TOWARD A LIFESPAN METRIC OF READING FLUENCY

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International Journal of Bifurcation and Chaos, Vol. 21, No. 4 (2011) 1173–1192c© World Scientific Publishing CompanyDOI: 10.1142/S0218127411028982

TOWARD A LIFESPAN METRICOF READING FLUENCY

SEBASTIAN WALLOTDepartment of Psychology, University of Cincinnati,

ML 0376, Cincinnati, OH 45221-0376, [email protected]

GUY VAN ORDENCenter for Cognition, Action & Perception,

University of Cincinnati, ML 0376,Cincinnati, OH 45221-0376, USA

[email protected]

Received February 22, 2010; Revised May 26, 2010

Much evidence suggests complexity in cognitive and motor task performances [Gilden, 2001].The present study builds upon this work, treating reading of text as a kind of complex coordi-nation or coupling between reader and reading conditions. Three self-paced reading conditionspresented connect text in units of different sizes: word, phrase, or sentence units, and repeatedlymeasure times between spacebar presses to advance the text. The three conditions reveal differ-ent patterns across the data. These patterns were evaluated using fractal analyses and RecurrentQuantification Analyses to distinguish highly fluent readers, PhD candidates in English litera-ture, from competent but less fluent undergraduate readers.

Keywords : Reading fluency; text reading; recurrence quantification analysis; fractal analysis.

“. . . to completely analyze what we do when we read would almost be the acme ofa psychologist’s achievements, . . . to unravel the tangled story of the most specificperformance that civilization has learned in all its history.”

[Huey, 1908]

1. Introduction

Whether reading a newspaper, a ballot, or the fineprint of a mortgage policy — competent reading isessential for success and well being in modern soci-eties. Reading is the foundation of elementary andhigher education, and the gateway to most kindsof employment, all the professions, and to a mean-ingful and independent life. Yet, despite its centralplace in modern society, more than a century ofresearch on reading has failed to yield a metric forgauging reading fluency that can generally contrast

different socioeconomic groups, different languages,or readers across different ages and at different lev-els of education.

On the one hand, to be called a fluent reader,a person must be well able to understand writ-ten text, to readily comprehend connected text andgrasp its meaning. On the other hand, fluency alsoimplies an effortlessness in the act of reading —written text is understood by the reader fairlyeasily, as a fluent reader can progress through atext quickly and flexibly. So, a minimal definition

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1174 S. Wallot & G. Van Orden

of reading fluency might encompass the termscomprehension, effortlessness, flexibility, and —superficially — reading speed.

The best predictors of reading fluency are rapidnaming or reading practice, yet reading fluencyis typically studied after it is achieved, so it isunclear how acquisition of fluency is related toits predictors. In this regard, reading fluency isnot sufficiently gauged by reading speed, nor sum-mary comprehension scores, or even vocabularybecause these measures do not reliably pick out flu-ent readers. For example, hyperlexic reading savantscan read aloud quickly yet understand nothing,whereas compensated developmental dyslexics existwho cannot accurately read a text aloud but havegood text comprehension (e.g. [Van Orden et al.,1990, 2001], are reviews).

Word identification in reading is crucial forreading acquisition, but it is not wholly predictiveof reading fluency. Also, while oral reading fluencyis predictive of reading comprehension of elemen-tary and junior high school readers, the relation-ship is weak for adults [Fuchs et al., 2001]. Thenature of adult reading fluency remains largely amystery. A critical gap in this respect is the lackof a metric that can capture the pattern of flow insilent reading. It is this concern that inspired thepresent study. Here, we begin to examine whethertime-series measures of Recurrence QuantificationAnalysis (RQA), together with fractal analyses,may characterize adult fluency and close this gap.

The present study departs somewhat from pre-vious efforts to study reading and is in that regardadmittedly exploratory, but also innovative in theuse of RQA to examine reading of connected text.RQA allows a quantitative analysis of time orderedrepeated measures, and we use RQA to analyzerepeated measures of self-paced reading times, com-paring performance between PhD candidates inEnglish Literature and freshman undergraduates.The RQA quantities are estimated from a recur-rence plot of the data-series. The recurrence plot isobtained through a method of time-delayed phase-space reconstruction and projection into higherdimensional space [Mane, 1981; Takens, 1981]. Sev-eral quantities based on the recurrence plot can beestimated, revealing information about the dynam-ics of the data series, including stability, complexity,and transitions between epochs of chaos and order(e.g. [Marwan et al., 2002; Webber & Zbilut, 2005]).

To complement the analysis of text readingthat follows, we also employ methods of fractal

estimation in time ordered reading data — manystandard experimental procedures used to examinecognitive and motor performance, including read-ing performance, have produced data that exhibitfractal signatures, as statistically self-similar fractaltime (e.g. [Gilden, 2001; Holden, 2002]). Additionalevidence exists that the fractal dimensions of cog-nitive and motor performance, estimated with scal-ing exponents, change with learning, development,skill acquisition and task difficulty ([Van Ordenet al., 2011] is a review). Thus fractal analysesare of potential interest to examine reading fluencyas well.

In the next section we discuss a problem thatconcerns the measurement of reading fluency on acharacteristic scale, such as reading speed. Then wedescribe the present method of a self-paced readingtask, the data that were gathered, and the resultsof traditional reading time analyses. Following that,we apply fractal estimation and recurrence quantifi-cation analysis to distinguish the different modes oftext presentation in simple or multiple readings ofthe same text by adult readers with different levelsof college education.

2. The Measurement Problem

All previous metrics to evaluate reading perfor-mance have assumed that a characteristic scale ofreading performance exists. The more abstract logicthat requires this assumption is a logic of concate-nated effects [Michell, 1999]. Concatenated effectsare those that share a common timescale and thatunfold in a time ordered fashion on that timescale.Thus, to read aloud a printed word, the compo-nents and subcomponents of sensation, perception,reading, and articulation are assumed to concate-nate their effects like a row of time-ordered fallingdominos, each affecting the next in its turn.

The abstract logic of concatenated effects justi-fies ordinary contrasts between the average times toread aloud, for example. Yet reading aloud is doneby a brain and body in which ubiquitous feedbackprocesses compose the nervous system, and in whichsimultaneous afferent and efferent processes controlthe eyes and mouth at the sensorimotor periph-ery of the reader. Moreover, feedback dynamicsself-organize rapid and even instantaneous changesacross the nervous system [Kelso, 1995], which putsthe nervous system on an entirely different range oftimescales than the time course of repeated mea-surements of behavior [Van Orden et al., 2011].

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Reading Fluency 1175

If this organization may dictate assumptions, thenthe measurement problem may be less one of tim-ing dominos, and more one of characterizing loopsand levels of interdependence in entangled cognitivephenomena [Bell, 1999].

