Working Memory, First Language, Second Language, and Mathematics

12 Pages·2016·0.36 MB·Turkish

Working Memory, First Language, Second Language, and
Mathematics: A Study of Relations

Ayşegül OKAY
Yıldız Technical University, Turkey

Özet
Bu çalışma, çalışma belleği (WM), ana dili (L1), ikinci dil (L2) ve matematik arasındaki ilişkiyi
inceler; amacı ile matematik ve L1 başarı daha sonraki L2 öğrenme performansı ile ilgili olup
olmadığını anlamak için; ve eğer öyleyse, WM bileşenleri (yani fonolojik döngü ve merkezi yürütme)
matematik ve dil arasındaki bu ilişkide rol oynar ister. Bu çalışmanın ikinci amacı bilgisayarlı Türk
Okuma Açıklık task.The katılımcıları 60 üniversite öğrencisi olduğunu bulmak oldu. veri 4 önlemler
sayesinde kantitatif toplanmıştır. WM bileşenlerini ölçmek için, bir bilgisayarlı Türk Okuma Dizisi
Görev ve Sayı Dizileri Görev; Matematik ve L1, Yükseköğretim Sınav puanları Geçiş başarıyı ölçmek
için; ve L2 başarıyı ölçmek için, hazırlık okul sınav puanları kullanılmıştır. Korelasyon L2 öğrenme
performansına matematiksel başarı (1) ilişki ortaya SPSS Sürüm 18.The veri analizi ile analizleri
yapılmıştır; ve (2) L2 öğrenme performansı L1 başarı ilişkisi. Bulgular matematik o başarı gösterir ve
L1 daha sonra L2 öğrenme performansı ile ilgilidir ve WM dil ve matematik arasındaki ilişki
açısından önemli bir faktördür. ; L1 için değil - Özellikle, fonolojik döngü özel fonksiyonlar L2 ve
matematik için temel bir öneme sahiptir ancak matematikte - merkez yürütme belirli fonksiyonları ise
L1 ve L2 daha önemli bir rol oynar.
Abstract
This study investigates the relationship among working memory (WM), first language (L1), second
language (L2), and mathematics; with an aim to understand whether achievement in mathematics and
L1 is related to performance in later L2 learning; and if so, whether WM components (i.e.
phonological loop and central executive) play a role in this relationship between mathematics and
language. A second objective of this study was to devise a computerized Turkish Reading Span
Task.The participants were 60 university students. The data were collected quantitatively through 4
measures. To measure WM components, a computerized Turkish Reading Span Task and a Digit Span
Task; to measure achievement in mathematics and L1, Transition to Higher Education Examination
scores; and to measure achievement in L2, the preparatory school exam scores were used. Correlation
analyses were performed via SPSS Version 18.The data analysis revealed (1) a relation of
mathematical achievement to performance in L2 learning; and (2) a relation of achievement in L1 to
performance in L2 learning. The findings indicate that achievement in mathematics and L1 is related
to performance in later L2 learning, and WM is a significant factor in terms of the relationship
between language and mathematics. In particular, the specific functions of the phonological loop are
of pivotal importance for L2 and mathematics – but not for L1; whereas the specific functions of the
central executive play more crucial role in L1 and L2 – but not in mathematics.
Keywords: working memory, first language, second language, mathematics, Turkish Reading Span
Task

Introduction
Language and mathematics are domain-specific abilities which require higher-order cognitive
functions that are unique to humans. Although first language (L1) is learned by all typically
developing children, and is acquired without explicit teaching; a later foreign/second language
(L2) after childhood can only be learned through extensive teaching. Just as for learning L2, a
specialized and intensive education is also required for the development of mathematical
skills. A crucial domain-general cognitive mechanism that has been constantly associated
with cognitive functions like language and mathematics is working memory (WM). Conway,
Jarrold, Kane, Miyake, and Towse (2008) state that WM is “fundamentally a form of
memory, but it is more than memory, for it is ‘memory at work’ encompassing a number of
components that perform several cognitive functions responsible for the storage and the
41
Turkish Journal of Psychology

