Common Core State Standards For Mathematics Research Articles

Interactive Homework: A Tool for Parent Engagement

Families have largely been excluded from the implementation of the Common Core State Standards in Mathematics (CCSSM), reducing their ability to extend their child’s mathematics learning. CCSSM emphasizes different instructional elements (e.g., pictorial representations, problem solving, multiple strategies for solving) that may differ greatly from how parents learned mathematics. In addition, many school officials have ineffectively engaged parents in the changes, further diminishing their capacity to participate in their child’s learning. This case study examined parent mathematics self-efficacy and parent mathematics knowledge for teaching, factors that influence the effectiveness of their engagement in their child’s mathematics learning. This study was also implemented to identify elements that the parent participant found helpful for their child’s mathematics learning. A thematic analysis was performed on the data sources, the interactive homework assignments, a survey, observations, a researcher’s journal, and an interview to conclude that the interactive homework assignments improved parent mathematics self-efficacy and parent mathematics knowledge for teaching. The parent participant also identified the assignments’ side-by-side examples, additional practice, and the easy access of the assignments as features of the intervention that enhanced her ability to support her child.

The Journey Continues: Mathematics Curriculum Analysis from the Official Curriculum to the Intended Curriculum

In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.

تحليل محتوى كتب الرياضيات المدرسية للمرحلة الثانوية في فلسطين في ضوء المعايير الأساسية الأمريكية المشتركة CCSSM

هدفت الدارسة إلى تحليل محتوى كتب الرياضيات الفلسطينية للمرحلة الثانوية في ضوء المعايير الأساسية الأمريكية المشتركة Common Core State Standards For Mathematics CCSSM، واستخدمت الباحثتان المنهج الوصفي التحليلي، وتكونت عينة الدارسة من محتوى كتب الرياضيات للمرحلة الثانوية (كتابي الصف الحادي عشر علمي وكتاب الصف الثاني عشر علمي) والتي تمّ اعتمادها في العام الدراسي 2019 /2020 في فلسطين. واستخدمت الباحثتان أداة تحليل المحتوى والتي تم إعدادها استنادا إلى المعايير الأساسية الأمريكية المشتركة CCSSM؛ وخلصت الدارسة إلى تضمين كتب الرياضيات للمرحلة الثانوية في فلسطين للمعايير الأساسية الأمريكية المشتركة CCSSM الخاصة بالمرحلة الثانوية بنسب قليلة، كما تفتقر الكتب لعدد من المعايير؛ ومن أهم توصيات الدارسة ضرورة إطلاع المختصين بالمناهج الدراسية على المعايير العالمية مثل المعايير الأساسية الأمريكية المشتركة CCSSM لتطوير المناهج وتحسين الجوانب ذات الضعف وإعادة النظر في المواضيع التي افتقرت إلى المعايير في كتب الرياضيات للمرحلة الثانوية وتعزيز نقاط القوة.

Solving for X: Constructing Algebra and Algebra Policy During a Time of Change

The year students take Algebra I historically determines how far they progress in secondary mathematics, creating complex equity issues around access to this course. By examining a case study of one large, urban school district adjusting to the Common Core State Standards in Mathematics (CCSS-M), we demonstrate how district leaders’ interactions, in combination with their organizational and institutional environments, led to an overhaul of the secondary mathematics course pathway, ending in detracked middle school mathematics. We find that district leaders’ deliberations of mathematics policy were constrained by organizational concerns around pedagogy, equity, logistics, and politics. In other words, the disruption created by the CCSS-M was limited by extant organizational priorities. This study has potential implications for theorizing disruptions and for better understanding equity-oriented mathematics policy and practice.

