Common Core in Mathematics

According to the Association of Mathematics Teacher Educators (AMTE, 2017), teachers should first try to see problems through their students' eyes, anticipate, understand, and analyze students' varied ways of thinking, and respond appropriately. In this study, we engaged preservice teachers (PTs) in planning to implement problem-solving tasks; explored how they identified problem-solving tasks; and characterized their anticipated responses to those tasks. PTs' competencies and deficiencies in selecting problem-solving tasks and anticipating solutions were described. The results inform the design of more effective interventions in math methods courses to help PTs to plan for implementation of problemsolving in their future teaching.

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.

According to the Association of Mathematics Teacher Educators (AMTE, 2017), teachers should first try to see problems through their students' eyes, anticipate, understand, and analyze students' varied ways of thinking, and respond appropriately. In this study, we engaged preservice teachers (PTs) in planning to implement problem-solving tasks; explored how they identified problem-solving tasks; and characterized their anticipated responses to those tasks. PTs' competencies and deficiencies in selecting problem-solving tasks and anticipating solutions were described. The results inform the design of more effective interventions in math methods courses to help PTs to plan for implementation of problemsolving in their future teaching.

This report describes the message of current publications in mathematics education. Eight documents were selected to be reviewed which provides a starting point for readers. Papers include: (1) "Principles and Standards for School Mathematics"; (2) "Adding It Up:

This study examines the effect of using Desmos on students’ performance in learning functions. An embedded mixed methods design was applied and involved 98 students from an upper secondary school in Sweden. Students’ assessments (pre- and post-test) and opinion polls were the two main data collection instruments. The results show that both groups (experimental and control) experienced a significant improvement in their post-test scores. However, the experimental group had a statistically significant improvement in comparison with that of the control group across the five constructs used in this study. The qualitative data revealed that the majority of the students ascribed a positive effect of the use of Desmos on their general understanding of function concepts, their ability to analyze functions and check their answers through visualization, which are difficult when working using paper and pencil.

* Significantly different (p < .05) from graduates who took algebra I during high school. NOTE: Data for graduates who did not take an algebra I course are not shown. Black includes African American, Hispanic includes Latino, and Asian/Pacific Islander includes Native Hawaiian. Race categories exclude Hispanic origin.

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 di...

Performance assessments are part of a robust assessment system in which students show what they know by writing an essay, curating a portfolio of work, or conducting original research. Ultimately, performance assessments can allow students to demonstrate college and career readiness through a culminating assessment-such as a graduate capstone or senior portfolio defense. The report on which this brief is based documents the work of three districts involved in the California Performance Assessment Collaborative: Los Angeles, Oakland, and Pasadena Unified School Districts. Through interviews, focus groups, and observations, we identify the key conditions needed to support the implementation of culminating performance assessments at the district, school, and classroom levels. We also examine students' and educators' perceptions of outcomes related to participation in performance assessment initiatives. Finally, we summarize lessons from the districts' experiences with performance assessments and present associated recommendations to district leaders and state policymakers.

To ensure conceptual learning in mathematics, teachers must shift many aspects of their instructional practices. We report on a two-year endeavor using a collaborative and responsive professional development model to help elementary school teachers enact seven shifts in classroom practice. We share evidence of teachers addressing the instructional shifts and discuss the promise of the approach used for those interested in co-constructing collaborations between and among universities and school districts.

A década em curso testemunhará, muito provavelmente, uma atenção sem precedentes sobre nos EUA. A adopção dos Common Core State Standards for Mathematics (CCSSM) por todos os estados, com poucas excepções, representa uma grande mudança na administração curricular. Pela primeira vez nos EUA, a grande maioria das escolas, professores e estudantes vão concentrar-se em objectivos de aprendizagem comuns específicos e estabelecidos por ano de escolaridade. Esta iniciativa, associada com as exigidas avaliações anuais comuns, também em cada ano de escolaridade, alinhadas com os CCSSM, poderá ter impacto em outros sistemas e factores importantes para a aprendizagem dos alunos, como o ensino e os materiais curriculares, a formação de professores e as políticas de escolha de cursos e graduação. Este artigo apresenta um resumo das iniciativas correntes de reforma curricular nos EUA, proporcionando um breve panorama do movimento actual tendo em vista as normas curriculares comuns (a nível nacion...

