Reading and mathematics equally important to science achievement: Results from nationally-representative data

Learning and Individual Differences 58 (2017) 1–9

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Learning and Individual Differences journal homepage: www.elsevier.com/locate/lindif

Reading and mathematics equally important to science achievement: Results from nationally-representative data

MARK

Lucy Barnard-Brak⁎, Tara Stevens, William Ritter Texas Tech University, P. O. Box 41071, Lubbock, TX 79410, United States

A R T I C L E I N F O

A B S T R A C T

Keywords: Reading Science Mathematics Achievement

We investigated the importance of reading and mathematics achievement in the prediction of science achievement across time. By studying models of these achievement variables while controlling for important variables, such as socioeconomic status and general knowledge, a better understanding of how reading and mathematics support science achievement over time emerged. Data from Early Childhood Longitudinal StudyKindergarten cohort was utilized as a nationally-representative and community-based sample of children across the United States. Findings provide a methodological improvement on previous literature by permitting the estimation of indirect effects, which provides the percent of the relationship accounted for at each time point. We found that reading achievement appears to significantly mediate the relationship between mathematics and science across time.

Science, technology, engineering, and mathematics are so commonly connected that even a single acronym, STEM, can be used to represent these fields as an aggregate. This high degree of relatedness suggests to educators that success in one area of STEM is associated with success in the others, and the research literature appears to support this conclusion. For example, mathematics achievement has been found to be highly correlated with science achievement and outcomes (e.g., Gustin & Corazza, 1994; Maerten-Rivera, Myers, Lee, & Penfield, 2010; O'Reilly & McNamara, 2007). The core knowledge required in STEM fields, however, does vary considerably. Despite some differences within the field of science itself, science educators typically focus on knowledge of the natural world, understanding of the processes used to generate knowledge of the natural world, and appreciation of the collaborative nature of science (Lehrer & Schauble, 2006; National Research Council, 2007). Although mathematical skills are often required in the process of knowledge generation, reading skills are necessary to learn about what has been discovered. The shared, social nature of scientific study further warrants a considerable amount of reading and sophisticated level of comprehension. Everyday words can take on new and very specific meanings in a scientific context, which further emphasizes the need for advanced reading levels when studying science (Newcombe et al., 2009). Interest in the association between reading and science achievement continues to emerge in the past decade (e.g., Bayat, Sekercioglu, & Bakir, 2014; Claessens & Engel, 2013; Kumtepe,

⁎

Kaya, & Kumtepe, 2009; Maerten-Rivera et al., 2010; O'Reilly & McNamara, 2007). These studies are limited, as reading achievement has been either investigated at a specific developmental level or included as a covariate rather than a variable of interest. Some longitudinal analyses have been conducted (e.g., Claessens & Engel, 2013; Kumtepe et al., 2009) with a focus on predicting science achievement at a later grade from reading achievement at kindergarten; however, these studies failed to include the associations of measured achievement at each grade level. By extending the investigation to focus on autoregressive models that includes both mathematics and reading achievement variables assessed into the middle level years, a better understanding of the relative importance of reading achievement and mathematics achievement in the prediction of science achievement will emerge. Although both mathematics and reading are implicated in children's successful science performance, initiatives to improve the science achievement of American youth are more likely to focus on mathematics alone. This strategy could be valuable as students approach secondary school science topics that rely more on mathematical applications to understand concepts. However, improving reading skills may, especially at the elementary level, be a more appropriate strategy to promote science achievement. The purpose of the present study was to investigate the relationship between reading, science, and mathematics achievement across four time points; kindergarten, third grade, fifth grade, and eighth grade. Specifically, the relative importance of reading and mathematics in the prediction of science achievement was

Corresponding author. E-mail addresses: [email protected], [email protected] (L. Barnard-Brak), [email protected] (T. Stevens), [email protected] (W. Ritter).

http://dx.doi.org/10.1016/j.lindif.2017.07.001 Received 13 October 2016; Received in revised form 28 June 2017; Accepted 11 July 2017 1041-6080/ © 2017 Elsevier Inc. All rights reserved.

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develop scientific knowledge on later achievement found little to no evidence to support this relationship (Kumtepe et al., 2009; Sackes, Trundle, Bell, & O'Connell, 2011). Thus, children's science knowledge development may depend on reading, especially in the context of public schools. Despite an increasing emphasis on project based science learning (Driscoll, Moallem, Dick, & Kirby, 1994), standardized and high-stakes testing continue to demand an emphasis on traditional classroom methods, including textbook reading. For example, 64% of teachers in a 2002 study (NEA, 2002) reported using the textbook for student homework. Concern arises, however, with the finding that 74% of 8th grade students did not perform beyond basic reading levels on the National Assessment of Educational Progress (NAEP) in 1998 (National Center for Educational Statistics, 1999). Thus, as reading achievement develops, science knowledge develops and assists in better science reading comprehension and ultimately science achievement over time, which suggests that the development of reading skills should be emphasized in the efforts of improving science achievement. Several researchers have documented the positive association between reading and science achievement. For example, O'Reilly and McNamara (2007) found that reading skill and reading strategy knowledge were positively associated with high school students' science achievement and reading skill helped students to compensate if their content knowledge was low. Therefore, the authors recommended that students read more about science in magazines and books to facilitate learning new information.

