Screening for Math in Early Grades: Is Reading Enough?

Abstract

Difficulties in reading and math are more likely to occur simultaneously than difficulties in either area alone; however, the research on that comorbidity is relatively sparse. The purpose of this study was to examine the relation between early reading skills as predictors of math achievement. A group of 102 kindergarten and 65 first-grade students were assessed with curriculum-based measures of early reading and early math, and a measure of broad math achievement. The results of multiple regression analyses indicated that when early numeracy was controlled for, the measures of early reading did not explain unique variance in math achievement among students. Interestingly, screening with only measures of early reading skills yielded acceptable area under the curve (AUC) values but did not yield accurate identification of students at risk for math difficulties (MD) when misclassification and specificity were taken into account. Results suggest that early math measures are most accurate in identifying students at risk for MD in early grades. Findings provide further insight into the relation between math and reading skills at the start of formal schooling. Authors provide recommendations for a combination of reading and math screeners to predict broad math achievement.

Keywords

early numeracy math early literacy screening

Early math skills at school entry are a robust predictor of later school achievement and college outcomes (Duncan et al., 2007). Unfortunately, many students experience math difficulties (MD) at the start of school. These difficulties tend to be stable and persistent overtime (Mazzocco, 2007), especially if such deficits are not remediated early. Of students with MD, an estimated one half to two thirds also have reading difficulties (RD; Badian, 1999; Geary, 2004; Jordan, 2007). The comorbidity of MD and RD adds to the complexity of identifying students at risk. Students with both MD and RD tend to have more severe deficits when compared with their MD-only peers (Jordan, Hanich, & Kaplan, 2003); however, researchers are still uncertain of the relation of reading and math achievement in regard to screening in multi-tiered systems of support (MTSS). Recent research is divergent on whether screening batteries should include measure of both reading and math. Furthermore, this research has not yet been extended to early screening measures. We aim to further explore this relation in this context in the current article.

Recent research and educational policy emphasizes the need to improve math instruction and better understand the development of math achievement (e.g., National Council of Teachers of Mathematics [NCTM], 2014; National Governors Association Center for Best Practices [NGA Center] & Council of Chief State School Officers [CCSSO], 2010). Understanding mathematical learning is not an easy task, as math does not require children to simply apply skills to perform a numerical operation. Rather, math involves a wide variety of both content-specific and interrelated general skills, and these skills increase in complexity by successive grade levels (Mazzocco, 2007). With aims to improve educational goals and math instruction, the NCTM (2000), and the Common Core State Standards in Math (CCSSM; NGA Center & CCSSO, 2010) have identified not only key content skills, but also a number of important processes or practices involved in mathematical learning. These process or practice standards include skills such as problem solving, representations, communication, modeling, and argumentation. Furthermore, the National Council for Teachers of Math (NCTM, 2000) suggests that conceptual understanding is a primary goal or strand of learning math, suggesting that computation skills are not enough and math today may include a multitude of skills.

Math often requires outside abilities, such as linguistic skills (e.g., communication). Furthermore, both general language ability and math-specific language may have different influences on student achievement (Vukovic & Lesaux, 2013); especially in the context of developing representations or models, and communicating or applying mathematical concepts to solve applied problems (NGA Center & CCSSO, 2010). Along with oral language and writing skills needed to express the solution to a problem, reading is often necessary to understand and interpret math problems. This occurs perhaps, even more so in the context of standardized achievement tests, which often present mathematical problems in the context of written language (Thurber, Shinn, & Smolkowski, 2002). Although reading may be an important skill in developing math proficiency, the standards do not explicitly mention the relation of reading skills and mathematical understanding (NCTM, 2000; NGA Center & CCSSO, 2010). Moreover, reading and math are often viewed as separate concerns in educational settings. As reading and math skills may influence each other, difficulties in one, the other, or both might represent similar problems or represent predictors of later difficulties.

Co-Occurrence of Math and RD

More than 40 years ago, a review of the research evaluating verbal factors and math learning indicated a positive and robust relation between reading and problem-solving arithmetic (Aiken, 1971). The review examined eight studies from 1952 to 1968 ranging from third to 11th grade. Four out of the eight studies examined the relation between verbal factors (e.g., reading) and math among sixth-grade students, and other studies evaluated the relation for third-, ninth-, and eleventh-grade students. The correlations between math and reading achievement across the eight studies were high (r = .40–.86, Mdn = .55). Some question if this positive correlation is attributed to general intelligence; however, when intelligence was partialled out, the correlations decreased but still had statistical and practical significance (r = .13–.48; Mdn = .38; Aiken, 1971).

As researchers continue to explore the complex nature of MD, a great deal of research has focused on the similarities and differences between students with MD and those with comorbid MD and RD. There are a number of hypotheses concerning the relation between MD and RD. Some researchers provided evidence that RD has a negative influence on the development of math achievement, but MD does not typically affect the development of reading (Jordan et al., 2003). Other evidence suggests that MD is simply a result of RD (Jordan, 2007). Some researchers propose that linguistic skills mediate math skills (Vukovic & Lesaux, 2013) while others posit that reading is a medium by which information in math is acquired and therefore influences the relation between reading and math (Shin, Davison, Long, Chan, & Heistad, 2013). In addition, researchers have speculated that language comprehension is reflected in RD among students with MD + RD and indicated that this may be related to some causal mechanism that make word problem solving difficult for that population (Anderson, 2008). Although there is some convergence of opinions among experts that reading and math skills are related, there is not substantial consensus as to the cause and implications of comorbidity, which may have important implications for screening within an MTSS framework.

