From Interpretation to Instructional Practice: A Network Study of Early-Career Teachers’ Sensemaking in the Era of Accountability Pressures and Common Core State Standards

Sample

We identified three states in the upper Midwest that varied in their level of implementation of the CCSS. Two of the states implemented CCSS starting in 2012–2013 and 2013–2014, respectively. These were considered CCSS states in Opfer et al. (2018). The last state first implemented CCSS in 2010, paused in May 2013, and then withdrew the policy in April 2014 (Torphy et al., 2019). This state was not considered a CCSS state; however, its mathematics standards were very similar to the CCSS.

Within each state, we sought two to four districts for participation in our study. Our goal was to recruit medium-sized districts in the three states that (a) served varying student populations with regard to race/ethnicity and socioeconomic status and (b) had at least 10 full-time core content elementary general education ECTs in Grades K–6 as of 2014–2015. While data collection was limited to eight districts due to limitations in resources, this provided a large enough sample of ECTs to have adequate power to detect moderate effects of ECTs or their networks. We provide the background characteristics of students in the districts in our study in Table 1. The districts served students ranging from 5.3% to 70% eligible for free/reduced-price lunch and from 28% to 92% White.

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Table 1

Background Characteristics of Students in the Districts

State	District	%FRL	%White	%Black	%Hispanic/ Latino/a	%Asian/ Asian Pacific Islander	%American Indian/ Alaskan Native	%Hawaiian Native/ Pacific Islander	%Two or more races	%ELL	%SPED	Total Enrollment	No. of Teachers Participating in the Study
1	1A	70	89	3	2	1	0.1	0.03	0.2	48	8	20,700	8
	1B	39	90	1	4	2	2	0.1	3	3	12	9,500	3
2	2E	23	75	10	5	2	0.2	0.06	5	1	12	8,700	21
	2F	14	75	7	6	6	0.2	0.1	5	2	11	21,500	5
	2G	61	28	41	20	1	0.1	0.07	7	12	14	15,400	27
	2H	72	29	49	13	1	0.1	0.1	7	7	16	12,100	33
3	3J	5.3	86	0.4	8	4	0.1	0.01	2	2	14	5,800	4
	3K	63	26	20	44	7	0.15	0.27	4	13	16	16,800	18

Note. FRL = free/reduced-price lunch; ELL = English language learner; SPED = special education.

In terms of standardized tests, each state administered its own state tests in reading/language arts and mathematics to students in Grades 3 to 8 on an annual basis. With regard to teacher evaluation, each state used data from classroom observations, student learning gains, and other data sources to evaluate teachers on a yearly basis. However, there was substantial variation among the districts in the details of their teacher evaluation systems, such as the weights given to each component of evaluation, the number of observations required, how each district used the teacher evaluation results, and so on. Such variation was in part due to the fact that the states allowed the districts to create their own system rather than employing a uniform state system (Kim, 2017). We acknowledge that the ways in which each state and/or district implemented CCSS varied, and thus, we include district fixed effects to account for such variation in the analysis. For example, using a fixed effect for District C accounts for anything commonly experienced by the teachers in District C, including the curriculum, the orientation of the central administration, the location, and so on.

Once a district agreed to participate, we requested a list of ECTs who might be eligible for our study. We defined an ECT as one who was in the first 4 years of teaching and taught at least some mathematics in a K–6 multiple-subjects classroom. We defined “early career” as the first 4 years of teaching because it takes about 4 years for most teachers to develop and refine their instructional repertoire (Feiman-Nemser, 2001) and because teachers in many states achieve tenure at the district level and/or professional licensure at the state level after about 4 years (Darling-Hammond et al., 2001; Goldhaber & Hansen, 2010). Given our definition of an ECT, we contacted the eligible ECTs within each district and solicited their participation. The ECTs were compensated $30 for each classroom observation and each survey. Ultimately, our study includes data from 14 ECTs from the school year 2014–2015, 95 ECTs from 2015–2016, and 49 ECTs from 2016–2017. This totaled 158 unique cases for a given teacher in a given year, although there were only 119 unique teachers, where 85 ECTs contributed 1 observation, 29 ECTs participated in 2 years and contributed 58 observations, and 5 ECTs participated in 3 years, contributing 15 observations.

The teachers in our data represent about 34% of the ECTs in the schools that we studied. The range was from 8% to 100% across schools, with lower response rates generally in schools where many ECTs worked. Our response rates did not vary with respect to the demographics of the school districts (response rate was correlated at .25 with %free/reduced-price lunch students and at −.36 with %White students, but these correlations were not statistically significant). Our sample size and sampling rate compare with those in Smith et al. (2018), who analyzed data from 61 ECTs, representing a response rate of roughly 50% but ranging lower in some analyses due to missing data. As such, our data afford one of the best opportunities to longitudinally study ECTs’ observed instructional practices, and perhaps they are the only such data to link ECTs’ instructional practices to attributes of their network members.

