Heterogeneity in Reading Achievement and Mindset of Readers with Reading Difficulties

Abstract

Recent research has focused on evaluating the relation between mindset and reading achievement. We used exploratory factor mixture models (E-FMMs) to examine the heterogeneity in reading achievement and mindset of 650 fourth graders with reading difficulties. To build E-FMMs, we conducted confirmatory factor analyses to examine the factor structure of scores of (a) mindset, (b) reading, and (c) mindset/reading combined. Our results indicated (a) a 2-factor model for mindset (General Mindset vs. Reading Mindset), (b) a 2-factor model for reading (Word Reading vs. Comprehension; four covariances), and (c) a combined model with significant correlations across mindset and reading factors. We ran E-FMMs on the combined model. Overall, we found three classes of students. We situate these results within the existing literature and discuss implications for practice and research.

Heterogeneity in Reading Achievement and Mindset of Readers with Reading Difficulties

The Simple View of Reading (SVR; Gough & Tunmer, 1986; Hoover & Gough, 1990) provides a theoretical model of the relation between critical components of reading. According to this model, reading comprehension is the product of decoding and linguistic comprehension (i.e., Decoding x Linguistic Comprehension = Reading Comprehension), which relate to print-focused and language-based skills. Studies conducted as part of the Reading for Understanding initiative (Institute of Education Sciences, 2009) validated and proposed extensions to the SVR model by identifying additional subcomponents of listening comprehension and word recognition, and by providing evidence of the contributions of oral language skills to reading comprehension (Cervetti et al., 2020). Although recent research has brought questions about the dynamic and complex relations among subskills that contribute to successful reading comprehension to the fore and researchers have conceptualized new models that attempt to capture that complexity (e.g., Active View of Reading; Duke & Cartwright, 2021), studies examining the validity of the SVR model provide evidence that decoding and linguistic comprehension do significantly contribute to the variance in reading comprehension scores in elementary grades (e.g., Cutting & Scarborough, 2006; Language and Reading Consortium [LARRC], 2015a; LAARC & Chiu, 2018; Lonigan et al., 2018).

Individual Differences in Reading Achievement

Students demonstrate reading profiles based on individual differences in these reading components (Aaron et al., 2008; Catts et. al, 2003; Hoover & Gough, 1990). SVR research suggests readers can be classified into four groups related to the strength (i.e., poor vs. good) of their linguistic comprehension and decoding abilities (Spencer et al., 2019). Some researchers have found that the same subgroups exist for readers with reading difficulties (RD), and that readers with RD tend to remain in the same subgroup across time (Catts et al., 2003; Leach et al., 2003). Similarly, Catts et al. (2012) examined the nature of late-emerging poor readers and identified subgroups of students with deficits in word reading, reading comprehension, or both.

However, other researchers have found that skill profiles of readers with RD may be different from typical readers, particularly for students in upper elementary and beyond. For older readers, there is a high prevalence rate of students struggling with reading comprehension who demonstrate weaknesses in other areas of reading as well (Brasseur-Hock et al., 2011; Capin et al., 2021; Clemens et al., 2017). For example, Brasseur-Hock et al. (2011) examined reading skill profiles for adolescent readers through a series of Latent Class Analyses. The authors found five subgroups within their students with below-average comprehension, defined by area and severity of reading difficulty (i.e., Readers with Severe Global Weaknesses, Moderate Global Weaknesses, Dysfluent Readers, Weak Language Comprehenders, and Weak Reading Comprehenders). In another Latent Profile Analysis, Capin et al. (2021) examined reading profiles of fourth graders scoring below the 16th percentile in reading comprehension, the majority (90%) of whom demonstrated concurrent, moderate difficulties in word reading (decoding) and listening (linguistic) comprehension. Only 10% of their sample fit into subgroups that reflected more severe deficits in one component of the SVR and moderate deficits in the other, indicating a pattern of relative strength within the below average performance across measures.

These results are in line with evidence indicating high levels of shared predictive variance (41–69%) of reading comprehension accounted for by decoding and linguistic comprehension for upper elementary readers (Foorman et al., 2018; Lonigan et al., 2018). Collectively, these studies indicate that there is variation in the reading achievement of students with RD, but that this variation is different than the four subgroups early literature indicated (i.e., Catts et. al, 2003) and also may be unique from the reading profiles of typical readers.

The Relation between Mindset and Achievement

Petscher et al. (2017) reported that variability in the extent to which reading comprehension can be explained in the SVR (e.g., linguistic comprehension and decoding) may be related to other factors outside of reading and language. These factors may be important to consider when constructing student profiles if reading difficulties in each subgroup relate to different underlying mechanisms. The Component Model of Reading (Aaron et al., 2008) and the Direct and Indirect model of reading (DIER; Kim, 2020) contextualize the SVR within a framework that considers additional components (e.g., cognitive, psychological, and ecological) that influence heterogeneity in reading achievement and the underlying mechanisms of RD. Mindset is one factor related to these additional components that may influence the variation in students’ reading profiles.

Mindset theory relates to an individual’s belief in or understanding about intelligence, learning, and skills (Dweck, 2006; Sisk et al., 2018). Individuals with a growth mindset believe that intelligence and skills can be developed across time through effort and practice; individuals with a fixed mindset believe that intelligence and skills are static. There is an increasing trend in schools related to understanding and addressing students’ social-emotional learning (SEL), which encompasses many factors including mindset (West et al., 2020). Additionally, there has been an increase in school-based use of mindset-related interventions (Farrington et al., 2012). Although mindset is not the only non-cognitive SEL-related construct, it may be uniquely different from similar constructs. For example, West et al. (2016) examined four non-cognitive constructs (i.e., grit, growth mindset, conscientiousness, self-control) and found that growth mindset was most strongly related to eighth grade test scores and uniquely different from the other measures. West et al. (2020) also found that growth mindset tends to increase with age, unlike other SEL-related measures (i.e., self-efficacy, self-management, social awareness). Given the unique nature of mindset and the relevance to current school context, researchers have continued to investigate its relevance to student achievement, particularly in specific academic areas.