Early Identification of MD

Difficulties in math can be observed as early as kindergarten and have the potential to persist through primary and secondary grades as well as further into adulthood (Geary, 2004). The prevalence and persistence of such difficulties are less likely with early identification and prevention. Early identification and prevention might be achieved with systematic screening and intervention programs, which are often conceptualized as MTSS or response-to-intervention (RtI) frameworks (D. Fuchs & Fuchs, 2006). There has been substantial research and development of screening tools for early reading skills in kindergarten and first grade. Thus, students who are identified to be at risk for RD have increased opportunity to receive additional early intervention and supports in school (Gersten, Jordan, & Flojo, 2005). Fortunately, researchers have begun to attend to examining options for the screening of early math achievement. Although much of the focus continues to be in regard to computation, there have been recent improvements in the development of measures that address early skills or more complex concepts and applications (Christ, Scullin, Tolbize, & Jiban, 2008; Foegen, Jiban, & Deno, 2007).

Although the importance of screening in early math was asserted almost over a decade ago (Gersten et al., 2005) and there are currently reliable and valid screening tools available (see Gersten et al., 2012), many schools continue to focus their screening resources in the area of reading. In 2010, it was reported that almost 90% of surveyed elementary schools implemented RtI practices in reading, but the prevalence was only 59% for math (Spectrum K12 School Solutions, 2010). Another illustration can be seen from AIMSweb, a popular assessment system of curriculum-based measures (CBMs), which shows substantially more use of universal screening measures in early reading compared with in math. Specifically, their norm samples, derived from schools that use universal screening, included nearly 2.5 times as many administrations of the letter sound measure compared with the Number ID measure in kindergarten. In first grade, the trend was similar; over 3.5 times as many students administered the letter name fluency measure compared with quantity discrimination (AIMSweb, 2012).

Similar patterns were apparent among those who used the FastBridge Learning assessment system. Just over half the number of kindergarten (53%) and first-grade students (58%) who were screened using the earlyReading measure were also screened using CBMs of early math. Furthermore, recent examination of the norm sample suggests that about 80% more students were screened in early reading skills compared with early math skills (FastBridge Learning, 2017).

Although CBMs in early math have made recent progress in terms of development, the tools are underused. The lesser use of math screeners relative to reading may relate to the priorities of local educators and the resources available to screen all students in both academic areas. The cost and potential implications of screening practices that exclude math are not well documented at early grades. This warrants further examination so that practitioners can best identify students at risk for MD at early grades.

Influence of Reading in Math Screening

As improved measurement of early math skill development begins to emerge (Gersten et al., 2012), there is also interest and need to discern the association between reading skills and math achievement (Gersten et al., 2005). Fletcher (2005) asserted that “given the comorbid association of reading, [and] math . . . measures sensitive to reading. . . . difficulties may be necessary in early screening batteries for math disabilities” (p. 308). Examining the influence of reading skills in developing math proficiency and identifying students may be especially important at an early age, when the reading load of instruction is substantially less compared with later grades. Dependent on the findings, there may be two major implications in the context of math screening. If reading screening does not significantly predict math scores beyond an early numeracy screener, the reading measure may be unnecessary in the context of math. On the contrary, if math screening does not predict math achievement beyond a measure of reading, an argument of efficiency may suggest that the math screener is unnecessary for initial screening. Another plausible conclusion may be that the addition of a reading-based assessment might add to the validity of math screeners for particular groups of students. This raises the question, “Can we use a measure of early reading to accurately screen for difficulties in math skills?”

Across elementary and middle school, a number of studies have estimated the predictive utility of reading achievement to predict math achievement (e.g., Betts, Pickart, & Heistad, 2009; Cormier, Yeo, Christ, Offrey, & Pratt, 2016; Crawford, Tindal, & Stieber, 2001; Jiban & Deno, 2007; Keller-Margulis, Shapiro, & Hintze, 2008; Purpura, Hume, Sims, & Lonigan, 2011; Rutherford-Becker & Vanderwood, 2009; Thurber, Shinn, & Smolkowski, 2002). Together, findings at the elementary grades suggest that when compared with using a math screening assessment only, using a reading screening assessment could significantly improve the accuracy of predicting broad math outcomes. This research was extended and findings suggest that CBM of reading (CBM-R) may be a significant mediator of student performance on state tests in math for students who perform at a lower level of achievement but not necessarily for those at or above expectations (Cormier et al., 2016). This may be perhaps due to the comorbidity of MD and RD. Another study examined the relation between CBM reading and math in a sample of seventh-grade students (Codding, Petscher, & Truckenmiller, 2015). Results provided evidence that across fall, winter, and spring seasons, CBM-R MAZE was the strongest predictor of State Test–Math performance even when compared with CBM of math (CBM-M). Furthermore, they found that CBM-M did not uniquely predict math outcomes above the CBM-R construct, suggesting that screening for reading may be enough to identify students at risk in math. Yet, this question has not yet been addressed in early grades in the context of screening.