To gauge our study sample relative to a national sample, in Appendix A (in the online version of this journal), we compare the teachers in our study with the ECTs in the National Teacher and Principal Survey (NTPS), the most recent national survey of teachers (employing the NTPS weights in the calculation of the test statistics to ensure national representation). The teachers in our sample were not statistically different from the NTPS ECTs in terms of being Black. They were less likely to be Hispanic (2% in our study vs. 10% in the national survey). They were also more likely to be female and more likely to have a general certification and a major in education (differences in the percentage having a master’s degree were not statistically different). We return to these differences in the Limitations, although we note here that the students in the districts we studied were diverse in terms of socioeconomic status and race. ³

Data Collection

As shown in Figure 3, in each of the three (2014–2015, 2015–2016, and 2016–2017) academic years, we collected classroom observation data from ECTs and survey data from both ECTs and their social network members. We observed each ECT twice in the fall/winter (between October and February) and twice in spring (between April and May) as they taught mathematics. The observations in a given season typically took place within 1 to 2 days of each other. We use the spring observations as our primary dependent variable and the fall observations as a baseline control. In almost all cases for a given ECT, the spring observations took place at least 3.5 to 4 months after the fall observations.

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Figure 3.

Timeline and structure of data collection.

Each ECT was also asked to complete three surveys in a given year. The fall and spring surveys included questions about planning mathematics instruction and about interpretations of state standards, evaluation, and the standardized tests that were used to construct the measure of the ECT’s interpretations of accountability pressures and curricular standards. The surveys also include measures of teacher background and other experiences that might affect instruction, which were used as covariates. Specifics are reported below in the measures section. In winter, the ECTs also completed an MKT survey (Hill et al., 2005). Since MKT was to be a covariate in our model, the winter measure best represented the ECT’s state of knowledge that might have effected change in instructional practices from fall to spring. If an ECT’s fall interpretations or interactions with network members between fall and winter affected the ECT’s MKT, then using a winter measure of MKT as a covariate leads to conservative estimates of the effects of interpretations on spring practices.

Also in winter, we contacted formal mentors and other teacher colleagues identified by the ECTs in the fall as network members. These data define a projected network, which we then confirm from the nominations an ECT made in spring (see description of the exposure term). We asked each member of the projected network to complete a survey that included the same items as in the fall ECT surveys, as well as items about their self-reported classroom practices (to be used as a covariate). The network members’ responses in winter represent the conditions to which the ECT was exposed during the school year, midway between the ECT’s baseline fall measure of instructional practices and the ECT’s spring measure, used as our primary dependent variable. ⁴ Furthermore, measuring the network members’ attributes in winter ensures that their attributes were measured prior to the dependent variable of the ECT’s spring instruction. This provides a sounder basis for causality by limiting reverse causality (wherein the ECT may select or influence network members based on the ECT’s spring instructional practices—see Frank & Xu, in press). In the measures subsection that follows, we describe how we use the projected network to obtain the data ultimately defining the network exposure term.

Measures

Dependent Variable

Teaching for Robust Understanding in Mathematics, or TRU Math

Our application of the sensemaking literature links interpretations of circumstances to instructional practices in the classroom. Correspondingly, our dependent variable is based on direct classroom observations using the TRU Math protocol. TRU Math is a subject-specific observational protocol developed to characterize powerful mathematics classroom instruction (Schoenfeld et al., 2014). TRU Math has five dimensions, of which we focused on the four in Figure 4.

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Figure 4.

TRU Math (Teaching for Robust Understanding in Mathematics) dimensions.

The following descriptions are from Schoenfeld et al. (2014).

The Mathematics (Dimension 1): The extent to which the mathematics in the lesson is focused and coherent and at grade level; connections between procedures, strategies, concepts, and contexts are addressed; and the lesson provides opportunities to engage in mathematical practices

Cognitive Demand (Dimension 2): The extent to which classroom interactions create and maintain an environment of productive intellectual challenge that is conducive to students’ mathematical development

Agency, Authority, and Identity (Dimension 4): The extent to which students are the source of ideas and discussion of ideas, as well as how student contributions are framed

Uses of Assessment (Dimension 5): The extent to which students’ mathematics thinking surfaces; the extent to which instruction builds on student ideas when potentially valuable or addresses misunderstandings when they arise

In addition to scores for each dimension, we constructed a combined measure by standardizing each dimension based on the spring ratings and then taking the average. As a set, the dimensions capture key elements of Lampert et al.’s (2010) conception of ambitious mathematics instruction. Dimensions 1 and 2 examine whether students are working on rigorous mathematics tasks that are at grade level. Dimensions 4 and 5 attend to how teachers create environments for students’ thinking to surface and be observed. Note that the highest levels on each dimension explicitly or implicitly include the potential for procedural and conceptual learning. For example, Level 3 of the mathematics dimension includes “connections between procedures, concepts and contexts.” It is this combination that creates the authentic learning opportunities emphasized in ambitious instruction.