evaluated through the evaluation of four models; a model with only mathematics achievement predicting science achievement at third, fifth, and eighth grade; a model with only reading achievement predicting science achievement at third, fifth, and eighth grade; a model including both reading and mathematics with mathematics serving as a mediator of reading achievement's prediction of science; and a model with both reading and mathematics with reading serving as the mediator of mathematics achievement's prediction of science. 1. The role of reading in science achievement Although reading requires a variety of skills ranging from phonological awareness to making inferences, the ultimate goal is to extract the intended meaning of the author from print through the development of cognitive representations. Reading at a basic or foundational level is a prerequisite to comprehension and the subsequent development of cognitive representations as students must first be able to decode text (García & Cain, 2014; Kendeou, Broek, Helder, & Karlsson, 2014). In this way, reading opens doors to learning, as text once decoded by the reader offers knowledge and even instructions for skill building. Thus, the finding that reading skill is associated with academic achievement is not surprising (Claessens, Duncan, & Engel, 2009; Cooper, Moore, Powers, Cleveland, & Greenberg, 2014; Duncan et al., 2006; Stevenson & Newman, 1986; Stevenson, Parker, Wilkinson, Hegion, & Fish, 1976). When considered in the context of the Model of Domain Learning (MDL, Alexander, 1997), reading becomes particularly relevant to the development of science knowledge, as “there is a mutually beneficial relation between one's linguistic knowledge, as represented in the person's domain knowledge, and his or her knowledge of topics encrypted by that language” (Alexander, 2005, p. 418). MDL describes how learners' interest, knowledge, and strategy use progress and develop from acclimation to competence and to eventual proficiency in a domain (Alexander, 1997). MDL acknowledges the unique developmental paths of learners by domain as some learners may be more progressed in one domain over another (Alexander, 2004). Interest serves the learning process and the development of expertise by providing an underlying motivation for learners to pursue knowledge, which may initially be situational and progressing to an individual interest (Alexander, 2004). As children develop reading strategies, such as developing inferences, their ability to fill in knowledge relevant to the content or topic of the text improves (O'Reilly & McNamara, 2002). Based on MDL as a theoretical perspective, students with better subject matter knowledge in both reading and science will benefit more from their homework reading, as they can fill in missing gaps and generate conclusions using reading strategies and existing knowledge. MDL also emphasizes the importance of strategic knowledge, which involves both general cognitive and metacognitive strategies (Murphy & Alexander, 2002). According to Murphy and Alexander, strategic knowledge is evident in general text-processing strategies, such as re-reading sections or, at a deeper level, relating what is read to existing knowledge. In view of MDL, reading ability would appear to be a pre-requisite to focusing the power of interest, enhancing knowledge, and executing strategies. Unfortunately, not all school textbooks devote sections to background content or explicit explanations of how concepts are related (VanLehn, 1990, 1995). This makes students' existing subject matter knowledge especially important as it offers connections and even a structure to newly introduced information. “In terms of academic achievement, the role of domain knowledge is probably most critical for helping students to interpret and comprehend their textbook” (O'Reilly & McNamara, 2007, p. 163). Therefore, children who already possess science knowledge will gain more from their reading and those who possess less knowledge will fall further behind as they do not benefit from their reading. Unfortunately, researchers investigating the positive influence of early science and nature experiences intended to

2. The role of mathematics in science achievement Success in science also depends upon strategic knowledge in mathematics, which is supported by the moderate correlations found between mathematics and science achievement (Gustin & Corazza, 1994; Maerten-Rivera et al., 2010, Wang, 2005). Advocates of integrated science and mathematics courses explain that mathematical language and tools allow for the understanding of science (Batista & Matthews, 2002). For example, a student's recreation a Galilean gravity experiment requires the measurement of the speed of falling objects made of the same material that differ based on size. Measurement, data organization, and data analyses, which are all mathematical tools, facilitate the student's understanding of gravity. Thus, as students' mathematical skills and strategies develop and improve, students' ability to understand and achieve in science should also increase. Ma and Ma (2005) provided empirical evidence to support this supposition. Using latent growth modeling as well as hierarchical analyses to control for individual and school characteristics, Ma and Ma found that growth in mathematics achievement between the seventh and twelfth grades was associated with growth in science achievement. They therefore concluded that science educators may need to look to mathematics assistance when helping struggling students such that, “improvement efforts of teachers in one subject without knowledge of students' learning problems in the other subject may not work at all” (Ma & Ma, 2005, p. 90). Although the relation between mathematics and science achievement is apparent, a review of the literature revealed only a few investigations conducted at the elementary school level when mathematical skill is still emerging. Maerten-Rivera et al. (2010) evaluated the association between mathematics and science achievement in a sample of elementary school students, but the sample was drawn from fifth grade students. Interestingly, the authors found that reading achievement was a stronger predictor of science achievement than mathematics. “The results from our study suggest reinterpretation of the relationship of science to reading and mathematics, respectively, since reading achievement did have a larger effect size on science achievement than mathematics achievement” (p. 958). Thus, an investigation of the question of how both reading and mathematics relate to science 2

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reading achievement as mediating the relationship between mathematics and science achievement. As there is evidence to indicate that science achievement requires more than mathematical skills, especially in the physical sciences like biology and geology (e.g., Reed, Petscher, & Truckenmiller, 2016; Sato et al., 2014; Wyss, Dolenc, Kong, & Tai, 2013), where the reading of complicated materials is required. Thus, reading achievement may mediate the relationship between mathematics and science achievement. Conversely, mathematics achievement may also mediate the relationship between reading and science achievement when considering the more direct connections examined between mathematics and science achievement (e.g., Gustin & Corazza, 1994; Singh et al., 2002; Uttal et al., 2013), which would suggest a more distal relationship with reading achievement. To examine these hypotheses, data from Early Childhood Longitudinal Study-Kindergarten cohort was utilized as a nationally-representative and community-based sample of children across the United States.