High school geometry textbooks’ proving opportunities of Common Core theorems

AbstractThe Common Core State Standards for Mathematics (CCSSM) explicitly states many specific theorems for students to prove across multiple domains (i.e., congruence, similarity, circles, and coordinates) in high school geometry. This study examined five high school geometry textbooks for how they approached proof of 17 theorems stated in the congruence domain focused on lines and angles, triangles, and parallelograms. Results showed that although textbooks provided 75 student opportunities to prove these theorems, no textbook provided student opportunities to prove all 17. Textbooks rarely had students write proofs from general conditional statements, and instead typically provided consistent hard scaffolding including the given, what to prove, and a diagram for all proof opportunities. Some of the textbooks used novel scaffolding such as partially completed proofs, flowchart proofs, second proofs, and hints in the back of the book. Textbooks need to continue shifting more responsibility to students proving the CCSSM theorems by incorporating more diverse scaffolding along with a process for removing the scaffolding as student learning progresses.

Algebra Instruction for Students with Learning Disabilities in the Era of Common Core

The Common Core State Standards in Mathematics (CCSSM) were released more than 10 years ago. This set of standards outlines the mathematics that all students should know and be able to do to prepare them for post-secondary education and employment. Students with learning disabilities (LD) continue to underperform in relation to their peers without disabilities in secondary mathematics. As high school Algebra I is a required course for the majority of students, research-based instructional practices should be utilized to support students with LD in Algebra I. This article summarizes recent research on instructional practices for teaching algebra content that aligns to the CCSSM. Specifically, three types of instructional practices have been found to promote progress in the high school algebra content: (a) concrete-representational-abstract integration, (b) virtual manipulative instruction, and (c) gestures and diagrams.

The role of instructional materials in the relationship between the official curriculum and the enacted curriculum

ABSTRACT 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.

지식의 구조로서 변환기하를 다루기 위한 성취기준 방향 탐색

While Korean students learn more about Euclidean geometry earlier than other countries, they learn transformation geometry less. Therefore, in this study, we proposed a way to find consistency and systematicness of the geometric curriculum in Korea, focusing on transformation geometry. For this reason, the importance of transformation geometry was discussed in terms of the structure of knowledge. Also, we analyzed the transformation-based perspective expressed in the curriculum standards of the Common Core State Standards for Mathematics(CCSSM) and the Korean 2015 revised mathematics curriculum in terms of curriculum articulation. As a result, the topics of transformation geometry that can be dealt with in school geometry were “congruent transformation”, “symmetry”, “similar transformation”, and “analytic approach to transformation”. In the case of CCSSM, the standards for each topic were structured to have a curriculum articulation, but in the case of Korea, the curriculum articulation of each topic was insufficient. Among the topics of transformation, 'similar transformation' was selected, which is important but not emphasized in Korea, and suggested what can be changed when the relevant standards are systemized into a transformation-based perspective.

Alignment Between Children’s Numeracy Performance, the Kindergarten Common Core State Standards for Mathematics, and State-Level Early Learning Standards

The current study examined preschoolers’ (N = 801) age-related performance on one measure of verbal counting and two measures of cardinality (“how many” and “give n”) aligned with the kindergarten Common Core State Standards for Mathematics (CCSSM) and included in the majority of states’ early learning guidelines for mathematics. Children were grouped into five age categories (3, 3.5, 4, 4.5, 5, 5.5), and within-age-group average rates of correct responses for each item within these three measures were calculated. Results demonstrated that the majority of children were already successfully meeting the CCSSM standards for both cardinal number knowledge tasks (86.5% and 53.3%, respectively) prior to kindergarten entry but that only 18.9% of the children were meeting the standard for verbal counting. Findings indicate potential misalignment between children’s existing capabilities and the CCSSM standards for cardinality and underscore the need to conduct large, nationally representative studies measuring children’s abilities on items that more closely assess the specific mathematics skills included in the CCSSM and early learning guidelines.