Some evidence suggests students’ mindset may relate to academic outcomes. Students with a growth mindset tend to demonstrate higher academic achievement than students with a fixed mindset (Blackwell et al., 2007; McCutchen et al., 2016; Yeager & Dweck, 2012). Additionally, academic achievement scores of students with a growth mindset have shown a slower decline across time than scores of students with a fixed mindset (McCutchen et al., 2016). Sisk et al. (2018) meta-analyzed the relation between mindset and academic achievement and found weak positive relations between mindset and academic achievement across the grades (elementary: r = .15; adolescent: r =.19) and a small, but significant effect of growth mindset interventions on academic outcomes (d = 0.08, p = .01). These results suggest that mindset interventions may improve outcomes for students who are academically at-risk and students from lower SES backgrounds (e.g., Claro et al., 2016). The results also suggest that even a weak relation between mindset and academic achievement may be important to consider, particularly for students with RD.

Mindset and Reading

Petscher et al. (2017) examined the relation between mindset and reading with fourth graders. First, the authors examined the factor structure of a survey (Mindset Assessment Profile; MAP) used with Brainology, a mindset training program (Blackwell et al., 2007), supplemented with additional survey items specific to reading (i.e., Reading Mindset as the belief in intelligence, learning and skills related to reading). Petscher et al. (2017) found that the mindset items had a complex structure, with a Global Growth Mindset (GGM) factor that consisted of more specific mindset factors for items about mindset generally or related to reading tasks (General Mindset and Reading Mindset, respectively). Additional analyses indicated the specific factors positively and significantly related to word reading and reading comprehension, even after controlling for word reading. Petscher et al. (2017) found that students with lower reading comprehension tended to have a fixed mindset. However, there was a stronger relation between GGM and reading comprehension for students with lower reading comprehension. In contrast, there was a stronger relation between Reading Mindset and reading achievement for students with higher reading comprehension. Other researchers have found similar associations between achievement and mindset other to academic areas (Costa & Faria, 2018; Gunderson et al., 2017)

These results suggest that mindset may be multi-dimensional and specific factors may be more predictive of achievement than global mindset; however, there may also be other explanations for the relation between mindset and achievement. For example, Cho et al. (2019) extended the work of Petscher et al. (2017) by considering indirect pathways from mindset to reading comprehension. The authors found that the pathway was mediated by student’s goals related to achievement (mastery and performance-avoidance goals) and emotional engagement; however, the authors only used three fixed mindset items from the MAP in their analyses, and did not consider reading-specific mindset as a distinct construct. Later, Cho et al. (2021) found that reading-specific mindset was not predictive of sixth grade students’ initial reading comprehension scores or growth in those scores across time, but based reading-specific mindset scores on only three general mindset questions and three reading-specific mindset questions, fewer than the eight general and seven reading-specific mindset items Petscher et al. (2017) developed.

Given the mixed results from the literature, researchers have continued exploring mindset and the role it may play in understanding profiles of readers at-risk for RD. Of course, understanding reader profiles is only as strong as the tools used to measure reader characteristics. Therefore, Tock et al. (2021) sought to validate a Reading Mindset measure, which included items such as “If I make a lot of mistakes while reading, I quit trying.”. The authors refined the measure and tested whether the scores significantly and uniquely predicted variance in standardized measures of reading for a sample of fourth graders. Overall, the authors found that the Reading Mindset measure significantly and positively predicted word reading and reading comprehension. The measure continued to uniquely and significantly predict the variance in reading comprehension after controlling for word reading, suggesting reading-specific mindset may be one component relevant to reader profiles.

Other researchers have investigated mindset profiles in ways that complement reader profile literature. For example, Petscher et al. (2021) analyzed the MAP (Blackwell et al., 2007) scores of 431 fourth graders. They found that MAP scores weakly correlated with standardized measures of word reading, vocabulary, and reading comprehension. However, the correlation between reading scores and lower MAP total scores (i.e., fixed mindset) was stronger than that of reading scores and higher MAP total scores (i.e., growth mindset). The authors also found five mindset profiles, which differed by reading scores. Students with a growth mindset and above average effort tended to have higher scores on all reading outcomes than students with a fixed mindset. This work began to explore the integration of mindset profiles with reading outcomes for elementary-aged students; future work that integrates the understanding of the variation in mindset and reading for students with RD may further elucidate the relation between profiles to inform intervention development and implementation.

The Current Study

The purpose of this current study was to extend the work of those doing profile analyses of reading (e.g., Capin et al., 2021) and mindset (e.g., Petscher et al., 2021). Specifically, we examined the factor structure of mindset survey items, and the relation between these factors and students’ reading achievement scores for fourth graders with RD (below the 30th percentile in reading comprehension). To create our sample, we drew upon pretest data from previously published work (Wanzek et al., 2021; Wanzek et al., 2020). We extend the work in both publications by considering the heterogeneity in pretest reading achievement and mindset for the students across both samples. Our research questions (RQs) include: (1) What factor structures of (a) mindset, (b) reading, and (c) mindset/reading combined exist for readers with RD when they begin fourth grade?; and (2) Using the combined mindset/reading factor models, what profiles exist for these readers?

Method

Participants

We created our sample based on pretest data collected from two federally-funded research projects (Wanzek et al., 2021; Wanzek et al., 2020), both of which adhered to human subjects principles and received human subjects approval from the institutional review board. Both projects examined the efficacy of multicomponent reading interventions for fourth graders with RD. Students in both projects attended public elementary schools situated in urban and suburban settings in the south-central and south-east regions of the United States. Our sample included students who were pretested in September and early October of each year and were later assigned to treatment or control conditions in the respective projects. Wanzek et al. (2021) included readers with severe difficulties in reading comprehension who scored below the 15th percentile on a standardized measure of reading comprehension. Wanzek et al. (2020) included readers with moderate to severe difficulties in word reading and word reading fluency who scored below the 30th percentile on a standardized measure of word reading and decoding fluency. Out of this larger sample, we selected students with reading comprehension difficulties who scored below the 30th percentile on the Reading Comprehension subtest of the Gates-MacGinitie Reading Tests (GMRT; MacGinitie et al., 2006). We removed three students who did not take that subtest. Our final sample included 650 fourth graders (M age = 9.76 years [SD = 0.46]). Table 1 summarizes demographic information.

Table 1.

