Factors Underlying Middle School Mathematics Teachers’ Perceptions About the Ccssm and the Instructional Environment Free

Our review of research begins with a description of the conditions that have spurred our nation’s interest in STEM education and the current instructional environment in middle school mathematics and science classrooms. We move on to describe how the CCSSM differ from prior standards documents. Next, we describe key findings from previous surveys examining teachers’ perceptions of the CCSSM. Last, we discuss surveys examining teachers’ perceptions of large-scale assessment and teacher evaluation. These sections summarize our current understanding of teachers’ perceptions and point out the need for more information regarding the factors underlying these constructs and how they are related to one another.

There has been an increased concern in recent years that the United States is not producing enough individuals with degrees in STEM (Kuenzi, 2008). While the causes of this phenomenon are certainly multifaceted, policy makers have drawn attention to the performance of U.S. students on national assessments such as the National Assessment of Educational Progress (NAEP), performance of U.S. students on international assessments such as the Programme for International Student Assessment (PISA), and the number of degrees awarded in STEM fields (Committee on Prospering in the Global Economy of the 21st Century, 2007). For instance, out of 65 countries, the mean mathematics performance of 15-year-old U.S. students on the 2012 administration of the PISA was below average while the reading literacy and science performance of these students was average (Organization for Economic Co-operation and Development, 2014). Moreover, the majority of middle school mathematics teachers (69%) do not have a major in mathematics (National Center for Education Statistics, 2003).

Given the achievement of U.S. students described above, an important question is: What is the instructional environment in U.S. mathematics classrooms? Middle school mathematics teachers tend to focus on number and operations and provide more emphasis on facts, concepts, skills and procedures than on reasoning or communication (Mitchell, Hawkins, Jakwerth, Stancavage, & Dossey, 1999). Middle school mathematics teachers are also more likely to use textbooks than middle school science teachers. Middle school mathematics teachers were more likely to focus on state standards when crafting instruction than middle school science teachers. This focus on standards by middle school mathematics teachers underscores the importance of understanding how this group of educators perceives the CCSSM.

Efforts to design and implement the CCSSM differ from prior articulations and implementations of standards for three primary reasons. First, the CCSSM are associated with high-stakes assessments through the Race to the Top competition, which requires that states adopt the CCSSM, design high stakes assessments based on the CCSSM, and tie teacher evaluations to student performance on those standardized tests (Duncan, 2009). As of 2013, 38 states required student achievement data to be used in teacher evaluations and in 23 of these states, student achievement accounted for at least half of teachers’ evaluation information (Hull, 2013). The association with high stakes testing and teacher evaluations distinguishes the CCSSM from prior standards documents, such as the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000), which had substantial national (Reys, 2006) influence in articulating characteristics of curriculum and instruction, but which were not tied to assessment and evaluation policies on a large scale. For an examination of the degree of STEM integration in a variety of different state and national standards, see STEM Integration in Mathematics Standards (Capraro & Nite) in this volume.

Second, the CCSSM bring some uniformity to state standards, which, prior to the implementation of the CCSSM, ranged considerably with respect to key dimensions such as content, rigor, coherence, and focus (Reys, 2006; Smith, 2011). Although states still have flexibility to add to the CCSSM, up to an additional 15% (Sloan, 2010), researchers now have an unprecedented opportunity to study teachers’ instructional and assessment practices with respect to a relatively uniform set of standards, rather than a potpourri of standards.

Third, the CCSSM were developed and adopted with great rapidity, reducing opportunities for input, testing, and revision. There has subsequently been a dearth of data regarding how teachers and districts are interpreting and implementing the CCSSM, and critics have charged that using untested standards as the basis for high-stakes testing and teacher evaluations could harm educational opportunities for students (Ravitch, 2013). Consequently, more needs to be known about how teachers and districts perceive the CCSSM in order to better support them in implementing the challenging features of the CCSSM.

Given the high stakes involved with the CCSSM and the considerable attention they are receiving in educational policy debates at the local and national level, it is important to understand the ways teachers perceive the standards and related assessment and accountability systems. Furthermore, it is imperative that researchers explain their methods so that educators, researchers, and policy makers can better understand the assumptions and findings in order to extend the research on the implementation of the CCSSM and consider the implications of this research.

