PSYC 565 Psychology of Learning

https://doi.org/10.1177/1534508417730822

Assessment for Effective Intervention 2018, Vol. 43(3) 182 –192 © Hammill Institute on Disabilities 2017 Reprints and permissions: sagepub.com/journalsPermissions.nav DOI: 10.1177/1534508417730822 aei.sagepub.com

Article

Researchers have spent decades studying the link between aptitudes and various educational treatments. An aptitude was defined as a measurable underlying personal character- istic that resulted in a predisposition to respond to tasks in a specific way (e.g., intelligence, personality, motivation, and learning styles; R. E. Snow, 1991). Researchers have long interpreted aptitudes to be fixed traits that were most often assessed with cognitive measures such as intelligence and memory (Snowman, McCown, & Biehler, 2008). The goal of the current research is to compare acquisition of words to measures of memory and to less fixed relevant traits such as reading skills. Below, we will discuss research around apti- tudes and educational treatments, skills and educational treatments, and acquisition of words.

Aptitude-by-Treatment Interaction

Cronbach and Snow (1977) and R. E. Snow (1991) proposed that an aptitude-by-treatment interaction (ATI) framework could be used to identify interventions for groups of students. An ATI was deemed to have occurred when interventions

were differentially effective for groups of students based on measures of aptitudes (Cronbach & Snow, 1977). Cronbach famously dedicated much of his career to finding an ATI, but failed to do so (Cronbach & Snow, 1977), and research con- ducted before 2000 generally failed to demonstrate an ATI (Kavale & Forness, 2000). Moreover, Petersen-Brown, et al. (2016) found a small effect (g = 0.17) for deriving interven- tions from measures of aptitude, and meta-analytic research of more than 200 studies since 2009 found small effects (d = 0.27) for interventions based on measures of aptitudes, which were most frequently measures of intelligence or memory (Burns, 2016).

730822 AEIXXX10.1177/1534508417730822Assessment for Effective InterventionBurns et al. research-article2017

1University of Missouri, Columbia, USA 2Brandon Valley School District, SD, USA 3ServeMinnesota, Minneapolis, USA 4Ball State University, Muncie, IN, USA

Corresponding Author: Matthew K. Burns, Associate Dean for Research, University of Missouri, 109 Hill Hall, Columbia, MO 65211, USA. Email: [email protected]

The Relationship Between Acquisition Rate for Words and Working Memory, Short-Term Memory, and Reading Skills: Aptitude-by-Treatment or Skill-by-Treatment Interaction?

Matthew K. Burns1, Katherine Davidson2, Anne F. Zaslofsky3, David C. Parker3, and Kathrin E. Maki4

Abstract The amount of information that students successfully learn and later recall from each intervention session is limited and is called the acquisition rate (AR). Research has consistently supported the effects of modifying intervention set sizes with AR data, but research with AR is in its infancy. The current study compared the relationship between AR while learning words with working memory, short-term memory, and reading skills. Participants were 52 fourth- and fifth-grade students with and without learning disabilities (LDs). Working memory (r = .34), short-term memory (r = .41), and word reading skills (r = .57) all moderately correlated with AR, but word reading skills accounted for 32% of the variance and the other two scores added little unique variance. The corrected correlation coefficients were higher for the word reading with AR than with any other variable and were essentially equal for both groups (r = .73 for average readers and r = .75 for students with an LD in reading). Thus, the data not only support the validity of making decisions with AR data but also suggest that AR is more consistent with a skill-by-treatment interaction framework than an aptitude-by-treatment interaction approach. Potential applications, directions for future research, and limitations are discussed.

Keywords achievement assessment, reading/literacy

Burns et al. 183

Reading has been linked to specific aptitudes such as long-term memory retrieval, fluid reasoning (Fiorello, Hale, & Snyder, 2006; Floyd, Evans, & McGrew, 2003; Floyd, Shaver, & Alfonso, 2004), and working memory (Feifer, 2008). Recent research has used more sophisticated assess- ment models of these constructs and have suggested potential positive benefits. For example, Fuchs et al. (2014) found that students with weak working memory learned fractions better with conceptual activities, but children with higher working memory responded better to fluency-building activities. Training in cognitive processes that were believed to underlie reading (e.g., attention, auditory processing, planning, pro- cessing speed, visual processing, and working memory) led to some acceleration, but the research did not support training in cognitive processes to intervene in reading (Kearns & Fuchs, 2013). Although there is reason to be skeptical, ATI appears to be an area in need of additional research.