The linguistic structure of a written text mayalso motivate loops and levels of interdependencein reading behavior. When words are read in suc-cession they influence each other in complicatedways. Conventionally, exacting laboratory controlsare used to strip away the complication, and sim-ple laboratory tasks and measurement proceduresare chosen to minimize task effects. Nonetheless,even the simplest reading tasks discover compli-cated interactions in which the interacting factorsmay either amplify, reduce, or even eliminate eachother’s effects. Merely presenting two words in suc-cession can be enough to create complicated inter-actions, due to their relation in meaning, spelling,pronunciation, or in more than one of these.

For example, a key-press response in a simplereading task, to indicate that the word pepper isindeed a word (with respect to English spelling) willbe about 48 msec faster (on average) if pepper is pre-ceded by the word salt (compared to a control con-dition that precedes pepper by an unrelated wordsuch as loan [Neely et al., 1998]). This is a largeeffect, given that a single word is easily read withinabout 200 msec from first sight. However, if salt ispresented twice in succession, in the same task, justbefore pepper appears, the large facilitation effectvanishes [Balota & Paul, 1996; Neely et al., 1998].If this was merely an isolated oddball finding then itmight be of little consequence, but all simple read-ing tasks reveal such complicated nonlinear patternsof interaction among the factors that reading scien-tists study (see [Bargh, 2006; Pickering & Ferreira,2008], for reviews and discussions).

A slight variation in a laboratory readingcontext — the introduction of a new factor intoan experimental paradigm — and the entire land-scape of reading effects can change [Van Orden &Kloos, 2005]. Nonetheless, the default assumptionin all this research has been that the impact of acontributing factor to reading, whether the prop-erty of a text or of the reader, will be additiveand proportional to its magnitude. A less skilledreader should require proportionally more time andeffort on the same text, and a more difficult textshould require proportionally more time and effortto read. But reading may comprise a heterarchy ofoverlapping and interacting capacities, such that

different combinations may even compensate fordeficiencies, insofar as reading speed or comprehen-sion are concerned.

The measurement problem as we see it maystem from the absence of a characteristic scaleof reading. Related concerns have arisen in otherareas of cognitive research where compensatorydata procedures have been proposed (e.g. [Faustet al., 1999; Fisher & Glaser, 1996]). The pro-cedures are patches or workarounds within thecommon practice, however, that skirt narrow prob-lems, none proving sufficiently reliable or generalto replace the common practice. An alternativewould be to use scale-free measures [Gottlob, 2007].Scale-free measures are invariant under scale trans-formation. For example, normative measures, suchas z-scores, become scale-free after one subtractsfrom each score the population mean and dividesby the standard deviation. But normative scalesare not inherently scale-free and the same assump-tion about concatenated effects must yet be true forconventional analyses.

Nonetheless, the suggestion to use scale-freemeasures appears to be the right suggestion, so longas the measured phenomena are inherently scale-free. This rationale stands behind our use of scale-free fractal analyses and Recurrence QuantificationAnalysis (RQA) and allows us to relax the assump-tions of linearity and proportionality of effects. Thenonlinear measures can be highly robust [Riley &Turvey, 2002; Webber & Zbilut, 1994, 1996, 2005;Zbilut & Webber, 1992] and have been used suc-cessfully to evaluate other cognitive and behavioralphenomena where multiple factors interact in a pre-sumably nonlinear fashion (e.g. [Shockley et al.,2007; Riley & Clark, 2003]), as we hypothesizeabout reading.

3. The Reading Data

We collected data in a self-paced reading task, muchused in psycholinguistic studies of language andreading. In this self-paced reading task, the readeradvances through a text by pressing the space-bar of a keyboard. The times between spacebarpresses estimate reading times of the text units.The reading times we collected were sampled froma single story divided into text units that wereeither word units, phrase units, or sentence units.Each time a participant reader pressed the space-bar, the next unit of text in sequence appeared onthe computer screen, so text accumulated on the

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screen either word by word, phrase by phrase, orsentence by sentence.

The participant readers were 24 (PhD candi-date) graduate students of English Literature, and24 freshman undergraduates, attending the Univer-sity of Cincinnati. All reported being unfamiliarwith the story they read and had normal or cor-rected to normal vision. We assumed that the grad-uate students were more fluent readers overall, butthe specific expectation with respect to the presentexploratory study was that they may exhibit reli-able differences in reading performance from under-graduates. Additionally, 12 of the graduate studentsand 12 of the undergraduates read the story morethan once. Text repetition effects are among themost reliable and pronounced effects in laboratoryreading tasks (e.g. [Gilden, 2001; Holden, 2002])and reports exist of changes in fractal dimensionwith task repetition (e.g. [Wijnants et al., 2009]).Differences in reading skill between graduate stu-dents and undergraduates, as well as the repetitionmanipulation supply a kind of backdrop of ordinaryreading effects within which to situate the results ofthe new analyses. Again, we are mostly concernedwith producing standard reading performances thatcan be examined further using estimates of scalingexponents (fractal dimensions) and also RecurrenceQuantification Analysis.

The story read by participants in our investi-gation was The Arelis Complex by DeGrado [2003].This story is about the fictive intergalactic politicsof the Arelians. The Arelians were nearly wiped

out previously in a conflict with another civiliza-tion. Star ship officer Drakh Norh, charged withthe safety of the Arelian’s home planet, overseesthe interception of an unmanned alien space ves-sel. The vessel is traced back to a “blue planet”whose inhabitants had been deemed incapable ofsuch technology. Officer Drakh concludes eventuallythat the alien race may develop into a threat andleads a war fleet to destroy the inhabitants of the“blue planet”. The attempt fails, however, leavingthe Arelians facing an uncertain future.

The Arelis Complex consists of 13 930 words,1696 phrases, and 1042 sentences. Each phrase wasa sequence of words demarcated by any punctua-tion (comma, period, colon, semicolon, parenthesis,question mark, exclamation mark, or dash). Textunits were presented in Times New Roman font(13.5 pt.) on a standard computer monitor, pacedby the reader’s spacebar presses. The graduate andundergraduate participants read the story whilebeing seated before the computer monitor, pressingthe spacebar to bring text to the screen. Figure 1illustrates the self-paced reading procedure.

Reading the story took between 30 min and80 min, depending on the individual. Participantswere compensated for their participation in classcredit and cash. After reading the story each readercompleted an exam, of which they had been fore-warned, to assess story comprehension and memory.The exam required a written summary of the storyplot, indicating characters and their roles in thestory, plus a multiple-choice sentence completion

Fig. 1. Illustration of the self-paced reading task for sentence-units.

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task. Items for the sentence completion task cov-ered the entire story.

4. Average Reading Times

We expected that graduate students could be fasterreaders on average than undergraduates (239 msecversus 271 msec for word units, 1757 msec ver-sus 1915 msec for phrase units, and 2534 msecversus 3655 msec for sentence units). Also readerswho read the story only once would read moreslowly on average than those who read it multi-ple times (267 msec versus 243 msec for word units,2137 msec versus 1535 msec for phrase units, and3682 msec versus 2507 msec for sentence units). Andwe expected that the average reading times forword units would be much shorter than the aver-age reading times for multi-word phrase or sentenceunits (M = 255 msec; SD = 50 msec, for words,M = 1835 msec; SD = 591 msec, for phrases, andM = 3095 msec; SD = 1402 msec, for sentences,F (2, 45) = 13.62, p < 0.001). These expectationswere all borne out.