Mathematics education researchers have historically used Likert-scale surveys to investigate mathematics teachers’ conceptions (Philipp, 2007), and more recently Likert-scale surveys have been used to assess teachers’ perceptions with regard to the CCSS and the CCSSM (Choppin et al., 2013; Cogan et al., 2013; Davis et al., 2013; EPE Research Center, 2013; Hart Research Associates, 2013). Surveys have found that teachers do not perceive that their current textbooks are well aligned with the CCSS or the CCSSM. In general, teachers do not feel well prepared to teach the CCSS or the CCSSM or to teach the CCSS to certain student groups (e.g., students with disabilities). Teachers also perceive that their districts have not done enough to prepare them for the CCSS or the CCSSM.

Overall, there appears to be a shift in teachers’ perceptions regarding the quality of the CCSSM in comparison to their previous state standards. For instance, Cogan et al. (2013) reported that of the 12,000 mathematics teachers in Grades 1-12 they surveyed in 2011, 77% stated that a selection of the CCSSM standards that they were provided with in the survey were the same as their former state standards. In February 2013, a survey involving 403 middle school mathematics teachers found that 39% perceived that a sample of the CCSSM Content Standards provided in the survey were similar to their previous state standards (Davis et al., 2013). In addition, the majority of middle school mathematics teachers stated that they viewed the CCSSM Content Standards (86.3%) and the CCSSM Standards for Mathematical Practice (87.4%) as more rigorous than their previous state standards.

Survey research has not deeply explored teachers’ perceptions with regard to state-based or national assessments. In recognition of this gap, the Gates Foundation and Scholastic (2012) completed an online survey in 2011 involving more than 10,000 teachers. A total of 60% of the teachers stated that standardized tests have a major impact on the classroom learning environment. A little over half of the teachers agreed that standardized tests could be used as meaningful benchmarks for teachers to judge student progress (51%) or to judge schools against one another (43%). Only 26% of teachers agreed that standardized assessments are an accurate portrayal of student achievement. While teachers agreed that student growth should be used in measuring teacher performance (85%), they largely rejected the use of standardized tests as this measure of student growth (64%).

Choppin et al. (2013) surveyed 366 middle school teachers about their perceptions with regard to state assessments and teacher evaluation. The sample agreed or strongly agreed that the new state-based assessments would be aligned with the CCSSM Content Standards (91.2%) and the CCSSM Mathematical Practice Standards (83.8%). Additionally, they stated that the state-based assessments associated with CCSSM would influence their instructional decisions (92%). The middle school mathematics teachers agreed or strongly agreed that teacher evaluation would influence their instructional decisions (65.1%) and assessment practices (64.2%).

The majority of the work on teachers’ perceptions with regard to the CCSSM or the CCSS has been in the form of nationwide surveys, but the extent of the reporting from these surveys has been limited, with simple descriptive analyses involving frequency counts within different Likert-scale categories. In addition, these surveys have not been examined to determine the structure underlying teachers’ CCSSM perceptions. This study uses a more sophisticated statistical technique, exploratory factor analysis, than descriptive analyses in order to identify the factors under-girding middle school mathematics teachers’ perceptions of the CCSSM. Specifically, this study was designed to answer the following research question: What factors help to explain middle school mathematics teachers’ responses in two national surveys addressing Mathematics Teachers’ Perceptions about the CCSSM and the Instructional Environment?

This study describes our efforts to understand the factors underlying middle school mathematics teachers’ perceptions of the CCSSM based upon surveys developed in 2012 and 2013. This section of our article is composed of four components. First, we describe the theoretical underpinnings for the questions included in the first survey. Second, we describe how the second survey was constructed by revising the first survey. Third, we provide readers with the demographics concerning the sample of middle school mathematics teachers completing each survey. Fourth, we describe the procedures for completing the exploratory factor analyses used to identify the factors underlying each set of survey responses. Our focus in the surveys was on gathering information on middle school mathematics teachers’ CCSSM perceptions, yet these perceptions do not occur within a vacuum. These perceptions are closely connected to the instructional environment that teachers work within and the CCSSM-related assessment and teacher evaluation systems introduced into the educational system by policy advocates. Thus, in understanding middle school mathematics teachers’ CCSSM perceptions we argue that their perceptions with regard to these other components must also be taken into consideration.

In 2012, we developed a survey to examine what we refer to as Mathematics Teachers’ Perceptions about the CCSSM and the Instructional Environment. We theorized that such a survey would contain five main components: perceptions of the CCSSM, beliefs about teaching mathematics (Philipp, 2007), professional development experiences (Sowder, 2007), instructional planning practices (Blomeke et al., 2008; Morris, Hiebert, & Spitzer, 2009), and curricular practices (Banilower et al., 2013; Grouws & Smith, 2000; National Research Council, 2001; Tarr et al., 2008).