achievement as students advance through the elementary school years appears warranted. 3. The association of emerging reading, mathematics, and science Claessens and Engel (2013) identified advocates' and researchers' growing interest in early mathematics skills and noted that little is known about how these early skills influence students' later achievement. Using hierarchical regression analyses of data from the Early Childhood Longitudinal Study—Kindergarten 1998–1999, Claessens and Engel (2013) predicted eighth grade mathematics and reading achievement from kindergarten mathematics and reading proficiency scores. They found that kindergarten proficiency, especially related to pattern recognition and understanding of advanced number and measurement, was a strong predictor of not only eighth grade mathematics achievement but also reading achievement, and the strength of this association was actually stronger for the prediction of eighth grade achievement in comparison to achievement in early grades. Perhaps their most interesting finding was that kindergarten mathematics proficiency, particularly at levels one and two, was a stronger predictor of eighth grade reading achievement and science achievement than kindergarten reading proficiency, which they accounted for by the greater reliance on pattern recognition and extrapolation that are foundational for the abstract thinking that emerges during the middle school years. Although Claessens and Engel (2013) conducted their analyses at multiple time points, including first, third, and fifth grade, their emphasis was on what types of early mathematical skills offered the strongest prediction of eighth grade achievement. Thus, they did not evaluate models that allowed for the influence of achievement at earlier grades to be included in their analyses. The authors also chose to include only mathematics proficiency scores as predictors rather than the overall mathematics scores. In addition to finding that certain mathematical skills were stronger predictors of science achievement than early reading, they also found that the strength of the association between some mathematical skills and science were quite similar to that found between early reading and science. For example, a proficiency estimate of kindergartners' ability to read two-digit numbers, recognize the next number in a sequence, find the ordinal position of objects, and solve simple word problems was actually a quite weak predictor of science achievement. Understanding which mathematical skills lead to later achievement is important; however, an investigation of how overall mathematics achievement influences later achievement is still needed. By breaking down proficiency skills in mathematics, researchers may tap into the underlying constructs fundamental to mathematics achievement rather than achievement itself. Pattern recognition, for example, is a common task on intelligence tests due to its relation to fluid ability, which is an aspect of g, or general intelligence (Carroll, 1993). Therefore, the purpose of the present study was to investigate the relative importance of reading and mathematics achievement in the prediction of science achievement across time. By studying models of these achievement variables while controlling for important variables, such as socioeconomic status and general knowledge, a better understanding of how reading and mathematics support science achievement over time will emerge. First, we hypothesize that when examined separately and exclusively that mathematics achievement will be more related to science achievement than reading achievement across time. Though the literature appears to acknowledge the role of reading achievement, the literature appears to emphasize mathematics over reading in its association with science achievement (e.g., Gustin & Corazza, 1994; Singh, Granville, & Dika, 2002; Uttal, Miller, & Newcombe, 2013). Second, we hypothesize that either reading or mathematics achievement will serve as a mediating variable in the relationship to science achievement. We will examine mathematics achievement as mediating the relationship between reading and science achievement. Then, we will examine

4. Method 4.1. Sample Data from Early Childhood Longitudinal Study- Kindergarten (ECLSK) cohort was utilized (Tourangeau, Nord, Lê, Sorongon & Najarian, 2009). As the data are all publicly available and fully de-identified, no human subjects approval was required by the Institutional Review Board at the authors' institution. The sample included 21,409 children, which with the application of the appropriate weight represent approximately 3,865,946 children across the United States. Beginning in the 1998–1999 academic year, these children were followed longitudinally from kindergarten through eighth grade concluding in the 2006–2007 academic year. Approximately 49% (n = 10,446) of the sample were female while 51% (n = 10,950) were male. With regard to ethnicity, approximately 55% (n = 11,788) of the sample identified as White, Non-Hispanic, 15% (n = 3224) were Black or African American, Non-Hispanic, 18% (n = 3826) were Hispanic, 6% (n = 1366) were Asian, 1% (n = 224) were Native Hawaiian or Pacific Islander, 2% (n = 381) were American Indian or Alaska Native, and 3% (n = 549) identified as more than one race. 4.2. Measures All measures were obtained from the ECLS-K. Science achievement was measured at three time points (e.g., third, fifth, and eighth grades). Reading and mathematics achievement was measured at each of the seven time points (e.g., kindergarten-fall, kindergarten-spring, 1st grade-fall, 1st grade-spring, 3rd grade-spring, 5th grade-spring, and 8th grade-spring). Reading achievement reliabilities ranged from α = 0.87 to α = 0.97 for the data obtained while the mathematics achievement reliabilities ranged α = 0.91 to α = 0.95 for the data obtained across the seven time points (Najarian, Pollack, & Sorongon, 2009). Since science achievement was our primary area of interest, we delimited analyses to those common time points with science achievement. Science achievement reliabilities ranged from α = 0.84 to α = 0.88 for the data obtained across the three time points (Najarian et al., 2009). We utilized IRT (Item Response Theory) scaled scores in analyses as being measurement free and taking into account item difficulty, item discrimination, and pseudo-guessing in the three parameter logistic IRT models employed (Baker & Kim, 2004). To establish the construct validity of these achievement domains, test information functions indicate continuum of item difficulties being measured with standard errors in an acceptable range (Najarian et al., 2009). For the ECLS-K data set, IRT-scaled scores are deemed the most appropriate for longitudinal examination (Najarian et al., 2009, Sections 5–26). IRT is particularly well-suited as items can be equated across time points according item parameter values. We also statistically controlled for general knowledge via IRT scaled 3