A more informative effect appears in Fig. 2as a three-way interaction among graduate versusundergraduate X phrase versus sentence units Xone versus multiple readings (F (1, 24) = 4.79, p <0.05). The benefit to graduate students’ averagereading time of reading the story more than onceis most pronounced when they are presented withphrase units (F (1, 12) = 2.20, p = 0.16). In con-trast, undergraduate readers benefit from multiplereadings in their average reading times to sentences(F (1, 12) = 2.65, p = 0.13).

These simple main effects of one versus multi-ple readings, in the phrase- and sentence-unit con-ditions, would likely have been statistically reliablewith a larger sample size of readers. At present,however, these contrasts between one and multiplereadings are between different participants readingthe story with different text units than their firstreading, and any statistical contrast comparing dif-ferent participants in different conditions will haveless statistical power than a contrast between thesame individuals in the different conditions.

The graduate versus undergraduate distinction,our speculative fluency distinction, appears to bemost salient in differences between the phrase-unitand sentence-unit conditions. The salient differ-ences between these larger text unit conditions isreplicated and clarified by the nonlinear analysesthat follow.

(a) Reading times (words)

(b) Reading times (phrases)

(c) Reading times (sentences)

Fig. 2. Average reading times and standard errors for(a) word-units, (b) phrase-units and (c) sentence-units.Response times are grouped by readers (PhD candidates andundergraduate students) and number of readings.

5. Power Spectral Analysis

Figure 3 illustrates a spectral analysis of one par-ticipant’s repeatedly measured word-unit readingtimes. The outcome of the analysis is a log–log spec-tral plot of the decomposed data series. The slope

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(a) (b)

Fig. 3. Example of the estimation of scaling in word unit response times. (a) 8192 word reading times (normalized). (b) Log–logspectral plot with least square regression line.

of the fitted, least square, regression line estimatesa scaling relation that can be used to quantify thefractal dimension of the pattern of variation acrossthe data. The negative slope −α = −0.66 in Fig. 3corresponds to a scaling exponent of α = 0.66,which lies between the scaling exponents of ideal-ized white noise (slope = 0, scaling exponent ofα = 0, fractal dimension = 1.5) and idealized pinknoise (slope = −1, scaling exponent of α = 1, frac-tal dimension = 1.2).

Scaling exponents of human performance havebeen widely studied, providing a background inwhich to situate new outcomes. For example, self-paced tapping of a key alone, without reading,yields scaling exponents close to that of Fig. 3 onaverage, though possibly a bit closer to α = 1.Repeatedly measured simple reaction times yieldscaling exponents very close, on average, to α =0.66 (Mean α = 0.66, SD = 0.22, see [Van Ordenet al., 2003]). Were we to reorder the words fromthe story, present them individually in a randomorder, and record the naming times word by word,generating a trial series of naming times, the aver-age scaling exponent would be closer to the α =0 of white noise (Mean α = 0.29, SD = 0.04,see also [Van Orden et al., 2003]). These absolutescaling exponents tend to be relatively uninforma-tive by themselves, however. Human performancesproduce a wide range of scaling exponent valuesthat depend upon tradeoffs among the integrity ofsystem dynamics, the task demands, the partici-pant skills, and the availability of other constraints.Tradeoffs make it difficult to interpret absolute val-ues of exponents, and encourage manipulations toinduce changes in scaling exponents that are more

revealing in their direction of change [Van Ordenet al., 2011].

Spectral analyses like that portrayed in Fig. 3,together with standardized dispersion analysesand detrended fluctuation analysis, were used toestimate scaling exponents and fractal dimen-sion for each time series. The methods all entailworkarounds because they are linear methods, atheart, that are used here to analyze nonlinear phe-nomena. Each method has weaknesses that anothermethod compensates for. When all goes well, theoutcomes of the three analyses are redundant, asthey were in the present data. Because they wereredundant, we report the detailed results of thescaling exponents from the spectral analyses exclu-sively. Data were preprocessed only as necessary, assuggested in [Holden, 2005].

5.1. Scaling exponents acrosstext units

Figure 4 presents summary results of the spectralanalyses. As is apparent in Fig. 4, when the storywas presented in word units, the corresponding dataseries exhibited 1/fα scaling exponents much closerto α = 1 than in the other conditions. The α = 1scaling relation was less present in sentence read-ing times and even less so in the phrase readingtimes, and a reliable trend was observed across theseconditions, away from α = 1 and toward α = 0(F (2, 36) = 24.60, p < 0.001).

We conducted surrogate data analyses to testwhether the scaling exponents we obtained from thereading time data differed reliably from α = 0. Sur-rogate data were created by shuffling the order of

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Fig. 4. Average scaling exponents and standard errors of word units, phrase units, and sentence units across all groupsof readers.

the data-series, thus destroying the temporal struc-ture of the data while preserving mean values andstandard deviations. We shuffled each participant’sdata once to create yoked pairs of surrogate ver-sus original data series to be contrasted with eachother. A statistical test using the scaling exponentsof the original data, compared to their surrogates,revealed an interaction effect between reading units(i.e. word, phrase, sentence) and ordered versus sur-rogate data series (F (2, 36) = 21.05, p < 0.001).

Planned contrasts found that reading timesin the word unit condition produced relativelyhigher scaling exponents (Mean α = 0.52;SD =0.20), compared to other conditions. The substan-tially higher scaling exponents indicate a substan-tial difference in how the word unit pacing affectedreading. One possible source of different scalingexponents would be inherent differences among thedifferent text units. Although the word and sentencelengths from Arelis Complex lie well in the rangeof standard English prose [Fengxiang, 2007; Sigurdet al., 2004] they may yet differ in variety from eachother. The various words and sentences differ inlength, for example, and sentences vary more unsys-tematically than words. Word units vary by numberof letters, and words in the story ranged from oneletter in length to 16 letters (M = 4.56;SD = 2.38).Sentence units vary by their number of words, andsentences in the story varied from one word to50 words in length (M = 13.36;SD = 7.89).

Reading times are partly due to the physicallength of a given text unit. If the wider variationacross sentence lengths is also more unsystematic,it would yield less systematic reading times andscaling exponents closer to α = 0 [Holden et al.,2010]. Effectively, unsystematic changes in reading

times are perturbations to the spectral analysesthat bias the estimates of scaling exponents in thedirection of random white noise. We tested for dif-ferential bias effects of variation in length for word,phrase, or sentence lengths by contrasting the text-ordered counts of number of letters in words, andnumber of words in phrases and sentences, con-ducting spectral analyses on these data-series. Thescaling exponent for the number of letters in eachword was α = −0.03, the number of words inphrases yielded a scaling exponent of α = 0.15,and sentences yielded α = 0.18. None of these val-ues could be distinguished reliably from α = 0 insurrogate analyses conducted using 20 surrogatesof each data series. In contrast, the word and sen-tence reading times yielded scaling exponents reli-ably different from their surrogates and α = 0 (allt(6) > −3.89, p < 0.05). Thus, the pattern of scal-ing exponents across these text units is not due todifferences in surface variation of length.