executive control of information” (p.3). Alloway (2006) asserts that WM plays a key role in
supporting children’s learning over the school years, and beyond this into adulthood. This
means that a domain-general ability like WM seems to be closely related to domain-specific
abilities like mathematics (Alloway & Passolunghi, 2011; Holmes & Adams, 2006; Raghubar,
Barnes, & Hecht, 2010) and language (Fuchs et al., 2005, 2008, 2010; Purpura, Hume, Sims,
& Lonigan, 2011). In some studies, general language skills seem to be the predictor of, and
related to, a variety of mathematical performance across different age groups (Hooper,
Roberts, Sideris, Burchinal, & Zeisel, 2010; Purpura et al., 2011). In their study, for instance,
Reimann, Gut, Frischknecht, and Grob (2013) have shown that deficits in general language
skills or WM can often co-occur and result in broader impairment in mathematical
functioning. In their review, Raghubar et al. (2010) also conclude that WM is indeed related
to mathematical performance in adults and in typically developing children; and cognitive
functions like language might mediate or moderate the relations between WM and
mathematics.
Background to the Study
The most influential WM model has been that of Baddeley and Hitch’s (1974) WM model. In
their model, they proposed a WM model comprising of three components: the central
executive (CE), and two slave systems: the phonological loop (PL) and the visuo-spatial-
sketchpad (VSSP). The CE was represented as a control system of limited attentional capacity
that is responsible for the manipulation of information within WM and for controlling two
subsidiary storage systems: the PL and the VSSP. The PL was assumed to be responsible for
the storage and maintenance of information in a phonological form, while the VSSP was
dedicated to the storage and maintenance of visual and spatial information (Repovš &
Baddeley, 2006). Based on a number of empirical findings a fourth component, the episodic
buffer (EB), was later added to the model (Baddeley, 2000). The EB is assumed to be a
limited capacity store that is capable of multi-dimensional coding, and that allows the binding
of information to create integrated episodes. Overall, WM is viewed as a comprehensive
system that unites various short- and long-term memory (STM/LTM) subsystems and
functions (Baddeley, 1986).
As regards the research carried out with an aim to investigate the relationship between WM
and academic achievement in various subjects; it is clear that WM plays a prominent role in
mathematical achievement of children (Holmes & Adams, 2006; Miller & Bichsel, 2004;
Purpura & Ganley, 2014; Smedt et al., 2009; Zheng, Swanson & Marcoulides, 2011). Other
empirical investigations have consistently implicated WM as a central deficit in children with
mathematical disabilities (Andersson & Lyxell, 2007; D’Amicoa & Guarnera, 2005; McLean
& Hitch, 1999; Peng, Congying, Beilei & Sha, 2012).
Regarding first/native language (L1), WM also plays a fundamental role in children in terms
of vocabulary (Baddeley, Gathercole & Papagno, 1998; Gathercole, Service, Hitch, Adams, &
Martin, 1999; Gathercole, Willis, Emslie, & Baddeley, 1992); and spoken language (Adams
& Gathercole, 2000); and in adults in terms of verbal achievement (Daneman & Carpenter,
1980; Friedman & Miyake, 2004); and reading comprehension (Cohen-Mimran & Sapir,
2007; Turner & Engle, 1989).
Second/foreign (L2) language and WM is also related in terms of vocabulary acquisition
(Gupta & MacWhinney, 1997; Masoura & Gathercole, 1999, 2005), reading comprehension
(Alptekin & Erçetin, 2010; Daneman & Carpenter, 1980; Payne, Kalibatseva & Jungers,
2009; Turner & Engle, 1989); listening comprehension (McInnes, Humphries, Hogg-Johnson
42
Turkish Journal of Psychology