Castañeda v. Pickard mandated that educational programs for emergent bilinguals be tested for program efficacy. As English language development (ELD) curricular materials are one part of an instructional program, we assess this mandate by examining the effectiveness of ELD materials in Texas, a large, diverse U.S. state with large numbers of emergent bilingual (EB) students. Using local linear matching, we find robust evidence that schools that do not purchase any ELD curricula have significantly lower English language proficiency scores relative to schools that purchase state-adopted ELD materials. In contrast, there is no significant difference between schools that adopt the two most popular ELD curricula in the state. This study suggests that curriculum materials matter for EBs’ English proficiency and implies that states should take a more active role in ensuring students have access to these materials.

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by engaging students in structured group activities or collaborative problemsolving activities. But encouraging students to work together on a problem-solving task can be difficult. Many teachers can probably identify with attempting to have students work in groups only to have one student take charge while the others sit back and observe. One way of helping students to learn to think and work collaboratively is to present them with "groupworthy" problems (Horn 2005, p. 219). Such problems meet the following criteria:

Leadership is one of the most examined concepts in the literature, and while the study of social networks is also gaining interest, the intersection between leadership and online social networks has received limited attention. The key notion underlying most leadership research is that the behaviors or attributes of a leader matter for a variety of outcomes. While offering valuable insights, this dominant view of leadership behavior and attributes underestimates the impact of social networks. Scholars are increasingly recognizing the importance of social processes involved in leading. Leadership has often been conceptualized as a process of influence toward an outcome. Social relationships through networks may provide leaders with the necessary infrastructure to access resources in achieving outcomes. Leadership from a network perspective emphasizes the interdependence reflected by a network of ties, which may ultimately moderate, influence, or determine the activity and movement of ...

Social media, such as microblogging, is a powerful medium for sharing information and organizing response in times of crisis or extreme events. We propose methods to integrate topical and social information and behavior derived from social media to improve situational understanding during an extreme event. Using Twitter data from the 2011 London riots, we analyze emergent social networks directly relating to response to crisis. We construct social networks from these tweets based on talking to (directed communication), quoting (retweeting), and talking about (mentioning) behaviors. We examine networks of riot response oriented around cleanup or prayer activities. These networks differ in size, structure, and membership. We identify prominent network actors and assess their similarity. These methods may enable more effective response during disasters or other emergency events.

This mixed methods study explored elementary teachers' (n 5 73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation to use the standards; implementation of the standards, including incorporation and teacher change; and tensions associated with enactment of the standards. Notably, the teachers believed in the merit of the standards but were constrained by their inadequate content knowledge, limited aligned curricular resources, lack of student readiness, and a perceived mismatch with ELLs. The results illuminate the professional needs of teachers during this critical time of transition to the standards and also add to the scant research on this national-scale reform in mathematics education.

athematics is a mental activity interested in patterns, proof, problem posing and solving, logical and critical thinking, to understand the world in which we live and to make use of that understanding in our daily life situations. Programme for International Student Assessment (PISA, 2009, 85) indicated, "Mathematics is concerned with the ability of students to analyze reason and communicate ideas effectively as they pose, formulate, solve and interpret mathematical problems in a variety of life situations". Therefore, "since mathematics have both utilitarian and intrinsic value, all students have a right of access to its benefits which provide powerful numeric, spatial, temporal, symbolic, communicative and other conceptual tools, skills, knowledge, attitudes and values to analyze; make and justify critical decisions; and take transformative action" (Paulsen,2006, 44). Students in modern societies, such as USA and UK, master general and basic information of mathematics with the enough level required for mathematical literate life. They also master skills of mathematical literacy and can apply mathematical rules in their common daily life situations.

GeoGebra is an interactive mathematics program for teaching and learning mathematics from early school years up to the university level. The program is considered dynamic mathematics software that enables student to see and explore mathematical concepts, their relations, and theories. The main objective of this study is to examine the effect of using GeoGebra on students’ understanding of Quadratic Functions in 10 grade Emirati students in Al Ain, United Arab Emirates. A quasiexperimental design was employed to collected data using a pre-test and post-test tool to evaluate the effectiveness of the GeoGebra software intervention. Eighty-five (n=85) participants were randomly divided into two groups of control and experimental. The result of the post-test indicated a statistically significant point of preference of using GeoGebra for the experimental group over the control group. Specifically, results revealed that students who were exposed to GeoGebra achieved a higher average score ...