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0.44 0.46 0.48 0.54 0.72 0.77 0.72 0.58 0.60 0.61 0.63 0.71 0.74 0.70 0.84 1 0.48 0.49 0.50 0.56 0.74 0.73 0.67 0.60 0.62 0.61 0.63 0.71 0.68 0.64 1 0.43 0.45 0.47 0.55 0.66 0.70 0.73 0.57 0.61 0.65 0.66 0.80 0.85 1 0.46 0.49 0.52 0.58 0.69 0.73 0.67 0.63 0.67 0.71 0.73 0.87 1 0.51 0.54 0.56 0.63 0.74 0.71 0.64 0.68 0.73 0.76 0.78 1 0.54 0.57 0.59 0.67 0.65 0.63 0.55 0.72 0.78 0.82 1 0.61 0.65 0.67 0.68 0.65 0.63 0.56 0.81 0.86 1 0.64 0.68 0.67 0.66 0.64 0.62 0.54 0.83 1 0.72 0.67 0.67 0.66 0.63 0.60 0.52 1 0.43 0.45 0.48 0.56 0.74 0.78 1 0.49 0.54 0.56 0.68 0.85 1 0.54 0.58 0.61 0.73 1

Reading for 3rd grade

Reading for 5th grade

Reading for 8th grade

Math for Kindergarten Fall

Math for Kindergarten Spring

Math for 1st grade Fall

Math for 1st grade Spring

Math for 3rd grade

Math for 5th grade

Math for 8th grade

Science for 3rd grade

Science for 5th grade

Science for 8th grade

scores as well. General knowledge was measured across the first four time points of the ECLS-K (e.g., kindergarten-fall, kindergarten-spring, 1st grade-fall, and 1st grade-spring). General knowledge reliabilities ranged from α = 0.88 to α = 0.89 for the data obtained across the four time points (Rock & Pollack, 2002). The general knowledge scale is not a direct measure of cognitive ability but it would appear to be related to cognitive ability as a domain general measure to approximate a g factor (Brunner, 2008). Kaufman, Reynolds, Liu, Kaufman, and McGrew (2012) found that a domain general measure of cognitive ability was well correlated with a domain general measure of achievement, r = 0.83 across two separate batteries: the Woodcock Johnson III and the Kaufman Assessment Battery for Children. Additionally, Duckworth, Quinn, and Tsukayama (2012) found that IQ scores as measure of cognitive ability predicted overall achievement well across time. Other studies have also found similar results correlating domain general cognitive ability with both domain general and domain specific achievement (e.g., Karbach, Gottschling, Spengler, Hegewald, & Spinath, 2013; Kriegbaum, Jansen, & Spinath, 2015; Marks, 2016). All achievement tests were derived from a combination of national and state level standards. Items were appropriated from the National Assessment of Educational Progress as well as other commercially available assessment with permission such as the Woodcock Johnson Tests of Achievement-Revised (Woodcock, McGrew, & Mather, 2001), Primary Test of Cognitive Skills (Huttenlocher & Levine, 1990), and the Peabody Individual Achievement Test-Revised (Markwardt, 1989). Items were aligned with standards from the National Council of Teachers of Mathematics, American Association for the Advancement of Science, and the National Academy of Science. Specific information on item-by-item sourcing is not available from the ECLS-K yet all items underwent extensive field testing as documented by the psychometric and technical reports of ECLS-K when combining items from different measures (Najarian et al., 2009, Tourangeau, Lê, Nord, & Sorongon, 2009). Achievement tests were administered in two stages. First, a shorter, routing test was utilized to determine the child's level of achievement with 10 items and then a longer, second stage test adapted to their level of achievement was administered to better and more precisely measure the child's achievement that designed to be completed in 80 min (Tourangeau, Nord, et al., 2009). Table 1 provides the descriptive statistics for science achievement, mathematics achievement, reading achievement, and general knowledge scales. Table 2 provides the correlations among reading, mathematics, and science

0.41 0.42 0.45 0.52 0.69 0.73 0.77 0.54 0.57 0.59 0.59 0.70 0.74 0.78 0.74 0.80 1

L. Barnard-Brak et al.

4

0.68 0.77 0.83 1 0.79 0.91 1 0.83 1 1

22.23 (7.51) 27.08 (7.89) 30.20 (7.95) 34.35 (7.70) 35.21 (10.20) 46.46 (14.04) 53.33 (18.20) 77.36 (23.87) 126.67 (28.04) 150.10 (26.39) 171.05 (27.59) 25.91 (9.10) 36.27 (12.00) 43.26 (14.39) 61.26 (18.09) 98.72 (24.72) 123.69 (24.79) 142.22 (22.01) 50.16 (15.14) 64.58 (15.71) 84.75 (16.03)

C1R4RSCL C2R4RSCL C3R4RSCL C4R4RSCL C5R4RSCL C6R4RSCL C7R4RSCL C1R4MSCL C2R4MSCL C3R4MSCL C4R4MSCL C5R4MSCL C6R4MSCL C7R4MSCL C5R2SSCL C6R2SSCL C7R2SSCL