As the survey focused on teachers’ familiarity with and perceptions of the CCSSM we included questions from previous surveys in this area such as teachers’ familiarity with the CCSSM content standards (e.g., Cogan et al., 2013). Due to the importance of choosing and implementing high cognitive demand tasks (Stigler & Hiebert, 2004) we asked teachers about the appearance of complex problems in the CCSSM. As one of the main features of the CCSSM is the Standards for Mathematical Practice (SMP) we included questions asking about teachers’ familiarity with these practices. Due to the importance of communication and exploration in mathematics in national reform documents (e.g., NCTM, 2000) and their connections to the SMP we included survey questions in these two areas as well. We also chose to examine teachers’ perceptions of the CCSSM with regard to conceptual and procedural fluency, as this has been a focus in mathematics education (National Research Council, 2001) in addition to an organizing principle of the CCSSM (CCSSI, 2010).

While the majority of states adopted the CCSSM in 2010, assessments associated with these standards will not be implemented until the 2014-2015 school year. Given this lengthy implementation time, it makes sense that school districts would provide opportunities for teachers to learn about these standards through professional development experiences. Additionally, previous surveys examining teachers’ perceptions of the CCSS (EPE Research Center, 2013; Hart Research Associates, 2013) and the CCSSM (Cogan et al., 2013) have included questions concerning their professional development experiences vis-á-vis these standards.

Another important influence on teachers’ classroom environments is their instructional planning practices (Blomeke et al., 2008; Morris et al., 2009), especially the examination of student work (Jacobson, 2010; Tobia, 2007). These findings led to the inclusion of a set of questions in both surveys addressing these characteristics of teachers’ classroom preparations.

A large body of research points to the importance of curricular resources within mathematics teachers’ instructional environments in terms of focusing teachers on particular articulations and sequencing of content (Banilower et al., 2013; Grouws & Smith, 2000; National Research Council, 2001; Tarr et al., 2008). There has also been an increase in the recognition of digital curriculum resources as valid instructional materials by states (Fletcher, Scaffhauser, & Levin, 2012). Accordingly, we added a set of questions involving teachers’ primary, secondary, and digital curriculum materials. Specifically, we asked teachers to indicate the level of consistency between their primary curriculum materials and the CCSSM content standards, SMP, and computational/procedural fluency. Prior research suggests that mathematics teachers supplement their primary textbooks in a number of different ways (Tarr et al., 2008). We developed two categories of teacher curricular supplementation: inquiry-based activities and remediation of skills. Open-ended items were included in the survey to determine the name of the resources used in both types of supplementation. Likert scale items were used to determine teachers’ perceptions regarding the alignment between these supplementary materials and the CCSSM.

In total there were seven different categories of Likert item responses on the first survey. Six of these categories consisted of four different item responses while one contained five different item responses. Different questions necessitated the use of a variety of Likert categories in the survey. For instance, we asked middle school mathematics teachers the following question: How familiar are you with the CCSSM content standards?

The second survey was developed during March 2013 using factors identified in the first survey. These factors are described later in the results section of the paper. Several components of the first survey, such as teachers’ beliefs, did not appear as factors; therefore, these sets of questions were not used in the development of the second survey. We also made changes to the format of questions appearing in the second survey. These questions were standardized so that the same set of Likert item responses could be used with as many of the items as possible.

In the second survey, we also included additional items that had appeared as themes in interviews with middle school mathematics teachers regarding the CCSSM that were conducted as other parts of our larger study (Choppin, Davis, Drake, & Roth McDuffie, 2012). These themes involved the influence of CCSSM-aligned state assessments and state-based teacher evaluation systems connected to the CCSSM. We also included items that had appeared in the CCSSM surveys created by other groups (e.g., Cogan et al. 2013) regarding teachers’ perceptions of their preparedness to teach the CCSSM. As a result, this second survey was also considered to be a measure of Mathematics Teachers’ Perceptions about the CCSSM and the Instructional Environment with a slightly expanded set of perceptions to include state assessment and evaluation tied to the CCSSM.

In total there were four different categories of Likert item responses on the second survey. Two of these categories consisted of four different item responses while one category contained five different item responses and one category contained six different item responses.