Working Memory

Many contemporary studies regarding ATI focus on mea- sures of and training in working memory (Fuchs et al., 2014; Kearns & Fuchs, 2013; Peng & Fuchs, 2017). Working memory is defined as the cognitive system that holds and manipulates information (Diamond, 2013), and is different than short-term memory, which is classically defined as the aspect of the total memory model that holds small amounts of information to be immediately used (Atkinson & Shiffrin, 1968). Research has consistently demonstrated that children identified with a learning dis- ability (LD) exhibited working memory difficulties relative to their nondisabled peers (Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; Hitch & McAuley, 1991; Swanson, 1993, 2003; Swanson & Jerman, 2007).

Although there seems to be a relationship between work- ing memory and reading (Feifer, 2008), the relationship between working memory and increased student learning is not well understood. For example, Perfetti’s (1985, 1992) verbal-efficiency theory suggests a link between efficient word reading and working memory because efficient decod- ing frees up working memory resources for comprehension, which could be a fundamental way in which controlled and automatic processes interact when reading (Walczyk, 2000). However, training in verbal working memory did not lead to a significant effect in listening comprehension (Peng & Fuchs, 2017), and multiple meta-analyses found that work- ing memory training led to small effects for reading (d = 0.13 to 0.21, Melby-Lervåg & Hulme, 2013; d = 0.15 to 0.21, Schwaighofer, Fischer, & Bühner, 2015).

Short-Term Memory

Short-term memory is also clearly linked to reading and contributes variance that is unique from phonological

awareness (Ozernov-Palchik et al., 2017). However, short- term memory has not correlated well with reading because it was most frequently measured with recall of digits within a digit span task and not with tasks that aligned with reading (Swanson, Zheng, & Jerman, 2009). Research with working memory usually involves manipulating information before recalling it, but short-term memory tasks usually involve the direct and immediate recall of verbally or visually pre- sented information without any opportunity to use or manipulate the information (Brown, Neath, & Chater, 2007; Davelaar, Goshen-Gottstein, Haarmann, & Usher, 2005; Diamond, 2013). There are two aspects of short-term mem- ory that should be measured, the capacity to recall items and the order in which they are presented, and order recall in kindergarten predicted independent variance in decoding in first grade (Perez, Majerus, & Poncelet, 2012).

Skill by Treatment Interaction

Research has yet to consistently identify an ATI, but there have been documented differential treatment effects for groups of students, which Burns, Codding, Boice, and Lukito (2010) called a skill-by-treatment interaction (STI). STI was defined as systematically identifying and manipulating environmental conditions that were directly related to the problem to isolate skill deficits and suggest appropriate interventions matched to student needs (Burns et al., 2010). For example, interventionists could predict which type of intervention might be more effective from a 3-min sample of oral reading or by examining completed mathematics problems.

There have been several examples in the literature of a researcher using pre-intervention scores in a particular skill such as reading decoding, reading comprehension, word reading, and mathematical computational fluency to identify an appropriate intervention. Connor, Morrison, and Katch (2004) were among the first to study a potential STI, which they called a child-by-treatment interaction, and found that students’ reading decoding skills and vocabulary knowledge predicted which type of instruction (teacher managed or child managed) was more effective for 108 first-grade students. The study relied on multiple sources of data to identify a general instructional strategy for groups of students.

Additional research has studied STI within the context of interventions, rather than instructional approaches for an entire classroom. Students who scored low on a pre- intervention mathematics assessment responded better to interventions that involved high modeling than interven- tions that focused on timed practice (Burns et al., 2010), and a modeling intervention for reading was more effective for students with low reading accuracy, but a reading fluency intervention was more effective for students with high read- ing accuracy (Parker & Burns, 2014). McMaster et al.

184 Assessment for Effective Intervention 43(3)

(2012) found an STI with reading comprehension because elaborators (students who made frequent inaccurate elabo- ration about text) responded best to training with causal questions, and paraphrasers (students who paraphrased or repeated text rather than make elaborations) benefited more from training in connecting text to other parts of the read- ing. Finally, Szadokierski, Burns, and McComas (in press) found that pre-intervention accuracy and rate predicted the reading intervention to which students would better respond. Students who read 32 words per minute with 85% accuracy or higher responded better to a practice intervention (i.e., repeated reading) and those who scored below those criteria responded better to a modeling intervention (i.e., listening passage preview with error correction).

Previous meta-analytic research also supported an STI paradigm. Burns, Petersen-Brown, et al. (2016) found small effects for deriving interventions with data consistent with an ATI, but measures of reading fluency (g = 0.43) and pho- nological skills (g = 0.50) were much larger. The compara- tive strength of interventions derived from direct measures of reading supports the idea of an STI, because STIs involve the use of pre-intervention measures of achievement to pre- dict intervention effects (Burns et al., 2010). Moreover, meta-analytic research found a low correlation between stu- dent reading growth and IQ (r = .11) but a significantly stronger correlation between reading growth and baseline measures of reading fluency (r = .37) and word attack (r = .36; Scholin & Burns, 2012). Finally, Swanson, Trainin, Necoechea, and Hammill (2003) meta-analyzed 35 studies and found that word reading correlated with IQ at r = .35 and with memory at r = .31, but with word attack at r = .61, spelling at r = .70, and reading comprehension at r = .64.