Kindergarten Fall – General Knowledge Kindergarten Spring – General Knowledge 1st grade Fall – General Knowledge 1st grade Spring – General Knowledge Kindergarten Fall – Reading Achievement Kindergarten Spring – Reading Achievement 1st grade Fall – Reading Achievement 1st grade Spring – Reading Achievement 3rd grade Spring – Reading Achievement 5th grade Spring – Reading Achievement 8th grade Spring – Reading Achievement Kindergarten Fall – Mathematics Achievement Kindergarten Spring – Mathematics Achievement 1st grade Fall – Mathematics Achievement 1st grade Spring – Mathematics Achievement 3rd grade Spring – Mathematics Achievement 5th grade Spring – Mathematics Achievement 8th grade Spring – Mathematics Achievement 3rd grade Spring – Science Achievement 5th grade Spring – Science Achievement 8th grade Spring – Science Achievement

Reading for 1st grade Spring

C1RGSCAL C2RGSCAL C3RGSCAL C4RGSCAL C1R4RSCL C2R4RSCL C3R4RSCL C4R4RSCL C5R4RSCL C6R4RSCL C7R4RSCL C1R4MSCL C2R4MSCL C3R4MSCL C4R4MSCL C5R4MSCL C6R4MSCL C7R4MSCL C5R2SSCL C6R2SSCL C7R2SSCL

Reading for 1st grade Fall

M (SD)

Reading for Kindergarten Spring

Description

Reading for Kindergarten Fall

Name

Table 2 Correlations among reading, mathematics, and science achievement.

Table 1 Descriptive statistics for continuous variables.

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(Rasch, 1980), other measures of fit were also evaluated. Values for the Comparative Fit Index (CFI) and Tucker Lewis Index (TLI, also known as the Non-Normed Fit Index) above 0.95 were considered as indicative of acceptable fit. Root Mean Square Error of Approximation (RMSEA) values at or below 0.08 were considered as indicative of acceptable fit while Standardized Root Mean Residual (SRMR) values at or below 0.09 as well (Little, 2013). Higher values of both the RMSEA and SRMR are indicative of less adequate or poorer model fit in contrast to values of the CFI and TLI. In conducting the current study, we first compared models of reading predicting science achievement versus mathematics predicting science achievement. In making comparisons of non-nested models, we evaluated Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) values such that lower values indicate better model fit (Kuha, 2004). Even though differences in BIC values > 10 have been indicated significantly different (Kuha, 2004), we calculated a Kass and Wasserman (1995) probability value to provide the level of statistical significance. We then examined mathematics versus reading as mediating the relationship to science achievement. As the ECLS-K is a complex data set, weights were applied and design effects adjusted to avoid the under-estimation of standard errors thereby reducing the likelihood of committing a Type I error (Claessens et al., 2009). Individual standardized path coefficient values may be interpreted similar to Pearson r values where an r value < 0.30 may be considered as small, a value > 0.30 and < 0.50 may be considered as moderate, while a value > 0.50 may be considered as large (Gravetter & Wallnau, 2016).

Table 3 Summary of fit statistics by model. Model

χ2

df

CFI

TLI

RMSEA

SRMR

Reading predicting Science Mathematics predicting Science Mathematics mediating Reading to Science Reading mediating Mathematics to Science

4291.42 3886.00 4677.22

55 55 86

0.982 0.939 0.976

0.976 0.917 0.968

0.09 0.09 0.08

0.16 0.15 0.16

4533.24

86

0.977

0.969

0.08

0.15

achievement. We also statistically controlled for socioeconomic status. The variable of socioeconomic status had a standardized mean of 0.105 (SD = 0.70), which was a composite of parents' education, occupations, and household income (Tourangeau, Lê, et al., 2009, Tourangeau, Nord, et al., 2009, Section 5–25). The variable concerning whether the student had an Individualized Education Plan (IEP) was also statistically controlled, which may be considered an indication of student having a disability that demonstrates educational need requiring special education services. Approximately 5% (n = 6159) of parents reported their child having an IEP and indication of a student having a disability. As typical in any longitudinal data set such as the ECLS-K, a certain amount of attrition was present from time point to time point. From kindergarten to eighth grade, the unweighted response rate was approximately 78% for the child assessment and interview data and approximately 73% for the parent interview data (Tourangeau, Lê et al., 2009; Tourangeau, Nord et al., 2009). Differences in study attrition did not appear according to type of school (e.g., public versus private), locale (e.g., urban, suburban, or rural), school size, percent of nonwhite students enrolled per school, or region (e.g., Northeast, Midwest, South, etc.) (Tourangeau, Lê et al., 2009, Tourangeau, Nord et al., 2009, Section 6–1).

5. Results We first examined models of reading and mathematics respectively predicting science achievement exclusive of each other. Table 3 provides a summary of the model fit statistics for each model individually. Both of these models fit the data reasonably well (see Table 2) but the model of mathematics predicting science achievement exclusive of reading achievement appeared to fit the data significantly better, p < 0.001 (see Table 4). Table 3 provides the summary of model comparisons. As for the model of reading mediating the relationship between mathematics and science versus the model of mathematics mediating relationship between reading and science, these models individually appeared to fit data well (see Table 3). The model of reading mediating relationship between mathematics and science appeared to fit the data better than the model of mathematics mediating the relationship between reading and science, p < 0.001 (see Table 3). Upon determining the best fitting model where reading achievement mediated the relationship between mathematics and science achievement, we next examined the individual paths. All paths were statistically significant at the 0.05 level or less. Table 5 provides the standardized path coefficient values for this model where reading achievement mediated the relationship between mathematics and science achievement along with statistically controlled variables. We have provided ECLS-K names for variables parenthetically in Table 5 for the purposes of study replication. The relationship of mathematics and reading achievement with science achievement appeared to be strongest as of the eighth grade indicating an increasing interdependence of domain specific knowledge and skills. This increasing relationship