A Systematic Review of Interventions for Algebraic Concepts and Skills of Secondary Students with Learning Disabilities

AbstractImproving the algebraic concepts and skills of secondary school students with learning disabilities is critical for their success in college and in the job market. This research reviewed 12 studies to examine interventions for students with learning disabilities in relation to algebraic notions and competencies. The results indicate that in regard to the Common Core State Standards for Mathematics (CCSSM) Content Standards, the majority of the studies address linear equations and expressions, linear inequalities, and quadratic expressions; they show that following interventions, students’ performance improved with respect to algebraic concepts and skills. The Tau‐U and Hedges’ g of the intervention effects computed were typically large or very large. The most commonly used instructional components in the interventions were multiple representations, a sequence and/or range of examples, and explicit instruction. Limitations and suggestions for future research are discussed.

Day by Day: Investigating Variation in Elementary Mathematics Instruction That Supports the Common Core

The Common Core State Standards for Mathematics (CCSS-M) aim to engage students in complex mathematical practices, including modeling, reasoning, and argumentation. Currently, little is known about how teachers’ daily instruction supports these practices. This study draws upon data from daily logs completed by third-, fourth-, and fifth-grade mathematics teachers from 39 states to learn about students’ engagement in standards-aligned mathematical practices. We find that there are both substantial fluctuations in students’ engagement in these practices and reported cognitive demand from day to day, as well as large differences across teachers. Practices in which students engage are related to teachers’ perceptions of student ability. These findings offer a broad perspective on how CCSS-M–based instruction unfolds across a range of states and policy environments.

A Comparative Study of Mathematics Education in the United States and Nepal

The purpose of this paper is to compare four domains of mathematics education-curricular materials, pedagogical process, teacher education, and assessment of students’ learning in the United States of America (USA) and Nepal. I applied categorical thinking for document analysis from the literature to find some key concepts related to the four categories of comparison. The Common Core State Standards for Mathematics (CCSSM) is a major curriculum standard implemented in many states in the USA, whereas, the National Curriculum Framework (NCF) is the major policy document that guides school mathematics curricula in Nepal. Mostly, classroom practices are student-centred with problem-solving, reasoning and critical thinking in the USA, but it is mostly drill-and-practice in Nepal. Preservice mathematics teacher education in the USA and Nepal are conducted by universities, but there is a vast difference in the courses offered in these countries. Assessment of students’ learning in mathematics is continuously done in classroom activities and exams including some standardized exams in selected grades in the USA, whereas, assessment in Nepal is done with periodic and final exams including standardized district and national tests in selected grades. I discussed some implications of the study.

A Learning Progression for Geometric Transformations

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these transformation as functions. The learning progression developed here is designed to be in alignment with the Common Core State Standards in Mathematics (CCSSM), in that a student who is placed at a particular level in the learning progression would have mastered the Common Core standards at the corresponding grade level. The description of the learning progression also includes sample tasks at each level that are intended to target that level of the progression.

Using the Theory of Planned Behavior to explore teachers’ intentions to engage in ongoing teacher professional learning

The purpose of this study was to examine the factors influencing teachers’ intentions to engage in professional learning on the mathematics Common Core State Standards (CCSS). The aim was to identify specific factors teachers encounter that impinge upon or facilitates implementing new instructional practices. Ajzen’s (1991) theory of planned behavior was used to examine the influence of three constructs (attitude toward the behavior, subjective norms, and perceived behavioral control) on teachers’ intentions to implement the instructional expectations associated with the CCSS in mathematics. Data for this quantitative study was collected from 152 teachers in an urban school district in California. The result of the study provides support for the adequacy of the theory of planned behavior for predicting and understanding teachers’ behavioral intention toward professional learning. Intention was predicted significantly by perceived behavioral control, subjective norm and attitude toward the behavior.