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The United States is undergoing another large-scale reform as an attempt to improve education. The goal of this study was to investigate the sense that mathematics high school teachers make of this new reform, Common Core State Standards for Mathematics (CCSSM). Using the sensemaking theoretical framework, I investigated how teachers interpret, adopt, and enact this national education reform. Furthermore, I studied how the interactions of internal and external factors affected the practice of teacher leaders. This mixed-method study consisted of two phases. For Phase One, all mathematics teachers in one district were invited to participate. Five teachers who were identified as teacher leaders at their schools and supporters of CCSSM were selected for Phase Two. Both qualitative and quantitative methods were used to analyze the different data sources. The results of the study indicate that interactions between teachers&#39; internal and external factors mediate teacher sensemaking of...

The California Collaborative on District Reform, an initiative of American Institutes for Research, was formed in 2006 to join researchers, practitioners, policymakers, and funders in ongoing, evidence-based dialogue to improve instruction and student learning for all students in California’s urban school systems. After nearly three years of the Local Control Funding Formula (LCFF), California educators still struggle to communicate district plans to parents, teachers, and other members of the school community. Local Control Accountability Plans (LCAPs), state-mandated LCFF documents presenting districts’ spending and programmatic decisions, have ballooned into jargon-laden stacks of tables well over 100 pages long, impenetrable to all but the most sophisticated reader. Envisioned as a tool to improve transparency, the LCAP as implemented has instead left many parents and community members utterly confused.

to improve instruction and student learning for all students in California's urban school systems. Common Core Implementation: Units of Study in Sacramento City The Common Core State Standards introduce a new set of opportunities and challenges to the K-12 education landscape. The new standards

In this article, we discuss the roles users play in political conversations on Twitter. Our case study is based on data collected in three dates during the former Brazilian president Lula’s corruption trial. We used a combination of social network analysis metrics and social capital to identify the users’ roles during polarized discussions that took place in each of the dates analyzed. Our research identified four roles, each associated with different aspects of social capital and social network metrics: activists, news clippers, opinion leaders, and information influencers. These roles are particularly useful to understand how users’ actions on political conversations may influence the structure of information flows.

In this article, we discuss the roles users play in political conversations on Twitter. Our case study is based on data collected in three dates during the former Brazilian president Lula’s corruption trial. We used a combination of social network analysis metrics and social capital to identify the users’ roles during polarized discussions that took place in each of the dates analyzed. Our research identified four roles, each associated with different aspects of social capital and social network metrics: activists, news clippers, opinion leaders, and information influencers. These roles are particularly useful to understand how users’ actions on political conversations may influence the structure of information flows.

In this article, we discuss the roles users play in political conversations on Twitter. Our case study is based on data collected in three dates during the former Brazilian president Lula’s corruption trial. We used a combination of social network analysis metrics and social capital to identify the users’ roles during polarized discussions that took place in each of the dates analyzed. Our research identified four roles, each associated with different aspects of social capital and social network metrics: activists, news clippers, opinion leaders, and information influencers. These roles are particularly useful to understand how users’ actions on political conversations may influence the structure of information flows.

This article describes findings from a survey completed by 250 K-12 grade teachers from eight states (i.e., Kentucky, Minnesota, Michigan, Maine, Delaware, North Carolina, Georgia, and Mississippi) that had fully implemented the Common Core State Standards (CCSS) by spring 2013. The survey was designed to examine teachers’ perceptions about their preparedness to teach the CCSS in Writing as well as provide information about what teachers perceived as barriers to implementing the standards, their perceptions of the positive and negative effects of CCSS implementation, and their professional development experiences related to implementing the standards. The results of the analyses indicate that teachers vary in their current level of acceptability regarding the CCSS in Writing according to the grade level they teach, their years of teaching experience, and the amount of professional development they have received. Significant differences were not found between teachers from different ...

According to the Association of Mathematics Teacher Educators (AMTE, 2017), teachers should first try to see problems through their students' eyes, anticipate, understand, and analyze students' varied ways of thinking, and respond appropriately. In this study, we engaged preservice teachers (PTs) in planning to implement problem-solving tasks; explored how they identified problem-solving tasks; and characterized their anticipated responses to those tasks. PTs' competencies and deficiencies in selecting problem-solving tasks and anticipating solutions were described. The results inform the design of more effective interventions in math methods courses to help PTs to plan for implementation of problemsolving in their future teaching.