4.3. Analyses Structural equation modeling techniques were employed via MPlus (v. 7.30; Muthén & Muthén, 2012). While a latent growth model would have enabled the examination of the trend across time as estimated by latent factors of intercept and slope (Grimm, Mazza, & Mazzocco, 2016), we selected an autoregressive cross-domain model whereby we longitudinally examined the relationship of each time point to the next that permits the estimation of indirect effects at each time point (e.g., Chen, Yeh, Hwang, & Lin, 2013; George, 2006: Liem, 2016). For general knowledge, we utilized latent growth modeling as we simply wanted to statistically control for the trend across time. In latent growth modeling, the intercept refers to the initial level while the slope refers to the rate of change (or growth) (Jung & Wickrama, 2008). In evaluating model fit, models should be evaluated holistically (e.g., Barrett, 2007; Byrne, 2013; Kline, 2015; Schermelleh-Engel, Moosbrugger, & Müller, 2003) so a variety of statistics were evaluated. The chi-square (χ2) goodness of fit statistic was evaluated in terms of statistical significance with a non-significant chi-square value indicative of acceptable model fit. As the chi-square statistic has been indicated as being sensitive to sample size and model complexity Table 4 Summary of model comparisons. Model

# of free parameters

BIC

AIC

Kass & Wasserman p value

Mathematics predicting Science versus Reading predicting Science

38 38 57 57

456,614.37 462,933.48 625,571.29 625,369.90

456,336.96 462,669.95 625,175.99 624,974.60

p < 0.001

Mathematics mediating Reading to Science versus Reading mediating Mathematics to Science

5

p < 0.001

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the sum of direct and indirect effects. For fifth grade, the estimated indirect effect was 0.054 (SE = 0.004) with the direct effect of 0.219 (SE = 0.010) indicated that approximately 20% of the relationship between mathematics and science achievement may be accounted for by reading achievement. For eighth grade, the estimated indirect effect was 0.100 (SE = 0.007) with the direct effect of 0.327 (SE = 0.017) indicated that approximately 23% of the relationship between mathematics and science achievement may be accounted for by reading achievement.

Table 5 Standardized path estimates. Paths General Knowledge at each time point Intercept BY General Knowledge for Fall of Kindergarten Intercept BY General Knowledge for Spring of Kindergarten Intercept BY General Knowledge for Fall of 1st grade Intercept BY General Knowledge for Spring of 1st grade Slope BY General Knowledge for Fall of Kindergarten Slope BY General Knowledge for Spring of Kindergarten Slope BY General Knowledge for Fall of 1st grade Slope BY General Knowledge for Spring of 1st grade General knowledge statistically controlled on Achievement Reading for 3rd grade ON General knowledge Intercept Reading Achievement for 3rd grade ON General Knowledge Slope Mathematics Achievement for 3rd grade ON General knowledge Intercept Mathematics Achievement for 3rd grade ON General knowledge Slope Science Achievement for 3rd grade ON General knowledge Intercept Science Achievement for 3rd grade ON General knowledge Slope Reading and Mathematics Achievement predicting Science Achievement Science Achievement ON Reading Achievement for 3rd grade Science Achievement ON Reading Achievement for 5th grade Science Achievement ON Reading Achievement for 8th grade Science Achievement ON Mathematics Achievement for 3rd grade Science Achievement ON Mathematics Achievement for 5th grade Science Achievement ON Mathematics Achievement for 8th grade Past Achievement predicting Subsequent Achievement Science Achievement for 5th grade ON Science Achievement for 3rd grade Science Achievement for 8th grade ON Science Achievement for 5th grade Mathematics Achievement for 5th grade ON Mathematics Achievement for 3rd grade Mathematics Achievement for 8th grade ON Mathematics Achievement for 5th grade Reading Achievement for 5th grade ON Reading Achievement for 3rd grade Reading Achievement for 8th grade ON Reading Achievement for 5th grade Gender statistically controlled on Achievement Mathematics Achievement for 3rd grade ON Gender Reading Achievement for 3rd grade ON Gender Science Achievement for 3rd grade ON Gender Socioeconomic Status statistically controlled on Achievement Mathematics Achievement for 3rd grade ON Socioeconomic Status (W5SESQ5) Reading Achievement for 3rd grade ON Socioeconomic Status (W5SESQ5) Science Achievement for 3rd grade ON Socioeconomic Status (W5SESQ5) IEP Status statistically controlled on Achievement Mathematics Achievement for 3rd grade ON IEP status (U2RIEP) Reading Achievement for 3rd grade ON IEP status (U2RIEP) Science Achievement for 3rd grade ON IEP Status (U2RIEP)