& Tannock, 2003); speech production (Finardi & Prebianca, 2006; Fortkamp, 1999); written
language production (Kellogg, Olive & Piolat, 2007; Swanson & Berninger, 1996) and
overall language proficiency (Gilabert & Muñoz 2010; Kormos & Sáfár, 2008).
The current study
Despite this large number of studies investigating the relationship between WM, language,
and mathematical achievement; they have certain limitations which need further research.
First of all, in terms of the relationship between mathematical achievement and WM, most of
the studies are carried out with young children (at primary school), very young children (4-5
years old), or children with specific disorders. Secondly, while the CE is generally found to be
influential in mathematical achievement, the role of the PL remains unclear. Some studies
support the role of the PL (Andersson & Lyxell, 2007; Peng, et al. 2012; Rasmussen &
Bisanz, 2005; Zheng, et al. 2011); whereas others claim that the PL is not the major factor in
explaining arithmetical difficulties (D’Amicoa & Guarnera, 2005; Holmes & Adams, 2006;
McLean & Hitch, 1999).
Concerning the relationship between WM and L2, studies are relatively fewer and the
findings about the relation between the PL and L2 are controversial. For example, in some
studies, the measures of the PL (i.e. simple span tasks, such as digit or word span) do not
correlate with language measures (Daneman & Carpenter, 1980; Turner & Engle, 1989);
whereas in other studies it does (Baddeley, Papagno & Vallar, 1988; Masoura & Gathercole,
1999, 2005). Besides, measures of the CE (i.e. complex span tasks, such as Reading Span
Task or Operation Span Task) also show, though rarely, non-significant correlations with
language skills. For example, in Fortkamp’s (1999) study, Speaking and Reading Span Tests
did not correlate with any L2 fluency task.
As for the relationship between L1 and L2, Palladino and Cornoldi (2004) assert that children
with foreign language learning difficulties typically seem to have problems with L1 learning;
and Hulstijn and Bossers (1992) also support the relationship between L1 and L2
achievement. Besides, the studies on the relationship between language and mathematics are
usually carried out with young or very young children, and they usually investigate the early-
developmental stages of L1 and mathematics, or L2 and mathematics. In other words, the
number of studies done with young adults who are beyond the acquisition process of L1 and
advanced concepts in mathematics are limited. Furthermore, the studies investigating the
relationship among L1, L2, mathematics, and WM are scarce.
Therefore, this study tries to contribute to this research stream by exploring the relationship
among WM, language, and mathematics in young adults. To this end, our first aim is to find
out whether general achievement in mathematics and L1 is related to the performance of later
L2 learning in young adults (i.e. preparatory school students at university), whose first/native
language is Turkish (L1) and who have started to learn English as their second/foreign
language (L2). The second aim is to explore whether there is a relationship between WM
components (namely the PL and the CE) and achievement in L1, L2, and mathematics.

Method
Participants
60 voluntary students (24 males and 36 females) participated in this study. Their ages ranged
from 18 to 23 (M = 19.55; SD = 1.17). They were students in an English preparatory school
of a university in Turkey. The first/native language (L1) of all students was Turkish. All
participants were classified as monolingual on the basis of a questionnaire examining their
43
Turkish Journal of Psychology

language history. They all started learning English as a foreign language (L2) in the prep
school and they were at elementary (CEFR A1) level. Participants gave their written informed
consent prior to their inclusion in the study.
Measures
Digit span task (DSPAN). In this task, the participants were presented with a series of digits,
beginning with three digits (e.g., 8, 3, 4) and then they were immediately required to recall the
digits in the order they were presented. When they did this successfully, they were given a
longer list (e.g., 9, 2, 4, 0). The length of the longest list a person could remember was that
person's digit span. In this study, a computerized version of the DSPAN
(www.cambridgebrainsciences.com) was administered to the participants in a computer lab by
the researcher, who informed the participants and showed them a demo before they did the
task.
Reading span task (RSPAN). Different from the original RSPAN of Daneman and
Carpenter (1980), a revised and computerized version of this RSPAN was created from
scratch in this study. The sentences were written in Turkish – not translated - and the number
of the words in sentences ranged from 14 to 17. The number of letters in these sentences
ranged from 91 to 98.
In the original RSPAN, the participants were required to remember the last words of each
sentence. Newer RSPAN tasks (see Conway et al. 2005; Kane et. al, 2004; Sanchez et. al,
2010; Unsworth, Heitz, Schrock, & Engle, 2005) require participants to recall unrelated letters
instead of the last words of the sentences. Therefore the RSPAN devised specifically for this
study also required participants to remember (consonant) letters (i.e. F, G, T, Z, etc.) instead
of words.
Additionally, grammaticality judgment was ensured. Of 60 sentences, half was written
sensical and half nonsensical so that the participants had to determine whether the sentence
was sensical or nonsensical. As an example, whereas “Yaşlı adam balkonda oturmus çayını
yudumlarken, birden karsı apartmandan bir çocuğun kendisine el salladığını farketti.” (As the
old man was sitting on his balcony and sipping his tea, he realized a boy waving at him from
the opposite house) is a sensical sentence; “Sabahları erken kalkıp evimizin karsısındaki
yemyesil tepside yürüyüs yaptığım zaman kendimi çok iyi hissediyorum.” (I feel myself very
good when I get up early and take a walk in the very green tray opposite our house) is
nonsensical. Nonsensical sentences were created by simply changing one word (e.g. “park” to
“tray”) from an otherwise meaningful sentence. There are many studies which use sensicality
judgement in their studies (Alptekin & Erçetin, 2010; Conway et al. 2005; Kane et. al, 2004;
Sanchez et. al, 2010; Unsworth et al., 2005).
Finally, the RSPAN was devised as a computer program so that a time restriction (maximum
7 seconds for each sentence) could be ensured. This computerized and Turkish version of the
RSPAN was administered to the participants in a computer lab by the researcher who
informed them and showed a demo to them before they did the task.
The procedure was approved by the Ethics Committee of the University.
L1 and mathematics. To measure their achievement in L1 (Turkish) and mathematics, the
participants’ scores in Transition to Higher Education Examination were used. It is a
standardized exam for the admission to higher education in Turkey administered by
Measuring, Selection and Placement Center. The only way to enter a university in the Turkish
education system is through this exam, in which there are 4 subject areas; namely, Turkish,
44
Turkish Journal of Psychology