We made four related modifications to adapt TRU Math to our context. These involved measurement in terms of 10-minute intervals, not measuring the third dimension of TRU Math because of inadequate interrater reliability (IRR), adaptation to elementary school classroom activities, and creating a finer 5-point scale including 5 points for which we were able to sustain IRR. See the technical Appendix B (available online) for details.

To establish baseline IRR, we first calibrated an expert rater team of three project members who all had mathematics education expertise. Once the expert team had reached a threshold of 0.50 weighted kappa on their ratings across all dimensions, we then measured IRR by calculating the intraclass correlations for a single typical rater and compared the weighted kappas of each team member with each of the expert raters. Raters were considered reliable if the team met acceptable thresholds of intraclass correlations (~.60) and a team member had a weighted kappa of about 0.50 with at least one expert team member (Bell et al., 2014). After reaching a baseline threshold for IRR in October 2015, we monitored for rater drift by asking the raters, usually twice per quarter, to rate the same class period video from a participating ECT to confirm that the raters continued to meet our thresholds for defining reliability. If particular raters did not meet the thresholds, the video episodes were discussed with an expert team member and the drifting rater rated a set of three episodes from another video (rated by other team members) until acceptable IRR was achieved (for further details, see Bieda et al., in press).

Data Analysis

We begin by presenting descriptive statistics for the four dimensions of TRU Math we have selected and for each of the teacher-level predictors in our models. We then estimate models with the different dimensions of TRU Math as the dependent variable, as well as a combination of all the dimensions with the ECTs’ own interpretations and that of their network members as the key predictors. Last, we present a descriptive model of the teachers’ exposure to their network members’ interpretations.

Model of Ambitious Instruction (TRU Math)

Corresponding to our measurement of TRU Math in episodes of 10 minutes, we estimated the following model for episode (i) and teacher (j):

Spring TRU Math i j k y = β 0 + β 1 ECT ’ s own interpretations j k y + β 2 Exposure to network members ’ s interpretations j k y + β 3 Out − degree j k y + β 4 Intensity of mathematics professional developme n t j k y + β 5 MKT j k y + β 6 TRU Math score in previous fall j k y + Γ ’ IND j k y + u k + θ j + α y + r i j k y .

(1)

In Equation 1, Spring TRU Math _ijky is the observation score on a TRU Math dimension (or combined across dimensions) for episode i for ECT j in district k within year y. Ultimately, the data included 1,856 episodes of mathematics instruction within 158 teacher-years (a given teacher in a given year) for 119 unique teachers. We used clustered standard errors at the teacher level to evaluate the estimated effects of the network exposure term.

In Equation 1, the term β₁ represents the relationship between an ECT’s own interpretations of accountability pressures and curricular standards and the ECT’s instructional practices, as in Research Question 1. This would be consistent with the sensemaking process represented by the white arc in Figure 1. A positive value of β₁ would indicate that ECTs who had more positive interpretations of accountability pressures and curricular standards were more likely to increase their ambitious instruction and ECTs with negative interpretations were more likely to decrease their ambitious instruction. Similarly, the term β₂ represents the relationship between an ECT’s network members’ interpretations of accountability pressures and curricular standards and the ECT’s instructional practices, as in Research Question 2. A positive relationship would be consistent with the transitional arc in Figure 1.

The term μ_k represents district fixed effects, recognizing that teachers may be affected by the particular circumstances of their districts, including the student demographics, curricular policies, and leadership. For example, district fixed effects would account for the unusually low levels of ambitious instruction in spring in District A due to the curriculum or limited professional development in District A. The terms β₁ and β₂ can then be interpreted as applying to teachers within the same district who had different interpretations of external circumstances or different networks, respectively. The term θ_j represents 9 fixed effects for the teachers who appeared in our sample in more than 1 year and whose fixed effects estimates were statistically different from those of the group of teachers measured only once (including 34 fixed effects for all teachers who participated in more than 1 year would have overtaxed the degrees of freedom). Fixed effects account for the dependencies due to repeated observations on a given teacher (Wooldridge, 2010) and have been used extensively in education research (e.g., Evans, 2019; Hurwitz et al., 2019; Ronfeldt et al., 2013). The term α_y represents the fixed effects for the year of data collection as well as a single fixed effect for Year 3 in a specific district that had a dramatic change in curriculum and corresponding professional development. The r_ijky represent random errors for the episodes and are assumed to be N(0, σ²). Although Equation 1 is specified for TRU Math generally, we estimated one model for each dimension separately and then one for all the dimensions combined. In each case, we controlled for the corresponding prior measure of TRU Math averaged across all the episodes in the preceding fall (for the combined score, the fall scores were standardized based on the means and standard deviations for the spring scores, thus maintaining consistency in the construction of the measure over time).