There are surely differences in addition tolength among the three text units and those differ-ences could also affect the pattern of reading times.As we already noted, the absolute estimates of scal-ing exponents in human performance are not usu-ally informative by themselves due to confoundedsources of bias in the estimate. We next turn tothe more informative patterns of change in scalingexponents associated with our manipulations.

5.2. Differences among scalingexponents

In the present study, readers entrain to the struc-ture of a story. Story structure includes any instanceor source of systematic or unsystematic change in

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the progression of the story, as well as in the pre-sentation conditions of the story. In the latter case,the previous variation in the unit lengths of words,phrases and sentences becomes a powerful source ofunsystematic change. Unit lengths could not be dis-tinguished from random noise in the previous surro-gate analyses, for example, and sources of randomnoise will greatly reduce scaling exponents towardα = 0 [Holden et al., 2010].

When the present analyses discover scalingexponents different from α = 0 (and soon theoutcomes supporting recurrence, determinism, andattractor strength) they do so against a backgroundof random perturbations that might have over-whelmed any structure in the performance. In thislight, the scaling exponents for phrase unit read-ing times only differed reliably from α = 0 forgraduate readers, reading the story more than once(t(6) = −4.02, p < 0.05). Otherwise the variationacross reading times to phrase units did not differfrom white noise, so perhaps phrases are subopti-mal linguistic units for reading, producing unsys-tematic reading times and perturbing the spectralanalysis. Among other things, phrases are relativelymore ambiguous in meaning, for instance, comparedto sentences.

While phrases may be suboptimal readingunits, graduates students nevertheless producedstatistically reliable fractal structure in multiplereadings. Other work has shown that practiceand improved performance on novel cognitive ormotor tasks moves scaling exponents away from theα= 0 of random patterns and toward the α = 1 oflong-range correlated, fractal behavior as practiceappears to do for phrase units. However, only theelite PhD candidates in English Literature showthe benefit of practice, which they also produced intheir faster reading times to phrase units in multiplereadings. Thus we may see in this result the greatercapacity of the graduate student readers to entrainto story structure presented in an unusual form,phrase by phrase. It would be interesting to explorefurther the number of readings of an identical textbefore undergraduate readers show this same degreeof entrainment to phrase unit presentations.

We asked one undergraduate to read the storyfour times, each time presenting phrase units oftext. The consequent changes in scaling exponentswere correlated with number of readings in the rightdirection (r = 0.48), and the maximum of α = 0.13was in the ball park of the graduate student scal-ing exponents in multiple readings, but surrogate

analyses did not distinguish either of her four read-ings reading times from random noise.

The sentence and word unit conditions didnot produce reliable differences in scaling expo-nents, neither for graduate versus undergraduate

(a) Alpha estimates (words)

(b) Alpha estimates (phrases)

(c) Alpha estimates (sentences)

Fig. 5. Average scaling exponents and standard errors for(a) word units, (b) phrase units and (c) sentence units.Scaling exponents are grouped by readers (PhD candidatesand undergraduate students) and number of readings.

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readers nor for single versus repeated readings (allF (1, 12) < 2.64 — see Fig. 5). Nonetheless the aver-age scaling exponents of word unit reading timeschange in the same direction, toward α = 1, forboth graduate students and undergraduates. Scal-ing exponents to sentence units, by contrast, trendaway from α = 1 toward α = 0 (although under-graduates vary widely in the scaling exponents ofmultiple readings).

Scaling exponents appear to gauge the coordi-nation of participants with the temporal demands oftasks, and coordinations more in synch with a newtask are also closer to α = 1 [Holden et al., 2010;Kloos & Van Orden, 2010]. In the present self-pacedreading task, enhanced coordination could mean atleast two different things, an enhanced capacity ofparticipants to entrain to the linguistic structureof the story, or an enhanced strategy of spacebarpressing to advance through the text.

Entrainment may apply to graduate studentswho produce a more reliable fractal pattern in mul-tiple readings. Word units on the other hand mayencourage strategic spacebar pressing, a hypothesisthat will become more salient across the remaininganalyses. One possibility is that participants canusually read individual words faster than they canadvance the text by pressing the spacebar. If so,then it is spacebar presses, not words, that are rate-limiting as participants advanced the story word byword.

6. Recurrence QuantificationAnalysis (RQA)

The unprocessed data were submitted to RQA.RQA parameters were estimated for each data setindividually. Mutual-average information was usedto estimate the delay parameter, which ranged fromone to 54, and false-nearest-neighbor analysis wasused to estimate the embedding dimension param-eter, which ranged from three to 11, using recom-mended procedures from Webber and Zbilut [2005].The radius parameters for each individual readers’data set was adjusted to produce 2% recurrence,which makes comparisons between readers possible.

Figures 6–8 portray results from each of thereading units for the RQA quantities of %DETer-minism and MAXLine. %DET is computed fromthe number of diagonally adjacent points in therecurrence plot divided by the total number ofrecurrent points, and estimates the degree of orderin the data, the extent to which readers fall into

rhythms of sorts across text units. MAXL is thelength of the longest chain of adjacent, diagonal,recurrent points and estimates the strength of thestrongest attractor. MAXL estimates the degree ofstability in the reading times and in the coordi-nation between the participant and the self-pacedreading task.

Reliable differences were found between read-ing times to the word units, phrase units, andsentence units, respectively, in the overall level of%DET (F (2, 45) = 147.35, p < 0.001) and MAXL(F (2, 45) = 49.31, p < 0.001). Reading timesto word units exhibited a much higher percent-age of deterministic structure and stronger attrac-tion to stable reading times compared to phrasesand sentences, which may be further evidence thatword units induce a different reading strategy thanphrases or sentences.

6.1. Word units

Despite the fact that word properties change fromword to word, and that the story context changes aseach new word appears, the estimated reading timesof word units appear relatively uniform in their pat-tern over time. Figure 6 displays the results for wordunits of %DET and MAXL and the high values for%DET and MAXL in word reading suggest a pre-ponderance of orderly, repeated, equivalent, read-ing times in the word unit condition. Participantsappear to discover a strategy of space bar pressingto advance the text, that is relatively unreflectiveof reading itself.

Word reading times are expected to be ratelimiting of spacebar presses, as the logic of self-paced reading experiments dictates, but the oppo-site appears to be true. Apparently the executionof a spacebar press usually takes more time thanthe time it takes to read a single word, so spacebarpresses are the effective rate limiting behavior. Thisis a concern because word unit presentation is thetypical mode of presentation in self-paced readingexperiments. This discovery also presents an oppor-tunity because the strategy distinguishes graduatestudents from undergraduates.