Recent evidence suggests that these findings are consistent across Grades 3 through 8, such that a reading screening assessment measuring word recognition, vocabulary knowledge, syntactic knowledge, and reading comprehension may predict math outcomes as measured by a broad normative math assessment with accuracy similar to other math screeners (Truckenmiller, Petscher, Gaughan, & Dwyer, 2016). In addition, Truckenmiller et al. (2016) concluded that screeners of reading achievement could identify students who are at risk for MD. Furthermore, they concluded that schools might adopt that practice to save instructional time through more efficient screening. Although this practice might take less time, it is difficult to justify the use of a reading screener as the sole indicator of math risk from a validity perspective (Kane, 2013). Specifically, is using a measure of reading to identify students at risk for MD acceptable, given that it does not aim to measure the construct of math and content that is aligned to the curriculum? Notably, with the exception of Truckenmiller et al., much of the other research on early math screening (e.g., Codding et al., 2015; Cormier et al., 2016; Purpura et al., 2011) has yet to address the use of reading screeners for this purpose or the use of both reading and math screeners together. The results and conclusions of Truckenmiller et al. warrant further examination. Perhaps the use of both reading and math screeners together may produce the most accurate identification of risk status and a more balanced consideration of validity. More research is needed to consider the diagnostic accuracy of such screening options, as that methodology is arguably the most important to evaluate screening measures and practices. As such, the present article is timely to fill an important gap in the research literature. Furthermore, more research in kindergarten and first grade is still needed to facilitate a greater impact in early identification of difficulties and to identify the best combinations of measures considering the accuracy, administration time, and content validity.

Purpose

The purpose of this study was to examine the patterns and predictive utility of early reading and early math screening scores, especially as it relates to the identification of MD. The study addressed the following questions:

Research Question 1: What is the predictive validity of early reading and early math skills in regard to broad math achievement in kindergarten and first grade? Specifically, to what extent do reading skills explain variation in math performance above and beyond numeracy.

Research Question 2: What is the utility of early reading and early math screeners to identify risk and predict MD? This question was examined with respect to the use of each measure on its own along with composite scores of multiple measures with each of the reading and math domains.

Method

Participants

A sample of kindergarten (n = 102; 40% male) and first-grade students (n = 65; 52% male) in two suburban districts in the upper Midwest participated in this study. Participants were from classrooms in two schools across these districts that volunteered to participate in a pilot study of the earlyMath measure. Participating schools already used the earlyReading screening measure for their kindergarten and first-grade students and agreed to administer two additional math measures in the 2013–2014 school year. In the kindergarten sample, 26% of students were eligible for free or reduced-price lunch (FRL), and 6% were eligible for special education services. The majority of the sample was White (77%), with the remaining students being Black (10%), Asian (6%), Hispanic (4%), or Native American (3%). In the first-grade sample, 31% of students were eligible for FRL and 10% were eligible for special education. Similar to kindergarten, the majority of the sample was White (68%), with the remaining students being Black (20%), Hispanic (6%), Asian (5%), or Native American (3%).

Measures

Early reading (earlyReading)

The earlyReading assessment is part of FastBridge Learning’s Formative Assessment System for Teachers (FAST; Theodore J. Christ and Colleagues [TJCC], 2015). It was developed to screen and monitor prereading and early reading skills among students in kindergarten and first grade and includes a set of subtests to measure different elements of early literacy (e.g., concepts of print, alphabetic principle, decoding, and phonemic awareness). FAST recommends the use of a composite measure as the most robust, reliable, and valid indicator of early reading ability. The earlyReading winter composite measures for both kindergarten and first grade were used. The winter composite includes Onset Sounds (identifying the beginning sounds of words; untimed), Letter Sounds (fluency of matching letters with letter sounds), Word Segmenting (phonemically taking apart words; untimed), and Decodable Real Words (reading fluency of consonant-vowel-consonant words; for example, sat) in kindergarten and Word Segmenting, Decodable Real Words, Sight Words (reading fluency of common grade-level sight words), and CBMReading (rate of accurate oral reading) in first grade. All measures are individually administered to students. Of these measures, four of them involve a timed administration of 1 min: Letter Sounds, Decodable Words, Sight Words, and CBMReading. The composite scores are vertically scaled across fall, winter, and spring testing sessions (M = 50, SD = 15). While the measures vary by year, the composite is indicative of developmentally appropriate skills in early reading.

Evidence provided by the publisher supports the reliability and validity of the earlyReading composite measures. Delayed test–retest for the composite range from .68 to .91 in kindergarten, and .88 to .97 in first grade (TJCC, 2015). Internal consistency reliability for individual subtests is generally high with coefficient alpha and split-half reliabilities ranging from .75 to .99. Interrater reliability is also high ranging from .83 to .99 (Mdn = .98). The composite also shows evidence of criterion-related validity with the Group Reading Assessment and Diagnostic Evaluation and other statewide tests (r = .68 to .83; TJCC, 2015).

In addition to the earlyReading composite measure, we also examined the predictive utility of a quicker and more commonly used CBMs. For kindergarten, we utilized the Letter Sounds measure. This measure is rate based and students identify as many letter sounds as they can in 1 min. In first grade, we utilized the CBMReading measure in which students read a passage for 1 min and the total number of words read correctly is calculated.

Early math (earlyMath)

Similar to earlyReading, the earlyMath assessment was developed by FAST and is intended for use among students in kindergarten and first grade (TJCC, 2015). The earlyMath assessment measures early numeracy skills from three math domains (Number, Relations, and Operations) defined by the National Research Council (2009). Like earlyReading, the composite measures of earlyMath are robust indicators of early numeracy skills in kindergarten and first grade. The winter composite measure in kindergarten included measures of Numeral Identification (fluency of identifying written numerals from 1 to 31), Number Sequence (counting forward, backward, and understanding the mental number line; untimed), and Decomposing (composing and decomposing quantities using images in five and 10 frames; untimed). The first-grade composite included Place Value (writing and identifying numbers based on their base-10 representations), Number Sequence, and Decomposing (fluency of composing and decomposing numerals and quantity representations [i.e., dots]). Most measures were administered individually with the exception of Place Value, which was administered in a whole group format. These subtests are combined by FAST to create the composite score that is vertically scaled across fall, winter, and spring (M = 50, SD = 15). Of these measures, two of them involve a timed administration of 1 min: Numeral Identification and Decomposing (first grade). The Place Value measure included a timed administration of 2 min while the other measures were untimed in their administration.