Correlates of Exposure to Network Members’ Interpretations

To explore the factors related to an ECT’s exposure to network members’ interpretations of accountability pressures and curricular standards, we examined how each of the variables in our main model was correlated with the ECT’s exposure to network members’ interpretations. Thus, we considered how ECTs might be very deliberate in cultivating their social networks that provide specific knowledge or information (Spillane et al., 2012; Wilhelm et al., 2016) or allow them to express vulnerability (Baker-Doyle, 2011). These networks may be very influential in determining how reforms are implemented in schools (Daly et al., 2010; Frank et al., 2004; Frank, Xu, et al., 2018; Penuel et al. 2009), and they are critical to teacher retention (Baker-Doyle, 2010; Smith & Ingersoll, 2004). We also explored the relationship between exposure to network members’ interpretations and several other measures (e.g., use of social media, math anxiety, self-efficacy, collective efficacy).

Preliminary analyses indicated that the strongest correlates of exposure to network members’ interpretations were based on the ECTs’ survey responses to these items: “I need to earn a high teacher evaluation score to keep my job” and “I enjoy thinking about different ways to solve a mathematics problem.” The responses were on a 4-point Likert scale, with 1 = strongly disagree, 2 = strongly agree, 3 = agree, and 4 = strongly agree. After we had identified potential factors associated with the interpretations of network members, we included them in a model predicting the network exposure term, controlling for the one district that varied significantly (p = .07) from the others, year fixed effects, fixed effects for the teachers with multiple years of data whose estimates differed significantly from those of the teachers who were measured only once, the ECTs’ TRU Math scores in the fall, and the ECTs’ interpretations of accountability pressures and curricular standards.

Descriptive Statistics

Descriptive statistics are shown in Table 2. The mean overall TRU Math scores ranged from 1.415 for Dimension 4 (Agency, Authority, and Identity) to 1.953 for Dimension 1 (The Mathematics). The combined measure has a mean near 0 because it was based on standardized scores of the individual dimensions. The means and standard deviations for each dimension were stable from fall to spring. There were 3% to 4% missing data on any given dimension. The ECTs’ own interpretations of accountability pressures and curricular standards had a mean of −0.007 with a standard deviation of 0.675 (recall that this was based on the mean of the standardized items). The exposure term mean was 0.919 with a standard deviation of 3.055, although there is no simple metric for this term because it is a function of frequency of interaction and interpretations of the network members. Out-degree ranged from 0 to 10, with a mean of 3.418. The mean of MKT was near 0 (−0.09 on the item response theory metric), with a range of about 4.5 points.

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Table 2

Descriptive Statistics

	M	SD	Minimum	Maximum
Dimension 1: The Mathematics (spring)	1.953	0.365	1	3
Dimension 2: Cognitive Demand (spring)	1.714	0.371	1	3
Dimension 4: Agency, Authority, and Identity (spring)	1.415	0.287	1	2.25
Dimension 5: Uses of Assessment (spring)	1.449	0.327	1	2.875
Combined (spring): mean of standardized scores	−0.021	0.562	−1.101	2.007
ECTs’ own interpretations	−0.007	0.675	−1.751	1.310
Exposure to network members’ interpretations	0.919	3.055	−9.117	10.058
Covariates
Out-degree	3.418	2.180	0	10
Professional development	3.610	1.421	1	6
Exposure to network members’ self-reported practices	7.002	2.511	2.714	15
MKT	−0.090	0.876	−2.007	2.513
Dimension 1 (fall): mean across episodes	1.931	0.384	1	2.917
Dimension 2 (fall): mean across episodes	1.688	0.373	1	2.75
Dimension 4 (fall): mean across episodes	1.408	0.304	1	2.5
Dimension 5 (fall): mean across episodes	1.473	0.349	1	2.714
Combined (fall): mean of standardized scores	−0.024	0.599	−1.210	1.857
Missing flag_ECTs’ own interpretations	0.209	—	0	1
Missing flag_ network members’ interpretations (nominated network members but no information from them)	0.209	—	0	1
Missing flag_network members’ self-reported practices	0.247	—	0	1
Missing flag_D1(fall)	0.044	—	0	1
Missing flag_D2(fall)	0.044	—	0	1
Missing flag_D4(fall)	0.038	—	0	1
Missing flag_D5(fall)	0.038	—	0	1
Missing flag_combined (fall)	0.038	—	0	1

Note. N = 158 (teacher-years). ECT = early-career teacher; MKT = mathematics knowledge for teaching.

Model of Ambitious Instruction (TRU Math)

Estimates from our model predicting TRU Math are shown in Table 3. Regarding Research Question 1, the estimated effect of an ECT’s own interpretations of accountability pressures and curricular standards was considerably less than its standard error on each dimension as well as the combined dimensions; there is no evidence of an effect of an ECT’s own interpretations on changes in the ECT’s instructional practices.

