Transitioning to the Common Core State Standards for Mathematics: A Mixed Methods Study of Elementary Teachers’ Experiences and Perspectives

This mixed methods study explored elementary teachers’ (n = 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. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

Preservice mathematics teachers' conceptions and enactments of modeling standards

Mathematical 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.     

Relationship Between Professional Development,Teachers' Instructional Practices,and the Achievement of Students in Science and Mathematics

The purpose of this study was to examine the relationship between different types of professional development, teachers' instructional practices, and the achievement of students in science and mathematics. The types of professional development studied included immersion, examining practice, curriculum implementation, curriculum development, and collaborative work. Data regarding teachers' instructional practices and the amount of professional development were collected using teacher surveys. Ninety‐four middle school science teachers and 104 middle school mathematics teachers participated in the study. Student achievement was measured using eighth grade state science and mathematics achievement test data. Regression analyses suggested that for both science and mathematics teachers, examining practice and curriculum development were significantly related to the use of standards‐based instructional practices. Only curriculum development for mathematics teachers was significantly related to student achievement. Implications of results for the professional development of science and mathematics teachers are discussed.     

Finding Alignment: The Perceptions and Integration of the Next Generation Science Standards Practices by Elementary Teachers

Preparing elementary‐level teachers to teach in alignment with the eight Next Generation Science Standards (NGSS) practices could prove to be a daunting endeavor. However, the process may be catalyzed by leveraging elements of teacher science instruction that inherently attend to the practice standards. In this study, we investigated the science instruction of three grade 3–5 elementary‐level teachers. We used observation, interviews, and surveys to determine the level to which the teachers perceived they taught and engaged in teaching science aligned with the eight NGSS practices. We found that the teachers were partially, and intrinsically implementing several of these practices in their instruction, and at the same time could not articulate the eight NGSS practices. Our results suggest there may be ample opportunity to build on the current science instruction of elementary‐level teachers to bring their instruction into alignment with the NGSS. We found that teachers’ perceive professional development, school culture, and access to additional instructional resources to be essential to their adoption of the NGSS practices.     

Examining Instructional Practices of Elementary Science Teachers for Mathematics and Literacy Integration

Integration of content in core disciplines is viewed as an important curricular component in promoting scientific literacy. This study characterized the current practices of a group of elementary teachers relative to their development of interdisciplinary links between science, mathematics, and literacy. A qualitative analysis of survey data showed that there were substantial differences in the use of a well‐developed process for integrating instruction. Teachers also lacked a conceptual connection to integration, showed contradictions in the importance placed on hands‐on experiences, used measurement as the primary interdisciplinary connection between mathematics and science, and did not use instructional strategies designed specifically for nonfiction/expository text. The findings underscore the need for professional development that assists teachers in changing their conceptual perspectives to integration while also building pedagogical knowledge related to integration of science, mathematics, and literacy.     

Integrating Science,Mathematics, and Technology in Middle School Technology‐Rich Environments: A Study of Implementation and Change

The GTECH project, funded through a grant from the GTE Foundation, prepared school teams of science, mathematics and technology teachers and an administrator to set goals for their local schools regarding implementation of electronic technology and integration of content across curricular areas. A variety of teacher‐centered staff development strategies were used to enable participants to achieve local school objectives, model and encourage active learning environments involving technology, develop integrated curriculum and provide training to their peers. GTECH staff provided workshops and summer institutes based on teacher feedback and classroom observations. Data from the Stages of Concerns Questionnaire assisted the staff in designing effective staff development activities. Over the 2‐year period, teacher teams developed and implemented integrated instructional materials and developed skills in using HyperStudio, PowerPoint, telecommunications applications, and instructional resources from the Internet. They also linked instruction to new state and national standards in science, mathematics, and technology. GTECH teachers reported that their students have expanded their knowledge and skill in problem solving, teamwork, technical expertise, and creativity.     

Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator use in Mathematics Instruction

This study investigated K‐12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.     

