utilize tools that make the systemic inquiry they engage in transparent, allowing for other researchers, practitioners, and stakeholders to see the complete design process and make use of the findings for their local context. Implications for this process as a tool for those who pilot and scale professional development are raised and addressed.

... For example, many organizations are developing curricula and PD aligned to the standards and used across districts and states (Hodge et al., 2016). Thus, one crucial test of the implementation of the CCSS lies in evaluating the extent of "vertical"-between goals and policies at different levels-and "horizontal"-across individuals and groups at each level-alignment between the standards and the curriculum, assessments, incentives, and learning opportunities for educators and students in different communities (Polikoff, 2015;Porter et al., 2011). By contrast, coherence reflects the sense that individuals and groups make of particular aspects of their experience and the extent to which they perceive those aspects as consistent and understandable. ...

In this study, we aim to deepen understanding of what it would take to develop the relationships, common understandings, and collective expertise that might support district-wide improvement efforts by examining the implementation of the Common Core and a teacher evaluation policy. Drawing on three years of social network data in three districts, we find that administrators were more likely to be talking together about teacher evaluation than the Common Core. Further, administrators with more positive views of the potential impact of these policies and their access to the human and technical resources necessary for implementation were more likely to engage in positive information seeking behaviors. These findings have important implications for policies intended to increase instructional coherence in schools and districts.

The transition to new assessments aligned to the Common Core State Standards was a significant turning point in the standards’ implementation. Concerns about the transition led districts to suspend the use of value-added scores for evaluating teachers, but changes to other measures, such as classroom observations, were rare. Using data from the Washington, DC Public Schools, I evaluate the effect of the assessment transition on teachers’ practice. I find substantial declines in instructional practice, ranging from 13% to 20% of a standard deviation, for teachers in tested grades and subjects when the new exam was introduced. These results suggest that policymakers should consider the ramifications of testing changes on a wider array of teaching outcomes than value-added scores alone.

Curriculum reform brings new approaches to classroom practice. As changes to the curriculum are implemented, teachers need to receive additional support from textbooks and other materials. In the study presented in this paper, we explored the use of resources during the process of educational reform in Croatia. The focus was on the use of a mathematics textbook set as the main resource, but the use of other material and non-material resources was also examined. The study also dealt with the social factors that influenced the use of these resources. It was designed as a case study of one mathematics teacher and her students, examined at three time points, before the reform, in the preparation period, and subsequent to the implementation of the reform. The results showed that the textbook set is a stable resource over the time periods, although it did undergo some changes towards digitalization. The teacher’s professional development was shown to be an important non-material resource during the period of change. The research also revealed that the participants’ decisions concerning the use of resources depended on some social issues, such as norms concerned with being a teacher or a student. The study showed that longitudinal monitoring of the use of resources in the period of curricular change may contribute to a better understanding of the processes of instructional transformation and development.

Социально-экономическое, политическое развитие нашего государства, интеграция в мировое сообщество являются важнейшими факторами, обусловливающими объективную необходимость качественных преобразований в системе профессионального педагогического образования. Насущной является необходимость создания условий для подготовки специалистов, ориентированных на выполнение социального заказа общества, конкурентоспособных на международном рынке труда, способных к профессиональному саморазвитию, самокоррекции в меняющихся условиях. Направления реформирования этой отрасли специального образования отражают общие тенденции развития образовательной практики в мире. Проблема формирования и развития профессиональной компетентности учителей рассматривается в контексте личностно ориентированной модели обучения, существенным признаком которой является такая организация усвоения содержания образования субъектом, во время которого происходит снятие объективного значения материала и выявление в нем субъективного смысла личностно утверждающих ценностей. Цель статьи заключается в раскрытии специфики, видов и технологии проведения интерактивных семинаров как формы активизации учебно-познавательной деятельности студентов вуза. В научно-педагогической литературе интерактивными принято называть средства, обеспечивающие непрерывное диалоговое взаимодействие субъектов образовательного процесса.
Socio-economic and political development of our state, integration into the world community are the most important factors that determine the objective need for qualitative changes in the system of professional teacher education. There is an urgent need to create conditions for training specialists focused on fulfilling the social order of society, competitive in the international labor market, capable of professional self-development, self-correction in changing conditions. The directions of reforming this branch of special education reflect the general trends in the development of educational practice in the world. The problem of formation and development of professional competence of teachers is considered in the context of a personality-oriented learning model, an essential feature of which is such an organization of the assimilation of the content of education by the subject, during which the objective meaning of the material is removed and the subjective meaning of personality-affirming values is revealed in it. The purpose of the article is to reveal the specifics, types and technologies of interactive seminars as a form of activation of educational and cognitive activity of university students. In the scientific and pedagogical literature, it is customary to call interactive means that ensure continuous dialog interaction of the subjects of the educational process.