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Table 3

Factors Predicting Ambitious Mathematics Instruction as Measured by TRU Math in Spring

	Model (1)	Model (2)	Model (3)	Model (4)	Model (5)
	Dimension 1: The Mathematics	Dimension 2: Cognitive Demand	Dimension 4: Agency, Authority, and Identity	Dimension 5: Uses of Assessment	All Dimensions Combined
ECTs’ own interpretation	0.010 (0.046)	0.013 (0.044)	0.011 (0.040)	0.003 (0.036)	0.013 (0.067)
Exposure to network members’ interpretation	0.015 (0.009)	0.023 ** (0.008)	0.011 (0.007)	0.015 (0.008)	0.032 ** (0.012)
Missing flag_ (nominated network members but  no information from them)	0.063 (0.102)	−0.028 (0.113)	0.040 (0.101)	0.058 (0.114)	0.033 (0.180)
Covariates
Out-degree	0.006 (0.015)	0.009 (0.015)	−0.008 (0.011)	−0.008 (0.013)	0.004 (0.022)
Professional development	−0.022 (0.018)	−0.032 (0.018)	0.003 (0.015)	0.003 (0.018)	−0.025 (0.028)
MKT	−0.063 (0.033)	−0.014 (0.030)	−0.006 (0.025)	−0.035 (0.032)	−0.050 (0.050)
Exposure to network members’ self-reported practices	−0.007 (0.012)	−0.008 (0.011)	−0.009 (0.009)	−0.010 (0.010)	−0.015 (0.017)
Prior (fall) of TRU Math	0.345 *** (0.072)	0.315 *** (0.074)	0.209 *** (0.075)	0.340 *** (0.089)	0.336 *** (0.072)
Constant	1.487 *** (0.281)	1.181 *** (0.349)	1.310 *** (0.289)	0.939 ** (0.297)	−0.155 (0.445)
Observations (N of episodes)	1,828	1,809	1,793	1,799	1,856

Note. Missing flags of all the variables above were included. Fixed effects for the 3 years and eight districts and a single fixed effect for Year 3 in a specific district that had a dramatic change in curriculum, and teacher fixed effects for the teachers whose estimates were statistically different from those for the group of teachers measured only once (N = 9) were included. The number of teachers is 158. ECT = early-career teacher; TRU Math = Teaching for Robust Understanding in Mathematics; MKT = mathematics knowledge for teaching.

*

p ≤ .05. **p ≤ .01. ***p ≤ .001.

Regarding Research Question 2, the coefficient for exposure to network members’ interpretations of accountability pressures and curricular standards is positive on each dimension of TRU Math, ranging from .011 on Dimension 4 (Agency, Authority, and Identity) to .023 on Dimension 2 (Cognitive Demand, p ≤ .01), with a coefficient of .032 (p ≤ .01) for the combined measure. Because the metric of the exposure term is difficult to interpret, we compare the standardized coefficients for the exposure term with the standardized coefficients for the corresponding prior TRU Math scores (Frank et al., 2004), as ECTs balance how they respond to others versus retaining their own tendencies (Frank et al., 2010). The coefficients for the exposure term range from 22% of the size of the estimated coefficient for prior behavior (fall TRU Math) for the mathematics dimension (coefficients of .08 for exposure and .37 for prior behavior) to 43% of the size of the estimated coefficient for prior behavior for the combined dimension (coefficients of .10 for exposure and .23 for prior behavior). These are consistent with other estimates of network effects, which are typically small to moderate for teachers but present across many domains (Frank, Xu, et al., 2018). We emphasize that a positive coefficient for exposure to others’ interpretations implies that those who are exposed to colleagues who report more positive interpretations may increase ambitious instructional practices while those who are exposed to colleagues who are at low levels of interpretation may fail to improve or may even decrease their levels of ambitious instructional practice.

Note that the estimated effect of exposure to network members’ interpretations is net of the relevant prior measure of TRU Math in the fall, the ECT’s out-degree, the ECT’s MKT, the ECT’s intensity of professional development, the ECT’s own interpretations, colleagues’ self-reported practices, as well as fixed effects for districts and year of study. ⁷ Not surprisingly, the ECTs’ prior level of TRU Math in the fall was a strong predictor of their TRU Math scores in spring across all dimensions. None of the substantive covariates were statistically significant (p ≤ .05), although we made the conservative choice to retain them in the models because they partly explain the effect of exposure to network members’ interpretations (when the covariates were removed, p ≤ .01 for the network exposure estimate on the cognitive demand dimension and p ≤ .015 for the combined dimension). All inferences were essentially sustained when we analyzed only those who did not have missing data on the exposure term (see the online Appendix D for details).

Causal Inference

We recognize that there could be omitted variables partly responsible for the estimated effect of exposure to network members’ interpretations of accountability pressures and curricular standards on ECTs’ instructional practices. We have attempted to account for some of these by controlling for an ECT’s prior levels of TRU Math, which might reflect prior levels of motivation, training, anxiety, and so on. Therefore, one way to interpret the estimated effect of the exposure term is to say that for two ECTs of comparable levels of ambitious instruction in the fall, the ECT who can draw on her colleagues as a source of support is more likely to increase her ambitious instruction in spring. Furthermore, we controlled for covariates (e.g., out-degree, MKT), some of which may be concurrent with exposure to colleagues (e.g., professional development), making our estimate of the network exposure effect conservative.