The earlyMath assessment exhibits strong reliability and validity evidence comparable to similar academic-based screening measures. The publisher reports that test–retest reliability for the composite measures range from .62 to .87 in kindergarten, and from .71 to .91 in first grade. Internal consistency reliability for individual subtests is generally high with coefficient alpha and split-half reliabilities ranging from .52 to .98. Average interrater reliability is high, ranging from .91 to .99 (Mdn = .95). The composite measures show evidence of moderate to strong criterion-related validity across kindergarten and first grade (r = .56–.72; TJCC, 2015).

Similar to earlyReading, we identified a common and quick screening measure as another indicator of performance in math. For both kindergarten and first grade, we examined the Numeral Identification measure as it is a 1-min rate-based measure and is recommended per the FastBridge Learning system. Students read as many numerals printed on a page as they can in 1 min. Scores are reported as numerals identified correctly per minute. The kindergarten included numerals from 1 to 31 and the first-grade measure includes numerals up to 120. Further technical information for the earlyMath and earlyReading measures can be accessed by contacting the publisher at fastbridgelearning.org.

Group Math Assessment and Diagnostic Evaluation (GMADE)

The GMADE (Williams, 2004) is an untimed, group administered, nationally norm-referenced, standards-based test of math achievement for children in preschool through Grade 12. Coefficient alpha and split-half reliabilities are high ranging from .91 to .99 (Mdn = .96). Alternate form and test–retest reliabilities are high, with a median of .89 and .90, respectively. Criterion related and predictive validities with the TerraNova and Iowa Tests of Basic Skills are moderately high, ranging from .63 to .90 (National Center for Response to Intervention [NCRtI], 2015).

Unique when compared with tests typically used in the previously reviewed research literature (e.g., Stanford Achievement Test–10; Test of Mathematical Abilities), the standardized instructions of the GMADE indicate that questions are read orally while students responded on paper–pencil test forms in a whole group format. Kindergarten students took the Level R assessment, which consisted of two subtests: Concepts and Communication (CC) and Process and Applications (PA). First-grade students took the Level 1 assessment, which was composed of three subtests: CC, PA, and Operations and Computation (OC). The CC subtest measures students’ understanding of the language and vocabulary of math as well as the ability to identify appropriate representations. The PA subtest measures the ability to apply mathematical concepts and use reasoning and operations to solve word problems. In first grade, the OC subtest measures students’ ability to compute addition and subtraction of whole numbers. Each subtest contains 24 to 28 questions. The sum of these two (kindergarten) or three (first grade) subtests yields the total test score. The total test scores are then converted to standard scores (M = 100, SD = 15) and percentiles. The total test scores are representative of math content aligned with NCTM (2000) content and process standards. We selected this measure as it includes a number of key components of math including those that are (e.g., Process and Applications) and are not (e.g., Computation) related to reading skills.

Procedures

Participants were administered the earlyReading and earlyMath assessments during the winter screening period (i.e., January). We selected the winter screening period for two reasons: (a) previous research suggests that it provides a more accurate measure for screening (e.g., Gersten et al., 2012; VanDerHeyden, Codding, & Martin, 2017) and (b) for some kindergarten students fall was their first exposure to formal schooling and we wanted to limit that confounding influence on results. Trained school staff (e.g., school psychologists, interventionists, reading specialists) administered the earlyReading composite assessments as part of typical educational practices. The earlyMath and the GMADE measures were introduced to the schools and were administered by the research team. Trained graduate and undergraduate students administered the earlyMath assessments with high interrater reliability (r = .92 to .99), which was calculated by having two raters present for about 20% of the administrations and calculating the correlation between scores. Finally, in the spring, two graduate students in educational psychology with training in assessment standardization administered the GMADE to students in their regular classrooms. Classroom teachers remained in the room to help with behavior management of some students. Data collectors across the three measures were trained and passed tests of fidelity both during training and in the schools. Prior to analysis, undergraduate students entered the data and graduate students checked 100% of the data for administration errors, data entry errors, and aberrant values.

Data Analysis Plan

Descriptive statistics for the earlyReading, earlyMath, and GMADE assessments were found. Descriptives were also provided to describe the proportion of students at risk for difficulties in early math, early reading, and both in the current sample. In addition, correlations between the measures were computed.

To address the research questions, the data were modeled with multiple linear regressions using a sequential procedure in R: A Language and Environment for Statistical Computing (R Core Team, 2017). The outcome variable was the GMADE total score. The predictors included the earlyMath and earlyReading composite scores. Demographic information was evaluated in the model as covariates. Covariates included sex (0 = male, 1 = female) and FRL status (0 = not eligible for FRL, 1 = eligible for FRL). Furthermore, we used a logistic regression to determine the accuracy of using different combinations of screening measures to identify students at risk in broad math achievement.