In this survey paper we focus on mathematics learning in Chinese contexts, as a way to contribute to broader discussions about mathematical learning. We first review the features of Chinese students’ mathematical learning depicted in the literature, followed by a review of student mathematical learning in recent Chinese research journals. This leads to an introduction of the papers on Chinese students’ learning in this issue. For Chinese students’ learning contexts, we discuss four aspects, namely, classroom instruction, teachers’ professional learning, curriculum materials, and learning outside of school. For each context, we review the literature findings on the identified features, introduce emerged practices and most recent policies under the reformed era, and discuss the relevant papers in this special issue. Whenever possible, we connect findings on Chinese students’ learning with the associated contexts and relate these findings in the Chinese contexts to findings in the broader world context. We conclude this survey paper with possible lessons learned from Chinese students’ learning features and from the varied Chinese contexts. In particular, we discuss these aspects from culturally contextualized and semantically decontextualized dimensions, which is expected to facilitate broad international discourse centering on the three questions proposed at the end of this paper.

The vast majority of U.S. teachers supplement their officially adopted curriculum materials with unofficial materials. Despite this, the body of supplementation-relevant literature tends not to focus on supplementation specifically, so lacks cohesion, and sometimes fails to capture all aspects the phenomenon. I systematically review supplementation-relevant literature from 2015 to 2020 and report seven areas of consensus in the literature around (1) who is involved in teacher-level curriculum supplementation, (2) important dimensions of supplementation, and (3) the educational value of supplementation. To provide future researchers a common starting point for studying teacher curriculum supplementation, I propose the Teacher Curriculum Supplementation Framework, a flexible yet testable analytical tool for systematizing scholarly inquiry around teacher curriculum supplementation and its effects on teachers and students.

This article analyzes the Common Core State Standards initiative as an innovation network. Using narrative data and quantitative analysis of hypertext linkages on the World Wide Web, we describe a network of about 3200 organizations that arose to scale up the Common Core State Standards and link them to aligned academic resources such as assessments, instructional materials, and professional development. By 2017, this network developed a “core-periphery” topology. The article describes structures and processes at the core of the network that created strong pressures for construction of a coherent ecosystem of instruction for American education and processes at the periphery that that worked against use of this system by most organizations in the network.

In this paper, we study the presence of systematic differences between teacher non-blind assessments and external blindly graded standardized tests as a measure of grading misalignment. Using a large administrative database covering two student cohorts (N = 31, 183 pupils) from publicly-funded schools in the Basque Country (Spain), we explore the grading gaps found between these two type of assessments for several student characteristics using fixed effects modeling. We find that, after controlling for standardized achievement, systematic teachers’ under-assessment exists for student groups that, on average, lag behind in school: boys, children from an immigrant background, and low SES students. The observed data patterns withstand several robustness checks, including the use of instrumental variables approach (IV) and other alternative regression specifications.

Textbooks are a widely used educational intervention that can affect student achievement, and the marginal cost of choosing a more effective textbook is typically small. However, we know little about how textbooks get from the publisher to the classroom. The purpose of this paper is to investigate the ways mathematics textbook adoption practices vary and predict adoption decisions. We use interviews with district leaders in a stratified random sample of 34 California school districts. We find isomorphic, highly formalized adoption processes in most districts. However, we observe some differences along dimensions of district size, technological interest/infrastructure, and English learner concentration. We recommend states produce and update lists of high-quality materials early and often, and that they use a highly rigorous evaluation process. We also recommend states experiment with encouraging similar districts to partner on textbook evaluation and adoption to respond to district demands for information and capacity building around curricula.

This chapter serves as an introduction to this volume. It introduces the idea of curriculum analysis and situates the work of this volume in the Improving Curriculum Use for Better Teaching (ICUBiT) project. After providing a brief historical overview of the evolution of mathematics curriculum materials in the USA, beginning in 1990, we detail the framework guiding our analysis of five elementary mathematics programs, along with a set of assumptions that undergird our approach. We then locate our approach to curriculum analysis in the wider body of such work, identifying several key methodological questions that researchers consider when undertaking analysis of curriculum materials. Finally, we introduce the five curriculum programs that are the focus of our analysis and provide an overview of key aspects of our methodological approach. We conclude with an overview of the remaining chapters in the volume.

This study investigates the alignment between curriculum standards and textbooks, based on a standards-based science education context. The analysis sample includes the High School Biology Curriculum Standards and five editions of biology textbooks in China. Porter's alignment model is used to construct a two-dimensional (content areas and cognitive levels) matrix of curriculum standards and textbooks to calculate alignment indices and marginal discrepancies between the two dimensions. The results show that 1) alignment between curriculum standards and textbooks has not been achieved; 2) textbooks are highly consistent and statistically significant, but independent of curriculum standards; 3) the distribution of curriculum standards and textbooks across various core concepts and cognitive levels is unbalanced; 4) both curriculum standards and textbooks overemphasise the cognitive levels of remembering and understanding, while minimally representing the applying, analysing, evaluating, and creating levels. This study examines the development of curriculum alignment in the context of current worldwide standards-based science education reforms and provides a framework for alignment research based on content analysis.