Although %DET did not differ reliably betweengroups of readers or repeated readings of thetext (all F (1, 12) < 1.71), MAXL reveals a sta-tistically reliable 2 × 2 interaction (F (1, 12) =10.85, p < 0.01), as can be seen in Fig. 6(b).Graduate students’ space bar presses became lessstrongly attracted in multiple readings to the

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(a) RQA %DET (words) (b) RQA MAXL (words)

Fig. 6. Reading performance to word units of text in (a) average %DETerminism and (b) average MAXLine (with standarderrors) by graduate versus undergraduate students reading the story once or multiple times.

strategic rhythm of space bar presses to advance thetext. Undergraduate readers change in the oppo-site direction to become more strongly attracted torhythmic pressing to advance the text. These oppo-site effects of multiple readings for graduate versusundergraduate readers, are generally comparable toother findings concerning less skilled versus moreskilled, fluent behavior.

For instance, perhaps the more fluent graduatestudent readers relax their strategic voluntary con-trol of spacebar pressing into a least effort, moreflexible, but less systematic form of control. Havingread a story more than once, they do not require thesame degree of voluntary effort to read the storyagain or to advance the text while reading. Stud-ies comparing more or less skilled performance ofother tasks have discovered a similar outcome usingscaling exponents as the outcome variable ([VanOrden et al., 2011], is a review). Initially, in skill

acquisition, there is a strong correlation betweenskill and scaling exponents. Greater skill equals scal-ing exponents that converge toward α = 1 (e.g.[Wijnants et al., 2009]). In the most highly skilledperformance, however, the performance of so-calledautomatic behaviors, scaling exponents appear tofind a place of “least effort”, retreating from α = 1to a value in the direction of α = 0. Scaling expo-nents may back off from α = 1 to increase flexibility,for instance, as skill reduces the need for voluntarycontrol [Kloos & Van Orden, 2010].

This fluency hypothesis explains the perfor-mance of undergraduates as well. Undergradu-ates show an effect opposite to graduate students,becoming more stably attracted to their strategyof advancing the text in multiple readings. Theyhave not yet reached the pinnacle of flexible read-ing fluency that graduate students have achieved.Consequently, undergraduate readers require more

(a) RQA %DET (phrases) (b) RQA MAXL (phrases)

Fig. 7. Reading performance to phrase units of text in (a) average %DETerminism and (b) average MAXLine (with standarderrors) by graduate versus undergraduate students reading the story once or more than once.

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(a) RQA %DET (sentences) (b) RQA MAXL (sentences)

Fig. 8. Reading performance to sentence units of text in (a) average %DETerminism and (b) average MAXLine (with standarderrors) by graduate versus undergraduate students reading the story once or more than once.

voluntary control of reading and advancing the textin all conditions and actually benefit from multiplereadings toward a more orderly, controlled, strategyof spacebar presses to advance the text.

6.2. Phrase units

In contrast to the results from word units, phraseunits are a sufficiently unnatural mode of text pre-sentation that all readers have an opportunity toincrease their task skills in self-paced reading. Con-sequently, both graduate and undergraduate read-ers exhibit more order in the pattern of readingtimes in multiple readings [i.e. increased %DET inmultiple readings of the text, F (1, 12) = 15.03, p <0.01, and no reliable interaction effect, as portrayedin Fig. 7(a)], and both graduate and undergraduatereaders are more strongly attracted to the orderlypattern of reading times in multiple readings [i.e.increased MAXL in multiple readings of the text,F (1, 12) = 4.66, p = 0.052, and no reliable interac-tion effect, as portrayed in Fig. 7(b)]. This specula-tion agrees as well with the outcome of the analysesof scaling exponents, that phrase unit presentationswere the most disruptive of the fractal pattern ofcoupling between reader and text in self-paced read-ing. Recall that the spectral analyses only found afractal pattern of coupling in the reading times ofthe more fluent graduate student readers, and thenonly in multiple readings.

6.3. Sentence units

When presented with the more natural text unit ofsentences, highly fluent PhD candidates in EnglishLiterature can read more flexibly and with lesseffort than undergraduates, and benefit little or

not at all from multiple readings. This outcomefor reading times to sentence units again reinforcesour speculation that undergraduates are less fluentreaders who enhance their skill in the self-pacedreading task in multiple readings, which we see as astronger more stable pattern in the self-paced read-ing times of sentence units. With sentence unit pre-sentation, PhD candidates do not gain appreciablyfrom multiple readings, while undergraduates pro-duce more orderly and stable sequences of readingtimes in multiple readings (i.e. visible increases inaverage %DET and MAXL, see Fig. 8, that are sta-tistically reliable in %DET, F (1, 12) = 11.99, p <0.01). This outcome is also the source of a reli-able main effect of multiple readings on %DET,(F (1, 12) = 11.94, p < 0.01), which appears tobe localized (marginally) in undergraduate readingtimes (F (1, 12) = 3.36, p = 0.092).

7. Cross Recurrence QuantificationAnalysis (CRQ)

Cross-recurrence analysis was developed to inves-tigate the shared dynamics of two systems thatmay be revealed in their respective repeated mea-surements [Shockley et al., 2002]. In the presentstudy we used CRQ to examine the shared dynam-ical structure among different readers who readthe same text under the same conditions. So, forinstance, we can ask whether two undergraduatesproduce shared patterns of change in repeated mea-surements because they read the same text, advanc-ing it identically, unit by unit in spacebar presses.

The abduction behind this analysis is that read-ers may entrain to a text in self-paced reading,and shared dynamics are detected in CRQ due to

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the common text. The CRQ analysis of repeatedlymeasured reading times used %REC, the percent-age of reading times located in the phase space (ofz-scores) that are nearly identical, %DET, the per-centage of recurrent points that fall on the samediagonal, and MAXL, the longest line of recurrentpoints on the same diagonal. All three quantitiesmay gauge the strength of shared entrainment inself-paced reading. Each condition included fourreaders and we examine all possible pairings, whichyield 4!/(2! ∗ (4 − 2)!) = 6 possible pairings in eachcell of identical reading conditions.

Every data series was z-transformed before sub-mitting the data to CRQ to control for differences inaverage spacebar press times on the shared dynamicstructure of each time-series. To explore differencesin percent recurrence (%REC), the parameters fordelay, dimension and radius were fixed to the aver-age values derived from the individual fittings ofRQA. To explore differences in %DET and MAXL,

the radius parameter was adjusted to equate crossrecurrence (again at 2%) across every pair of par-ticipants’ paired data series. Cross recurrence mustbe equated because %DET and MAXL are directlyaffected by differences in the percentage of recur-rent points. As with RQA, the overall magnitudes ofthe measures %REC (F (2, 69) = 27.02, p < 0.001),%DET (F (2, 69) = 31.84, p < 0.001), and MAXL(F (2, 69) = 84.26, p < 0.001) were greater for wordunit conditions compared to phrase unit and sen-tence unit conditions (see Figs. 9–11).

