How is anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3 children

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Cognition and Emotion

ISSN: 0269-9931 (Print) 1464-0600 (Online) Journal homepage: http://www.tandfonline.com/loi/pcem20

How is anxiety related to math performance in

young students? A longitudinal study of Grade 2 to

Grade 3 children

Elisa Cargnelutti, Carlo Tomasetto & Maria Chiara Passolunghi

To cite this article: Elisa Cargnelutti, Carlo Tomasetto & Maria Chiara Passolunghi (2017) How is

anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3

children, Cognition and Emotion, 31:4, 755-764, DOI: 10.1080/02699931.2016.1147421

To link to this article: http://dx.doi.org/10.1080/02699931.2016.1147421

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BRIEF ARTICLE

How is anxiety related to math performance in young students? A

longitudinal study of Grade 2 to Grade 3 children

Elisa Cargnelutti

, Carlo Tomasetto

and Maria Chiara Passolunghi

Department of Life Sciences – Psychology Unit “Gaetano Kanizsa”, University of Trieste, Trieste (TS), Italy;

Department of

Psychology, University of Bologna, Cesena (FC), Italy

ABSTRACT

Both general and math-speciﬁc anxiety are related to proﬁciency in mathematics.

However, it is not clear when math anxiety arises in young children, nor how it

relates to early math performance. This study therefore investigated the early

association between math anxiety and math performance in Grades 2 and 3, by

accounting for general anxiety and by further inspecting the prevalent directionality

of the anxiety–performance link. Results revealed that this link was signiﬁcant in

Grade 3, with a prevalent direction from math anxiety to performance, rather than

the reverse. Longitudinal analyses also showed an indirect effect of math anxiety in

Grade 2 on subsequent math performance in Grade 3. Overall, these ﬁndings

highlight the importance of monitoring anxiety from the early stages of schooling

in order to promote proﬁcient academic performance.

ARTICLE HISTORY

Received 9 July 2015

Revised 21 January 2016

Accepted 23 January 2016

KEYWORDS

Math anxiety; general

anxiety; math performance;

math precursors; early

assessment

Basic mathematical skills are regularly used in every-

day life, and their deﬁciency affects both employ-

ment opportunities and socio-emotional well-being

(e.g. McCloskey, 2007 ). As adulthood math compe-

tence is the end result of the math skills acquired

early in life, many studies have sought to identify

the factors responsible for math difﬁculties in

children.

Research in the ﬁeld is mainly focused on those

cognitive abilities that underpin math learning and

are potentially impaired in individuals with math difﬁ-

culties (e.g. Fuchs et al., 2010; Passolunghi, Cargnelutti,

& Pastore, 2014). Conversely, the role of the affective

aspects such as anxiety is frequently neglected or

underestimated when dealing with young students

(e.g. Liew, McTigue, Barrois, & Hughes, 2008). Our

study was aimed at ﬁlling this gap, by longi tudinally

investigating the relation between both general and

math-speciﬁc anxiety and math performance in chil-

dren from Grade 2 through Grade 3.

Anxiety and its relation with academic and

math performance

General anxiety

Anxiety, broadly deﬁned as a disproportional and dys-

functional response to a situation perceived as threa-

tening, is already present in preschool children with

a preva lence of around 10% (Egger & Angold, 2006).

Even though many factors ma y moderate the inter-

play between anxiet y and performance in the aca-

demic context, the negative consequences of

anxiety alone are proven, with particularly damaging

effects in children with learning difﬁculties, typically

more anxious than their no rmall y achieving peers

(e.g. Fisher, Allen, & Kose, 1996).

This trend was observed not simply when referring

to test anxiety, a subtype of anxiety experienced in

testing situations (see Hembree, 1990), but also to

general anxiety. These ﬁndings outline how academic

performance can also be affected by trait dispositions

CONTACT Elisa Cargnelutti [email protected]

Supplemental data for this article can be accessed 10.1080/02699931.2016.1147421.

COGNITION AND EMOTION, 2017

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of the individual, such as general anxiety, and not

merely by factors tightly associated with the academic

context.

Math anxiety

Math anxiety is a distinct subtype of anxie ty which can

be experienced even in the absence of both general

and test anxiety (Hembree, 1990). It is deﬁned as a

negative emotional response occurring in situations

involving math, and can produce stress and avoidance

behaviour (Ashcraft & Ridley, 2005). Math anxiety is

not infrequent, and recent data report it to be experi-

enced at a high degree by approximately 17% of the

population (Ashcraft & Moore, 2009). Its effects tend

to endure over time also causing repercussions on

work choices (Ma & Xu, 2004).