With the recent adoption of the Common Core standards in many states, there is a need for quality information about textbook alignment to standards. While there are many existing content analysis procedures, these generally have little, if any, validity or reliability evidence. One exception is the Surveys of Enacted Curriculum (SEC), which has been widely used to analyze the alignment among standards, assessments, and teachers’ instruction. However, the SEC can be time-consuming and expensive when used for this purpose. This study extends the SEC to the analysis of entire mathematics textbooks and investigates whether the results of SEC alignment analyses are affected if the content analysis procedure is simplified. The results indicate that analyzing only every fifth item produces nearly identical alignment results with no effect on the reliability of content analyses.

We describe an innovative automated test construction algorithm for building aligned achievement tests. By incorporating the algorithm into the test construction process, along with other test construction procedures for building reliable and unbiased assessments, the result is much more valid tests than result from current test construction practices. The test construction process is efficient and versatile in its application. The target domain could be state content standards, a particular curriculum, or even an intervention. The algorithm, which draws on Surveys of Enacted Curriculum (SEC) procedures, can be employed in the context of English language arts and reading, mathematics, or science. We demonstrate the algorithm's use and benefits for constructing tests, guiding item writing, and creating subtests from an existing test such that the subtests.

The alignment among standards, assessments, and teachers’ instruction is an essential element of standards-based educational reforms. The Surveys of Enacted Curriculum (SEC) is the only common tool that can be used to measure the alignment among all three of these sources (Martone & Sireci, 2009). Prior SEC alignment work has been limited by not allowing for significance tests. A recent article (Fulmer, 2011) provided a first attempt to address this shortcoming of the SEC, but that work was limited in several ways.We extend Fulmer’s simulation approach by accounting for important elements of the SEC procedures, including the proper framework size, number of standards and assessment points, number of raters, rater cell-splitting rates, and rater agreement results. The results indicate that inferences about relative alignment may be heavily influenced by features of the alignment procedures. Thus, our method should be broadly applied to future SEC alignment investigations.

Coherence is the core principle underlying standards-based educational reforms. Assessments aligned with content standards are designed to guide instruction and raise achievement. The authors investigate the coherence of standards-based reform’s key instruments using the Surveys of Enacted Curriculum. Analyzing 138 standards-assessment pairs spread across grades and the three No Child Left Behind tested subjects, the authors find that roughly half of standards content is tested on the corresponding test and roughly half of test content corresponds to the standards. A moderate proportion of test content is at the wrong level of cognitive demand as compared to the corresponding standards, and vice versa. Between 17% and 27% of content on a typical test covers topics not mentioned in the corresponding standards. Policy and research implications are discussed.

State content standards are the backbone of the standards-based reform movement. Content standards provide teachers with a set of guidelines for what students are expected to know and be able to do, defining the intended curriculum. And although the current 50-state system of education gives each state the task of setting content standards, there has been little empirical investigation of the similarities and differences among state content standards. This analysis uses the content analysis procedures of the Council of Chief State School Officers/State Collaboratives on Assessment and State Standards to consider whether there exists a de facto national curriculum as defined in state content standards. Data from English/language arts and reading (ELAR), science, and mathematics for Grades 4, 8, and K—8 are used. Results suggest considerable variability among states in the content of content standards, particularly in individual grades, but also for the aggregated standards. Further analysis suggests that state standards are no more well aligned to national professional standards (i.e., National Science Education, National Council of Teachers of Mathematics) than to other states’ standards. Still, there exists a small “core curriculum” across states in each content area. The level of focus of the state standards varies substantially across states, and the redundancy of the standards is such that alignment within state, across grades is often as high as alignment within grade, across states. Policy implications are briefly discussed.

School accountability decisions based on standardized tests hinge on the degree of alignment of the test with the state’s standards documents. Yet, there exist no established criteria for judging strength of alignment. Previous measures of alignment among tests, standards, and teachers' instruction have yielded mixed results that are difficult to interpret and to compare across studies. This article reports findings from a simulation study to determine critical values for Porter’s alignment index, suitable for hypothesis testing at alpha levels of .05 and .10, as is familiar to many scholars. It then reexamines the results of previous alignment studies and demonstrates how these findings may be compared through the use of these critical values. The tables of critical values will be useful to researchers or policymakers who seek to judge strength of alignment of standards, assessments, and instruction. The article also describes directions for future research in establishing objective criteria for the interpretation of alignment indices.

The Common Core standards released in 2010 for English language arts and mathematics have already been adopted by dozens of states. Just how much change do these new standards represent, and what is the nature of that change? In this article, the Common Core standards are compared with current state standards and assessments and with standards in top-performing countries, as well as with reports from a sample of teachers from across the country describing their own practices.

The authors (a) discuss the importance of alignment for facilitating proper assessment and instruction, (b) describe the three most common methods for evaluating the alignment between state content standards and assessments, (c) discuss the relative strengths and limitations of these methods, and (d) discuss examples of applications of each method. They conclude that choice of alignment method depends on the specific goals of a state or district and that alignment research is critical for ensuring the standards-assessment-instruction cycle facilitates student learning. Additional potential benefits of alignment research include valuable professional development for teachers and better understanding of the results from standardized assessments.