Transitioning from practicing teacher to teacher leader: a case study

ABSTRACTGiven US students’ lack of international competitiveness in mathematics and science, many states have adopted the Common Core State Standards for Mathematics (CCSSM). To help ensure that the Standards for Mathematical Practice within the CCSSM and effective teaching practices are implemented appropriately, many teachers are emerging as teacher leaders with the intent of supporting teachers with this implementation. Unfortunately, not all of these teachers are necessarily prepared in the field of teacher leadership. Recognizing the importance of having well-prepared teacher leaders, this article describes the case of Ms. Hodges, as she transitioned from mathematics teacher to teacher leader. Data revealed that several factors affected Ms. Hodges’ transition, some positively and others negatively. These results as well as implications for teacher leader development are provided.

Preservice mathematics teachers' conceptions and enactments of modeling standards

AbstractMathematical modeling has been highlighted recently as Common Core State Standards for Mathematics (CCSSM) included Model with Mathematics as one of the Standards for Mathematical Practices (SMP) and a modeling strand in the high school standards. This common aspect of standards across most states in the United States intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers (M‐PSTs) who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their attendance in the same course sections during a teacher preparation program. This result led us to investigate the ways the M‐PSTs understood modeling standards, which could provide insights into better preparing teachers to teach mathematical modeling. We present the contrasting ways in which M‐PSTs presented modeling related to their conceptions of mathematical modeling, choices of problems, and enactments over an academic year, connecting their practices to extant research. We consider this teaching and research experience as an opportunity to make significant changes in our instruction that may result in our students enhanced implementation of mathematical modeling.

U.S. Middle School Mathematics Teachers’ Perceptions of the Standards for Mathematical Practice by Textbook Type

An important component of the Common Core State Standards for Mathematics (CCSSM), used by the majority of states in the U.S., are the eight standards for mathematical practice (SMPs). While surveys have investigated teachers’ perceptions of the CCSSM few have investigated middle school mathematics teachers’ (MSMTs’) (grades 6-8) perceptions of the SMPs. Similar to other countries, teachers in the United States frequently use mathematics textbooks. Two different types of textbooks have been in use in the United States, conventional and standards-based. The latter were designed on the basis of earlier standards documents including versions of the SMPs. As a result of these changes to the educational system in the U.S., we sought to characterize MSMTs’ perceptions of the SMPs and investigate if these perceptions differed by the type of textbook teachers used. We found that MSMTs struggled in naming the SMPs, misinterpreted the modeling SMP, and conflated components of reform-oriented instruction with the SMPs. MSMTs using a standards-based textbook were more likely to view their textbooks as aligned with the SMPs, and to view the SMPs as an instructional philosophy for the CCSSM, Fisher’s Exact Test = 3.881, p = .05. The implications of these results are discussed.

Comparing Turkish Early Childhood Education Curriculum with Respect to Common Core State Standards for Mathematics

Increasing recognition of mathematics in society and its effects in development of children takes attention to early childhood education and as a result early childhood curriculum. Although children have informal mathematical knowledge before they begin formal schooling, a qualified mathematics education during early childhood will enrich and prevent learning difficulties in further years. For this purpose, the aim of the study was to compare Turkish Early Childhood Education Curriculum (TECEC) objectives with respect to kindergarten level Common Core State Standards for Mathematics (CCSSM). The study carried out as a document analysis method. Results are presented under five domains of CCSSM; counting and cardinality, operations and algebraic thinking, number and operations in base ten, measurement and data, and geometry. Results of the study indicate that TECEC and CCSSM for kindergarten level have both similarities and differences. While CCSSM dedicate more time numbers than other topics, TECEC gives significance to many mathematical skills not specifically the numbers like geometry, measurement, etc. About numbers topic in CCSSM have in depth expectations from children. Some other differences are also seen in patterning topic in TECEC and in place value topic in CCSSM. More similarities are found in geometry domain in both TECEC and CCSSM.

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.

Analysis on Middle School Mathematics Curriculum of USA: Probability and Statistics

This study aimed to investigate middle school mathematics curriculum of USA and to discuss ideas for curriculum research and development. For this study, we analyzed mathematics curriculum of USA, Common Core State Standards for Mathematics(CCSSM) announced in 2010. In order to investigate the curri...