Student Demographics

Demographic Variable	Number of Participants (%)
Gender
Female	304 (46.77%)
Male	308 (47.38%)
Missing	38 (5.85%)
Race/Ethnicity
Hispanic	251 (38.62%)
Non-Hispanic White	50 (7.69%)
Non-Hispanic Black	268 (41.23%)
Other	11 (1.69%)
Missing	70 (10.77%)
Free/Reduced Lunch
Yes	471 (72.46%)
No	106 (16.31%)
Missing	73 (11.23%)
English Learner
Yes	105 (16.15%)
No	423 (65.08%)
Missing	122 (18.77%)
Special Education
Yes	86 (13.23%)
No	465 (71.54%)
Missing	99 (15.23%)

Note. All students were in the fourth grade and had scored at or below the 30th percentile on the Gates-MacGinitie Reading Tests Comprehension subtest. All data were collected in the fall.

Measures

Research assistants (RAs), trained to 100% reliability in administration and scoring, administered reading and mindset measures to students within a 3-week window in September/October of each year prior to the start of interventions. Testing sessions ranged from 45 to 90 min, with counterbalanced assessment order in the testing battery across participants. RAs read mindset measures aloud to students as they completed it.

Mindset Measures

To measure students’ general mindset, we used the modified version of the MAP of the Brainology® intervention (Blackwell et al., 2007) from Petscher et al. (2017). Petscher et al. had revised the original survey to align with the needs of fourth graders, who are younger than students for whom the original survey was developed. Revisions included modifications such as substituting words (e.g., “smart” vs. “intelligent”) to increase readability (e.g., “No matter who you are, you can always change how smart you are”) and reducing the number of items by removing items with redundant wording. We also used items from the Reading Mindset measure (Tock et al., 2021), which Petscher et al. (2017) had used to assess reading mindset (e.g., “Even if you’re not a good reader, you can always get better if you work hard”). For each item, students responded on a Likert scale (6 = Agree a lot, 5 = Agree, 4 = Agree a Little, 3 = Disagree a Little, 2 = Disagree, 1 = Disagree a lot). For analyses, we reverse-coded applicable items so that lower scores represented fixed mindsets and higher scores represented growth mindset. Tock et al. (2021; p. 285) categorized scores of 5 or 6 as being more “positive mindset-oriented” (i.e., growth) and scores of 1 or 2 being more “negative mindset” (i.e., fixed). By extension, scores between 3 and 4 may indicate a more mixed mindset.

Petscher et al. (2017) reported a final measure that included eight General Mindset items and seven Reading Mindset items (α = .76 and .74, respectively). In the current study, General Mindset had poorer reliability (α = .47) with the eight items. We excluded two items (item 2 and 8; see Table 2) based on item correlations. After that, General (6 items) and Reading Mindset (7 items) measures had acceptable internal reliability (α = .72 and .77, respectively). See Table 2 for the modified MAP items.

Table 2.

Modified Mindset Assessment Profile (MAP) Survey

Survey Item
General Mindset Items
Your intelligence is something you can’t change very much. O, R1
I like school work that I’ll learn from even if I make a lot of mistakes. O
You can learn new things, but you can’t really change how smart you are. E, R2
An important reason why I do my school work is because I like to learn new things. O
No matter who you are, you can change how smart you are a lot. E, R1
I like school work best when it makes me think hard. O
The harder you work at something, the better you will be at it. O
If an assignment is hard, it means I’ll probably learn a lot doing it. O
When something is hard, it just makes me want to work more on it, not less. O
When I have to work hard at my schoolwork, it makes me feel like I’m not very smart. E, R1
You know you’re good at something when it comes easily to you. E, R2
If you’re not good at a subject, working hard won’t make you good at it. O, R1
It doesn’t matter how hard you work- if you’re not smart, you won’t do well. O, R1
Reading Mindset Items D
Even if you’re not a good reader, you can always get better if you work hard.R1
If a book is hard to read, I stop reading it.
I like school work best when I can do it perfectly without any mistakes.R1
I like reading even if I make a lot of mistakes.R1
I feel like I am one of the worst readers in my class.
I like reading.R1
If I have to read out loud in class, I feel scared.
If I make a lot of mistakes while reading, I quit trying.
I feel like I am one of the best readers in my class.R1
When I have to work hard at reading, it makes me feel like I am not very smart.
When someone reads better than me, I’m jealous.
don’t like when my teacher corrects me when I’m reading.
I can always get better at reading.R1

Note.

^O=Part of original Mindset Survey (Blackwell et al., 2007).

^E=Edited from original by Petscher et al. (2017) for younger students.

^D=Developed by Petscher et al. (2017) to capture Reading-Specific Mindset.

^R1=Removed from Petscher et al. (2017) Modified MAP based on reliability metrics.

^R2=Removed from our analyses to support adequate reliability.

Test of Word Reading Efficiency

We used the Sight Word Efficiency (SWE) and Phonemic Decoding Efficiency (PDE) subtests of the Test of Word Reading Efficiency (TOWRE; Torgesen et al., 2012) to assess students’ word reading. Test-retest reliabilities for the TOWRE range from .83–.96. In both subtests, students have 45 seconds to read a list of words (Real words in SWE; Pseudowords in PDE). Student scores reflect the number of words read correctly within the time limit. The PDE subtest has concurrent validity estimates of .86 with the Word Attack subtest of the Woodcock Reading Mastery Test-Revised (WRMT-R; Woodcock, 1987) for fourth graders. The SWE subtest has concurrent validity estimates of .89 with the Word Identification subtest of the WRMT-R for fourth graders. We categorized these subtests as Word Reading.

Gates-MacGinitie Reading Tests - 4th Edition

We used the Reading Comprehension and Vocabulary subtests of the GMRT (MacGinitie et al., 2006) to assess reading comprehension and vocabulary. On the Comprehension subtest (GMRTC), students answer multiple choice questions about expository and narrative passages of increasing length. On the Vocabulary subtest (GMRTV), students select the meaning of words they read in context. For fourth graders, the internal consistency of the GMRT ranges from .91–.96. We categorized these subtests as Comprehension.

Woodcock Johnson Test of Achievement

We used the Letter Word Identification (LWID), Word Attack (WA), and Passage Comprehension (PC) subtests from the third (Wanzek et al., 2020) and fourth (Wanzek et al., 2021) editions of the Woodcock Johnson Test of Achievement (WJ; Schrank et al., 2013; Woodcock et al., 2001). The WJ is an individually administered, untimed, norm-referenced test. The LWID subtest measures real word reading. The WA subtest measures decoding skills, beginning with single letter sounds and increasing to complex pseudowords. On the PC subtest, students read a passage and select missing key words that would make sense (i.e., a cloze measure). The split-half reliability of the WJ-IV for five to 11 year olds is .83–.96. The test-retest reliability of the WJ-III for fourth grade is .86. We categorized LWID and WA as Word Reading and PC scores as Comprehension.