Studies of teachers’ use of mathematics curriculum materials are particularly timely given the current availability of reform-inspired curriculum materials and the increasingly widespread practice of mandating the use of a single curriculum to regulate mathematics teaching. A review of the research on mathematics curriculum use over the last 25 years reveals significant variation in findings and in theoretical foundations. The aim of this review is to examine the ways that central constructs of this body of research—such as curriculum use, teaching, and curriculum materials—are conceptualized and to consider the impact of various conceptualizations on knowledge in the field. Drawing on the literature, the author offers a framework for characterizing and studying teachers’ interactions with curriculum materials.

This book offers in-depth information resulting from the Third International Mathematics and Science Study (TIMSS). Launched in 1995, the TIMSS examines elementary and secondary mathematics and science achievement in 40 countries. The book explains that curriculum has a profound effect on student achievement and plays a crucial role in providing opportunities for student learning. The 11 chapters examine: (1) "How Does Curriculum Affect Learning?"; (2) "A Model of Curriculum and Learning"; (3) "Measuring Curriculum and Achievement"; (4) "The Articulation of Curriculum"; (5) "Curriculum Variation"; (6) "The Structure of Curriculum"; (7) "A First Look at Achievement"; (8) "Learning and the Structure of Curriculum"; (9) "Curriculum and Learning Gains across Countries"; (10)"Curriculum and Learning Within Countries"; and (11) "Schools Matter." The book concludes that reform efforts should be redirected to create challenging curriculum across all years of schooling for all students. The four appendixes focus on: TIMSS mathematics and science curriculum frameworks; relationship between content measurement categories for TIMSS framework, teachers, and TIMSS test; TIMSS framework codes and number of items for each mathematics and science test sub-area; and supplemental material related to the two-level analysis of mathematics achievement: chapter 10. (Contains 96 references, 56 tables, and 32 figures.) (SM)

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of classroom practice--teaching--and presents the results of two studies of randomly selected, nationally representative U.S. eighth-grade mathematics lessons that were videotaped as part of the TIMSS 1995 and 1999 Video Studies. (Contains 4 figures, 6 tables and 11 footnotes.)

This analytic essay draws on research about the effectiveness of current education policies as well as observations about developing policy systems in a number of states. The chapter begins with several observations about policy and school-level success, examines current barriers to school improvement and proposes a design for a systemic state structure that supports school-site efforts to improve classroom instruction and learning. The structure would be based on clear and challenging standards for student learning; policy components would be tied to the standards and reinforce one another in providing guidance to schools and teachers about instruction. Within the structure of coherent state leadership, schools would have the flexibility they need to develop strategies best suited to their students. The systemic school reform strategy combines the ‘waves’ of reform into a long-term improvement effort that puts coherence and direction into state reforms and content into the restructuring movement.

Instructional policy reforms that focus on standards and assessments have gained popularity in the last two decades. State governments, which had previously left most instructional matters to local governance, set challenging learning standards and developed related assessments and curricular frameworks. Despite their popularity and persistence, standards-based reforms face the challenge of successful local implementation. Occupying an intermediary position between the statehouse and the schoolhouse, the local school district has significant potential to influence standards implementation. It is important to consider the consequences for classroom instruction of what districts do in response to standards. While states may set standards and provide incentives for implementing them, district policies often determine how teachers comprehend the standards.
This issue of CPRE Policy Briefs summarizes the findings of a recent book, Standards Deviation: How Schools Misunderstand Education Policy (Spillane, 2004), that examines state and local government relations as the standards move from the statehouse to the district policymakers and teachers who attempt to make sense of them. It takes a case study approach, focusing on a single state, Michigan, and strategically sampled school districts. The study is based on empirical data from a four-year examination of approaches to the use of standards in nine Michigan districts between 1992 and 1996. The sample included three midsize city districts, two suburban districts, and four rural districts. Mixed methods, including semistructured interviews, questionnaires, and observations, were used to gather data at state, district, and school levels on implementation of math and science standards.
This overview of the study's findings first frames the subject of standards-based reform, and then moves to a discussion of the Michigan math and science standards. Variation in the progress of standards among districts is explored next, followed by a cognitive explanation for the variation and a discussion of districts' resources. Next, variation in teachers' beliefs about and implementation of the standards is analyzed. The overview closes with implications of the study for policy outcomes, analysis, and design.

While numerous recent authors have studied the effects of school accountability systems on student test performance and school “gaming” of accountability incentives, there has been little attention paid to substantive changes in instructional policies and practices resulting from school accountability. The lack of research is primarily due to the unavailability of appropriate data to carry out such an analysis. This paper brings to bear new evidence from a remarkable five-year survey conducted of a census of public schools in Florida, coupled with detailed administrative data on student performance. We show that schools facing accountability pressure changed their instructional practices in meaningful ways. In addition, we present medium-run evidence of the effects of school accountability on student test scores, and find that a significant portion of these test score gains can likely be attributed to the changes in school policies and practices that we uncover in our surveys.