TEACHERS&#39; PERCEPTIONS ON PREPAREDNESS AND SUPPORTS TO IMPLEMENT THE ENGLISH LANGUAGE ARTS COMMON CORE STATE STANDARDS by Maria Clara Fernández The purpose of this study was to: (1) describe elementary teachers&#39; perceptions on their preparedness to implement the English Language Arts Common Core State Standards (ELA-CCSS); (2) determine how perceptions influenced changes in instructional practices; and (3) to explore ELA-CCSS implementation challenges and/or barriers in supporting teacher development. This study was conducted using a multi-methods research design involving quantitative data from a survey, and qualitative data from interviews. The conceptual framework for this study centered around a history of the Common Core State Standards, education reform implementation research, understandings about the Common Core State Standards, and reconstructing teacher practice. Results revealed that professional development effect on instructional practice was limited; preparednes...

We describe the process and outcomes of a project aimed at bringing together a set of diverse experts to generate a set of design recommendations for what should be considered when creating, sustaining, and assessing professional development systems to support the Common Core State Standards in mathematics. Although the recommendations were generated in mathematics, the underlying guiding principles for professional development are generalizable to other disciplines. As such, we discuss implications for professional development more broadly.

The purpose of this case study was to examine how one teacher supported her students in making contributions to whole-class discussions in an Iranian classroom. Data were analysed using a grounded theory approach and include field notes from all classroom observations and three teacher interviews collected over five weeks in a Year 11 classroom. Findings indicated that in spite of the differences in context, the Iranian teacher’s practice shared substantial elements with the ‘five practices’ of orchestrating productive mathematical conversations outlined by Stein et al. The results suggest that proactive support of students’ mathematical understandings is an achievable goal worth pursuing in Iran.

The Instructional Leadership Corps (ILC) is an innovative professional learning project in which teacher leaders in California collaborate to lead sustainable professional development to support implementation of new student standards within their districts. Over more than 4 years, the ILC has served over 100,000 teachers. The responses of these educators to ILC conferences and trainings have been overwhelmingly positive. This brief describes how the ILC has changed the professional development landscape in four communities, offering lessons about how teacher-led learning can motivate shifts in practice, enhance teachers’ professionalism and efficacy, and create supportive systems and strategic relationships that can sustain change.

This mixed methods study explored elementary teachers' (n 5 73) experiences with and perspectives on the recently implemented Common Core State Standards for Mathematics (CCSS-Mathematics) at a high-needs, urban school. Analysis of the survey, questionnaire, and interview data reveals the findings cluster around: familiarity with and preparation to use the standards; implementation of the standards, including incorporation and teacher change; and tensions associated with enactment of the standards. Notably, the teachers believed in the merit of the standards but were constrained by their inadequate content knowledge, limited aligned curricular resources, lack of student readiness, and a perceived mismatch with ELLs. The results illuminate the professional needs of teachers during this critical time of transition to the standards and also add to the scant research on this national-scale reform in mathematics education.

Performance assessments are part of a robust assessment system in which students show what they know by writing an essay, curating a portfolio of work, or conducting original research. Ultimately, performance assessments can allow students to demonstrate college and career readiness through a culminating assessment-such as a graduate capstone or senior portfolio defense. The report on which this brief is based documents the work of three districts involved in the California Performance Assessment Collaborative: Los Angeles, Oakland, and Pasadena Unified School Districts. Through interviews, focus groups, and observations, we identify the key conditions needed to support the implementation of culminating performance assessments at the district, school, and classroom levels. We also examine students' and educators' perceptions of outcomes related to participation in performance assessment initiatives. Finally, we summarize lessons from the districts' experiences with performance assessments and present associated recommendations to district leaders and state policymakers.

We studied how the distal policy mechanisms of curricular aims and objectives articulated in official curriculum documents influenced classroom instruction, and the factors that were associated with the enactment of those curricular aims and objectives. The study was set in the U.S. context, where there is an ambitious effort to transform curriculum and instruction via the Common Core State Standards for Mathematics (CCSSM). The CCSSM represented the curricular aims and objectives in most of the U.S. at the time of the study. We analyzed enactments of this official curriculum in terms of the rigor of mathematical activity in 47 middle school mathematics lessons from multiple state and curriculum contexts. The enactment of the CCSSM was not uniform across contexts, and the lack of uniformity was associated in part with the type of instructional materials used by teachers. The use of instructional materials classified as delivery mechanism was associated with activity we characterized as routine procedural rigor. In lessons involving instructional materials classified as thinking device, we found greater variation and more occurrences of non-routine forms of rigor. These differences between types of instructional materials occurred despite the finding that teachers across the sample held similar views of the CCSSM. We conclude that the teachers responded more to features in the instructional materials than to the curriculum aims and objectives articulated in the CCSSM while planning and enacting lessons, which has implications for policy makers who aim to influence instruction through national standards and for school districts as they select materials.