Social Sciences, Mathematics, and Physical Sciences; and 40 multiple choice type questions
each.
In the Turkish component of the Transition to Higher Education Examination (THEET from
here afterwards) there are 40 multiple choice questions, assessing the students’ verbal ability
in their L1. The content of the questions are based on grammar, vocabulary, and reading.
Listening, writing, and speaking skills are not measured in this exam.
In the Mathematic component of the Transition to Higher Education Examination (THEEM
from here afterwards) there are 40 questions assessing the students’ ability in advanced
concepts of mathematics and geometry.
L2. To measure their L2 (English) verbal achievements, the participants’ Achievement Exam
(AE) scores at the preparatory school were used. This exam is administered once at the end of
each term. It comprises of reading, writing, listening and use of English parts and in total
accounts for 100 points. However, because the content of the questions in THEET is based on
grammar, vocabulary, and reading; only the grammar, vocabulary and reading parts of AE
were taken into account.

Results
In this part, firstly, the descriptive statistics will be provided for all measures (RSPAN:
Reading Span Task, DSPAN: Digit Span Task, THEET: Transition to Higher Education
Examination Turkish Component, THEEM Transition to Higher Education Examination
Mathematics Component, and AE: Achievement Exam).
In the second part of this section, in order to describe the strength and direction of the linear
relationship between the measures, the results from the analyses of Pearson product-moment
correlation coefficients (r) will be presented.
General Descriptive Statistics
Descriptive statistics for the results of RSPAN, DSPAN, THEET, THEEM, and AE measures
are provided in Table 1.

Table 1. Descriptive statistics for all measures
M SD Minimum Maximum
RSPAN 43.18 10.09 12 18
DSPAN 7.54 1.50 4 11
THEET 34.81 2.94 25 40
THEEM 29.52 6.61 14 40
AE 75.00 11.59 51.50 97.50

Correlation Analyses
Figure 1 below presents the results from Pearson product-moment correlation analysis, which
was computed to assess the relationship between all variables. There were significant,
positive, and from moderate to strong correlations between all variables except for RSPAN-
THEEM, DSPAN-THEET, and THEET-THEEM.
45
Turkish Journal of Psychology

* p < .05.
** p < .01.
Figure 1: Correlation analyses for all measures.