A Splintered Vision: An Investigation of U.S. Science and Mathematics Education is the US report on the curriculum analysis component of the Third International Mathematics and Science Study (TIMSS) which was sponsored by the International Association for the Evaluation of Educational Achievement (IEA).
The report summarizes data from the TIMSS curriculum analysis and integrates it with teacher questionnaire data from the US, Japan, and Germany on science and mathematics topic coverage and instructional practices.
The authors of A Splintered Vision discuss and provide evidence of the unfocused nature of US mathematics and science curricular intentions, textbooks, and teacher practices. They offer the premise that producers of US textbooks and curriculum guides have attempted to answer calls for curricular reform by adding new content to already existing materials instead of devoting time to restructuring the materials. The authors also suggest that US teachers, inundated with a myriad of competing visions, are attempting to cover all the topics they confront in their resource documents and to meet all the instructional demands placed on them by those with a stake in education. In keeping with the `incremental assembly line' philosophy in American society, US teachers also tend to lean toward a piecemeal approach to education. The authors speculate on what such practices may mean for the mathematics and science achievement of US students.
The work is sure to spur discussion among educational researchers, policy makers, and others concerned about the future of mathematics and science education in the US.

What is “teaching to the test,” and can one detect evidence of this practice in state test scores? This paper unpacks this concept and empirically investigates one variant of it by analyzing test item–level data from three states’ mathematics and reading tests. We show that NCLB-era state tests predictably emphasized some state standards while consistently excluding others; a small number of standards typically accounted for a substantial fraction of test points. We find that students performed better on items testing frequently assessed standards—those that composed a larger fraction of the state test in prior years—which suggests that teachers targeted their instruction towards these predictably tested skills. We conclude by describing general principles that should guide high-stakes test construction if a policy goal is to ensure that test score gains accurately represent gains in student learning.

The authors comment on Porter, McMaken, Hwang, and Yang’s recent analysis of the Common Core State Standards for Mathematics by critiquing their measures of the focus of the standards and the absence of an assessment of coherence. The authors then consider whether the standards are an improvement over most state mathematics standards by discussing whether the core mathematics ideas on which they focus are appropriate, whether individual standards are organized into coherent learning progressions, and whether their implementation is feasible. They question whether schools and districts currently have the capacity to support effective implementation, and they call for improvement-oriented investigations that can inform the development of effective implementation models.

The alignment of instruction with the content of standards and assessments is the key mediating variable separating the policy of standards-based reform (SBR) from the outcome of improved student achievement. Few studies have investigated SBR’s effects on instructional alignment, and most have serious methodological limitations. This research uses content analyses of state standards and assessments and survey data on more than 27,000 teachers’ instruction in mathematics, science, and English/language arts (ELA) to investigate changes in instructional alignment between 2003 and 2009. Fixed-effects models indicate that alignment in grades K–12 mathematics increased by approximately 0.19–0.65 standard deviations, depending on the grade and target. Alignment also increased to grades K–12 standards in ELA and grades 3–8 standards in science, though the magnitudes were smaller. Multiple alternative specifications support the findings of increased alignment. Implications for research and SBR policy are discussed.

This article is a report of a study of relationships between intended, implemented, and tested curricula of 84 classes of United States eighth-grade mathematics students in 1981-82. It is based on data from the Second International Mathematics Study (SIMS, Population A) and the SIMS test: 180 multiple-choice questions covering topics in arithmetic, algebra, geometry, measurement, and statistics. The study focused on three areas: (a) coverage of the SIMS test items in six nonalgebra textbooks, (b) teacher reports of whether students had the opportunity to learn the SIMS items, and (c) teacher expectations for student success on the SIMS items. Of special concern was the challenge presented to students as measured by textbook and teacher coverage of new, versus reviewed, mathematics topics. The analysis indicated that the SIMS test for eighth graders was not representative of the curriculum defined by students' texts. The books were heavily biased toward a review of arithmetic and away from algebra or geometry items. Items new to texts were among the least covered. Teacher expectations for student success mirrored the textbook coverage of SIMS items and indicated a high degree of reliance on textbooks for topic sequencing. Teachers using nonbasal texts had higher expectations than teachers of basal texts. Teachers reported that they taught more old items than new items and more arithmetic and algebra items than geometry, measurement, or statistics items.