Synthesis

Researchers have yet to consistently identify an ATI for reading or mathematics, but recent research is more promis- ing. First, as stated above, Fuchs et al. (2014) identified an ATI between teaching fractions and working memory. Second, the STI framework has repeatedly identified pre- dictors of intervention success (Burns et al., 2010; Connor, Morrison, & Petrella, 2004; McMaster et al., 2012 Szadokierski et al., in press). Aptitude, within ATI, was defined as a personal characteristic that results in a predis- position to respond to tasks in a specific way (Snow, 1991), which has been subsequently refined to mean fixed traits rather than dynamic performance of particular skills (Snowman et al., 2008). Thus, the fundamental difference between ATI and STI is that the data used to predict inter- vention effects are either representations of a fixed trait (ATI) or a momentary sample of a specific skill that is both dynamic and representative of the academic domain in question (STI).

Acquisition Rate

Perhaps one reason why working memory research has inconsistently influenced student outcomes was that the instructional link between working memory and student learning was indirect and treated as a fixed trait. An assess- ment approach called Curriculum-Based Assessment for Instructional Design (CBA-ID; Burns & Parker, 2014) pro- poses a direct way to measure student academic skill to facilitate intervention design. CBA-ID assesses the interac- tion between a student and an assigned task to determine whether it is appropriately challenging and includes the limits of memory within the dynamic momentary sample of behavior (Gravois & Gickling, 2008), by assessing an acquisition rate (AR; Gickling & Thompson, 1985). The AR is the amount of information that a student can success- fully rehearse and later recall (Burns, 2001). Assessing a student’s AR involves teaching new items (e.g., words, let- ter names, or mathematic facts) to an individual student until the student makes three errors while rehearsing any one new item (Burns, 2001). The total number of items suc- cessfully rehearsed before the three errors occurred is the student’s AR, and would be used to determine appropriate intervention set sizes for individual students.

AR is based on Cesaro’s (1967) seminal finding that teaching students a number of words that exceeded their individual limit resulted in an inability to learn the new information and reduced retention of previously learned material. Cesaro called this phenomenon retroactive cogni- tive interference, which has been consistently supported in subsequent research (Chandler, 1989; Dewar, Cowan, & Della Sala, 2007). AR data resulted in delayed alternate- form reliability estimates while teaching word recognition with a 2-week test–retest interval of .76 for first-grade stu- dents, .91 for third graders, and .91 for fifth graders (Burns, 2001). Criterion-related validity for AR data was estimated for third- and fourth-grade by correlating AR data to data from a standardized measure of verbal memory and non- verbal memory, which resulted in coefficients of r = .58 and r = .72, respectively (Burns & Mosack, 2005). Finally, AR data followed predicted developmental trends because the mean AR for first graders (M = 3.23, SD = 1.15) was smaller than for third graders (M = 5.17, SD = 2.07), who in turn had a smaller mean AR than fifth graders (M = 6.63, SD = 1.97; Burns, 2004).

AR data have direct implications for intervention. Teaching a number of items that exceeded a student’s AR resulted in learning fewer sight words (Haegele & Burns, 2015) and mathematic facts (Burns, Zaslofsky, Maki, & Kwong, 2016). Moreover, using AR data to determine intervention set sizes with students with significant behav- ioral difficulties resulted in higher percentages of task-rel- evant behavior during a word recognition intervention (Burns & Dean, 2005).

Burns et al. 185

Although the potential intervention implications of AR are clear, research is in its infancy. There are multiple student aptitudes and environmental conditions that could affect AR. For example, there is a reciprocal rela- tionship between working memory and cognitive inter- ference (Lewis, Vasishth, & Van Dyke, 2006), and the amount of information retained is affected by various developmental factors (Gathercole & Baddeley, 1993; Miller & Vernon, 1996). However, differences in the amount of information retained has also been linked to prior experience with the information (Rabinowitz, Ornstein, Folds-Benett, & Schneider, 1994) and content of the material (Scweickert & Boruff, 1986; Semb & Ellis, 1994).