Data Analyses

We conducted a series of analyses in SPSS 21.0 (IBM Corp, 2012) and Mplus 8 (Muthén, & Muthén, 1998–2017). We ran descriptive statistics to capture the demographic characteristics (Table 1). To build a foundation of testing exploratory factor mixture models (E-FMMs; Muthén, 2008), we ran a series of confirmatory factor analysis (CFA) for the mindset variables, reading variables, and combined mindset/reading variables. We conducted a CFA for mindset variables and reading variables to test the factor structure of the items from the modified MAP and the factor structure of standardized raw reading scores across measures, respectively. Based on the selected CFA models of mindset and reading in isolation, we ran a CFA for the combined mindset/reading variables to test the factor structure of a combined mindset/reading model and establish the final CFA model for E-FMMs. We considered the previous literature on the relations between mindset and reading (e.g., Petscher et al., 2017) to build the combined mindset/reading models.

We revised and improved the CFA models with appropriate item and factor covariances by considering the modification indices and the significance of parameters. We compared the model fits of Mindset CFA models (i.e. 1-factor, 2-factor, and bi-factor), Reading CFA models (i.e. 1-factor, 2-factor, and bi-factor), and Combined Mindset/Reading CFA models for each step across model fit indices: Akaike Information Criterion (AIC; Akaike, 1987), Bayesian Information Criterion (BIC; Schwarz, 1978), Sample Size Adjusted Bayesian Information Criterion (aBIC; Sclove, 1987), χ², the root mean square error of approximation (RMSE; Steiger, 1990; Steiger & Lind, 1980), Comparative Fit Index (CFI; Bentler, 1990), and Tucker-Lewis Index (TLI; Bentler & Bonett, 1980; Tucker & Lewis, 1973). We used the information criterion (AIC, BIC, aBIC) to compare non-nested models, but applied χ²-based model fit indices when comparing nested models and evaluating model fits of individual models. We did not compute AIC, BIC, and aBIC for Combined Mindset/Reading CFA models given that a model was nested within another. We selected the most appropriate CFA model for each analysis by considering model fit indices, previous literature, model appropriateness, parsimony principle of a model, and further statistical analyses (i.e. model complexity of E-FMMs).

Next, we used E-FMM (Muthén, 2008) to investigate the number of categorized groups that, based on measurement invariance, best represented group-based individual differences in mindset and reading latent variables among our sample. The E-FMM is a method to estimate latent classes based on a factor structure model. This hybrid model of latent class analysis (LCA) and factor analysis (FA) has advantages over LCA and FA because it has fewer required assumptions (e.g., conditional independence assumption) and considers heterogeneity within a class (Clark et al., 2013). Based on the Combined Mindset/Reading factor model we identified in the prior analyses, we estimated two to four classes. We assumed measurement invariance across potential classes to investigate factors across classes in a consistent and comparable manner. We selected a final model based on model fit indices: AIC, BIC, aBIC, Entropy (Celeux & Soromenho, 1996), (Vuong)-Lo-Mendell Rubin likelihood ratio test (VLMR), Lo-Mendell-Rubin Adjusted test (aLMR) (Lo et al., 2001), and Parametric Bootstrapped likelihood ratio test (BLRT; McLachlan & Peel, 2000).

In the E-FMM, factor mean scores of each class are relative to those of a referent group. The referent group represents the last class of the sample, which often has the largest or smallest threshold (Muthén, 2008). For our analyses, the referent group was the class representing the largest proportion. The referent group latent means are fixed at 0 and factor mean scores are centered at the referent group mean, which makes interpretation challenging. To descriptively capture the meaning of each profile’s mindset and reading scores compared to normative samples, we also reported observed sample mean scores across variables for each group.

We used the Mplus default estimators for conducting each analysis: weighted least squares means and variance adjusted (WLSMV) for mindset CFA models and combined Mindset/Reading CFA models, Maximum Likelihood (ML) for reading CFA models, ML estimation with robust standard error (MLR) for the LPA.. The Mplus default estimators were determined based on types of items (i.e. categorical, continuous, or mixed) in a model and the analysis efficiency (i.e., time). We added additional analyses for mindset CFA models using Maximum Likelihood (ML) to calculate AIC, BIC, and aBIC due to the limitation of calculating model fit indices in a model with ordinal variables using WLSMV.

Models with lower AIC, BIC, and aBIC values indicate better model fits (Akaike, 1987; Schwarz, 1978; Sclove, 1987). A CFI and TLI greater than or equal to .95 and RMSEA less than .08 indicates reasonable model fit (Hu & Bentler, 1999). Entropy above .8 indicates that each profile was distinguishable in the model. The VLMR, aLMR, and Parametric Bootstrap indices assess difference between k model and k-1 model, where a significant p value (p < .05) indicates the k model is significantly better than the k-1 model (Samuelsen & Saczynski, 2013). We used full information maximum likelihood (FIML) to handle a small percentage of missing data (i.e., within 2.5%) in the mindset items for the CFAs and E-FMMs.

Results

Descriptive Statistics

Table 3 summarizes descriptive statistics and correlations between variables. The correlation between mindset measures was small but significant (r = .14, p <.01). General Mindset scores had small and significant correlations with all Word Reading measures (SWE, PDE: r = .17 ~ .21, p <.01; LW, WA: r = .08 ~ .09, p <.05) and with GRMTV (r = .14, p <.01). Reading Mindset scores were small but significantly correlated with SWE (r = .15, p <.01) and PDE (r = .20, p <.01) in Word Reading and GMRTV (r = .10, p <.05) in Comprehension. The reading measures were significantly correlated, but the correlation coefficients varied from small to large (r = .15 ~ .73, p <.01). There were large correlations between reading measures within Word Reading (r = .57 ~ .73, p <.01); the correlations between the reading measures in Comprehension were moderate (r = .34 ~ .48, p <.01).

Table 3.