Estimate

0.94 0.95 0.98 0.99 0.00 0.13 0.27 0.41

6. Discussion The present findings are consistent with the existing literature that supports moderate associations between mathematics and science achievement (e.g., Gustin & Corazza, 1994; Maerten-Rivera et al., 2010; O'Reilly & McNamara, 2007; Singh et al., 2002; Uttal et al., 2013) and reading and science achievement (Bayat et al., 2014; Claessens & Engel, 2013; Kumtepe et al., 2009; Maerten-Rivera et al., 2010; O'Reilly & McNamara, 2007). The model of mathematics achievement predicting science achievement exclusive of reading achievement did fit the data better than the model of reading predicting science achievement exclusive of mathematics achievement. This result was not surprising as hypothesized given the breadth of literature associating mathematics and science achievement. In comparing models of mediation, the model where reading achievement mediated the relationship between mathematics and science achievement fit the data significantly better than the model of mathematics achievement mediating the relationship between reading and science achievement. There did appear to be fluctuations in the degree of mediation however across time. This result may be explained by the nature of the science curriculum across ages. The science curriculum in the elementary years is quite different than the physics and chemistry content of secondary coursework. For example, first graders might be asked to observe differences in materials (e.g., liquids versus solids) and to identify the different types of environments inhabited by various species of animals whereas secondary students are expected to apply mathematical formulas and advanced measurement to understand scientific phenomena (National Governors Association Center for Best Practices and Council of Chief State School Officers: Common Core State Standards Initiative, 2010). The elementary science curriculum does require mathematics, especially measurement; however, classroom practice may limit discovery learning and mathematical applications as many elementary schools do not devote a comparable amount of time across academic subjects. The focus of the early elementary years is reading, and science is not always taught on a daily basis (Tilgner, 1990). Standardized testing and the resulting high stakes are also focused on reading and mathematics rather than science (Abrams, Pedulla, & Madaus, 2003), which means that science instruction is too frequently limited to reading textbooks and related materials at the elementary level (Tilgner, 1990). This would suggest that mathematics achievement would become more important to science education as students advance through school, especially in areas of science such as physics as compared to other areas such as biology and geology. Because the present analyses did not include achievement scores beyond eighth grade, an increase in the influence of mathematics on science might not have been captured by the study. The model of reading achievement mediating the relationship between mathematics and science achievement revealed that mathematics achievement's relation to science was weakest at third grade and strongest at the eighth grade level. Therefore, the role of mathematics in science may very well increase in the later secondary school years. When reading achievement acts as a mediator of mathematics achievement's influence on science, students might possess mathematics skills but their science achievement still depends on whether they can read well enough to apply those skills. As the science vocabulary expands, children's reading and reading comprehension skills

0.71 0.26 0.23 0.10 0.58 0.19

0.24 0.21 0.29 0.16 0.22 0.32 0.56 0.38 0.71 0.66 0.85 0.78

−0.15 0.12 −0.09 0.08 0.14 0.02

0.03 0.09 −0.02

would also appear to be indicative of a fanspread effect or Mathew effect present in many achievement data sets (Walberg & Tsai, 1983). The model with reading mediating the relationship between mathematics and science achievement was evaluated. As indicated in Table 3, the model appeared to fit the data well. A review of the estimated indirect effects revealed that all standardized path coefficients were statistically significant at the 0.05 level or less. Fig. 1 provides the path diagram with standardized path coefficients. For third grade, the indirect effect of reading mediating the relationship between mathematics and science achievement was 0.115 (SE = 0.007). In combination with the estimated direct effect of 0.161 (SE = 0.011), this value indicates that approximately 41% of the relationship between mathematics and science achievement may be accounted for by reading achievement. The percent of the effect that was mediated was calculated by the value of indirect effect divided by the total effect, which is

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0.473 Math 3rd grade 0.16 1

Reading 3rd grade

Total Effect = 0.276 (Total Effect = Direct + Indirect Effect) Direct Effect = 0.161 .115* 0.242 Indirect Effect = 0.115 Mediation = 41% Science (Mediation = Indirect Effect /Total Effect) rd 3 grade

Reading 5th grade

0.26 Math 5th grade

0.05 Science 5th grade

0.22

0.36 Math 8th grade

0.21

Reading 8th grade 0.28

0.10 0.33

Fig. 1. Path diagram of mathematics predicting science mediated by reading. * Indirect effects are in bold. ** Dashed lines indicate the indirect path.

Total Effect = 0.27 (Total Effect = Direct + Indirect Effect) Direct Effect = 0.22 Indirect Effect = 0.05 Mediation = 18% (Mediation = Indirect Effect /Total Effect)

Total Effect = 0.43 (Total Effect = Direct + Indirect Effect) Direct Effect = 0.33 Indirect Effect = 0.10 Mediation = 23% (Mediation = Indirect Effect /Total Effect)

Science 8th grade

with science achievement. Our findings extend the literature base to emphasize that first, elementary mathematics achievement is important to science achievement but second, mathematics and reading achievement are both necessary in the prediction of science achievement. Finally, the present results show that these relationships are significant as children advance through elementary and middle school. Reading achievement continues to be important to science achievement even when most believe that mathematics achievement is central to science learning. For example, Gustin and Corazza (1994) found that the composite verbal SAT score for gifted seventh grade students was a stronger predictor of a standardized posttest score on a science measure than the mathematical reasoning SAT score. The authors explained that the strongest association, which occurred between verbal reasoning and biology, was due to the heavy reliance on reading in biology instruction relative to chemistry and physics. Despite the attention received by mathematics in the role of science achievement at both the elementary and middle levels, the development of reading skills must be considered important to science. “Research indicates that skilled readers generate more inferences than less skilled readers because skilled readers are more strategic and have more knowledge of reading strategies” (O'Reilly & McNamara, 2007, p. 164). Science reading demands the generation of inferences, yet the reading skills of American youth has been reportedly declining (see Perie, Grigg, & Donahue, 2005). At a time when achievement in the STEM fields is highly prized and encouraged, reading achievement simply cannot be ignored. Even so, proposed strategies to increase STEM engagement can range from incorporating video game learning (Mayo, 2009) to engaging early elementary school children in cooking (see Kumtepe et al., 2009; Sackes et al., 2011); however, few studies focus on improving reading skills. Evidence is emerging to support the improvement of science through reading interventions. Schneps, O'Keeffe, Heffner-Wong, and Sonnert (2010) utilized a computerized intervention that limited the visual distractibility associated with reading to improve the chemistry knowledge of eight college students diagnosed with dyslexia. The authors pointed out that individuals with dyslexia and other disorders associated with limits in executive functioning can do well in science if