Nonetheless, there could be other explanations for the size of our estimated network effect that we have not considered. In response, we quantify what it would take to change our inference. Using Frank, Maroulis, et al. (2013), 28% of the estimated effect of network exposure on combined TRU Math would have to be due to bias to invalidate our inference of an effect of network exposure on TRU Math. This is already conditioned on TRU Math in the fall and our other covariates. The inference for an effect of network exposure on Cognitive Demand is slightly more robust (33% of the estimated effect would have to be due to bias to invalidate the inference). These values are approximately at the median of the observational studies reported by Frank, Maroulis, et al. Using Frank (2000), an omitted variable would have to be correlated at .28 with both exposure and combined TRU Math to invalidate our inference (for an impact on the network exposure term defined by the product .28 × .28 = .078). In contrast, our strongest covariate was professional development, which was correlated at −.1 with exposure to network members’ interpretations and at −.04 with combined TRU Math (for a product of .004), partialling for fall TRU Math; the impact of the omitted variable would have to be about 20 (.06/.004 is about 19.5) times larger than the impact of our strongest covariate to invalidate our inference of an effect of exposure to network members’ interpretations on combined TRU Math. While such an omitted variable may exist, we believe our inference is robust to most plausible omitted variables.

Specific Cases of Network Exposure and TRU Math

While our quantitative evidence shows a general relationship between exposure to network members’ interpretations and TRU Math scores, we contrast a kindergarten ECT whose TRU Math score increased with a second-grade ECT whose TRU Math score decreased to illustrate. The ECTs were chosen based on their specific values of combined spring TRU Math scores and network exposure term, conditional on their fall TRU Math scores. They are from the same district, ruling out differences in their changes in instruction that might be due to the district curriculum or personnel. The teachers were observed 1 year apart, but the district curriculum and personnel changed little over the 1 year. The professional development did change between the years of observation, but both teachers participated in only 1 to 2 hours of mathematics-based professional development during the academic year, making it unlikely that any differences in the content of the professional development were responsible for the dramatic differences in the changes in their teaching practices.

Increase in TRU Math, positive interpretations of network members: In the fall of 2015, the kindergarten ECT taught lessons focused on describing shapes. Her lessons were roughly on grade level (Mathematics mean = 1.86) and characterized by limited cognitive demand (mean = 1.36). The ECT asked students to select a shape, then describe the shape they chose to their classmates. While the students were able to express their ideas, their ideas were not built on by others (Agency, Authority, and Identity mean = 1.29), nor was student thinking solicited (Uses of Assessment mean = 1.29). For example, the ECT asked the students, “What shape is this?” And the students responded with short answers, identifying their chosen shape.

In the spring of 2016, this teacher indicated having interacted with an experienced teacher one to three times per month during the past academic year (coded “2”). In the winter of 2016, the experienced teacher reported that the expectations associated with state standards and tests both supported her instruction and that she always used curricula standards in planning. She did not respond to how frequently she used the performance criteria used in teacher evaluation or teacher evaluation results for planning. Her overall interpretation score based on the sum of observed standardized items was 0.68. The corresponding exposure term for this ECT (when the sum of the standardized responses was multiplied by the frequency of interaction) was 2 × 0.68 = 1.36. The ECT’s MKT measured in winter was −0.678.

Different from the fall, in spring, the kindergarten ECT introduced the students to subtraction problems, with physical models and writing of equations (especially focusing on the equals sign and what it means). Spring lessons were consistently on grade level and also supported meaningful connections for real-world meeting (Mathematics mean = 3). The students each had their own set of manipulations and acted out the subtraction, which supported their productive engagement (Cognitive Demand mean = 2.94). Generally, the students were able to share their answers in a chorus, but the ECT was the primary driver of the conversation, and the students were not supported to build on one another’s ideas (Agency, Authority, and Identity mean = 1.56). The ECT did not actively pursue student thinking consistently throughout the spring lessons; during small groups, the teacher was able to see the students thinking through manipulative representations, yet the discussion that ensued tended to be corrective in nature, leading the students to the correct answer (Uses of Assessment mean = 1.63).

Decrease in TRU Math, negative interpretations of network members: The average scores for the second-grade ECT’s instruction on each TRU Math dimension in the fall were relatively high, close to 2.3. The ECT taught lessons involving addition and subtraction word problems, on grade level. The students explained their ideas and responded to one another’s ideas. The ECT asked the students to explain how they had solved the problems, and clarified strategies for the class. The ECT was intentional about hearing from different students. During one moment, a student provided an incorrect answer. The ECT asked direct questions to help get the student on track, yet the ECT did not scaffold away challenge or give the student the answer.

The second-grade ECT interacted with two colleagues daily between the fall of 2016 and the spring of 2017, as reported in the spring of 2017. In the winter of 2017, the first colleague reported that the expectations associated with state standards and tests are inhibiting to some extent or had no effect (scoring a 0, lower than the average in our study), while the network member used evaluation criteria, results, and state standards for planning frequently or always (about average for our study). The interpretation score for this colleague was −0.111. The second colleague held more negative interpretations, with a score of −0.5. In addition, the ECT named two colleagues for whom we did not have data. Thus, the exposure term was (−0.111 × 5) + (−0.5 × 5) = −3.1 when frequency of interaction and number of colleagues were taken into account. The ECT’s MKT measured in winter was −0.557.