The leading school reform policy in the United States revolves around strong accountability of schools with consequences for performance. The federal government's involvement through the No Child Left Behind Act of 2001 reinforces the prior movement of many states toward policies based on measured student achievement. Analysis of state achievement growth as measured by the National Assessment of Educational progress shows that accountability systems introduced during the 1990s had a clear positive impact on student achievement. This single policy instrument did not, however, also lead to any narrowing in the Black-White achievement gap (though it did narrow the Hispanic-White achievement gap). Moreover, the Black-White gap appears to have been adversely impacted over the decade by increasing minority concentrations in the schools. An additional issue surrounding stronger accountability has been a concern about unintended outcomes related to such things as higher exclusion rates from testing, increased dropout rates, and the like. Our analysis of special education placement rates, a frequently identified area of concern, does not show any responsiveness to the introduction of accountability systems.© 2005 by the Association for Public Policy Analysis and Management

International comparisons have highlighted that the U.S. mathematics curriculum, both in terms of curriculum influences (e.g., textbooks, standards) and actual instruction, is broad and shallow. Standards-based reform is explicitly designed to improve coherence and reduce redundancy across grades. This article evaluates the redundancy of mathematics instruction after the early years of standards-based reform, using survey data from over 7,000 teachers. Instruction for teachers in consecutive grades in the same school is compared, and the redundancy of instruction is compared with the redundancy of state standards. Results indicate continuing problems of instructional redundancy, with upwards of 60% of instructional time at each grade on content taught in previous grades. Topics are continually introduced to the curriculum but leave more slowly; middle school instruction is broader and more redundant than elementary school instruction. State standards are also highly redundant, though there is no apparent relationship between the redundancy of state standards and the redundancy of instruction.

Opportunity to learn (OTL) is rare among the many concepts that education researchers use to depict the complexity of the schooling process. Although designed as a technical concept to ensure valid cross-national comparisons, OTL has changed how researchers, educators, and policymakers think about the determinants of student learning. This article examines the evolution of OTL from a research concept to a policy instrument. It describes OTL’s intellectual origins in the IEA studies and the role of OTL research in education indicator development. The article then outlines OTL’s emergence as a potential policy tool, and assesses its political and technical feasibility.

In this work, we explored the relationship of the Common Core State Standards in Mathematics (CCSSM) to student achievement. Building on techniques developed for the Third International Mathematics and Science Study (TIMSS), we found a very high degree of similarity between CCSSM and the standards of the highest-achieving nations on the 1995 TIMSS. A similar analysis revealed wide variation in the proximity of state standards in effect in 2009 to the CCSSM. Finally, we used regression and analysis of covariance techniques to assess the relationship between the proximity of a state’s standards to the CCSSM and performance on the 2009 National Assessment of Educational Progress (NAEP). After adjusting for cut-points on state assessments and controlling for state demographics related to socioeconomic status and poverty, we found that states with standards more like the CCSSM, on average, had higher NAEP scores.

Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks
designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of
the books, the structure of the lessons, and the nature of the mathematical problems presented. Findings showed USA and Kuwaiti
mathematics textbooks are larger than Japanese textbooks; this larger size is consistent with a great deal of repetition.
The Japanese texts do not address fractions until the third grade; they use linear models and connect fractions with measurement.
In the USA and Kuwait, fractions are introduced in the first grade. The Harcourt text uses concrete material to help students
learn fraction procedures. For the Kuwaiti series, the lessons depend on using some pictorial representation of the area model
to illustrate fraction ideas. All these textbooks focus on standard algorithms as the main computational methods.

The purposes of this investigation were to (a) describe teachers' styles of textbook use and (b) examine the overlap between content taught and textbook content in elementary school mathematics. Using daily teacher logs and a three-dimensional classification system as guides, trained raters generated detailed classifications of all problems presented in books and all content presented to students over the course of an entire school year. The results of analyses of overlap between textbook content and content taught challenge the popular notion that elementary school teachers' content decisions are dictated by the mathematics textbooks they use In each classroom studied, there were important differences between the curriculum of the text and teachers' topic selection, content emphasis, and sequence of instruction.

Low-achieving, low-income students are typically tracked into dead-end math courses in high school. In this article, the authors evaluate the success of "transition" math courses in California and New York, which are designed to bridge the gap between elementary and college-preparatory mathematics and to provide access to more challenging and meaningful mathematics for students who enter high school with poor skills. The authors hypothesize that the transition courses-Math A in California and Stretch Regents and UCSMP Math in New York-allow students to keep pace with those who enter college-preparatory courses by covering rigorous mathematical content using a range of cognitive strategies. Data from 882 students in 48 math classes are analyzed using a three-level hierarchical linear model. The results show that growth in student achievement is significantly lower in general-track classes than in college-preparatory classes. Achievement in transition classes falls in between: not significantly lower than in college-preparatory classes, but not significantly greater than in general-track classes. More rigorous content coverage accounts for much of the achievement advantage of college-preparatory classes. The transition classes are judged a partial success in meeting their goal of upgrading the quality of mathematics instruction for low-achieving, low-income youth.

Studies of 4 fourth-grade teachers in 2 urban schools in a single school district provide the data for this article. Questions about the roles textbooks play in elementary education and how they come to play those roles were addressed using an ecologically based research approach (interviews and classroom observations)-one that considered teachers' thought and action and the relationships between these, teachers' work within and across subjects, and the fuller context of teachers' conditions of work. Using this approach, we found that the influence of textbooks on classroom instruction and teachers' thinking was somewhat less than the literature would have us expect, that patterns of textbook use and thinking about these materials were not necessarily consistent across subjects even for a single teacher, and that the conditions of elementary teachers' work encouraged selective and variable use of textbook materials.