must be at a reasonable level. However, mathematics can also mediate the relation between reading and science achievement. If students read well but do not possess the mathematical skills to make scientific comparisons, for example, their science achievement will suffer. These findings support that reading and mathematics skills work in concert to support science learning. The present results seem to suggest that improving the reading and mathematics skills of students may also result in improvements in science achievement, especially given how reading appears to be mediate the relationship between mathematics and science achievement. However, it is important to note that the results of this study were correlational and not causal. Future research is required to determine the precise causal connections between mathematics, reading and science. Although these findings are not necessarily surprising, they do point out value of reading achievement in the prediction of science achievement when the common recommendation is to promote science achievement typically emphasizes only the role of mathematics. For example, Ma and Ma (2005) found strong evidence to support mathematics' role in science achievement and recommended that educators look to mathematics performance to understand students' lack of success in science; however, they did not include reading achievement in their analyses. Claessens and Engel (2013) also emphasized the importance of mathematics over reading in their study of predictors of science achievement. Although they found stronger estimates of the association between kindergarten mathematics proficiency and fifth grade science achievement than what was found for kindergarten reading, their analyses included only kindergarten mathematic proficiency scores that focused on specific skills rather than overall achievement. This approach revealed that skills associated with pattern recognition were consistently the strongest predictors of later science achievement; however, these skills could also be considered indicators of general intelligence (Carroll, 1993). Claessens and Engel (2013) findings offer an important contribution, as they emphasize the importance of developing kindergarten students' mathematics proficiency at a grade level when the focus is typically on children's reading. However, this might be the only grade level when reading is emphasized over mathematics in its association 7

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Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42(5), 815–824. Batista, B., & Matthews, S. (2002). Integrated science and mathematics professional development programs. School Science and Mathematics, 102(7), 359–370. Bayat, N., Sekercioglu, G., & Bakir, S. (2014). The relationship between reading comprehension and success in science. Education in Science, 39, 457–466. Brunner, M. (2008). No g in education? Learning and Individual Differences, 18(2), 152–165. Byrne, B. M. (2013). Structural equation modeling with Mplus: Basic concepts, applications, and programming. Routledge. Campbell, D. T., & Stanley, J. C. (2015). Experimental and quasi-experimental designs for research. Ravenio Books. Carroll, J. B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge University Press. Chen, S. K., Yeh, Y. C., Hwang, F. M., & Lin, S. S. (2013). 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their reading challenges are addressed. Therefore, future researchers should continue to explore how gains in reading skill can support and promote science achievement. Future researchers should also expand on the present study to address limitations associated with the global nature of achievement measures used, especially as more specific investigations may identify the reading skills necessary to succeed in the differing areas of science. Reading achievement is comprised a variety of skills, ranging from decoding to comprehension and inference making. For example, O'Reilly and McNamara (2007) focused on the role of reading comprehension strategies in science achievement, as they hypothesized that such strategies are useful across many scientific areas. Researchers should continue to identify associations between specific skills and science achievement outcomes. Of further concern is the correlational nature of the present study. The correlational design of the study precludes the examination and estimation of causal effects. In the current study, there was no manipulation of an independent variable and that there was limited control of extraneous variables such as socioeconomic status, general knowledge, and disability status after the fact as statistical covariates rather than by design (see Campbell & Stanley, 2015 for more information on experimental and quasi-experimental designs). As a result, paths may not be interpreted as one variable causing another but rather correlational. Another limitation may be that we did not utilize a cross lag modeling approach. While prior reading, mathematics, and science achievement were statistically controlled on subsequent reading, mathematics, and science achievement respectively (see Table 4 for individual path estimates), we did not take into account the longitudinal nature of the data via cross lag modeling. Given the two year gap between 3rd and 5th grades and the three year gap between 5th and 8th grades, cross lag models were limited in their ability to detect relationships, especially as children transitioned from educational contexts (e.g., classrooms and both classrooms and schools when considering the gap between 5th and 8th grades). We have revised the manuscript to note this limitation of the current study. Finally, the sample's inclusion of only elementary and middle level students prevents the understanding of the reading and science association as children advance into high school. As children enter the high school years, science coursework becomes considerably varied to include specific chemistry, physics, and biology classes. The role of reading may be different depending upon scientific content, and future investigators should account for this in their research design. In conclusion, reading achievement was found to be an important predictor of science achievement, even as children advanced through the middle level years. Mathematics and reading achievement worked in concert as reading achievement appeared to mediate the relationship between mathematics and science achievement. Educators as well as policy makers who are invested in advancing STEM outcomes for public school children should therefore not ignore the value of reading achievement, even as children advance through school. Acknowledgement None of the authors have any conflict of interest. References Abrams, L. M., Pedulla, J. J., & Madaus, G. F. (2003). Views from the classroom: teachers' opinions of statewide testing programs. Theory Into Practice, 42(1). Alexander, P. A. (1997). Mapping the multidimensional nature of domain learning: The interplay of cognitive, motivational, and strategic forces. Advances in Motivation and Achievement. 10. Advances in Motivation and Achievement (pp. 213–250). Alexander, P. A. (2004). A model of domain learning: Reinterpreting expertise as a multidimensional, multistage process. Motivation, emotion, and cognition: Integrative perspectives on intellectual functioning and development (pp. 273–298). . Alexander, P. A. (2005). Psychology in learning and instruction. Prentice Hall. Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques. CRC Press.

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