Different from the fall, in the spring of 2017, the students were learning to tell the time to the hour and half-hour. The ECT’s instruction was procedural, characterized by the students providing short answers to the ECT’s questions—for example, “What time is it?” and “Write 9:00 on the digital clock.” The ECT scaffolded away challenge for the students by telling them directly what the time was. The ECT did not ask the students how they got to the answer or solicit student thinking. Noticeably, the ECT’s scores for all areas of TRU Math declined (Mathematics = 1.75; Cognitive Demand = 1.38; Agency, Authority, and Identity = 1.29; Uses of Assessment = 1.33).

Focusing on changes in the cognitive demand dimension (which had the strongest results in our quantitative models), the first ECT’s score increased from 1.36 to 2.94, while the second teacher’s score decreased from 2.33 to 1.38. Furthermore, their MKT scores were almost identical (−0.678 for the first, −0.557 for the second, with the difference less than 0.14 standard deviation). Therefore, any underlying capacities and dispositions that might affect their ambitious instruction likely overlapped considerably. But critically, the first ECT increased her level of ambitious instruction in the presence of colleagues who had positively interpreted curricular standards, standardized tests, and evaluation criteria. The second reduced her ambitious instruction level—especially on Cognitive Demand; Agency, Authority, and Identity; and Uses of Assessment—in the presence of colleagues who had negative interpretations of accountability pressures and curricular standards. Most important, these ECTs demonstrate a specific connection between interpretation of colleagues and changes in practices. And because they taught in the same district, the differences were not due to the district’s choice of curriculum, provision of professional development, or central office policies. While these are just two examples, what we observe for these two teachers is consistent with the trends we observe across the data, which also includes controls for district contexts.

Correlates of Exposure to Network Members’ Interpretations

Our previous results illustrate how exposure to others’ interpretations of accountability pressures and curricular standards predicts an ECT’s classroom instruction. Therefore, here we explore the correlates of exposure to others’ interpretations to gain an initial understanding of how ECTs might cultivate resources and supports in their networks. In Table 4, we report the results for two predictors of interest separately as a basis for future exploration (the two are correlated at −.1). Interestingly, the ECTs’ interpretations of evaluation pressure were positively related to the interpretations of their network members. This could be because those who perceive evaluation pressure sought colleagues with positive interpretations they could draw on (although it is also possible that those with colleagues who had positive interpretations of standards and tests came to perceive more evaluation pressure). Second, the ECTs who reported enjoying solving mathematics problems were less likely to identify network members who positively interpreted curricular standards and standardized tests. It may be that the ECTs who enjoyed solving mathematics problems on their own were less likely to seek help in interpreting curricular standards and standardized tests (although it could be that teachers whose network members are less supportive come to enjoy solving problems on their own). Again, we emphasize that these analyses are exploratory and should only be interpreted as indicators of foci for future study.

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Table 4

Exploratory Factors Associated With Exposure to Network Members’ Interpretations

	Model (1)	Model (2)
ECTs’ own interpretations	−0.193 (0.454)	0.277 (0.452)
Mean TRU Math in the fall	−0.055 (0.957)	0.251 (0.960)
Evaluation pressure	0.884 * (0.362)
Enjoy solving mathematics problems		−0.966 * (0.419)
Constant	−1.436 (1.751)	3.227 (2.037)
Observations (N of teachers)	95	96

Note. Models include fixed effects for year and for districts as well as indicators for three teachers who had multiple years of data and differed significantly from those who had only 1 year of data. Only cases with no missing data were used. ECT = early-career teacher; TRU Math = Teaching for Robust Understanding in Mathematics.

*

p ≤ .05. **p ≤ .01. ***p ≤ .001.

Implications

Our results have important implications for the distribution of support for ECTs. If critical support comes from immediate networks, then an ECT with a more supportive network, in terms of positive interpretations of accountability pressures and curricular standards, should have greater potential for enacting ambitious mathematics instruction. The success of ECTs depends not merely in applying their preparation to their classroom but also in cultivating a network that can provide insights and support based on experience that they do not yet have.

But much of social capital is formed as a by-product (Coleman, 1988) of other behaviors and actions chosen for their immediate contribution to productivity. Therefore, administrators should consider the implications of other decisions such as room assignments (Spillane et al., 2017) and implementation of innovations (Frank, Xu, et al., 2018) for their unintended effects on the formation of teachers’ networks. Of course, many schools face immediate demands for specific actions. Therefore, we call on other stakeholders to give administrators the discretion to balance immediate demands with investment in social capital for future needs (Frank, 2014).