Correlations between Mindset and Reading Variables

	Mindset		Word Reading				Comprehension
	1 General Mindset	2 Reading Mindset	3 SWE	4 PDE	5 LW	6 WA	7 PC	8 GMRTc	9 GMRTv
1
2	.14**
3	.21**	.15**
4	.17**	.20**	.67**
5	.09*	−.01	.71**	.62**
6	.08*	.05	.57**	.72**	.73**
7	.03	−.05	.57**	.35**	.72**	.52**
8	.04	−.05	.31**	.15**	.32**	.20**	.35**
9	.14**	.10*	.46**	.36**	.51**	.41**	.48**	.34**
M	4.71	3.85	50.21	18.11	43.96	15.12	22.71	12.03	13.31
SD	.97	1.27	12.89	9.70	7.43	5.51	4.75	3.93	5.50

Note.

^**p < .01

^*p < .05

Confirmatory Factor Analysis

Table 4 provides the model fit indices of all CFA models. We used robust weighted least squares (WLSMV) or maximum likelihood (ML) for each. Figures 1–3 illustrate the CFA models explored for mindset, reading, and combined mindset/reading, respectively. Figure 4 provides the final CFA models selected.

Table 4.

CFA Models

	AIC	BIC	aBIC	χ 2	df	RMSEA 90% CI	CFI	TLI
Mindset CFA
1-factor	25280.56	25629.77	25382.12	1121.88**	65	.158 [.150, .166]	.72	.67
2-factor	24742.82	25096.50	24845.67	121.60**	64	.037 [.027, .047]	.99	.98
Bi-factor	24729.87	25137.27	24848.35	91.56 **	52	.034 [.022, .046]	.99	.99
Reading CFA
1-factor	10835.07	10929.09	10862.41	361.88**	14	.196 [.178, .213]	.86	.79
2-factor	10800.11	10898.61	10828.76	324.92**	13	.192 [.174, .210]	.87	.80
Bi-factor	10548.91	10669.79	10584.07	63.72**	8	.104 [.081, .128]	.98	.94
Rev. 1-factor	10524.60	10641.00	10558.45	41.41**	9	.074 [.052, .098]	.99	.97
Rev. 2-factor	10517.10	10633.50	10550.95	33.90**	9	.065 [.043, .089]	.99	.98
Rev. Bi-factor	10513.21	10643.04	10550.96	24.01**	6	.068 [.041, .097]	.99	.97
Combined Mindset/Reading CFA
Correlation Model 1	-	-	-	376.07**	160	.046 [.040, .052]	.95	.94
Correlation Model 2	-	-	-	362.12**	162	.044 [.038, .05]	.96	.95

Note.

^**p <.001

Figure 1. Confirmatory Factor Analysis Models for Mindset.

Note. I: Unidimensional Model, II: 2-factor Model, III: Bi-Factor Model

Figure 3. The Combined Mindset/Reading Confirmatory Factor Analysis Models.

Note. I: Correlation Model of Mindset and Reading Skill, II: Revised Correlation Model, FR: Foundational Reading Skills. GR: General Reading Skills

Figure 4. Final Confirmatory Factor Analysis Models.

Note. I = CFA for Mindset; II = CFA for Reading; III=CFA for Combined Mindset/Reading

Comp = Comprehension

Mindset

The one-factor mindset CFA model did not have good model fit χ² (65) = 1121.88, RMSEA = .158, CFI = .72, TLI = .67). Both 2-factor model and bi-factor model had appropriate model fits across different model fit indices (the 2-factor model: χ² (64) = 121.60, RMSEA = .037, CFI = .99, TLI = .98; the bi-factor model: χ² (52) = 91.56, RMSEA = .034, CFI = .99, TLI = .99). However, there was not a clear difference between the two models in this sample of readers with RD and each model had different benefits related to explaining the structure of the two mindsets. The bi-factor model had advantages over the 2-factor model in terms of χ²- based model fit. On the other hand, the 2-factor model had advantages over bi-factor model based on information criteria (BIC, aBIC) and the parsimony principle (i.e., larger degree of freedom). Considering that model fits of bi-factor models can be overestimated (Decker, 2021; Reise et al., 2016) and the advantages of the 2-factor model for further analyses, we chose the 2-factor model for analysis in our mixture models.

Reading

We estimated three reading CFA models (1-factor, 2-factor, and bi-factor model) and revised these models with appropriate item covariance by considering modification indices in each model. The revised 1-factor model included five relevant residual covariances: WA & PDE, PDE & SWE, LW & PDE, WA & LW, GMRTV & GMRTC. We added four item covariances to the 2-factor model (SWE & PDE, PDE & WA, PDE & LWID, GMRTV & GMRTC). We included one item covariance in the bi-factor model (SWE & PDE). All the item covariances were theoretically appropriate, given that some reading measures shared more similarities with others because they were from the same assessments (GMRTV & GMRTC, SWE & PDE), or they shared similar reading tasks (PDE & WA, PDE & LWID). Similar to CFA results for mindset, the revised 2-factor model and the revised bi-factor model had the most reasonable model fit (2-factor model: AIC = 10517.10, BIC = 10633.50, aBIC = 10550.95, χ² (9) = 33.9, RMSEA = .065, CFI = .99, TLI = .98; bi-factor model: AIC = 10513.21, BIC = 10643.04, aBIC = 10550.96, χ² (6) = 24.01, RMSEA = .068, CFI = .99, TLI = .97). The revised one-factor model had the poorest model fit to the data (AIC =10524.60, BIC = 10641.00, aBIC = 10558.45, χ² (8) = 41.41, RMSEA = .074, CFI = .99, TLI = .97). Neither the revised 2-factor nor the revised bi-factor models showed clear superiority over the other across model fit indices. However, the revised 2-factor model had the advantage of the parsimony principle and showed a better model fit than the revised bi-factor model across all model fit indices except AIC. Therefore, we selected the revised 2-factor model for further analysis.

Combined Mindset/Reading CFA Model

We combined the CFA models from the previous sections and estimated the correlations across factors for the combined mindset/reading CFA. To improve model fit, we excluded an insignificant correlation between Reading Mindset and Comprehension and an insignificant item covariance between PDE and LWID in the correlated combined CFA model. The final combined CFA model had reasonable a model fit χ²(162)(=362.12, RMSEA = .044, CFI = .96, TLI = .95). The latent correlations between variables across mindset and reading in the final model were small (Reading Mindset & Word Reading: ψ = .15, p <.01; General Mindset & Word Reading: ψ = .18, p <.01; General Mindset & Comprehension: ψ = .11, p <.05). The latent correlations between mindset variables was small (ψ = .27, p <.01), but was large between reading variables (ψ = .86, p <.01).