Answering the call by developing an online elementary mathematics specialist program

The Association of Mathematics Teacher Educators adopted Standards for Elementary Mathematics Specialists calling for structured preparation of math coaches, specialists, and instructional leaders across the country (AMTE, 2013). The purpose of this paper is to illustrate the structure and design of our fully online Elementary Mathematics Instructional Leader (EMIL) graduate program for inservice teachers aiming to answer the call. Our graduates are teacher leaders and coaches who are responsible for supporting effective mathematics instruction and student learning at the classroom, school, district, or state levels. We will review formative data from our first cohort of graduates, the benefits and drawbacks to providing online (and grant-funded) courses, and the impact of participant attrition. Our goal is to offer guidance and information to other organizations as they move to develop programs of their own.     

Planning District‐Wide Professional Development: Insights Gained From Teachers and Students Regarding Mathematics Teaching in a Large Urban District

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work, homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth‐grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry‐based experiences, fewer student‐to‐student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district.     

Effective Professional Development and Change in Practice: Barriers Science Teachers Encounter and Implications for Reform

This study focused on two middle schools in the central US who participated in collaborative, sustained, whole‐school professional development in implementing inquiry as part of National Science Education Standards, or standards‐based instructional practices. Participants were involved in their second year of the professional development experience. The research question explored was, “What barriers do science teachers encounter when implementing standards‐based instruction while participating in effective professional development experiences?” Qualitative data collected in the form of teacher interviews and classroom observations were utilized and were analyzed using a barrier to reform rubric. Findings indicate that even with effective professional development, science teachers still encounter technical, political, and cultural barriers to implementation. More support is required for professional development efforts to be successful, such as resources and time, as well as administrative buy‐in and support. Findings also revealed that even the best intended professional development efforts do not reveal and address existing beliefs for all teachers. Implications for future science education reform stakeholders are discussed.     

Science and Mathematics Instruction in a Reform‐based Teacher Preparation Program

This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform‐oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi‐experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform‐oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform‐oriented instruction. Implications of results for large‐scale reform of science and mathematics teacher preparation are discussed.     

Online education for in-service secondary teachers and the incorporation of mathematics technology in the classroom

This paper reviews existing research on how in-service high school teachers have learned about, worked on or thought about the incorporation of mathematics technology into their teaching practices. The paper reviews different scenarios of instruction issuing from important research related to teacher professional development. Specifically, we will deal with contributions to online in-service mathematics teacher education that refer to the use of digital technologies in classroom teaching practices. The different articles reviewed belong to a range of teams of researchers from several universities and countries, and who have implemented distinct online education approaches. That work has allowed the gaining of knowledge on the specificities of using Web 2.0 tools for mathematics professional development (MPD), the function that online teacher interaction has in teacher learning, and the actual classroom conditions in which mathematics technology is incorporated into instructional practice. This paper describes and discusses the design features of those approaches emphasizing the main concepts and their underpinning theoretical frames, noting important design elements, and specific results. Finally, the paper discusses how some of these research findings are connected with emergent issues in the field of MPD.     

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

This quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.     

Mathematics teacher training at the State Technical University in Chile

During the fifties and sixties in Chile many mathematics graduates of Pedagogical Institutes became university instructors rather than high school teachers as intended. In the late sixties Masters level programmes began giving more advanced training for university mathematics instructors. A ‘modern’ mathematics curriculum including computer science was introduced in the high schools. The first significant attempt to adapt the training of Chilean high school mathematics teachers to the new academic and social realities was begun in 1976 at the State Technical University with the cooperation of Teachers College, Columbia University, and the support of the Organization of American States.

The four‐year programme leads to Licenciatura (Bachelors) in Mathematics and Computer Education. All courses are taught by faculty members of the Department of Mathematics and Computer Science. The three basic areas of instruction are mathematics, computer science, and mathematics education. Funds provided by the O.A.S. have helped to make possible the development of curricular materials in Spanish, and the acquisition of computing and video tape equipment.     

Mathematics Assessment: Practices and Reporting Methods

The curriculum, teaching, and assessment Standards of the National Council of Teachers of Mathematics advocate the use of various assessment techniques in mathematics, K-12. Practitioners from 35 school districts in two regions of a midwestern state completed a questionnaire and reported information about their assessment practices, reporting methods, and other issues that affect change in mathematics. The results of the survey suggest that current reporting practices are limiting the use of alternative classroom assessment practices. Delays in the use of alternative mathematics assessment practice can probably be expected until the reporting systems used in school districts become consistent with the assessment systems and teachers participate in ongoing professional development programs to learn more about alternative assessment practices.     