This article presents a theoretical analysis of how such class conditions as textbook organization and content, compositional characteristics of classes, instructional time, and teachers' beliefs influence the mathematics content that teachers introduce. Propositions concerning the relations among these conditions were examined in light of evidence from detailed case studies undertaken in 9 fourth-grade classes. Although textbook characteristics, class composition, and teacher beliefs were related to the amount and order in which content was presented, instructional time was not. Implications for further study of teacher decision making, textbook content and organization, and the use of instructional time are discussed.

We previously conducted a curriculum analysis of third-grade mathematics textbooks aimed at investigating the extent to which teaching the recommended methods for problem solving adhered to the 2000 National Council of Teachers of Mathematics (NCTM) Standards and instructional design criteria. In this article, we extend the previous findings by comparing the teaching of problem solving presented in the same textbooks published after the 2000 NCTM Standards to that in older editions published before the Standards were in effect. Results indicated that the changes in textbooks varied with regard to meeting the different Standards. However, results for instructional design criteria indicated more consistent changes, favoring the textbook series published after 2000. Additional findings and implications for practice are discussed.

This article describes tools for measuring the content of instruction, the content of instructional materials, and the alignment between these. Illustrative findings about the use of these tools are reported, and possible additional uses, both for research and practice, are discussed. The validity of data produced through use of these tools is found to be quite good. An agenda for future work is sketched—both for improvement of the quality and versatility of the tools and for use of the tools in research and practice.

Words have no inherent meaning. Instead, they signify ideas or actions ascribed to them by communities, and meanings for specific words often vary across those communities. Words that carry specialized meanings in one community can be interpreted differently by another, particularly where individuals in the second community have little access to dialogues in the first, or when forces in the second community compete to assign meaning to key words. Observations of one district’s mathematics curriculum writing committee suggested a disconnect of this sort occurred along the policymaker/teacher divide in one state. Where state standards used words like “construct” and “concept” to imply certain mathematics teaching methods, teachers reading these documents imputed more local, and sometimes conventional, definitions to these words. As a result, state standards lost their force. This article describes and analyzes the work of state-local policy reconciliation as it occurred in this committee, and appraises that work’s implications for reform efforts that rely on language as a medium for communication.

We use data from one of the few states where information on curriculum adoptions is available â€“ Indiana â€“ to empirically evaluate differences in performance across three elementary-mathematics curricula. The three curricula that we evaluate were popular nationally during the time of our study, and two of the three remain popular today. We find large differences in effectiveness between the curricula, most notably between the two that held the largest market shares in Indiana. Both are best-characterized as traditional in pedagogy. We also show that the publisher of the least-effective curriculum did not lose market share in Indiana in the following adoption cycle; one explanation is that educational decision makers lack information about differences in curricular effectiveness.

This paper utilizes data from U.S. districts that participated in the 1999 TIMSS-R study to explore the consequences of variation in opportunities to learn specific mathematics content. Analyses explore the relationship between classroom coverage of specific mathematics content and student achievement as measured by the TIMSS-R international mathematics scaled score. District level SES indicators demonstrated significant relationships with both the dependent variable of interest: mathematics achievement, and the classroom level measure of content coverage. A 3-level hierarchical linear model demonstrated a significant effect of classroom content coverage on student achievement while controlling for student background at the student level and SES at all three levels documenting significant differences in mathematics learning opportunities as a function of the U.S. education system structure.

The purpose of this large-scale, national study is to determine whether some early elementary school math curricula are more effective than others at improving student math achievement, thereby providing educators with information that may be useful for making adequate yearly progress (AYP). This report presents results from the first cohort of first grade in 39 schools participating in the evaluation during the 2006-2007 school year, with the goal of determining the relative effects of different early elementary math curricula on student math achievement in disadvantaged schools. The report also examines whether curriculum effects differ for student subgroups in different instructional settings. A competitive process was used to select four curricula Investigations in Number, Data, and Space; Math Expressions; Saxon Math; and Scott Foresman-Addison Wesley Mathematics) that represent many of the approaches used to teach elementary school math in the United States. An experimental design randomly assigned schools in each participating district to the four curricula, setting up an experiment in each district. The relative effects of the curricula were calculated by comparing math achievement of students in the four curriculum groups. Hierarchical linear modeling (HLM) techniques were used to conduct statistical tests to assess the significance of all the results. Curriculum implementation findings include: (1) All teachers received initial training from the publishers and 96 percent received follow-up training; combined training varied by curriculum and ranged from 1.4 to 3.9 days; (2) Nearly all teachers reported using their assigned curriculum as their core math curriculum and about a third reported supplementing their curriculum with other materials; (3) Eighty-eight percent of teachers reported completing at least 80 percent of their assigned curriculum; and (4) On average, Saxon Math teachers reported spending one more hour on math instruction per week than did teachers of the other curricula. Achievement findings include: (1) Student math achievement was significantly higher in schools assigned to Math Expressions and Saxon Math, than in schools assigned to Investigations in Number, Data, and Space and Scott Foresman-Addison Wesley Mathematics; and (2) Math achievement in schools assigned to the two more effective curricula was not significantly different, nor was math achievement in schools assigned to the two less effective curricula. Another 71 schools joined the study during the 2007-2008 school year and curriculum implementation occurred in both the first and second grades in all participating schools. A follow-up report is planned that will present results based on all 110 schools participating in the evaluation, and for both the first and second grades. The study also is supporting curriculum implementation and data collection during the 2008-2009 school year in a subset of schools, in which implementation will be expanded to the third grade. A third report is planned that will present those results. Four appendixes are included; (1) Data Collection and Response Rates; (2) Teacher-Reported Frequency of Implementing Other Curriculum-Specific Activities; (3) Glossary of Curriculum-Specific Terms; and (4) Constructing the Analysis Samples and Estimating Curriculum Effects. (Contains 66 footnotes, 10 figures and 43 tables.) A table of acronyms is included. [For Executive Summary of this report, see ED504419.]