Exploratory Factor Mixture Models (E-FMMs)

We considered E-FMMs with two through five class solutions. Results were mixed, depending on model fit indices (Table 5). The 2-class solution had the highest Entropy, but also had the highest AIC, BIC, and aBIC. The 4-class solution had the lowest AIC, BIC, and aBIC, but did not have appropriate Entropy (Entropy = .71). The 5-class solution showed worse model fits than the 4-class solution model, with higher AIC, BIC, aBIC, and nonsignificant p-value of VLMR, aLMR, and BLRT. In contrast, the 3-class solution had reasonable Entropy (Entropy = .79), with evidence of superiority compared to the 2-class solution and the 4-class solution based on VLMR and aLMR. Therefore, we selected the 3-class solution model.

Table 5.

Model Fits of Exploratory Factor Mixture Models

	AIC	BIC	aBIC	Entropy	VLMR	aLMR	BLRT
LPA 2	35239.45	35740.87	35385.27	0.854	0.0083	0.0094	0
LPA 3	35193.78	35717.58	35346.11	0.794	0.0208	0.0236	0.667
LPA 4	35152.28	35698.47	35311.12	0.709	0.0583	0.064	0.075
LPA 5	35153.65	35722.23	35319.00	0.755	0.2376	0.2440	0.150

Note. Bold= the lowest values in AIC, BIC, aBIC, the highest value in Entropy, or p < .05 in VLMR, aLMR, and BLRT

We used factor mean scores and observed sample means scores to describe each class in the 3-class solution model (see Table 6). Factor mean scores from the 3-class solution represent scores relative to a referent class (Class 3; Figure 5), which represented the largest proportion of students in our sample (all of whom scored <30th percentile on the GMRTC). The relative factor mean scores indicated how the factor means of Class 1 and Class 2 were different from the factor mean of the majority of the sample (Class 3). Because of this, factor mean scores do not allow comparison of groups’ scores relative to a normative sample. Hence, we also calculated the sample means from the observed data to interpret characteristics of each group compared to a normative sample.

Table 6.

Factor Means and Sample Means of Mindsets and Reading Measures by Each Class

	Class 1 (n=53)	Class 2 (n=74)	Class 3 (n =523)
Relative Factor Means
General Mindset (SE)	−.33 (.24)	.64** (.21)	0
Reading Mindset (SE)	−.52**(.18)	−2.73*** (.24)	0
Word Reading (SE)	−2.70***(.34)	.42 (.26)	0
Comprehension (SE)	−2.41***(.22)	.58** (.18)	0
Observed Sample Means
Mindset
General Mindset (SD)	4.36 (0.98)	5.21 (0.62)	4.67 (0.99)
Reading Mindset (SD)	3.65 (1.02)	1.75 (.57)	4.17 (1.06)
Word Reading
SWE (SD; percentile)	23.81 (9.72; < 1)	53.89 (8.68; ~10)	52.37 (10.46; ~8)
PDE (SD; percentile)	6.17 (4.75; < 1)	17.46 (8.46; ~5)	19.41 (9.41; ~6)
LWID (SD; percentile)	28.19 (4.93; <= 1)	47.99 (6.51; 20~48)	44.99 (5.62; 12~43)
WA (SD; percentile)	7.64 (3.69; 0.4~13)	16.14 (5.07; 19~35)	15.73 (5.15; 19~35)
Comprehension
PC (SD; percentile)	13.94 (3.22; <= 1.0)	25.18 (3.56; 8~26)	23.25 (4.04; 3~18)
GMRTC (SD; percentile)	9.53 (3.45; ≈ 4)	13.53 (3.78; ≈ 13)	12.07 (3.89; ≈ 8)
GMRTV (SD; percentile)	8.49 (3.85; ≈ 2)	14.72 (5.23; ≈ 15)	13.60 (5.43; ≈ 13)

Note. Observed sample mean scores in Word Reading and Reading Comprehension were reported with raw scores of each reading subtest at an individual level. Percentile rank estimates based on sample mean scores and their corresponding percentile ranks in our sample. Percentile ranks vary based on chronological age at time of testing. SWE = Sight Word Efficiency in Test of Word Reading Efficiency (TOWRE); PDE = Phonemic Decoding Efficiency in TOWRE; LWID = Letter Word Identification in Woodcock-Johnson Reading Mastery Test-Revised (WRMT-R); WA= Word Attack in WRMT-R; PC = Passage Comprehension in WRMT-R; GMRTC = Comprehension Subtest of the Gates-MacGinitie Reading Tests (GMRT); GMRTV = Vocabulary Subtest of the GMRT

^**p < .01,

^***p < .001

Figure 5. Factor Mixture Model of Combined Mindset/Reading Profile Means.

Note. Class 1 = Severe RD with Slight Growth General and Mixed Reading Mindsets (n= 53); Class 2 = Less Severe RD with Growth General Mindsets and Fixed Reading Mindsets n = 74); Class 3 = Reading Difficulties Reference (n = 523)

** p <.01

In the referent class (Class 3; n = 523), sample means of variables in Word Reading ranged from 8th to 19th percentile; in Comprehension, scores ranged from the 6th to 13th percentile. Mindset scores were based on Likert scale responses from 1 to 6, with higher scores indicating a growth mindset and lower scores indicating a fixed mindset. Class 3’s scores on General Mindset (M = 4.67, SD = .99) and Reading Mindset (M = 4.17, SD = 1.06) both fell between the Agree a Little (4) and Agree (5) response options on average, indicating a slight growth mindset (i.e., scores greater than 4, but not yet at 5; hereafter termed “slight growth mindset”).

Class 1 (n = 53) had relatively lower levels of Word Reading (M_{factor score}= − 2.70, SE = .34, p <.001) and Comprehension (M_{factor score}= − 2.41, SE = .22, p < .001) compared to Class 3, with sample mean scores in both areas corresponding to the <1st to 4th percentile in normative samples. Class 1 also showed lower (i.e., more fixed) scores on Reading Mindsets (M_{factor score}= −.52, SE = .18, p = .005) than Class 3, but similar scores on General Mindsets (M_{factor score}= − .33, SE = .24 p = .175) relative to Class 3. The sample means of mindsets indicated that Class 1 had a general growth mindset (M = 4.36, SD = .98) compared to normative samples. However, the reading mindset in Class 1 (M = 3.66, SD = 1.02) fell between the Disagree A Little (3) and Agree A Little (4) response options, indicating a mixed reading mindset (i.e., scores between 3 and 4).