Cut points were determined using the InformationValue package in R (Prabhakaran, 2016). Specifically, we chose to select the cut points that yielded the highest Youden’s index (Youden, 1950). This follows similar guidelines as Hintze and Silberglitt (2005) and cut points were selected with aims to improve sensitivity (e.g., at least .80) and find a balance between specificity. This methodology was selected as schools and districts may have different reasons for prioritizing sensitivity and specificity and these cut points show a balance between the two criteria. Those cut points were used to examine specificity (correct classification of those without MD), sensitivity (correct classification among those with MD), false negative rate (FNR; incorrect negative classification of those with MD), false positive rate (incorrect positive classification of those without MD), and misclassification error (total misclassifications). These statistics were used to determine the most accurate and quickest use of screening measures in the study sample.

Results

Descriptives and Correlations

Descriptive and correlational analyses were used to examine the relation between measures. Table 1 presents the means, standard deviations, percentiles, and correlations between the measures. Scores for each measure were normally distributed (z score <|1.96| or kurtosis < 3). The average scores of students in kindergarten and those in first grade performed at similar percentiles across all measures. The earlyMath and earlyReading assessments were significantly correlated (p < .05). These correlations were robust in kindergarten (r = .70) and first grade (r = .67). The validity coefficients (i.e., correlations) for earlyMath scores to predict spring GMADE total scores were .57 in kindergarten and .70 in first grade. As for earlyReading, coefficients were .51 in kindergarten and .65 in first grade. The earlyMath assessment was slightly more predictive of the GMADE compared with earlyReading, yet these coefficients were comparable.

Table 1.

Descriptive Statistics and Correlations Between Measures in Kindergarten and First Grade.

Measures	n	M	SD	Skew	Kurtosis	EM	ER	LS	NI	GMADE
Kindergarten
EM	102	52.15	12.66	−0.10	−0.84	—	.70	.63	.85	.57
ER	102	53.49	10.18	1.05	2.84		—	.73	.65	.51
LS	102	32.02	13.61	−0.10	−0.21			—	.67	.36
NI	102	33.21	12.68	0.23	−0.05				—	.45
GMADE	102	103.61	15.71	0.15	−0.38					—
						EM	ER	CBM-R	NI	GMADE
First grade
EM	65	48.21	12.84	−0.15	−0.86	—	.67	.65	.63	.70
ER	65	56.78	16.21	0.46	−0.83		—	.97	.62	.65
CBM-R	65	63.09	43.25	0.72	−0.36			—	.54	.66
NI	65	38.77	8.95	0.42	0.03				—	.51
GMADE	65	103.37	13.37	−0.39	−0.26					—

Note. All correlations were significant (p < .01). EM = earlyMath; ER = earlyReading; LS = Letter Sounds; NI = Numeral Identification; GMADE = Group Math Assessment and Diagnostic Evaluation; CBM-R = Curriculum-based measures of reading.

Base Rates of Difficulty

The proportion of students with RD, MD, or MD + RD was estimated and is shown in Figure 1. Students with scores below the benchmark for some risk as provided by the publisher were classified as at risk. Approximately 58% of kindergarten and 74% of first-grade students were at risk in math, reading, or both. Among those at risk on earlyReading, 84% of kindergarten and 90% of first-grade students were also at risk in math. Of those at risk on earlyMath, 81% of kindergarten and 75% of first-grade students were also at risk in reading; therefore, if earlyReading were used to identify math risk, 19% of kindergarten and 25% of first-grade students who performed within the at-risk range on earlyMath would not be identified as at risk. Among all those who performed within the at-risk range on either earlyReading or earlyMath, 70% of kindergarten and 69% of first-grade students had comorbid classifications for risk in both math and reading. Stated differently, 30% of kindergarten and 31% of first-grade students demonstrated a unique risk in either reading or math without comorbidity. Interestingly, in kindergarten the students with comorbid difficulties most scored below the 40th percentile on the GMADE (see Figure 1).

Figure 1.

Student performance on earlyMath and earlyReading screenings by risk status as determined by assessment benchmarks.

Prediction of MD

To address the research questions, the data were modeled with multiple linear regressions using a sequential procedure in R: A Language and Environment for Statistical Computing (R Core Team, 2017). The outcome was the GMADE total score. The predictors included the earlyMath and earlyReading composite scores and covariates included sex (0 = male, 1 = female) and FRL status (0 = not eligible for FRL, 1 = eligible for FRL). Although students were nested within only six classrooms in each grade, implying a potential lack of power for hierarchical modeling, we conducted a sensitivity analysis and confirmed that the ICC for the unconditional models were 0% to 8% (Mdn = 0%) for all outcome measures across grades. These results indicated that students nested within classes did not account for unique variance in the GMADE total score; therefore, simple multiple regression was sufficient to model the data (i.e., rather than a hierarchical model; Fox, 2008).

Analytic assumptions were examined prior to analysis. Predictors showed evidence of normality, homoscedasticity, and linearity. Furthermore, as earlyReading and earlyMath composite scores were significantly correlated (r_kindergarten = .70, r_{first grade} = .67, p < .001), tests of multicollinearity were run. The variance inflation factors were low in kindergarten (range = 1.03–2.65) and first grade (range = 1.18–2.09); therefore, multicollinearity likely did not inflate the explained variance (Fox, 2008).

Results for the multiple regression analyses are presented in Table 2. Sex was not a statistically significant predictor of GMADE performance. FRL, however, was a significant predictor in Model 3 in kindergarten (i.e., Sex, FRL, earlyReading) but not in first grade. Control variables alone (i.e., Sex and FRL) accounted for 13% and 9% of the variance in GMADE total scores in kindergarten and first grade, respectively. After controlling for early numeracy skills, reading was not a unique predictor of math achievement (R² change = .01) in kindergarten or first grade (R² change = .03). In first grade, early math skills explained an additional 18% of variance in GMADE total score. Across kindergarten and first grade, with reading controlled, early numeracy skills explained an additional 7% to 18% of variation in GMADE scores. Interestingly, reading alone explained 30% and 43% of the variation in GMADE scores in kindergarten and first grade, respectively.