Discussion
WM and L2: The role of the CE
This study reveals a positive and moderate correlation between RSPAN and AE. which
supports the claim that the CE component of WM plays an important role in L2 achievement.
As Daneman and Carpenter (1980) agree, the CE processes are probably one of the principal
factors determining individual differences in WM span. In one of his recent papers in 2012,
Baddeley analyzes these CE processes by proposing four suggestions about the functions of
the CE (p. 14):
- focusing attention
- dividing attention between two important targets or stimulus streams
- switching between tasks
- interfacing with LTM
These functions of the CE clearly relate to nearly all skills in L2 processing in WM. Hence, it
could be suggested that the correlation found between RSPAN and AE in this study evidently
reflects the relationship between the CE functions and L2 processing in WM.
WM and L2: The role of the PL
This study also shows positive and moderate correlation between DSPAN and AE. Baddeley
et al. (1998) state that the DSPAN measure provides a useful indication of the capacity of an
individual's PL (p. 18). As Baddeley (1998) states, “the PL correlates with the more
conventional measure of digit span” (p. 236). The PL involves “a sub-vocal rehearsal process”
which means silently maintaining the contents of the phonological store (Baddeley, et al.,
1998, p. 167). When answering questions in L2, it is obvious that the participants need to use
this inner-speech function of the PL in order to make sense of the questions they answered,
which also explains the positive and moderate correlation found between DSPAN and AE (i.e.
the PL and L2) in this study.
WM and L1: The role of the CE
46
Turkish Journal of Psychology

As shown in Figure 1, there is a positive and moderate correlation between RSPAN and
THEET (i.e. the CE and L1). Since both THEET and AE measure the same content areas
(reading, grammar and vocabulary), the relationship found between the CE and L2
achievement, thus, is also apparent in the relationship found between the CE and L1
achievement in this study.
WM and Mathematics: The role of the PL
In the present study, we found a strong correlation between DSPAN and THEEM (i.e the PL
and Mathematics).
The correlation between the PL and mathematics might be traced to the interface function of
the PL to LTM. As Baddeley (2012) states, information flows from LTM to the PL, as well as
the reverse (p. 11). From this reciprocal relationship between the PL and LTM, it follows that,
unlike very young children, since most adults readily know the answer to the sum 6+7 or the
product 3x4, without having to follow any form of calculation algorithm, the answers to these
problems are calculated and found by direct LTM access (Logie, Gilhooly & Winn, 1994).
The finding of this study that there is relationship between the PL and mathematics is also
consistent with those of Andersson and Lyxell (2007), Peng, et al. (2012), Rasmussen and
Bisanz (2005), and Zheng, et al. (2011).
WM and Mathematics: The role of the CE
Despite the fact that RSPAN and DSPAN (i.e. the CE and the PL) are strongly correlated with
each other, THEEM showing correlation only to DSPAN but not to RSPAN is noteworthy
(Figure 1). It is generally accepted that number-based WM span measures are more strongly
associated with mathematics than non-numerical span measures, such as those that use words
(i.e. RSPAN in this study). One explanation is that, as Holmes and Adams (2006) explain,
WM and mathematics are linked because the assessments of both involve either number
processing or direct access to numerical information (p. 343). Since the RSPAN measure in
this study consisted of only words and letters, this fact might explain the reason why there
was no correlation between RSPAN and THEEM (i.e. the CE and Mathematics).
Is there a relationship between L2 and Mathematics?
As shown in Figure 1, the correlation analyses in the present study revealed a high and
positive correlation between THEEM and AE (i.e. Mathematics and L2), which means that
there is a strong relationship between mathematical achievement and later L2 learning. At this
point it is important to note that, in the data analyses of the present study, while L2
achievement showed relationship both with the CE and the PL measures of WM;
mathematical achievement showed relationship only with the PL measures of WM (Figure 1).
Taking the previous discussions about these relationships into consideration; the most
important result to be drawn in terms of the relationship between L2 achievement and
mathematical achievement is that the role of the PL is critically important in both L2 and
mathematical achievement, which means that the PL might play a more prominent role than
the CE in the relationship among WM, mathematics, and L2.
Is there a relationship between L2 and L1?
The data analyses in the present study showed a positive and moderate correlation between
AE and THEET scores (i.e. L2 and L1). The correlation found between L1 and L2 (Figure 1)
might indicate that the cognitive functions while processing the first language may have an
impact on the learning processes of the second language. Here, the question arises whether
this relation is language-specific or not. Since the typologies of Turkish and English are
different, it can be argued that a transfer from Turkish (L1) to English (L2) does not seem
47
Turkish Journal of Psychology