7.1. Word units

Graduate students produce largely idiosyncraticdispersions of reading times to word units and thusshare less recurrence overall, compared to under-graduates [i.e. less %REC of spacebar press timesbetween paired graduate students than betweenpaired undergraduates, F (1, 20) = 15.49, p < 0.001,

(a) CRQ %REC (words) (b) CRQ %DET (words)

(c) CRQ MAXL (words)

Fig. 9. Reading performance to word units of text in (a) average %RECurrence, (b) average %DETerminism and (c) averageMAXLine (with standard errors), between reading times of pairs of graduate students versus pairs of undergraduate students,reading the same story either once or multiple times.

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(a) CRQ %REC (phrases) (b) CRQ %DET (phrases)

(c) CRQ MAXL (phrases)

Fig. 10. Reading performance to phrase units of text in (a) average %RECurrence, (b) average %DETerminism and (c) averageMAXLine (with standard errors), between reading times of pairs of graduate students versus pairs of undergraduate students,reading the same story either once or multiple times.

see Fig. 9(a)]. Nonetheless, despite less recurrenceoverall and fewer opportunities in which to discoverorder, paired graduate students share more orderlyand entrained patterns of reading times the firsttime they read the text, drifting away from eachother into strongly attractive, idiosyncratic pat-terns in multiple readings. Paired undergraduatesproduce reading times that recur (are equivalent)for fully 35% of word units, on average, in theirfirst reading, but a shared order among these sharedvalues only emerges in multiple readings, in whicha strongly attractive pattern of shared performancebetween paired undergraduates is present (i.e. reli-able 2 × 2 interaction effects were found betweengraduate versus undergraduate readers X singleversus multiple readings in both %DET, F (1, 20) =10.25, p < 0.01, and MAXL, F (1, 20) = 6.02,p < 0.05).

Either undergraduates are more stronglyentrained to the text in multiple readings or they

refine their spacebar tapping strategy for advancingthe story. The latter possibility agrees with theirslightly faster and more tightly dispersed spacebarpressing times [Fig. 2(a)] and the apparent changetoward α = 1 in undergraduate’s average scal-ing exponents [Fig. 5(a)]. The statistically reliablereduction in %REC [(F (1, 20) = 8.66, p < 0.01), seeFig. 9(a)] may even imply that the strategy of space-bar pressing has become more independent from thestructure of the text in multiple readings, reflectingmore exclusively the shared stable strategic pat-tern of advancing the text. Thus, either the textentrains more of undergraduate readers’ behaviorin the same way in multiple readings (compared tograduate students) or undergraduates hit on moresimilar strategies for pacing their spacebar presses.The latter hypothesis is in line with our previousresults. The strategy of using spacebar presses toadvance the text becomes less reflective of readingtimes in multiple readings. The common strategy

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(a) CRQ %REC (sentences) (b) CRQ %DET (sentences)

(c) CRQ MAXL (sentences)

Fig. 11. Reading performance to sentence units of text in (a) average %RECurrence, (b) average %DETerminism and(c) average MAXLine (with standard errors), between reading times of pairs of graduate students versus pairs of under-graduate students, reading the same story either once or multiple times.

is refined in multiple readings becoming the basisfor increases in shared order and stronger attrac-tion to shared patterns in paired undergraduates’performances.

7.2. Phrase units

We have speculated that phrase units are not opti-mal units for text presentation in the self-pacedreading task. The outcome of the CRQ analysesbears this out because no reliable effects of readingfluency or multiple readings were observed. If mean-ingful patterns emerge across phrase unit readingtimes they do not distinguish paired graduate stu-dents’ performance from paired undergraduates andthey are not affected by single versus multiple read-ings of the text (i.e. for %REC all F (1, 20) < 1.10,for %DET all F (1, 20) < 1.84, and for MAXL allF (1, 20) < 2.58, see Fig. 10).

7.3. Sentence units

We have suggested from previous results that sen-tences are optimal units for self-paced readingand that graduate students are clearly more fluentreaders than undergraduates. In the sentence unitcondition, the quantities of shared patterns of per-formance between graduate students remain con-stant across multiple readings. The entrainment totext that they share does not change with multi-ple readings (t(10) = 1.14, p = 0.28 for %REC,t(10) = 0.06, p = 0.96 for %DET, t(10) = 1.27, p =0.23 for MAXL). Constant results across single ver-sus multiple readings also agree with the resultsfrom individual RQA analyses of sentence unit read-ing times, which also found little change of gradu-ate student performances in multiple readings. Thismakes sense if graduate students are at the perfor-mance ceiling of reading fluency, which we can seemost clearly once the presentation units are right

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for revealing fluency in self-paced reading. Sentenceunits are natural units of story structure and theyare rate limiting compared to spacebar pressing.

The present sample of undergraduate read-ers are less fluent readers than the sample ofPhD students in English literature. By less fluent,we mean that the undergraduates have a greatercapacity for change in reading performance. Inthe CRQ analyses they show a shared capacityfor change, and multiple readings reveal this extracapacity for shared changes in paired undergrad-uate performances. The advantage they gain inmultiple readings makes sense if we imagine thatthe paired undergraduates better entrain to thecommon text, which produces a greater propor-tion of shared structure and stronger attractionto the shared structure in sentence reading times[i.e. an increase in shared %DET in multiple read-ings, t(10) = 4.85, p < 0.001, see Fig. 11(b), andan increase in shared MAXL in multiple readings,t(10) = 1.48, p = 0.17, see Fig. 11(c)].

8. Discussion

A logic of concatenated effects has guided readingresearch for over 100 years. This guiding logic is oneof divide and conquer, seeking to isolate effects that,in turn, identify the basic mental building blocksessential to reading fluency. The present alternativestrategy is to unravel and describe complex patternsof interdependence in data, to quantify changes inthe interactions between readers and texts. In thepresent study, we find evidence of complex higher-order relationships in the dynamics of story reading,discovered in the patterns of reading times. Basedon these results, we put forward two speculativehypotheses:

First, the three text units used in the self-pacedreading task — words, phrases, or sentences —impose different constraints on reading performanceand yield patterns of reading times that refer jointlyto task demands and readers. Although all threeinvolve reading, they reflect reading differently inthe reading time data they produce — so differ-ently that they cannot be equated along a com-mon quantitative dimension. Task demands in thesethree conditions are sufficiently different that theyessentially create three different tasks.

Second, PhD candidates in English Literature aremore fluent readers than freshman undergrad-uate students; the graduate students displayed

qualitatively different reading performance acrossthe three text-unit presentation conditions, andbetween single and multiple readings of the story.We summarize the basis of these conclusions next.

8.1. Task differences

Reading performances of the three types of textunits (words, phrases, and sentences) reveal qualita-tive differences in long-range correlational structure(i.e. fractal dimension), as well as dissociativechanges in participants’ performance over readingunits and multiple readings. Yet the ordinary goal oftask contrasts is to find their common core. Presum-ably the common core would refer to reading itself,distinct from the idiosyncrasies of reading tasks.Alternatively, why not take the complicated pat-terns that performance reveals closer to face value?In doing so, we may suggest that reading itselfchanges among the three tasks. No reading processis shared identically across the three tasks, at leastnone is revealed in the data.