Study Purpose

Given that AR is consistent with measures of memory (Burns & Mosack, 2005), it could be viewed from an ATI paradigm, but it is discussed from an STI perspective within the CBA-ID framework from which AR was born. A com- parison of the relationship between AR and aptitudes, and AR and skills could support the ATI or STI framework and could help better understand the potential underlying mech- anisms within AR such as working memory (aptitude), short-term memory (aptitude), or word reading (skill). Therefore, the current study was conducted to compare stu- dent ARs to measures of working and short-term memory, and to a measure of word reading skill. The following ques- tions guided the study:

Research Question 1: What is the relationship between AR and working memory for students with and without an LD in reading? Research Question 2: What is the relationship between AR and short-term memory for students with and with- out an LD in reading? Research Question 3: What is the relationship between AR and word reading for students with and without an LD in reading? Research Question 4: How much unique variance do measures of working memory, short-term memory, and word reading contribute to AR?

Method

Participants

The participants for the study were 52 fourth- and fifth- grade students attending one of three elementary schools in Minnesota. There were 25 (48%) females and 27 (52%) males, with a variety of ethnic backgrounds (3.8% African American, 5.8% Asian, 86.5% Caucasian, 1.9% Hispanic, and 1.9% Native American). The sample included students with an LD in reading to ensure adequate variability in

measures of memory and reading. Of the 52 students, 22 (42%) were identified with an LD in basic reading skills, and 30 were average readers. The 22 students with an LD in basic reading were identified by school personnel using Minnesota guidelines, which involved severe under- achievement in response to usual classroom instruction, a severe discrepancy between general intellectual ability and achievement, and a documented information processing disorder as determined by observation, anecdotal informa- tion, record reviews, or interpretation of scoring patterns on norm-referenced tests (Minnesota Department of Education, 1998). It should be noted that the Minnesota Department of Education was revising its LD identification guidelines when this study was conducted but that these guidelines were in place when the data were collected and all 22 students were identified with LD under these guide- lines. The 30 average readers were identified by classroom teachers and scored above the 25th percentile on school administered group achievement tests of reading.

Measures

Each participating student was assessed with three mea- sures. We assessed AR as the criterion variable for the study, and word reading, working memory, and short-term mem- ory as predictors.

Criterion—acquisition rate. The AR was assessed with pro- cedures outlined by Burns (2001). Each student was taught unknown words from a grade-level word list (Fry & Kress, 2006) that exceeded their current school grade by two levels (e.g., sixth-grade list for fourth-grade stu- dents). All words were written on 3-inch by 5-inch cards in black ink with a landscape orientation. Potential unknown words were individually presented to the stu- dent, who was then asked to orally read the word. Those that were not correctly read within 2 s were identified as unknown. Next, the students were presented a list of grade-level potentially known words with those correctly read within 2 s considered known.

After identifying known and unknown words, the unknown words were taught using the procedure used in previous AR research (Burns, 2001, 2004; Burns et al., 2016; Haegele & Burns, 2015) and outlined in Figure 1. Using AR data to determine intervention set sizes resulted in higher percentages of task-relevant behavior with students with sig- nificant behavioral difficulties (Burns & Dean, 2005), and a larger number of words (Haegele & Burns, 2015) and math- ematical facts (Burns et al., 2016) recalled.

First, each unknown word was presented to the student while verbally reading it. Second, the student was asked to restate the word and to use it in a sentence. If the student could not state a sentence that used the words in a semanti- cally correct manner, a sentence was modeled for the student, and the student was then asked to provide a different sentence

186 Assessment for Effective Intervention 43(3)

First Unknown Word First Known Word First Unknown Word First Known Word Second Known Word First Unknown Word First Known Word Second Known Word Third Known Word First Unknown Word First Known Word Second Known Word Third Known Word Fourth Known Word First Unknown Word First Known Word Second Known Word Third Known Word Fourth Known Word Fifth Known Word First Unknown Word First Known Word

Second Known Word Third Known Word Fourth Known Word Fifth Known Word Sixth Known Word First Unknown Word First Known Word Second Known Word Third Known Word Fourth Known Word Fifth Known Word Sixth Known Word Seventh Known Word First Unknown Word First Known Word Second Known Word Third Known Word Fourth Known Word Fifth Known Word Sixth Known Word Seventh Known Word Eighth Known Word

Figure 1. Incremental rehearsal sequence to rehearse unknown words within an acquisition rate assessment.

that used the target word. Third, the word was rehearsed with Incremental Rehearsal (Tucker, 1989) at a ratio of one new, unknown word to eight known words in the presentation pat- tern shown in Figure 1. Each time a new unknown word was introduced, the previous unknown word was treated as the first known word, the previous eighth known word was removed from the deck, the new unknown word was added to the set, and the process began over again. Any time a student did not correctly read a word that was written on the card, regardless if it was designated as “unknown” or “known,” it was immediately corrected and counted as an error.