possible. This means that a domain-general ability like WM appears to be closely related to
the domain-specific ability of language, regardless of the typology of the languages.
Is there a relationship between L1 and Mathematics?
As it can be seen in Figure 1, no correlation was found between THEET and THEEM, which
means that there is no meaningful relationship between L1 and Mathematics. Taken together,
we found relations of (1) the CE to L1 and L2; (2) the PL to L2 and mathematics; (3) L2 to
mathematics; and (4) L1 to L2. This means that the CE plays a role in the relationship
between L1 and L2, but not in L2 and mathematics. On the other hand, the PL plays a role in
the relationship between L2 and mathematics, but not in L1 and L2. Therefore, it can be
inferred that the reason why there was no correlation between L1 and mathematics in this
study might be traced to the role of the PL.

Conclusion
In this correlational study, we investigated the relationship among WM and achievement in
L1, mathematics, and L2. The main aim of the study was to find out whether WM
components and the achievement in mathematics and L1 are related to performance in later
L2 learning in young adults who are beyond the acquisition process of L1 and of advanced
concepts in mathematics.
The data analysis revealed (1) a relation of mathematical achievement to performance in L2
learning; and (2) a relation of achievement in L1 to performance in L2 learning. These results
indicate that achievement in mathematics and L1 is related to performance in later L2 learning
– regardless of the typology of the languages. In addition, WM has been shown to be a
significant factor in terms of the relationship between language and mathematics. In
particular, the specific functions of the PL are of pivotal importance for L2 and mathematics –
but not for L1; whereas the specific functions of the CE play more crucial role in L1 and L2 –
but not in mathematics.
Overall, we conclude that achievement in mathematics and L1 seems to be associated with
performance in later L2 learning; and WM components appear to underlie each of these high-
order cognitive processes.
Implications
These results have several implications in terms of WM and academic achievement in
general. Shipstead, Hicks and Engle (2012) state that if WM capacity limits performance in
academic areas, then a training program that increases WM capacity should result in
improvements in these areas. Although the studies carried out to find out whether WM
capacity could be improved by training are relatively recent (Holmes & Adams, 2006;
Klingberg, Forssberg, Westerberg, 2002; Klingberg, et al., 2005), they seem promising. In
their comprehensive review, Morrison and Chein (2011), for example, concluded that WM
training can be considered as a tool to enhance general cognitive abilities.
The findings in this study indicate that the growth of WM components (especially the PL in
line with the results of the present study) might result in an increase in achievement of
language and mathematics. Therefore, we believe that training WM and thus increasing the
capacity of its components would also increase achievement in mathematics and language.
48
Turkish Journal of Psychology

References
Adams, A. M., & Gathercole, S. E. (2000). Limitations in working memory: implications for
language development. International Journal of Language and Communication Disorders,
35(1), 95-116.
Alptekin, C., & Erçetin, G. (2010). The role of L1 and L2 working memory in literal and
inferential comprehension in L2 reading. Journal of Research in Reading, 33(2), 206-219.
Alloway, T. P. (2006). How does working memory work in the classroom? Educational
Research and Reviews, 1(4), 134-139.
Alloway, T. P., & Passolunghi, M.C. (2011). The relations between working memory and
arithmetical abilities: A comparison between Italian and British children. Learning and
Individual Differences, 21, 133-137.
Andersson, U., & Lyxell, B. (2007). Working memory deficit in children with mathematical
difficulties: A general or specific deficit? Journal of Experimental Child Psychology, 96,
197-228.
Baddeley, A. D. (1986). Working Memory. Oxford: Oxford University Press.
Baddeley, A. D. (1998). Recent developments in working memory. Current Opinion in
Neurobiology, 8, 234-238.
Baddeley, A. D. (2000). The episodic buffer: a new component of working memory? Trends
in Cognitive Science, 4(11), 417-423.
Baddeley A. D. (2003). Working memory and language: an overview. Journal of
Communication Disorders, 36, 189-208.
Baddeley A. D. (2012). Working Memory: Theories, Models, and Controversies. Annual
Review of Psychology, 63, 1-29.
Baddeley, A. D., Gathercole, S. E., & Papagno, C. (1998). The phonological loop as a
language learning device. Psychological Review, 105(1), 158-173.
Baddeley, A. D., & Hitch, G. (1974). Working memory. In G.H. Bower (Ed.), The
psychology of learning and motivation: Advances in research and theory, 8, 47-89. New
York: Academic Press.
Baddeley, A. D., Papagno, C., & Vallar, G. (1988). When long term learning depends on
short-term storage. Journal of Memory and Language, 27, 586-595.
Cohen-Mimran, R., & Sapir, S. (2007). Deficits in working memory in young adults with
reading disabilities. Journal of Communication Disorders, 40, 168-183.
Conway, A. R. A., Jarrold, C., Kane, M. J, Miyake, A., & Towse, J. N. (2007). Variation in
working memory: An introduction. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake
& J. N. Towse (Eds.), Variation in Working Memory (pp 3-17). New York: Oxford
University Press.
Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R.W.
(2005). Working memory span tasks: A methodological review and user’s guide.
Psychonomic Bulletin & Review, 12, 769-786.
D'Amico, A., & Guarnera, M. (2005). Exploring working memory in children with low
arithmetical achievement. Learning and Individual Differences, 15, 189-202.
Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and
reading. Journal of Verbal Learning and Verbal Behavior, 19(4), 450-466.