Conditions that advance the text in word unitsdiffer greatly from both phrase unit and sen-tence unit conditions. The fractal pattern acrossspacebar press times is much stronger for wordunit presentations. As we already suggested, theprominent fractal pattern is consistent with the ideathat spacebar pressing takes longer, on average,than word reading times. The average spacebarpress time of roughly 250 msec to word units is notmuch longer than average simple reaction times,for instance, when participants are dedicated exclu-sively to producing a rapid response. On this basis,we interpreted the spacebar press to be rate lim-iting; the spacebar press primarily shapes perfor-mance across word reading trials, not the otherway around. The likely effect on spacebar pressingperformance by text and word properties is to occa-sionally perturb the pattern of spacebar pressingsuch that it departs toward slower reading times.This might happen to rare words or in difficult pas-sages of text, but it cannot have happened too oftengiven the average pressing time.

Moreover, undergraduate readers fall into anincreasingly rigid mode of responding, as theyentrain more stably to spacebar pressing taskdemands. Perhaps they see the task as emphasiz-ing a rigid pace to reveal word units, dealing withthe consequences as they come, as concerns read-ing the story. This may explain why undergrad-uates share more stable dynamic structure across

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spacebar press times in multiple readings, wherethe text is now familiar. Graduate students do notperform an identical task, however; they do not dis-cover so rigid a pace. In contrast, graduate studentsadapt more flexibly to the word unit conditionsand their performance exhibits a less stable, moreflexible mode of spacebar pressing, also close inspeed to simple reaction times. Altogether then self-paced reading of word units exhibits unique dynam-ics compared to the other reading conditions andbetween graduate and undergraduate readers.

Conditions that advance the text in phraseunits differ from sentence unit conditions, aswell. The prominent fractal pattern of word unitconditions is absent in almost all phrase unit condi-tions, and only differs from surrogate data in mul-tiple readings by graduate students. Local detailsof phrase units themselves dominate reading times,such as the number of words that compose eachphrase. For instance, although lacking the higher-order structure that nonlinear analyses reveal, thelinear correlations between phrase lengths and read-ing times were statistically reliable (average r2 =0.44 for undergraduates first reading and r2 = 0.37in multiple readings; average r2 = 0.43 for gradu-ate students first reading and r2 = 0.50 in multiplereadings).

Perhaps the close reading of phrases is neces-sary because phrases are more ambiguous than sen-tences — i.e. reading the phrase “Drakh knew itmeant time away from his family,” provides a basisto foster expectations about what will follow, butis by no means uniquely predictive of content orlength of the phrase that will follow. Also the prac-tical meaning of the phrase depends on what fol-lows thereafter (e.g. time away from his family couldbe something joyful, sorrowful, or simply unim-portant). Garden-path sentences are a prominentexample of such “feedback-loops” in text compre-hension, where ambiguity in one part of a sentenceis resolved through a word or phrase that comes latein the sentence (e.g. [Frazier & Rayner, 1982]). Sen-tence surprise endings might perturb on-going com-prehension of the story, when presented in phraseunits, requiring a closer reading in self-paced phraseunit conditions.

Dependencies between sentences exist as well,of course, which is the basis for higher order storystructure. Also, presently, the fractal pattern of per-formance is more prominent in sentence unit thanphrase unit conditions, so sentences are not giventhe close reading, to the same degree as phrase

units. In the next section, we discuss results fromsentence unit conditions that distinguish graduatestudent and undergraduate readers in fluency — atleast that is our hypothesis. Please note, however,we do not claim that sentence unit conditions repli-cate the standard reading conditions of continuoustext, or reading in any other context other than self-paced reading of sentence units. Maybe sentenceunits will prove better to distinguish adult fluency,but it could also turn out that word units betterdistinguish fluency in beginning readers.

Our discussion of how the three task condi-tions impose different constraints on participants,hopefully raises some concern about any claimthat a laboratory task is transparent to a cogni-tive process. We conclude, from these and otherresults, that reading performance is always consti-tuted in the light of contextual constraints and taskdemands, and is never transparent to a reading pro-cesses. Contextual constraints are not merely per-turbations of performance that can be minimized,context plays a constitutive role in reading andlanguage comprehension and in the performance ofall tasks that include printed text [Van Orden et al.,1999].

8.2. Reading fluency

Graduate students produced a pattern of scalingexponents consistent with greater fluency in thesentence unit condition; although, admittedly, ourinterpretation relies on what has been learned aboutother cognitive and motor behaviors, and in partic-ular fluent human gait [Van Orden et al., 2011].Presented with novel cognitive and motor tasks,participants’ scaling exponents generally approachα = 1 after much practice. But in adults’ pre-ferred gaits, the most fluent behavior studied todate, scaling exponents fall within a narrowly con-strained range of scaling exponents about α ≈ 0.60.Departures from adults’ preferred gaits, however,whether walking or running, or speeding up or slow-ing down, yield scaling exponents that reapproachα = 1, a finding that is reliably present acrossa variety of gait measurements [Hausdorff et al.,1996; Jordan et al., 2007a, 2007b]. Seemingly, flu-ent gaits find default scaling exponents like thoseof slightly whitened, or partly random, fractal pat-terns. Consequently, flexibility is enhanced at thatsame time that demands for voluntary control inpreferred gaits is reduced [Kloos & Van Orden,2010].

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Fluent reading may also find default scalingexponents that are slightly whitened. Yet preferredgait is usually measured on a treadmill, whichreduces uncontrolled sources of perturbation, togive a clearer default picture of fluent gaits. Here,however, reading time measurements were taken asthe story accumulated, in units that changed inlength randomly, in a pattern of change statisti-cally equivalent to white noise. Thus the superficialdefault for entrained reading times is a randomsignal; which reading times, of both graduate andundergraduate readers, track reliably (e.g. for sen-tence lengths and reading times, r2 = 0.64 andr2 = 0.58 for graduate student’s first and multi-ple readings, respectively, and for undergraduatesr2 = 0.58 and r2 = 0.54). Nevertheless, graduatestudents’ and undergraduates’ scaling exponents tosentence-units were reliably different from α = 0(see Fig. 5); so sentence reading times do not sim-ply reflect the default surface properties of text.

When reading sentence units, graduate studentand undergraduate readers differ after the first read-ing, as scaling exponents of graduate students movecloser to α = 0 in multiple readings. In contrast,when word or phrase units are presented in multi-ple readings, scaling exponents of graduate studentschange in the same direction as those of undergrad-uates, toward α = 1. The fact that graduate stu-dents’ change toward α = 0, when reading sentenceunits, does not stem from a closer reading of sen-tences with multiple readings; the random patternof sentence lengths is more strongly correlated withreading times in first readings for instance, as noted.Thus the change may reflect a greater capacity toflexibly entrain to the story structure, yet anothersource of perturbation to reading times, despite theodd presentation mode of one sentence unit at atime. This conclusion draws heavily on the analogywith fluent gait, of course; fluent reading expressesflexibility in a more whitened scaling exponent.