Table 2.

Regression Models for Predicting GMADE Total Score in Kindergarten and First Grade.

Predictors	Model 1B (SE)	Model 2B (SE)	Model 3B (SE)	Model 4B (SE)
Kindergarten
Intercept	103.93 (2.45)**	70.05 (6.06)**	68.17 (7.73)**	63.66 (7.44) **
Sex	4.50 (2.97)	3.44 (2.56)	1.59 (2.75)	2.55 (2.62)
FRL	−6.24 (1.84)**	−3.03 (1.67)	−3.79 (1.73)*	−2.79 (1.67)
earlyMath		0.63 (0.11)**	—	0.49 (0.14)**
earlyReading		—	0.68 (0.14)**	0.26 (0.18)
R²	.13	.36	.30	.37
ΔR² (Model 1)		.23	.17	.24
ΔR² (Model 2)			− .06	.01
ΔR² (Model 3)				.07
First grade
Intercept	105.91 (1.77)**	63.05 (5.34)**	75.72 (5.42)**	59.77 (5.37)**
Sex	0.03 (2.32)	1.36 (2.22)	−0.58 (2.59)	0.83 (2.16)
FRL	−4.77 (1.91)*	0.67 (1.46)	−1.51 (1.63)	0.85 (1.41)
earlyMath		0.82 (0.10)**	—	0.65 (0.12)**
earlyReading		—	0.51 (0.08)**	0.20 (0.09)*
R²	.09	.58	.43	.61
ΔR² (Model 1)		.49	.34	.52
ΔR² (Model 2)			.15	.03
ΔR² (Model 3)				.18

Note. Statistical significance for boldfaces values in Table 2 are all <.01 (**), with the exception of the “.09” in Model 1 for first grade. This one is significant at the .05 level “*.” GMADE = Group Math Assessment and Diagnostic Evaluation; FRL = free or reduced-price lunch.

p < .05. **p < .01.

Accuracy of Identification

Logistic regression and classification analysis were conducted to examine the decision-making accuracy of different combinations of screening measures in identifying students at risk for MD. Different combinations were created to examine measures of math and reading alone and together, as well as measures of different administration times to consider quickness. At-risk status was defined as the 40th percentile on the GMADE. This was the same method used to estimate published benchmarks for earlyMath (TJCC, 2015). Results are presented in Table 3.

Table 3.

Predictive Utility and Accuracy of Different Combinations of Screening Tools.

Screener/predictor	Time (min)	n	AUC	FPR	FNR	Se	Spec	ME
Kindergarten (BR = .34)
earlyMath	5–10	102	.86	.15	.20	.80	.85	.17
earlyReading	5–10	102	.82	.33	.20	.80	.67	.28
Numeral identification (ID)	1–2	102	.82	.27	.20	.80	.69	.27
Letter sounds	1–2	102	.75	.45	.14	.86	.55	.34
earlyMath + earlyReading	10–20	102	.87	.18	.20	.80	.82	.19
earlyMath + Letter Sounds	6–12	102	.85	.21	.17	.83	.79	.20
earlyReading + Numeral ID	6–12	102	.84	.27	.17	.83	.73	.24
Numeral ID + Letter sounds	2–4	102	.82	.22	.26	.74^a	.77	.24
First grade (BR = .25)
earlyMath	5–10	65	.90	.16	.12	.88	.84	.15
earlyReading	5–10	65	.82	.43	.00	1.00	.57	.32
Numeral ID	1–2	65	.78	.12	.31	.69^a	.88	.17
CBMReading	1–2	65	.84	.33	.00	1.00	.67	.25
earlyMath + earlyReading	10–20	65	.91	.14	.12	.88	.86	.14
earlyMath + CBM-R	6–12	65	.92	.12	.13	.88	.88	.12
earlyReading + Numeral ID	6–12	65	.84	.20	.19	.81	.80	.20
Numeral ID + CBMReading	2–4	65	.86	.37	.00	1.00	.63	.28

Note. AUC = area under the curve; FPR = false positive rate; FNR = false negative rate; Se = sensitivity; Spec = specificity; ME = misclassification error; BR = base rate of risk status on the outcome measure; CBM-R= Curriculum-based measures of reading.

Utilizing Youden’s index was unable to find an appropriate cut score to allow for Se to reach .80.

In kindergarten, screeners with the highest area under the curve (AUC) were as follows: earlyReading and earlyMath (AUC = .87), earlyMath (AUC = .86), and earlyMath and Letter Sounds (AUC = .85). These combinations of measures also yielded the lower rate of misclassification (i.e., .19, .17, and .20) and FNRs (.20, .20, and .17). This suggests that these combinations of measures yielded identification of risk status that resulted in the lower number of students being identified as not at risk in math when in fact they were at risk for MD based on their GMADE scores.

In first grade, screeners with the highest AUC were as follows: earlyMath and CBM-R (AUC =.92), earlyReading and earlyMath (AUC = .91), and earlyMath (AUC = .90). These combinations of measures also yielded the lowest rate of misclassification (i.e., .12, .14, and .15) and FNR (i.e., .13, .12, and .12). Again, these combinations of measures yielded identification of risk status that resulted in the lowest number of students being identified as not at risk in math when in fact they were at risk for MD.