New unknown words were added into the sequence until the student made three errors while practicing a new word. At this time, the number of unknown words successfully completed was recorded as the AR and that number was used for subsequent analyses. For example, if a student rehearsed the first four unknown words while making few errors, but made three errors while completing the fifth word, the student’s AR would be four. There is no maximum number of words set for teaching when considering an AR, but instead the number taught varied between students based on their AR. As stated earlier, previous research found that ARs can be reliably measured (delayed alternate form r > .90) for third- and fifth-grade students (Burns, 2001) and were highly correlated (r = .70) with a standardized norm- referenced measure of memory (Burns & Mosack, 2005).

Predictor—working memory. Two tasks were used to assess the memory of the students. Working memory was assessed with a rhyming task, and short-term memory was assessed with word span, both of which were used in previous mem- ory research (Swanson & Jerman, 2007). The rhyming task

involved presenting the participants with nine sets of rhym- ing words that ranged in size from 2 to 10 monosyllabic words. After presenting each set orally, the student was asked to recall whether a particular word was in the set, and then was asked to repeat the list of words. Data for the rhyming task were the number of sets correctly recalled (0 to 10). The median Cronbach’s alpha reliability coefficient for the rhyming task was .74 (Swanson & Jerman, 2007).

Predictor—short-term memory. The word span task was used to assess short-term memory, and involved verbally pre- senting monosyllabic words in increasingly longer sets (two to eight) and asking the participants to recall the words in the set. The assessment stopped once the student was unable to verbally recall the words presented in the given set. The number of total words recalled represented the data from the word span task (0 to 35). The median Cronbach’s alpha reliability coefficient from previous research for word span was .70 (Swanson & Jerman, 2007).

Predictor—word reading skills. Each student’s word reading skills were assessed with the Alphabet/Word Knowledge subtest of the Third Edition of the Diagnostic Achievement Battery (DAB-3; Newcomer, 2001). The Alphabet/Word Knowledge subtest contains 65 items that assess word rec- ognition skills by asking the students to identify individu- ally presented letters and words. All data were converted to an age-based standard score with a mean of 10 and a stan- dard deviation of 3. Cronbach’s alpha reliability estimates for the Alphabet/Word Knowledge subtest all exceed .92 for any age group, with a median coefficient of .95, and test– retest reliability estimates resulted in a mean coefficient of .96 (Newcomer, 2001).

Procedure

All data were collected by school psychology graduate stu- dents with advanced training in assessment and research pro- tocols. Each graduate student researcher was individually taught the procedures for collecting the data by one of the study authors during a 45-min training session during which each procedure was modeled and practiced until proficient.

The participants were taken to a quiet place within the school building but separate from their classroom (e.g., a desk in the hall). The researchers first obtained student assent, and then screened word reading skills with the Alphabet/Word Knowledge subtest of the DAB-3. Alphabet/ Word Knowledge scores for all 22 students identified with an LD fell at or below the 25th percentile, and the scores for the 30 average readers were all at or above the 37th percen- tile. Next, the AR assessment, rhyming task, and word span tasks were completed in a counterbalanced order. The order of the tasks did not affect the results for AR F (2, 53) = 0.04, p = .97, rhyming task F (2, 53) = 1.42, p = .25, or words span F (2, 53) = 0.54, p = .59.

Burns et al. 187

Table 1. Descriptive Data and Correlations Coefficients for Memory and Word Reading Data.

Variable M (SD) Skewness

(SE = 0.33) Kurtosis

(SE = 0.65) Rhyming

taska Word span

Word reading

Acquisition rate 5.16 (2.25) −0.20 −1.29 .34 .41* .57* Rhyming taska 2.38 (1.66) 2.56 7.81 .34 .14 Word span 9.80 (3.44) −0.02 −1.17 .46* Word reading 8.98 (2.67) 0.17 −1.00

aCorrelations were computed with a z score. *p < .01.

Fidelity and Interobserver Agreement

The procedures for assessing AR, rhyming task, and word span were observed by the first author for 25% of the data collection sessions using an implementation checklist. The total number of items correctly implemented was divided by the total number of items and resulted in 98% correct implementation for AR, and 100% for the rhyming task and word span.

Interobserver agreement was also computed by observ- ing 25% of the data collection sessions. The first author observed the session and also recorded whether or not words were stated (AR) or recalled (rhyming task and word span) correctly. The total number of words that were consis- tently recorded as correct or incorrect was divided by the total number of words presented in each task and resulted in 100% IOA for all three assessments.