Flexibility implies more behavioral options tochoose from to accomplish the same task, or toadjust reading behavior online, and will thus resultin more varied and variable outcomes. The subtleflexibility of expertise has not been captured in tra-ditional studies [Dreyfus, 1992]. In linear analyses,for example, the data features of flexible outcomeswill not be seen as positive facets of performance.They will appear superficially to be no change (flex-ible adjustments to sustain performance), instabil-ity (multiple means or ways to produce successfuloutcomes), or possibly nonstationary data outcomes

(multiple choices among strategies). The data out-comes of the graduate student readers, when read-ing sentence units, illustrate this kind of patternthroughout.

For instance, the primary characteristics of themore fluent graduate students include stable read-ing times of sentence units, scaling exponents thatbecome more idiosyncratic in multiple readings,and RQA and CRQ variables in sentence read-ing that show little or no change from single tomultiple readings. By comparison, when undergrad-uates read sentence units they produce the contrast-ing positive or null changes in the same variables,including faster reading times, more determinism,and equivalent or stronger attraction to the surfacestructure in multiple readings. We interpret thesedifferences between undergraduates’ and graduatestudents’ performances to indicate that the under-graduate participants have a greater capacity forimprovement toward reading fluency.

Additional evidence is present in contrastsamong sentence unit versus word and phrase unitconditions in graduate student performance, wheregraduate students appear more like undergraduatesin word and phrase unit conditions, although notidentical. Reading phrase units, for example, grad-uate students and undergraduates are qualitativelysimilar, changing in the same direction in multiplereadings, making positive or null gains in speed andstability of reading times. Also, in word unit con-ditions, neither graduate students nor undergrad-uates change appreciably in reading times (space-bar presses are rate limiting) and both producescaling exponents that change toward α = 1 inmultiple readings, consistent with gains in skill intheir spacebar-tapping text-advance strategy. Yetthe RQA and CRQ results suggest that under-graduates simply become more stable and morestrongly attracted to a strategic rhythm of tap-ping, to advance the text, whereas graduate stu-dents appear more flexible in using this strategywith multiple readings, and more idiosyncratic intheir patterns of responding.

Undergraduate reading performance increasesin stability with repeated readings, showing a latentcapacity to become more fluent, despite good com-prehension. And, as noted, comprehension scoresdo not reliably distinguish adults’ fluency [Has-brouck & Tindal, 2006]. Thus gains toward expertfluency are gains toward flexible, effortless, imme-diate accommodation of text structure. Fluent con-trol of behavior by experts is not only flexibly

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skilled, but also partly off-loaded to the availableconstraints of the tools and tasks in question, whichfor gait would include the steady pace of the tread-mill, and which for reading would include the storystructure. This emerging picture of fluent behavioris reminiscent of Martin Heidegger’s phenomenol-ogy of “ready-to-hand”, to describe tools and tasksthat are transparent to one’s intentions of use —the available constraints to the mind and body aretransparent at their interface to the required con-straints of the world, like hand in glove, so to speak[Dotov et al., 2010].

Thus, reading the story text in sentence-unitsseemed to situate graduate student readers best todemonstrate characteristics of reading fluency, as“ready-to-hand”, especially in contrasts with wordand phrase units. For instance, graduate studentsread phrase units more quickly in multiple read-ings, but not so sentence units in multiple readings.Given sentence units, graduate readers are suffi-ciently fluent in the first reading to perform at ceil-ing, “ready-to-hand”. Nonetheless, a more abstrusetext might have made them look like they gain insentence reading fluency in multiple readings, per-haps, as the phrase-unit conditions do, and this fluid“now you see it, now you do not” aspect of fluencyappears to be inevitable. Fluency must be measuredand measurements conflate the capacities of read-ers with the demands of reading tasks (cf. [Holdenet al., 2010; Van Orden et al., 2010]).

8.3. What next?

In designing this exploratory study, we naturallymade choices about where to start that limited thescope of the present research. One choice was tocontrol for text by using a single story in all con-ditions and examine readers at different skill levels.An obvious extension of the present study wouldbe to examine the same readers in all conditions,including texts that differ in difficulty. Variationsin difficulty of text might be particularly suited toilluminate the relationship between the dynamicsof the reading process, effort (or effortlessness) inreading, and actual text comprehension. We havenot yet conducted such a study.

Another important extension would be toexamine reading of children in the process of acquir-ing literacy (through cross-sectional and longitu-dinal investigation) or children who suffer fromdevelopmental dyslexia. In that regard, MaartenWijnants and Anna Bosman, colleagues at Radboud

University in Nijmegen, have observed changes inscaling exponents toward α = 1 that distinguishdyslexic children from nondyslexic children of thesame age in a word naming task. The scaling expo-nents of dyslexic children were not reliably differentfrom the α = 0 of white noise, the scaling exponentsof nondyslexic children were reliably different in thedirection of α = 1, but not so far in that directionas undergraduate readers performing the same task.

We should also cross-validate our results usingdifferent behavioral measures of reading. A read-ing study that measures eye-movements could pro-duce data amenable to nonlinear analyses. Whileeye-tracking studies of reading have been conductedfor many years, the aims of previous studies andtheir procedures and methods of linear analysis dif-fer decidedly from our approach. Measurement ofreading via eye-movements could also extend tostudies that do not present discrete text units. Wecould evaluate self-paced reading using literally self-paced eye movements. These are all goals that weare currently pursuing.

Finally, research in psycholinguistics has iden-tified many linguistic variables and word propertiesthat influence reading performance. These linguis-tic variables are interesting in the present contextas well, since they are cornerstones of conventionalideas about reading. Thus, how they may modulatethe dynamics of self-paced text reading will alsostipulate further theory development, and we arecurrently expanding our analyses to include promi-nent psycholinguistic variables used previously inreading research. Investigating the impact of thesevariables, as well as their relation to dynamic mea-sures of the reading process will be important tolink our findings to the large body of the existingliterature.

Of course the focus of this exploratory workhas been reading fluency, specifically, not just read-ing performance. Reading fluency develops over thecourse of each individual’s lifetime, from elemen-tary school, to high school, and — as our datasuggest — through university and beyond. Mini-mally, further details of the dynamics of readingbehavior while reading continuous text will fur-ther specify the subtleties of what fluent readingentails. With that goal in mind, we have intro-duced methods of complexity science amenableto study the dynamics of reading behavior. Thepresent modest success, distinguishing readingbehavior of elite PhD candidates in English Liter-ature from competent undergraduate readers, may

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promise refined metrics of reading fluency across thelifespan.

Acknowledgments

We thank Anna Haussmann for helpful commentson manuscript versions of this draft and we thankEleanor Logan for her contribution to data collec-tion. Preparation of this article was supported byNSF Grants to Guy Van Orden (BCS #0642716,BCS #0843133, DHB #0728743).

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TOWARD A LIFESPAN METRIC OF READING FLUENCY