The negative relation between math anxiety and

math achievement has been largely proved, with

high levels of anxiety demonstrated to be linked to

low performance (e.g. Faust, Ashcraft, & Fleck, 1996;

Ma & Xu, 2004). However, math anxiety is typically

monitored from middle school onward, and

assumed to interfere with the execution of complex

arithmetic operations (e.g. Faust et al., 1996). Math

anxiety has been therefore imputed to cause an affec-

tive drop, meaning a decline in performance attribu-

table to its presence rather than to inadequate

competence (e.g. Ashcraft & Moore, 2009).

Nevertheless, alternative accounts are also plau-

sible. Math anxiety may be interpreted as a result −

rather than the cause − of negative math experiences,

poor attainment, and failures (Ma & Xu, 2004). Math

anxiety, actually, may be simultaneously both the

cause and consequence of limited performance (e.g.

Ashcraft & Moore, 2009).

Math anxiety in young children

Even if we assume the link between math anxiety and

math performance to be bidirectional, the onset of

this relation is still almost unexplored. Until recently,

only a handful of studies involved children before

Grade 5. Moreover, outcomes about students during

the ﬁrst grades of primary school are divergent: It is

not clear how and when math anxiety arises, and,

more importantly, when it becomes relevant to math

performance. Some authors have indeed failed to

ﬁnd an early relation betwee n math anxiety and per-

formance. Among them, Thomas and Dowker (2000)

hypothesised an age-dependent relation between

the two variables, expected to surface after the age

of 9. Krinzinger, Kaufmann, and Willmes (2009)

instead proposed the link to possibly emerge only in

individuals with extremely high math anxiety conco-

mitant with very pronounced math difﬁculties.

On the other hand, evidence has also been found

for a signiﬁcant link between math anxiety and math

proﬁciency in the ﬁrst stages of schooling. Wu, Barth,

Amin, Malcame, and Menon (2012) and Wu, Willcutt,

Escovar, and Menon (2014) observed that math

anxiety predicted performance in Grades 2 and 3

even when controlling for general anxiety, and that

some math domains (e.g. those involving reasoning)

were more affected than others. The effects of math

anxiety were also detected in other studies, with

other constructs also proposed to moderate the

relation between anxiety and performance (e.g.

Harari, Vukovic, & Bailey, 2013; Jameson, 2014).

Current study

Given the sparse and contradicting ﬁndings on the

issue, our research was aimed at shedding light on

the relation between anxie ty and math proﬁciency

in the early primary grades. Our ﬁrst purpose was to

verify whether math anxiety, in particular, can

impact math performance even in young children,

and whether a possible reciprocal inﬂuence exists.

We collected data from children attending Grade 2

and subsequently Grade 3, attempting to deﬁne

both concurrent and developmental patterns.

Overall, this study advances prior works in several

ways. First, in contrast to Wu et al. (2012, 2014), we

explored the interplay between math anxiety and per-

formance by means of path analyses, with longitudinal

models aimed at shedding light on the causal path-

ways and prevalent directionality of this link. Second,

expanding upon Krinzinger et al. (2009), we also eval-

uated the role of general anxiety (as in Wu et al., 2012,

2014), in order to see whether math anxiety is inde-

pendent from it, and uniquely linked to math perform-

ance even in early schooling. Further, in contrast to

past research in which only computation was assessed

(Krinzinger et al., 2009; Thomas & Dowker, 2000), we

tested diverse math skills relevant to the early

primary school curriculum, in order to achieve a

more global and robust index of math competence.

In summary, our hypotheses were that math

anxiety, independently from general anxiety, could

impact math proﬁciency very early, with signiﬁcant

negative effects traceable even in Grade 2. Regarding

the directionality of the link, we expected math

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anxiety at this stage to already be both the cause and

consequence of low math performance.

Method

Participants

Two hundred and three children attending Grade 2

were recruited for the study. Children attended 10

different classes across 6 primary schools in Northeast-

ern Italy. These schools were located in urban non-dis-

advantaged areas and were attended mostly by

children from middle-income families. From the

initial sample, three children were excluded because

of neurological diseases, and two for atypical ages

for their grade. The resulting sample included 198 chil-

dren (105 males; mean age = 7 years 7 months).

Of this sample, 80 children (48 males; mean age = 8

years 4 months) were also included in the testing

phase in Grade 3. The remaining students did not par-

ticipate because of not-renewed school consent.

Procedure

The study took place at two different time points: The

second term of Grade 2 (April–May) and the ﬁrst term

of Grade 3 (December). The investigated constructs

(general anxiety, math anxiety, and math compe-

tence) were assessed collectively and on different

days within the same week, by randomly alternating

the order of the tasks.