Results

The AR scores were the criterion variable for the study, and the rhyming task score, word span score, and word reading standard score were the predictor variables. The descriptive data for the four variables are included in Table 1. The dis- tributions for three of the scores were adequately normal because the absolute value of the estimates of skew and kur- tosis were less than 2.00 and within two standard errors. However, the rhyming task data were not normally distrib- uted. Therefore, the rhyming task data were converted to a standard z score using the data from the two samples (LD and average readers) described below, which resulted in estimates of kurtosis and skew that were less than 2.00. The resulting z score was used for analyses.

Data were examined for grade-level differences before addressing the research questions. No significant differences were found between fourth- and fifth-grade students for AR t(50) = 1.22, p = .23, rhyming task score t(50) = 0.04, p = .97, word span score t(50) = 0.78, p = .44, or Alphabet/ Word Knowledge standard score t(50) = 0.77, p = .44. Thus, data for fourth- and fifth-grade students were combined for subsequent analyses.

The first three research questions inquired about the rela- tionships between AR and working memory (rhyming task), short-term memory (word span), and word reading skills for

students with and without an LD in reading. As shown in Table 1, word span (r = .41) and word reading (r = .57) both led to significant correlations with AR, but the standardized rhyming task score did not (r = .34). Because the standard deviation of the Alphabet/Word Knowledge subtest for the total sample was 2.67 and it was 3.00 for the population (Newcomer, 2001), there appeared to be a restriction of range for the data. Even small range restrictions can effect correlation coefficients. For example, a restriction from a standard deviation of .80 to .50 can reduce a correlation of r = .45 to r = .30 (Murphy & Davidshofer, 2005). Therefore, the correlations with word reading were corrected for range restriction with the formula presented by Murphy and Davidshofer (2005). The resulting corrected coefficients were r = .61 for AR and word reading, r = .45 for word span and word reading, and r = .38 for rhyming task and word reading. The magnitude of the corrected correlation between AR and word reading was compared with the coefficients for the correlations with AR and the rhyming task and AR and word span using a Fisher transformation. The correla- tion coefficients were not significantly different between AR and word reading (corrected) and AR and rhyming task (z = 1.76, p > .05), or between AR and word reading (cor- rected) and AR and word span (z = 1.35, p > .05).

The descriptive data for the students with and without an LD in reading are shown in Table 2. The mean score for each variable was significantly higher for the average reader group than the LD group. The correlation coefficients for each group are also shown in Table 2, and again the coeffi- cient for the correlation between AR and word reading was corrected for range restriction based on the standard devia- tions of the two groups. The corrected correlation coeffi- cient was higher for the word reading with AR than with any other variable and was essentially equal for both groups (r = .73 for average readers and r = .75 for students with an LD in reading). The magnitude of the corrected correlation between AR and word reading was again compared with the coefficients for the correlations with AR and the two mem- ory variables with a Fisher transformation. Among the aver- age readers, the correlation was significantly higher for AR and word reading than for AR and rhyming task (z = 1.99, p < .05), but was not significant between AR and word read- ing and AR and word span (z = 0.92, p > .05). Among the students with an LD in reading, the correlation was

188 Assessment for Effective Intervention 43(3)

Table 2. Descriptive Data and Correlations Coefficients for Memory and Word Reading Data for Average Readers and Students With an LD.

Variable Average readers

M (SD) LD

M (SD) t Acquisition

rate Rhyming

Taska Word span

Word reading

Word reading corrected

Acquisition rate 6.10 (2.04) 4.27 (2.07) 3.17* .37 .59* .51* .73* Rhyming taska 2.97 (1.99) 1.72 (0.70) 2.78* .38 .46 .35 .56* Word span 11.10 (3.17) 7.72 (2.91) 3.92* −.02 .29 .21 .36 Word reading 11.07 (1.66) 6.36 (1.05) 11.68* .37 .14 −.15 NA Word reading

corrected NA NA NA .75* .38 −.40 NA

Note. Coefficients above the diagonal are for the typical readers (n = 30) and those below the diagonal are for students with learning disabilities in reading (n = 22). Coefficients with Word Reading are corrected for range restriction. LD = learning disability. aCorrelations were computed with a z score. *p < .01.

significantly higher for AR and word reading than for AR and rhyming task (z = 1.98, p < .05), and between AR and word reading and AR and word span (z = 2.94, p < .05).

The final research question addressed the unique vari- ance for the three measures on AR. Word reading was added in first because it had the largest correlation with AR, and working memory (rhyming task z score) and short-term memory (word span score) were added in simultaneously in Model 2. As shown in Table 3, word reading accounted for 32% of the variance, which was significant and large. Adding in working and short-term memory (Model 2) resulted in an additional 4% of the variance, which was not significant and small. Word reading was the only significant predictor in either of the first two models. The order of the variables was reversed to further test the unique variance attributed to each model. Model 3 resulted in a significant and large amount of variance (26%), but adding in word reading still accounted for an additional 16% of unique

variance, which was significant. Moreover, short-term memory was a significant predictor in Model 3, but only word reading remained significant in Model 4.