The importance of textbooks to the U.S. mathematics curriculum cannot be overstated. The recent rejection by the California State Board of Education of all fourteen text series submitted for adoption illustrates the public perception of the importance of textbooks. Begle (1973) pointed to data from the National Longitudinal Study of Mathematical Achievement to emphasize the important influence textbooks have on student learning, citing evidence that students learn what is in the text and do not learn topics not covered in the book. The National Advisory Committee on Mathematical Education (1975) acknowledged the importance of textbooks as guides for teachers. Fey (1980) emphasized the important influence of texts and pointed out that text content is usually not ba ed on research. Investigators at the Insti tute for Research on Teaching offer evidence that, at the very least, texts are important exercise sources (see Porter et al. 1986). The overall picture is that to a great extent the textbook defines the content of the mathematics that is taught in U.S. schools.

This review of state English language arts (ELA) and mathematics standards is the latest in a series of Fordham evaluations dating back to 1997. It comes at a critical juncture, as states across the land consider adoption of the Common Core State Standards. These are the authors' major findings: (1) Based on their criteria, the Common Core standards are clearly superior to those currently in use in thirty-nine states in math and thirty-seven states in English. For thirty-three states, the Common Core is superior in both math and reading; (2) However, three jurisdictions boast ELA standards that are clearly superior to the Common Core: California, the District of Columbia, and Indiana. Another eleven states have ELA standards that are in the same league as the Common Core (or "too close to call"); and (3) Eleven states plus the District of Columbia have math standards in the "too close to call" category, meaning that, overall, they are at least as clear and rigorous as the Common Core standards. Appendices include: (1) Grading and Criteria; (2) Detailed Grades; and (3) 2005 to 2010 Comparisons. Individual sections contain footnotes. (Contains 12 tables and 2 figures.) [This paper was written with Daniela Fairchild, Elizabeth Haydel, Diana Senechal, and Amber M. Winkler. Foreword by Chester E. Finn, Jr. and Michael J. Petrilli is included.]

In recent years, US curriculum policy has emphasized standards‐based conceptions of curricula in mathematics and science. This paper explores the data from the Third International Mathematics and Science Study (TIMSS) to argue that the presence of content standards is not sufficient to guarantee curricula that lead to high‐quality instruction and achievement. An examination of the content topics covered in each grade of a group of six of the highest‐achieving TIMSS countries in mathematics and science shows a pattern in which new topics are gradually introduced, are a part of instruction for a few grades, and then often leave the curriculum as separate topics. This contrasts sharply with mapping of topics in the various US national standards in mathematics and science. Topics enter and linger, so that each grade typically devotes instructional attention to many more topics than is typical of the six high‐achieving countries; in addition, each topic stays in the curriculum for more grades than in the high‐achieving countries. An examination of mathematics and science content standards from 21 states and 50 districts in the US shows a pattern more like that of the US national standards than those of the high‐achieving TIMSS countries. While content standards have become integral to US curriculum development and reform, they have yet to reflect the coherence that is typical of countries that achieved significantly better than the US in the TIMSS study.

This article examines the reliability of content analyses of state student achievement tests and state content standards. We use data from two states in three grades in mathematics and English language arts and reading to explore differences by state, content area, grade level, and document type. Using a generalizability framework, we find that reliabilities for four coders are generally greater than .80. For the two problematic reliabilities, they are partly explained by an odd rater out. We conclude that the content analysis procedures, when used with at least five raters, provide reliable information to researchers, policymakers, and practitioners about the content of assessments and standards.

Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform?

- D L Ball
- D K Cohen

Choosing blindly: Instructional materials, teacher effectiveness, and the Common Core

- M M Chingos
- G J Whitehurst

Systemic educational policy: A conceptual framework

- W H Clune

New texts aim to capture standards

- S Sawchuk

The impact of No Child Left Behind on student achievement

- T S Dee
- B A Jacob

Access to textbooks, instructional materials, equipment, and technology: Inadequacy and inequality in California’s public schools

- J Oakes
- M Saunders