The first survey was conducted in February 2013 while the second survey was conducted in April and May 2013. Market Data Retrieval (MDR) conducted both surveys and used two primary sampling sources for each survey. The first sample source was MDR’s online educator panel consisting of teachers who agreed to participate in MDR survey research. The second source was MDR’s client e-mail sample of educators and was used to improve the representation of middle school mathematics teachers in the sample. While both samples consisted of middle school mathematics teachers from across the country we have no evidence suggesting that the sample was representative of middle school mathematics teachers in the United States. Survey invitations were randomized nationally based upon state. Private and parochial schools were excluded from the process. The order of questions was randomized during each administration of the survey. The response rate for the first survey was 39% while the response rate for the second survey was 29.5%. The lower response rate for the second survey was attributed to the timing of the survey as early May is a busy time for teachers nationwide.

The first survey (S1) included 428 elementary, middle school, and high school mathematics teachers. However, as we were interested in focusing on middle school mathematics teachers, we removed the responses of teachers who indicated that their primary teaching responsibility was at the elementary (Grade 5 or below) or high school (Grades 912) levels. This resulted in a total of 403 middle school mathematics teachers employed in 43 of 45 of the states that at the time had adopted the CCSSM. The second survey (S2) included 400 elementary, middle school, and high school mathematics teachers. In order to focus on middle school mathematics teachers, we again culled elementary and high school teachers from the S2 respondents. This process yielded a total of 366 middle school mathematics teachers employed in 42 of 45 CCSSM-adopting states at the time of the survey.

A factor analysis can be used for three purposes: to reduce a data set to a smaller subset of data that contains as much information from the original data set as possible; to develop a survey to measure a specific underlying variable; and to understand the structure of one or more variables (Field, 2009). For this study, we used SPSS 21.0 (2012) to conduct exploratory factor analyses on both surveys to better understand and describe the structure embedded within the collection of variables comprising each survey. Despite the different types of Likert item responses used in both surveys, we followed the precedent of Linden (1977), who conducted a factor analysis involving different decathlon events, some of which involve distances while others involve time. The procedures surrounding each factor analysis are described in the following paragraphs.

There is some disagreement about the sample size needed for a factor analysis. On the one hand, Nunnally (1978) recommends having 10 times as many participants as variables. On the other hand, Comrey and Lee (1992) describe 300 as a good sample size for a factor analysis. With 62 initial questions and 403 participants we met the second criterion but not the first. In S1, teachers were asked several questions concerning the supplementary materials that they used for remediation and inquiry-oriented activities. These questions were answered by at most 276 teachers. As we were likely to use listwise deletion to handle missing data for the exploratory factor analysis, we removed these questions because including them in the factor analysis would have reduced the sample size substantially. This resulted in a total of 54 questions in the first survey that were answered by all 403 teachers in the sample. Next, we followed Field’s (2009) suggestion and began looking at the correlation matrix involving all 54 questions. We retained those questions that had five or more correlations of between 0.3 and 0.9. This resulted in a total of 26 variables retained for the initial principal component analysis.

We retained factors that had eigenvalues greater than 1, and due to the fact that many variables referred to the CCSSM we hypothesized that factors could be related so we used an oblique rotation (direct oblimin). Cases were excluded listwise and coefficients were sorted by size with smaller coefficients suppressed with absolute values below 0.4. We also ran reliabilities using Cronbach’s alpha (1951) and specifically measured the reliability if an item was deleted from each of the factors. This work resulted in the elimination of four more variables from the data set as their exclusion from the data set resulted in a higher overall reliability. Altogether, 22 variables were retained for the S1 factor analysis.

There was a total of 33 questions addressing teachers’ perceptions surrounding the CCSSM. As there were only 366 total participants, the number of questions needed to be reduced. Similar to the first factor analysis, we examined the correlation matrix for these 33 questions to examine the number of correlations between 0.3 and 0.9. As there were fewer variables than S1, we retained those variables that had at least three correlations between 0.3 and 0.9. This resulted in a total of 22 variables retained for the initial principal component analysis. To investigate the relationship between different factors, we performed both an orthogonal (varimax) and an oblique (direct oblimin) rotation. The latter did not indicate any relationship between factors, so the orthogonal rotation is reported within the results section. Examining the reliability of each of the factors resulted in the removal of 3 variables from the factor analyses resulting in a total of 19 variables used in the S2 factor analysis.