Compared to Class 3, Class 2 (n = 74) was characterized by relatively higher levels of Comprehension (M_{factor score}= .58, SE = .18, p = .002), but comparable Word Reading (M_{factor score}= .42, SE = .26, p =.113). The sample mean scores indicated that students in Class 2 were placed in the 5th to 23th percentile in Word Reading and in the 10 to 15th percentile in Comprehension on average, compared to normative samples. Class 2 also had relatively higher General Mindset scores (M_{factor score}= .64, SE = .21, p = .002), but lower levels of Reading Mindset (M_{factor score}= −2.73, SE = .24, p < .001) compared to Class 3. The sample mean scores indicated that Class 2 had a general growth mindset (M = 5.21, SD = .62), but a fixed reading mindset (M = 1.75, SE = .57).

We termed Class 3 the Reading Difficulties Reference (RD Reference). Based on relative levels of reading achievement and mindset, we labeled the other two classes Severe RD with Slight Growth General but Mixed Reading Mindsets (Class 1) and Less Severe RD with Growth General Mindsets and Fixed Reading Mindsets (Class 2).

Discussion

The purpose of this study was to extend previous work in two ways. First, we examined the factor structures of mindset, reading, and mindset/reading combined for fourth graders with RD (RQ1). Second, we considered the heterogeneity in student profiles in the combined mindset/reading factor models (RQ2).

Connections to Prior Work

For RQ1, we investigated the factor structures of mindset alone, reading alone, and reading/mindset combined for fourth graders with RD. For mindset, a 2-factor model (General Mindset, Reading Mindset) best explained the data, indicating two correlated, but distinct areas of mindset: one related to students’ general mindset (beliefs about general abilities) and one specific to reading (beliefs about reading abilities). The existence of general and specific areas of mindset builds upon previous literature which has found that areas of mindset exist and may be relevant for predicting reading achievement (Petscher et al., 2017; Tock et al., 2021).

For reading, a 2-factor model best explained the structure of reading achievement. We found two distinct but related areas of reading ability aligned with the SVR: (a) Word Reading, including measures of decoding, word recognition and word reading fluency; and (b) Comprehension, including measures of passage comprehension and vocabulary. Our findings correspond to previous research findings demonstrating decoding and linguistic comprehension contribute to variance in reading ability (Cutting & Scarborough, 2006; Lonigan et al., 2018). Further, we found Word Reading and Comprehension factors were strongly, positively correlated (ψ = .89); performance in one factor predicted similar performance in the other factor. This result aligns with previous work indicating that co-occurring difficulties across these areas are common in older readers with RD (Capin et al., 2021; Cirino et al., 2013; Clemens et al., 2017; Hock et al., 2009) and are seen in populations of readers participating in interventions in the later elementary grades (Donegan & Wanzek, 2021). Upon combining the two models, we found a good fit to the data, building upon evidence that a combination of risk factors beyond reading achievement may contribute to the later development of RD (Catts & Petscher, 2021).

For RQ2, we investigated the presence of classes with unique reading and mindset profiles based on the combined factor structure. We found three classes of readers. Class 1 (Severe RD with Slight Growth General and Mixed Reading Mindsets) demonstrated the weakest reading performance, showing the greatest difficulties in Word Reading and Comprehension. Class 2 (Less Severe RD with Growth General Mindsets and Fixed Reading Mindsets) and Class 3 (RD Reference) demonstrated stronger reading performance when compared with Class 1 overall, but still demonstrated moderate difficulties in both Word Reading and Comprehension. This result is likely due to our sample of students with RD scoring below the 30th percentile on the GMRTC.

This result stands in contrast to other literature with samples of readers with and without RD, which has indicated that readers fall into one of four groups based on strength (i.e., poor vs. good) of their linguistic comprehension and decoding abilities (Catts et al., 2003; Leach et al., 2003; Spencer et al., 2019) but is more consistent with recent studies focused on older readers, which showed difficulties across reading domains are common in this population (Capin et al., 2021; Cirino et al., 2013; Clemens et al., 2017; Lonigan et al., 2018). For example, Capin et al. (2021) found the majority of fourth grade students with severe reading comprehension difficulties (90%) showed moderate difficulties in both word reading and listening comprehension. Several studies examining the reading profiles of middle schoolers with reading difficulties reported similar findings. Cirino et al. (2013) examined the reading achievement in decoding, fluency, and fluency/comprehension (i.e., timed Maze task) of middle school readers. Among readers who scored below benchmark on a state reading assessment, they found isolated skill difficulties were rare (1–12%) and that the vast majority of readers had difficulties in two or more skill areas. Similarly, Clemens et al. (2017) examined reading fluency and vocabulary of students with reading comprehension difficulties in middle school students. Out of the students they identified with reading comprehension difficulties, 80% demonstrated below-average scores in fluency. Further, 57% demonstrated difficulties with both fluency and vocabulary with estimated mean standard scores approximately 1 SD below the mean. The findings of Lonigan et al. (2018) indicate a substantial amount of variance in reading comprehension explained by both decoding and linguistic comprehension, which may have also reflected relatively comparable skill levels across both reading domains, as seen in our sample.

Across our classes of readers with RD, we found General Mindset scores that ranged from slight growth mindset (M=4.36 for Class 1) to growth mindset (M=5.21 for Class 2). This was a surprising finding considering research has indicated that similar samples of readers are more likely to demonstrate lower self-concept and motivation in reading (Becker et al., 2010; Cho et al., 2019; Torppa et al., 2020; Vaknin-Nusbaum et al., 2018). However, we found that readers with stronger reading abilities (Class 2) tended to show the highest scores in mindset, indicating growth General Mindset. In other words, there appeared to be a positive relation between General Mindset and reading ability in our sample.

In contrast, there was a pattern of fixed Reading Mindset observed across our sample. This aligns with the results of previous research examining reading behaviors, attitudes, self-concepts, and goals of readers with and at-risk for disabilities (Al Otaiba et al., 2021). Elementary-age readers with RD are likely to avoid difficult reading tasks (Greulich et al., 2014; Morgan et al., 2008) and show lower reading motivation (Lee & Zentall, 2012; Morgan et al., 2008; Toste et al., 2020). Further, upper elementary readers with RD with fixed mindsets are more likely to pursue goals related to avoiding failure and therefore may be more likely to avoid challenges needed to improve their reading ability (Cho et al., 2019). In addition, reading performance is correlated with reading self-concept (the perception of one’s competence towards reading tasks) and this relation strengthens as students’ progress through elementary school (Chapman & Tunmer, 1997).