Discussion

Few studies have examined the relation of early reading and math achievement at the start of kindergarten and first grade in the context of screening, which was the purpose of this study. The scores from the early reading and early math screeners had statistically significant correlations of moderate magnitude. The findings suggest that when early numeracy skills were controlled for, early reading skills did not significantly add variance to the prediction of broad math achievement in either kindergarten or first grade (ΔR² = .01, .03). In both grades, the combination of the early Math and early Reading composites yielded the most accurate identifications of students with MD, and earlyMath consistently outperformed earlyReading to predict MD although by only small margins. These findings are discussed further below.

Base Rates and Correlations

Early reading and early math skills were moderately correlated in both kindergarten (r = .70) and first grade (r = .67), which is consistent with previous research. For example, Betts et al. (2009) reported that performance on numeracy and literacy screeners in spring was highly related among kindergarteners (r = .88). In addition, the more the general relation between early reading and math performances on screeners, the more the classification of students as at risk was also related when using reading and math screeners.

In the present study, cormorbid MD+RD was observed for 45% of sample, which was generally consistent with previously published findings. For example, one study reported rates of comorbidity that ranged from 17% to 66% (Badian, 1999) and another reported a range of 50% to 66% (Barbaresi et al., 2005, as cited in Jordan, 2007). Among those with risk in math, 81% of kindergarten and 75% of first-grade students were also at risk in reading (see Figure 1). The high rates may further emphasize the importance to consider reading skills when identifying students with MD. While some suggest that MD may be a result of RD, in the present sample, 10% of students in kindergarten and 17% of students in first grade had MD but not RD (see Figure 1). Performance, achievement, and risk status within the domains of reading and math may be related, but they are not the same thing. It is clear that some portion of the population will be typically performing and not at risk in early reading while atypically performing and at risk for early math development.

Relation to Math Achievement

Findings did not support the expectation that reading improves the prediction of math achievement in kindergarten and first grade. A possible explanation may be that students in kindergarten are likely experiencing their first exposure to formal instruction. As such, their skills are in early development and they may not yet be able to automatically use reading or verbal skills to aide in their math learning and performance. If this is the case, the measures of early reading and numeracy may have been more representative of an indicator of school readiness. It was surprising that FRL, Sex, earlyMath, and earlyReading together only explained a 37% variation in scores on the GMADE.

Further studies of longitudinal design are warranted to extend the findings and investigate if these early reading skills in kindergarten are indicative of later math achievement.

Current findings may be a function of the specific measures used. For example, a study conducted in a similar geographic area (Betts et al., 2009) found that reading skills in kindergarten accounted for an additional 13% of variance in explaining math outcomes in addition to early numeracy. Betts and colleagues not only used similar measures of reading (Letter Names, Letter Sounds), but also included Rhyming and Alliteration tasks. To measure early numeracy, they utilized tasks of Number Sense, Pattern, and Spatial. The current study used measures that may target number sense; however, we did not evaluate the relation between other, more spatial or geometric skills. These skills may have been more closely aligned with the content included in the GMADE.

Possible differences across measures may be a larger issue of content validity, raising questions of whether schools are using screening measures representative of instructional goals for reading and math at early grades. While the early reading and numeracy measures used in this study were developed aligned with research-based theories to cover specific domains across grades (TJCC, 2015), a number of skills were not included (e.g., computation, problem solving, quantity discrimination). Cognitive skills (e.g., working memory, rapid automated naming) were also not examined in this study. While these cognitive skills have been identified as correlates to math achievement, they have not yet been strongly linked to educational decisions. Furthermore, we did not include a measure of listening comprehension, which is a skill some students may have used to understand items on the GMADE assessment.

While reading did not explain statistically significant variance above earlyMath, it was surprising that reading alone still explained 17% to 34% of variation in scores above the control variables (i.e., FRL, Sex). Even when the assessment was read aloud to students, this is evidence that early reading skills can explain some of the variance in broad math scores. This has implications for the practice many schools use, reading items aloud as a testing accommodation in math for students who may have difficulty in reading. This evidence suggests that reading items aloud may not completely eliminate the influence of reading skills in the context of math performance.

Screening Utility

The results of the logistic regression analysis provide important findings in regard to the screening utility of different combinations of reading and math measures in kindergarten and first grade. Expert groups (e.g., NCRtI, 2017) suggest that screening tools with an AUC of .85 or higher show convincing evidence of diagnostic accuracy. Combinations of measures that reached this threshold were as follows: earlyMath and earlyReading, earlyMath, and earlyMath and a narrow CBM in reading (i.e., Letter Sounds, CBMReading). While the combination of earlyMath and earlyReading yielded the most accurate prediction of at-risk status in both kindergarten and first grade, it also has the longest administration time of 10 to 20 min per student. Given the small difference in the improvement that earlyReading made when added to earlyMath in predicting MD, schools may select to use only earlyMath or earlyMath along with a more narrow measure of reading to identify students with MD.

In addition to examining the combinations of the earlyMath and earlyReading composite measures, we also examined briefer CBMs in aims for shorter time of screening. The use of Numeral Identification, Letter Sounds, CBMReading, or combinations of the three did not yield evidence to suggest that they alone should be used to accurately screen students for MD. These measures resulted in higher rates of misclassification error and higher false negative and false positive rates, suggesting that students who were at risk were not being identified, as well as students who were not truly at risk were being identified as at risk.