Discussion

The current study examined the relationships between AR and measures of word reading, working memory, and short- term memory. The current data suggested a stronger rela- tionship with skill (word reading) measures than with aptitude (memory) measures. There was a significant rela- tionship between AR and word reading, and between AR and short-term memory, but the relationship between AR and working memory was not significant. Thus, word read- ing skills appear to underlie how many words a student can learn and recall, but short-term memory also appeared to be a factor. Moreover, measures of skill (word reading) accounted for a large percentage of variance (32% when

Table 3. Regression Analyses for Word Reading (Alphabet/Word Knowledge), Working Memory (Rhyming Task z score), and Short- Term Memory (Word Span) on Acquisition Rates for Word Recognition.

Model 1 Model 2

B S.E. b t B S.E. b t

Constant 1.17 0.90 1.30 0.84 0.95 0.88 Word Reading 0.46 0.10 .56 4.82* 0.36 0.10 .44 3.56* Working Memory 0.47 0.27 .21 1.78 Short-Term Memory 0.13 0.08 .20 1.48 R2 = .32

F Change = 23.25* R2 = .36

F Change = 3.09

Model 3 Model 4

Constant 2.83 0.86 3.30* 0.84 0.95 0.88 Working Memory 0.46 0.30 .20 1.54 0.47 0.27 .21 1.78 Short-Term Memory 0.26 0.08 .40 3.07* 0.13 0.08 .20 1.48 Word Reading 0.36 0.10 .44 3.56* R2 = .26

F Change = 8.50* R2 = .42

F Change = 12.70*

*p < .01.

Burns et al. 189

entered first, and 16% when entered second), but the apti- tude (memory) measures only accounted for 26% when entered first or 4% when entered second. Therefore, the skill measures provided unique variance beyond measures of memory and predicted AR better.

All of the findings described above supported STI over ATI as the underlying framework for AR, which was also consistent with previous research. Cowan (2008) and Swanson and Jerman (2007) also found significant relation- ships between working memory, short-term memory, alpha- bet/word reading, and word acquisition, but there were stronger relationships between learning and academic skills than learning and measures of cognition (Burns, 2016; Scholin & Burns, 2012; Swanson et al., 2003).

The current study used teaching word recognition as the stimulus to measure AR because rapid word recognition is important (Carnine, Silbert, Kame’enui, & Tarver, 2004; Fuchs, Fuchs, Hosp, & Jenkins, 2001; Perfetti, 1992) and because word recognition is a frequent target for interven- tion research (Burns, 2007; Mechling, Gast, & Thompson, 2009; Nist & Joseph, 2008). Sight-words are those words that are recalled from memory as a single unit, and for which pronunciations and meanings are automatically remembered without cognitive effort (Ehri, 2005). Previous research also found a relationship between decoding skill and learning words, and that vocabulary predicted word learning with irregular words (Wang, Nickels, Nation, & Castles, 2013). The current study did not examine vocabu- lary, which suggests an area for future research. Moreover, the implications of measuring a student’s AR are much less clear for less memory-oriented topics like social studies, science, and more complex reading comprehension tasks, which also suggests areas for future research.

AR could be linked to cognitive load, which also sug- gests that the capacity of working memory is limited (Sweller, Van Merriënboer, & Paas, 1998), but we did not consider cognitive load in the current study. The limitations of working memory are not the same among novices and more expert learners because previously learned informa- tion stored in long-term memory can be activated and used to expand the capacity of working memory for that domain (Ayers & Paas, 2009). Research has consistently found larger working memory loads for more expert learners (Kalyuga, Chandler, & Sweller, 1998, 2001; Pollock, Chandler, & Sweller, 2002; Tuovinen & Sweller, 1999). Children with reading difficulties have fewer learned words from which to draw than more advanced readers and would therefore have to dedicate more cognitive resources. Thus, the students with LD had significantly lower word reading scores and likely had fewer words from which to draw. Future researchers could include self-reports of mental effort (Paas, Tuovinen, Tabbers, & Van Gerven, 2003) or could compare the effect that sets size has on mental effort.

Previous research demonstrated instructional benefits of determining how many new items to teach during one

lesson or intervention session (Burns & Dean, 2005; Burns et al., 2016; Haegele & Burns, 2015) and those data appear to be at least moderately related to word reading and mea- sures of memory. The moderate correlations support the validity of assessing AR and begin to explain its theoretical underpinnings. However, the final model that included all three sets of data still explained less than 40% of the vari- ance. Therefore, 60% of the variance remained unaccounted and suggested areas for future research.