Administrators can directly mitigate potential deficiencies in ECTs’ networks by helping ECTs cultivate supportive networks. This goes beyond assigning a formal mentor or formal induction program (Glazerman et al., 2010). Instead, administrators may provide the conditions for ECTs to identify the supports they need. This may come in the form of provision of instructional support staff (e.g., instructional coaches), who are ideally suited to play the translational role between pressures external to the school and practices within the school (Galey-Horn, in press). The school could gain extra leverage from instructional support personnel if they are specifically trained to work with ECTs. The school might also develop high-quality professional learning communities, from which ECTs might identify supportive colleagues (Horn et al., 2020) who can help improve teacher retention (Gu, 2014; Ingersoll & Smith, 2004; Le Cornu, 2013). Or the school can arrange for release time or monetary incentives for teachers identified by the ECT to provide support. Thus, our study helps identify critical new forms of support that schools might offer ECTs (Smith et al., 2018). Furthermore, we encourage teacher-training programs to consider helping ECTs learn to navigate and cultivate networks in their schools that will support high-level practice (Bausell & Glazier, 2018; Fox & Wilson, 2015; Mansfield et al., 2016), just as training programs for other young professionals do (Uzzi & Dunlap, 2005).

The provision of support is not isolated from other aspects of an ECT’s professional life. As colleagues provide professional support, they undoubtedly shape the identity of an ECT (Rodgers & Scott, 2008). Also, given the professional challenges ECTs face, professional support may also help sustain them emotionally (e.g., Lasky, 2005) and help ECTs maintain their commitment to the profession (Allensworth et al., 2009). Finally, those providing professional support may also convey other forms of support an ECT may need (Glazerman et al., 2010).

Even with these supports, ECTs may find it challenging to seek and access help within their schools. Frank et al. (2004) describe a social capital exchange in which novices exchange their conformity for access to expertise. Since ECTs have little local knowledge or relative expertise, they may feel compelled to adopt the norms and practices of others in their school in order to access the local knowledge critical for their success. Not surprisingly, many ECTs seek resources on social media outside their school (Opfer et al., 2018; Risser, 2013; Torphy & Drake, in press), in part because it is an arena in which they do not have to trade their conformity for access to expertise. Administrators must be thoughtful in guiding how ECTs use these interorganizational networks.

Limitations

We find that ECTs’ networks are related to their own disposition toward mathematics and their perceptions of evaluation pressures. There may be a causal link: Those who do not enjoy solving mathematics problems or who perceive external evaluation pressures may be more likely to seek helpful colleagues. But unlike our primary analysis, which is based on longitudinal data, this exploratory analysis is based on only cross-sectional data. Therefore, we are very cautious and call for further study of the factors affecting who teachers seek in their networks (e.g., Wilhelm et al., 2016), but with specific emphasis on ECTs.

Because our study is focused around ECTs, we have only a small number of focal teachers per school in our sample. As a result, we have limited capacity to examine the effects of collective sensemaking, or more broadly of school culture. This would likely include contributions from administrators and instructional coaches (Coburn, 2001; Domina et al., 2015; Galey-Horn, in press). Future studies might consider saturated samples of educators (including administrators, coaches, and teachers) in schools to fully explore the school-level social dynamics in which sensemaking occurs. We also focused on the sensemaking process that occurs from fall to spring within a single school year. Future studies could involve sustained data collection over multiple years to study ongoing sensemaking, although it is not clear what form of data collection would be optimal (e.g., repeated teacher interviews or surveys, teacher journals). Such studies would allow one to better track the diffusion of professional development experienced by school colleagues and then spilling over to ECTs (Sun et al., 2013). Such studies might also attend more carefully to the content of professional development (e.g., Desimone, 2009) and how professional development interacts with a teacher’s networks (Frank et al., 2011).

Our analyses are based on a sample of elementary teachers in the upper Midwest. We believe the sample is adequate to represent the intraschool processes we studied, but it may not represent broader populations, including middle or high school teachers, teachers in urban districts, or those in other parts of the country. Our sample is also more likely to have a general certification and to have majored in education than nationally representative teachers. It is possible that this makes our results conservative, as teachers with less training than those in our sample or with training in specific areas may well have greater need to rely on their colleagues to make sense of institutional pressures in unfamiliar contexts. But this should be studied further.

Our sample included mostly White teachers (90%), which is similar to the national average for elementary schools (86% White). But further studies should focus carefully on teachers from underrepresented populations and how they form and respond to their networks, affecting interactions with students (Skiba et al., 2014). In a theory of critical sensemaking, Helms-Mills et al. (2010) argue that there may be power differentials within an organization that affect whose sensemaking dominates a narrative. This may be especially profound when a power differential between an ECT and a veteran teacher intersects with race. Helms-Mills et al. further point out that organizations can accentuate or mitigate existing power differences by creating opportunities for interaction or influencing what is valued in the organization. Further study also is needed to generalize to urban contexts that may perceive stronger pressures on test scores and evaluation that might affect instruction (Crocco & Costigan, 2007; Diamond & Spillane, 2004).