This section contains two parts. The first part describes the factors undergirding Survey 1. The second part describes the factors under-girding Survey 2. Each section is prefaced by calculations involving the adequacy of the sample and if the sample is a candidate for exploratory factor analysis.

The Kaiser-Meyer-Olkin (KMO) measure verified the sampling adequacy for the analysis, KMO = .823, which is considered to be great (Hutcheson & Sofroniou, 1999). All KMO values for individual items were greater than .7, which is above the acceptable limit of .5 (Field, 2009). Bartlett’s test of sphericity %², indicated that correlations between items were sufficiently large for PCA and that the correlation matrix was statistically significantly different from an identity matrix.

As suggested by Cattell (1966) we examined solutions above and below the inflection point of the scree plot. Solutions involving four extracted factors resulted in a survey item appearing in two different factors. Solutions involving six extracted factors resulted in a factor involving only two survey items. As a result, we used a solution involving five factors, which converged in eight iterations. From the scree plot and application of the Kaiser-Guttman rule, five factors were extracted accounting for 65.9% of the variation in the sample. Table 1 shows the factor loadings after rotation for the pattern matrix.¹

The item clustering shown in Table 1 suggests the following five factors:

• Factor 1 – Extent to Which Digital/Electronic Curriculum Resources are Used;

• Factor 2 – Degree to Which Professional Development is Supported;

• Factor 3 – Level of Required CCSSMMathematical Processes and Perceived Rigor;

• Factor 4 – Extent to Which Digital/Electronic Curriculum Resources are Read;

• Factor 5 – Frequency of Teachers’ Collaborative Instructional Planning.

Factors 1 and 4 were negatively correlated with one another (r = -.542). That is, as middle school mathematics teachers’ responses to one factor increased, responses to the other factor decreased. The factors all had good reliability as their Cronbach Alpha scores were all in the .7 to .8 range (Kline, 1999).

The Kaiser-Meyer-Olkin (KMO) measure verified the sampling adequacy for the analysis, KMO = .731, which is considered to be good (Hutcheson & Sofroniou, 1999). All KMO values for individual items were > .6, which is above the acceptable limit of .5 (Field, 2009). Bartlett’s test of sphericity %², indicated that correlations between items were sufficiently large for PCA and that the correlation matrix was statistically significantly different from an identify matrix.

Similar to the exploratory factor analysis for S1, we explored solutions just above and below the point of inflexion of seven factors (Cattell, 1966). Analyses involving six and eight factors resulted in factors consisting of only one survey item. As a result, we used the Kaiser-Guttman rule to extract seven factors accounting for 73.4% of the variation in survey responses. The rotation converged in six iterations. Table 2 illustrates the factor loadings after orthogonal rotation. The item clustering suggests the following seven factors:

• Factor 1 – Extent to Which Digital/Electronic Curriculum Resources are Used;

• Factor 2 – Extent to Which CCSSM Requires Mathematical Processes;

• Factor 3 – Extent to Which State Assessment and Teacher Evaluation Influence Classroom Practices;

• Factor 4 – Extent of District Professional Development Support and CCSSM Familiarity;

• Factor 5 – Extent of Teacher Familiarity with and Preparation for the CCSSM;

• Factor 6 – Level of Perceived Rigor within the CCSSM; and

• Factor 7 – Extent of Alignment Among State Assessments, CCSSM, and Classroom Assessments.

Six of the seven factors had good reliability as their Cronbach Alpha scores were at least .7; factor 7 was slightly below this value at .6 (Kline, 1999) While this factor involving state assessments, classroom assessment and CCSSM-based assessment was slightly less reliable than the other factors, we retained it in our analysis as this was a key addition to S2. The slightly lower reliability of this factor may have been due to the fact that teachers were making predictions about state-based CCSSM assessments that they, at the time of survey completion, had not seen.

We designed and implemented two surveys to examine Mathematics Teachers’ Perceptions about the CCSSM and the Instructional Environment. A total of five different factors were found to undergird this construct explaining 65.9% of respondent variation in S1. In S2 a total of seven different factors were identified in the analysis, explaining over 73% of respondent variation. Across both surveys there was one similar factor: Extent to Which Digital/ Electronic Curriculum Resources are Used. The following sections interpret the meanings of these findings more closely.