It is essential that assessments be instructionally relevant and provide educators with the information they need to make modifications. There are many well-constructed mea- sures of working memory, and quicker, less formal approaches (e.g., rhyming task), though knowing that a stu- dent has low working memory might not lead to interven- tions that are readily relevant instructionally. Interventions for a student with a standard score of 90 may not differ from one with a standard score of 75, and previous research that studied academic interventions based on memory data resulted in small effect sizes (Burns, 2016). Alternatively, finding an AR of five while teaching word recognition sug- gests that the student would probably recall the words at a higher rate (Haegele & Burns, 2015), have less time off task (Burns & Dean, 2005), and may read them more fluently in text (Burns, 2007) when teaching five words rather than teaching six or more. Teachers may overestimate the appro- priate set size for students or may not teach enough new words to be most efficient. Among these fourth- and fifth- grade students, the mean AR was approximately five words with a standard deviation of 2. Thus, 68% of the students in this sample would probably respond best to set sizes of three to seven words. The one standard deviation range of three to seven words was quite large and suggested the potential for considerable individual differences within a group of same-aged students.

Limitations

Although these data are of interest to researchers, they should be considered within the context of study limita- tions. One potential limitation of the study was that students were identified with LD with a discrepancy model that has consistently been shown to lack validity and reliability (Aaron, 1997; Fletcher et al., 1998). Many state depart- ments of education and local school districts identify stu- dents with LD by monitoring response to research-based interventions (RtI). Thus, this study could be replicated with students identified with LD through an RtI process.

The finding that the strongest relationship existed between AR and word reading skills as compared with memory skills is consistent with previous research of direct and indirect assess- ments (Scholin & Burns, 2012; Swanson et al., 2003). However, additional research within a single population is nec- essary to ensure the relationships are similar and to determine the relative contribution of the indirect and direct measures to

190 Assessment for Effective Intervention 43(3)

AR. The current sample was too small to adequately examine the two subgroups, and the size of the sample should be con- sidered a limitation of the conclusions.

Another limitation stems from the use of just the rhym- ing task and word span task to assess memory. In using one assessment for each type of memory, we may have under- or mis-represented the memory constructs we desired to assess. Likewise, the conceptualization of working memory is subject to ongoing research, including Baddeley’s (2000) addition of the episodic buffer, which binds different types of processing information (i.e., visual, auditory, etc.) together in an integrated representation. The relationships of a comprehensively measured working memory with AR and word reading skills might be different with the addition of information about other working memory components. Finally, the study did not examine retention of the newly acquired words, and future researchers could conduct fol- low-up assessments.

The current study examined word reading skill in fourth- and fifth-grade students, but reading sight words is also an important skill for younger children (C. E. Snow, Burns, & Griffin, 1998). The absence of these students from the par- ticipant sample represents a limitation for generalizing the results to the whole of the population of readers for whom the relationship of AR and other memory constructs should be researched. Future research should consider whether dif- ferent results would emerge for students at earlier stages of reading development.

The study also did not examine the readability of the words or if they were regular or irregular. Students in fourth and fifth grade may have some knowledge of prefixes, suf- fixes, roots, common letter patterns, and may have been able to use that knowledge to chunk the new words. Future researchers could replicate the design with more tightly controlled word structures. We also only assessed if the stu- dents could correctly state the word within 2 s of presenta- tion and did not examine orthography, phonology, semantic similarity, or prior experience, which suggests areas for future research. Moreover, using different unknown words for individual students could have resulted in different level of difficulties across participants. The words were randomly selected from the same word list, but the comparability of the stimulus words is unknown and should be considered a limitation. Finally, participants who were diagnosed with LD all experienced deficits in basic reading skills, but we did not know if they were deficient in other areas as well. Thus, the potential effects of comorbid disabilities are unknown and suggest an area for future research.

Conclusion

The overall purpose of the research questions posed here was to better understand the potential mechanisms underlying the efficacy of basing set sizes on AR data. The results are con- sistent with previous research because they supported the STI

paradigm over ATI. Assessing an AR could be important to consider when teaching students words, but the correlational design of the study prohibits conclusions regarding the causal mechanisms behind the effects of using AR to modify the sizes of intervention sets. Given the consistent finding that students with learning difficulties often have difficulties with measures of memory, the lack of instructional implications of most measures of memory, and the number of students who experience reading difficulties in schools, additional research seems warranted.

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 disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The current study was funded by a grant from the Learning Disabilities Foundation.

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