Common Core State Standards in the Middle Grades: What's New in the Geometry Domain and How Can Teachers Support Student Learning?

The Common Core State Standards for Mathematics (CCSSM) is a primary focus of attention for many stakeholders' (e.g., teachers, district mathematics leaders, and curriculum developers) intent on improving mathematics education. This article reports on specific content shifts related to the geometry domain in the middle grades (6–8) mathematics curriculum. The methodology employed allows for comparisons of content across multiple standards documents. We report on some dramatic changes with regards to the geometry content taught in the middle grades. We found 52% of the middle grades geometry CCSSM learning expectations will be new to the respective grade level at which they are taught in at least six of the eight states analyzed in this study (57% in grade 6, 50% in grade 7, and 50% in grade 8). We also highlight three areas that represent “new” geometry content at the middle grades based on our analysis of CCSSM and pre‐CCSSM state standards.     

STEM Teachers' Planned and Enacted Attempts at Implementing Engineering Design‐Based Instruction

This study investigates grades 5 and 6 science, technology, engineering, and mathematics (STEM) teachers' planned and actualized engineering design‐based instruction, the instruments used to characterize their efforts, and the implications this work has for teachers' implementations of an integrated approach to STEM education. Participants included 23 STEM teachers from six schools (three rural, two suburban, and one urban). Data were gathered via lesson implementation plans and classroom observations. Teachers demonstrated strength in planning for standards‐ and engineering design‐based lessons, incorporating engineering practices within their respective implementation plans, and aligning their plans with content and design process standards. Missing from their plans was attention to science concepts and their placement, use, and application within a design task. Classroom observations indicated that the teacher participants gave priority to “front loading,” the design process by concentrating more of their instructional time on problem identification and planning and less time on testing designs, communicating performance results, and redesigning. Measures utilized in this study provided insight into the content of teachers' planning and subsequent instruction and suggest potential for capturing content planning in the context of classrooms in which teachers are attempting to integrate novel curriculum, such as the new standards for engineering practices.     

Mathematics coaching and instructional reform: Individual and collective change

Mathematics coaching initiatives are being implemented in schools and districts across the country, guided by the notion that these initiatives will foster individual teacher’s learning and thereby support system-wide instructional improvement in mathematics. This paper explores the evolving roles that mathematics coaches played in a system-wide instructional improvement effort focused on elementary mathematics education in a medium-sized suburban school district. Using social network analysis and qualitative analysis of interviews, we argue that coaches facilitated teachers’ implementation of a new mathematics curriculum by acting as brokers, first as intermediaries between the district office and schools, then as catalysts for collective inquiry. Further, we show how coaches’ work was both enabled and constrained over time by various organizational dimensions at the school and district levels. Overall, our findings suggest that district and school leaders should think beyond the roles and responsibilities of individual coaches, and consider how to support coaches as participants in system-wide networks focused on continuous learning and instructional improvement.     

Enhancing and Enacting Curricular Progressions in Elementary Mathematics

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of progressions—mathematical concepts, instructional activities, number choices, and student solutions—and that the progressions were embedded within each other. This study contributes to the field’s understanding of the ways in which expert teachers make use of curriculum- and research-based progressions in their teaching practices.     

Middle‐School Mathematics Teachers' Beliefs in NCTM's Vision

This study examined the extent to which seventh‐ and eighth‐grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in these documents. Quantitative data were collected through the Mathematics Standards Belief Survey (MSBS), a survey specifically designed to measure teachers' overall belief in NCTM's vision as well as in certain philosophical tenets of NCTM. Of the 82 seventh‐ and eighth‐grade mathematics teachers in the identified school district of Nevada, 73 (89.0%) participated in this study. The data revealed that, among seventh‐ and eighth‐grade mathematics teachers, secondary‐certified teachers had significantly higher MSBS scores than elementary‐certified teachers. A number of other findings were made, including significant differences among mean belief scores in the philosophical tenets of NCTM.