Within our sample of students with RD, we found that those with relatively stronger reading abilities were more likely to exhibit a fixed Reading Mindset than those with weaker reading abilities (e.g., Class 2). This finding stands somewhat in contrast to previous work demonstrating stronger relations between reading mindset and achievement for students with stronger reading abilities (Petscher et al., 2017), and that reading mindset positively predicts word reading and comprehension (Tock et al., 2021). In both prior studies, however, the samples included some typical readers, which may explain the differences we found in our results.

Other researchers have also had unexpected findings of reading specific mindset and other reading specific motivational predictors and the relation to reading skills and growth among readers with RD. Cho et al. (2021) found among sixth grade students, a reading specific growth mindset did not predict growth in reading comprehension or end of year outcomes. Toste et al. (2019) found readers with RD receiving reading intervention outperformed those who did not receive the reading intervention on measures of decoding, spelling, and word reading (ES = 0.25 – 0.90), and one measure of comprehension (ES = 0.26), but demonstrated lower reading self-concept than their peers in the control group. The authors suggested that the feedback received in the intervention may have elicited more accurate evaluations of students’ own reading abilities (Toste et al., 2019). Although all students in our sample performed below the 30th percentile in reading comprehension and thus are readers with reading difficulties, we are unsure what explains the lower Reading Mindset of our relatively stronger readers within this sample. Because the mindset and achievement data used in our analyses had been collected at the beginning of the school year, school-based interventions would not have occurred for long. It is possible other characteristics (e.g., motivational predictors [Cho et al., 2021]; active self-regulatory processes [Duke & Cartwright, 2021]; and listening comprehension, text characteristics, or oral language skills such as vocabulary, grammar, and morphology [Cervetti et al., 2020]) not captured by our study explain this difference in reading mindset for our sample.

Implications for Practice and Directions for Future Research

One purpose of this paper was to replicate and extend the earlier work of Petscher et al. (2017), which found a complex structure of mindset, with Global Mindset, General Mindset, and Reading Mindset factors. For our sample of readers with RD, the factor structure identified by Petscher et al. (2017) and the 2-factor model were similar in terms of model fit. We chose the 2-factor model over the global factor model for additional analyses in the name of parsimony. However, our results may have been different had we included a sample with a wider range of reading achievement as was done in Petscher et al. (2017), or with wider grade ranges.

There are three main implications of our results for practice. First, our sample had a relatively flat profile of reading achievement across both aspects of the SVR, namely Word Reading and Comprehension factors. This result lends support to the need for multicomponent reading interventions (i.e., interventions that include instruction in decoding/word reading alongside comprehension) for upper elementary readers with RD. Previous reviews have noted the promise of multicomponent reading interventions for improving the overall reading achievement of these older elementary readers (Donegan & Wanzek, 2021; Wanzek et al., 2010). Second, practitioners should note the lower levels of Reading Mindset (compared to General Mindset) observed across our sample. Readers with RD may be more likely than typical readers to demonstrate a fixed Reading Mindset, which may further impact their reading performance and reading behaviors. Fixed Reading Mindset may pose an additional challenge to accelerating the growth of these readers, even when they are participating in evidence-based reading interventions. Third, we found three distinct classes of students with reading difficulties which indicate practitioners may need to plan interventions to account for these general profiles, particularly for a smaller subgroup of readers with severe word reading and comprehension difficulties alongside a more fixed reading mindset (Class 1) who may be in need of the most intensive reading intervention.

This implication provides a direction for future research investigating the effects of reading interventions that include components targeting mindsets or related constructs (e.g., motivation, goal-setting). Several intervention studies examining the effects of reading interventions with added components show positive results for older elementary students. These studies show students who received a researcher-provided reading intervention that included added mindset or motivational components had better reading outcomes than students who received no researcher-provided reading intervention (Toste et al., 2017; Toste et al., 2019; Wanzek et al., 2021). However, these studies also compared the effects of researcher-provided reading interventions with and without these added components and found that students who received either intervention performed similarly on reading measures at post-test (Toste et al., 2019; Wanzek et al., 2021) which leaves lingering questions about the added benefit of mindset components in academic interventions.

Further, although results from some of these studies have shown that students receiving reading interventions with mindset or motivational components improve in mindset and related areas (Denton et al., 2020; Orkin et al., 2018; Toste et al., 2017), others have shown a lack of effects in these areas (Guthrie et al., 2009; Wanzek et al., 2021), and one study showed students receiving interventions performed worse (Toste et al., 2019). Work examining potential moderators of effects of mindset interventions has indicated contextual factors may impact outcomes and explain these differing effects reported in the literature (Jia et al., 2021; Yeager et al., 2019). For example, Yeager et al. found stronger effects of mindset interventions for moderate and low-achieving schools and in environments where peer norms supported challenge-seeking behaviors. In addition, Jia et al. found growth mindset predicted more adaptive learning behaviors in environments manipulated to be high-mobility (better odds in qualifying for a reward) compared to low-mobility.

Overall, the late elementary grades mark a critical juncture in development. Academic expectations shift as students progress to these grades. More research on how the reading and mindset profiles of readers with RD develop may provide a more complete view of the reader, particularly when considering the transition through middle and secondary school, with an increased focus on content area reading. Our results contribute to the growing body of research related to understanding variation in reading achievement that extends beyond reading factors only and includes additional components such as mindset for a more comprehensive understanding of the student (e.g., mindset as a resilience factor within a risk-resilience model; Catts & Petscher, 2021). This body of research may contribute to the development of reading interventions tailored to student needs across domains (e.g., reading and mindset). Eventually, work in this area may deepen the understanding of how to use these profiles to support practitioners’ selection of targeted reading interventions aligned with student profiles to improve reading achievement across time.

Figure 2. Confirmatory Factor Analysis Models for Reading Skills.

Note: I: Unidimensional Model, II: 2-factor Model, III: Bi-Factor Model, IV: Revised 2-Factor Model. V: Revised Bi-Factor Model. FR: Foundational Reading Skills. GR: General Reading Skills