Finardi, K. R., & Prebianca, G. (2006). Working memory capacity and speech production
49
Turkish Journal of Psychology

in L2: evidence from a picture description task. Revista de estudos da linguagem, 14(1),
231-260.
Friedman, N. P., & Miyake, A. (2004). The reading span test and its predictive power for
reading comprehension ability. Journal of Memory and Language, 51, 136-158.

Fortkamp, M. B. M. (1999). Working memory capacity and aspects of L2 speech
production. Communication and Cognition, 32, 259-296.
Fuchs, L. S., Compton, D. L., Fuchs, D., Hollenbeck, K. N., Craddock, C. F., & Hamlett, C.
L. (2008). Dynamic assessment of algebraic learning in predicting third graders’
development of mathematical problem solving. Journal of Educational Psychology, 100,
829-850.
Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005).
The prevention, Identification, and cognitive determinants of math difficulty. Journal of
Educational Psychology, 97, 493-513.
Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M.,…
Schatschneider, C. (2010). Do different types of school mathematics development depend
on different constellations of numerical versus general cognitive abilities? Developmental
Psychology, 46, 1731-1746.
Gathercole, S. E., Service, E., Hitch, G. J., Adams, A. M., & Martin, A. J. (1999).
Phonological short-term memory and vocabulary development: Further evidence on the
nature of the relationship. Applied Cognitive Psychology, 13, 65-77.
Gathercole, S. E., Willis, C., Emslie, H., & Baddeley, A. D. (1992). Phonological memory
and vocabulary development during the early school years: A longitudinal study.
Developmental Psychology, 28, 887-898.
Gilabert, R., & Muñoz, C. (2010). Differences in attainment and performance in foreign
language: the role of working memory capacity. International Journal of English Studies,
10(1), 19-42.
Gupta, P., & MacWhinney, B. (1997). Vocabulary acquisition and verbal short-term memory:
Computational and neural bases. Brain and Language, 59, 267-333.
Holmes, J., & Adams, J. W. (2006). Working memory and children's mathematical skills:
Implications for mathematical development and mathematics curricula. Educational
Psychology, 26, 339-366.
Hooper, S. R., Roberts, J., Sideris, J., Burchinal, M., & Zeisel, S. (2010). Longitudinal
predictors of reading and math trajectories through middle school for African American
versus Caucasian students across two samples. Developmental Psychology, 46(5), 1018-
1029.
Hulstijn, J. H., & Bossers, B. (1992). Individual differences in L2 proficiency as a function of
L1 proficiency. European Journal of Cognitive Psychology, 4, 341-353.
Kane, M. J., Hambrick, D. Z., Tuholski, S. W., Wilhelm, O., Payne, T. W., & Engle, R. W.
(2004). The generality of working memory capacity: A latent-variable approach to verbal
and visuo-spatial memory span and reasoning. Journal of Experimental Psychology:
General, 133, 189-217.
Kellogg, R. T., Olive, T., & Piolat, A. (2007). Verbal, visual, and spatial working memory in
written language production. Acta Psychologica, 124, 382-397.