Research suggests that mathematics teachers frequently use textbook resources when shaping and implementing classroom lessons (e.g., Banilower et al., 2013). However, our survey questions associated with the alignment between middle school mathematics teachers’ primary curriculum resources and the CCSSM were not connected to other questions in the survey. That is, there did not appear to be a factor involving middle school mathematics teachers’ primary textbook materials associated with their CCSSM perceptions. Moreover, both factor analyses reported here suggest that while textbooks may still drive middle school mathematics teachers’ classroom instruction, students’ experiences are increasingly mediated by teachers’ use of digital/electronic resources for student work, teacher resource information, and supplementary resources. As a result, professional development for middle school mathematics teachers in our current Common Core era may need to provide teachers with tools for helping them to discern and choose wisely amongst the wide spectrum of resources that are available online and to articulate the connections between the different kinds of resources they use to design instruction. Given the larger trend for teachers in the United States and elsewhere to locate activities from various websites when planning instruction (Selwyn, 2007), there are broad implications for professional development for STEM teachers to identify characteristics of high quality resources. Not only was professional support an important factor appearing in both surveys regarding middle school mathematics teachers’ perceptions of the CCSSM, it was also connected to other teacher actions that can positively influence student learning, such as teachers’ planning with colleagues, regularly discussing mathematics with colleagues, and frequently discussing student work. In S2, professional development focused on the CCSSM was associated with middle school mathematics teachers’ support for new instructional practices, CCSSM preparation, and familiarity with the CCSSM processes. Thus professional development focusing on the CCSSM that is connected to many aspects of middle school mathematics teachers’ work has the potential to pay multiple dividends to teachers that not only extend to a better understanding of the standards themselves but also to other factors that influence teachers’ instructional environments, such as a willingness to try new instructional approaches or engage in more collegial interactions focused on mathematics or student work.

In both surveys, middle school mathematics teachers drew connections between several mathematical processes and conceptual understanding. Specifically, teachers perceived that student exploration and communication were connected with conceptual understanding. At the same time, however, there were differences with regard to these processes across both surveys. In S1, these processes as well as complex problems were connected to middle school mathematics teachers’ perceptions of the CCSSM being more rigorous than their previous state standards. In S2, middle school mathematics teachers’ perceptions of rigor constituted a separate factor. It is not clear why these differences emerged across the two surveys. Although middle school mathematics teachers were asked to what extent the CCSSM emphasize or require procedural or computational fluency, these questions did not comprise a factor. In other words, middle school mathematics teachers did not perceive that procedural fluency was connected to conceptual knowledge or mathematical processes such as mathematical computation. These findings suggest that middle school mathematics teachers might benefit from professional development that seeks to connect mathematical processes, conceptual knowledge, and procedural knowledge. This is an especially relevant finding for all STEM subjects given the emphasis on science and engineering practices in the NGSS as a means to develop content.

The factor analysis on S2 illustrates the relationships between middle school mathematics teachers’ perceptions regarding teacher evaluation and state assessments. That is, middle school mathematics teachers perceive policy changes in the areas of teacher evaluation and state-based CCSSM assessments as influencing both their instructional decisions and assessment practices. Given the broad support for teacher evaluation across the United States, this finding serves as a call to the broader research community to more carefully investigate how these policies will affect teachers’ perceptions and the classroom environment. While the influence of state assessments on instructional decisions may not result in “teaching to the test,” it is indeed a powerful finding that middle school mathematics teachers perceive that these assessments will drive their practices before they have even set eyes on these tests or administered them to their students.

The questions comprising the factors in these analyses could be used by researchers to develop similar surveys examining the construct of Mathematics Teachers’ Perceptions of the CCSSM and Instructional Environment or they could be elaborated upon with additional questions to further clarify the extent of and boundaries around each factor. For example, Factors 6 and 7 in S2 contained two survey items each, which is atypical. Nonetheless we feel that these factors are important in understanding teachers’ perceptions of the CCSSM. For instance, researchers (Schmidt & Houang, 2012) as well as architects of the CCSSM (CCSSI, 2012) have used the word “rigor” to refer to these standards. As a result, survey items related to this factor should be included in future analyses. The alignment of two items to each of these factors suggests that these constructs are currently underrepresented in the survey. Future surveys addressing Mathematics Teachers’ Perceptions about the CCSSM and the Instructional Environment should create additional survey items to further understand these factors. Additionally, as our analyses involve middle school mathematics teachers’ perceptions of the CCSSM, these factors could be used to construct surveys aimed at elementary level and high school level mathematics teachers to determine the extent to which the CCSSM perceptions of these different populations of teachers are similar to or different from middle school mathematics teachers.