We also examined the accuracy of using only a screening measure of earlyReading to identify students at risk for MD. Although this practice does not necessarily have content validity, some researchers have suggested it as a possible option as an initial screening stage for schools that might not have resources to purchase high-quality screeners in both reading and math (e.g., Truckenmiller et al., 2016). In this sample, the use of earlyReading as a math screener yielded partially convincing AUC values of .82 in both kindergarten and first grade (NCRtI, 2017). The misclassification rate was .28 in kindergarten and .32 in first grade, suggesting that 28% of students in kindergarten and 32% of students in first grade were identified incorrectly. This suggests that earlyReading as a sole screener of math performance might be acceptable in regard to time of administration and classification based on the AUC, but it still is not as accurate as using a measure of math from a validity perspective and can also result in up to twice as many misclassified students. The earlyReading measure also yielded a higher false positive rate in both kindergarten (.33) and first grade (.43). This is concerning as it means that 33% and 43% of students identified as at risk for MD were incorrectly classified, which can be especially problematic in schools with limited resources.

Implications for Practice

Findings may have a number of implications for early identification and intervention frameworks of MD; however, as with most studies, these results should be replicated across different populations and extended to evaluate the generalizability of such claims. Researchers have suggested that including reading measures in math screeners may add to the utility of identifying students who may be at risk for MD (Fletcher, 2005; Gersten et al., 2005). Furthermore, some studies have suggested that reading screeners may be enough to accurately identify students at risk for MD for older grades (Codding et al., 2015; Truckenmiller et al., 2016). Our findings provide evidence that early math and reading skills are related and both should be considered when identifying students who are at risk for academic difficulties. Furthermore, the results suggest that reading alone may not be enough to accurately identify MD in younger populations.

Another consideration for practice is the important aspect of efficiency in regard to time and resources in school settings. Currently, many schools that have adapted MTSS and screening practices place emphasis on the use and interpretation of reading screeners. This may be because many districts have to balance cost of assessments and time of administration with instructional utility. Although previous research at older grade levels has found that this practice might be enough for identifying students with MD, the findings of this study suggest that only screening early skills in reading may be at the cost of misidentifying students. This may result in missed opportunities for early intervention and prevention of later difficulties, or inefficient use of resources. Using CBMs of both math and reading have the potential to increase early remediation of difficulties as well as provide more accurate identification of students, which in the end may help balance resources. If resources are a concern, schools should seek out screening measures of early math skills that have lower administration times and more feasible reports so that they are better able to serve their students with MD.

Limitations and Future Research

The current study has limitations that emphasize the need for future research. First, this study was conducted over the course of a single school year with limited sample size. As such, it is difficult to know the extent to which these findings generalize to other populations pending replication and extension of this study. Future studies may benefit from longitudinal design to examine the developmental changes in the association between math and reading skills. This may be especially important given the young age of the participating students and the high variability that is typically present in the math and reading development of young children. Future research might also examine the influence of class situations, instructional methods, student attitudes, and teacher effects on these results.

Another limitation is the use of a small set of measures. Although the publisher (TJCC, 2015) validated the earlyMath and earlyReading composite measures as reliable and robust indicators of math and reading skills in early grades, they only account for three to four constrained skills within each content area. As mentioned earlier, the observed relation between reading and math performance might vary if measured differently. Future research might follow the framework of Purpura and colleagues (2011) and more closely analyze the relations between specific subtests with alternate modeling procedures, such as factor analysis or structural equation modeling. A thorough analysis of both the cognitive and educational literature in MD and RD may enhance the selection of such measures for inclusion in future studies to further investigate the implications for screening.

Summary

In summary, after early numeracy skills were accounted for, early reading skills did not significantly add variance to predict broad math achievement in kindergarten and first grade. Further-more, screening with only measures of early reading skills yielded acceptable AUC values but did not yield accurate identification of students at risk for MD when misclassification and specificity were taken into account. In addition, we found that a large proportion of students in kindergarten and in first grade who had MD also had comorbid RD. Furthermore, these students with MD + RD consistently scored below the 40th percentile on the GMADE in kindergarten with more variability in first grade (see Figure 1).

At the time of this study, the research indicates a relation between reading and math achievement; however, the underlying causes or mechanisms are only speculative. Notably, with the exception of Truckenmiller et al. (2016), much of the other research on early math screening (e.g., Codding et al., 2015; Cormier et al., 2016; Purpura et al., 2011) has yet to address the use of reading screeners for this purpose or the use of both reading and math screeners together. Future studies are necessary to investigate the implications for early identification and intervention of MD and disabilities. There is strong evidence that students with comorbid MD + RD show more severe deficits (Jordan, 2007; Jordan et al., 2003); however, we must first better understand the nature of this comorbidity to best inform instruction to meet the needs of these students and to guide the development of early interventions to improve math achievement.

At this time, the best recommendation may be to use curriculum-based screening measures like earlyReading and earlyMath together in early elementary grades. Based on the results of the present study, other recommendations to use only measures of reading may not be generalized to younger graders at this time. Students who demonstrate dual low achievement are at the most substantial risk for long-term deficits and disabilities in both reading and math. Although the participants in this study were relatively high performing, many still had combined MD and RD. At the time of this study, the trend in education was standards-based reform to ensure all students are prepared for success. To this end, there are educational standards in both English language arts and math that begin in kindergarten. If those standards represent important educational values and skills in one domain substantially indicate skills in the other, then a robust dual screening system may be necessary at or before the beginning of school to facilitate early prevention and intervention.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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