Self-rating questionnaires were used to assess

general and math anxiety. Teachers’ ratings of chil-

dren’s general anxiety were also collected. This

measure was taken to check for potential discrepan-

cies with the ratings given by children of their affective

states. This was done purposely because general

anxiety, contrary to math anxiety, lacks speciﬁcity

(i.e. it can be experienced in several contexts and

can be determined by different stressors), thus

resulting in less reliable self-evaluations by young

students (White, Oswald, Ollendick, & Scahill, 2009).

Measures

Anxiety

General anxiety. Depression and Anxiety in Youth Scale

(DAYS, Newcomer, Barenbaum, & Bryant, 1994; Italian

ed., 1995). This questionnaire was developed for

youths from 6 years of age onward. Concerning the

self-rating scale (hereafter Anxiety-Self), we partly

modiﬁed the original version by removing or reformu-

lating some items in order to make it more suitable for

younger children (e.g. the sentence “I want to kill

myself.” was removed). The administered scale

resulted in eight items with four response options:

Never, sometimes, often, and always. Scoring ranged

from 0 (never )to3(always). The maximum score was

24 points.

The scale for teachers (hereafter Anxiety-Obs erved)

was kept in the original version and includes seven

statements (e.g. “He/she easily changes his/her

mood.”) with a dichotomous response modality (true

or false). Responses indicating the presence of an

anxiety symptom were scored 1 point, or otherwise

0 points. The maximum score was 7 points.

Math anxiety. Scale for Early Math Anxiety (SEMA,

translated and adapted from Wu & Menon, 2012).

This questionnaire includes 20 items requiring chil-

dren to imagine either having to solve a given math

problem (e.g. “What time will it be in 20 minutes?”),

or to be experiencing common situations occurring

during math lessons (e.g. “Your teacher give s you a

bunch of subtraction problems to work on.”). In both

cases, children had to indicate the level of nervous-

ness they would feel if these conditions were truly

happening.

This version provided four instead of the original

ﬁve response options: Not nervous at all, a little

nervous, somewhat nervous, and very nervous. The

choice was supported by pilot studies showing

pupils’ difﬁculty in selecting between ﬁve different

response options. Each response was scored 0 (not

nervous at all)to3(very nervous

) points, giving a

maximum

score of 60 points.

Math skills

Written computation. This test was developed in two

versions, one for each grade, by referring to the corre-

sponding math textbooks. Both versions are com-

posed of 16 arithmetic computations to be solved

within 10 minutes (additions and subtractions for

Grade 2, all operations for Grade 3). In both versions,

each correct solution received 1 point, giving a

maximum of 16 points.

Word problems (from Giovanardi Rossi & Malaguti,

1994). This test requires children to solve, within 15

minutes, six word-problem questions for Grade 2

(additions and subtractions), and eight for Grade 3

(all operations). Up to 1.5 points were assigned for

each correct answer (1 point for the correct set out

of the expression to be solved, plus 0.5 if also the

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computation procedure was correctly executed). The

maximum score was 9 points for Grade 2 and 12

points for Grade 3.

MAT-2 (from Amoretti, Bazzini, Pesci, & Reggiani,

2007). We administered the module Number, including

a wide spectrum of tasks to be performed within 20

minutes. The module consists of 11 tasks for Grade 2

(e.g. ranking numbers from the smallest, decomposing

numbers) and 13 tasks for Grade 3 (e.g. writing down

numbers in the rank of thousands, solving problems

involving the concepts of expenses and proﬁts).

Each exercise correctly solved was scored 1 point,

with a maximum score of 11 points for Grade 2 and

13 points for Grade 3.

Data analysis

Main statistical analyses were conducted by PAW Stat-

istics 21. AMOS 21 package was used to perform path

analyses. Missing data were imputed using a stochas-

tic procedure, and a maximum likelihood approach

was adopted for model estimation. A bias-corrected

bootstrap procedure with 2000 re-samples was run

to estimate conﬁdence intervals for direct, indirect,

and total effects.

Pertaining to general anxiety, Anxiety-Se lf and

Anxiety-Observed scores were treated separately,

being mildly cor related with each other and, more

importantly, differentially correlated with the other

variables (see Table 1). Concerning math performance,

we computed a unique composite score for each

grade, named Math, by averaging the scores of

Written computation, Word problems, and MAT-2.

Path models were ﬁrst estimated independently for

each grade to test the impact of anxiety on concurrent

math performance. The link causal ordering was

instead inspected in the longitudinal models including

both assessment times. For the deﬁnition of the longi-

tudinal relations, we tested different models with

alternative directionality solutions. All the models

were estimated with each variable in Grade 2

expected to predict the correspondent in Grade 3,

and by taking general anxiety as a covariate, to

control for its non-speciﬁc effects on Math.

In detail, Anxiety-Observed in Grades 2 and 3 was

hypothesised to be linked to correspondent math per-

formance (in Grades 2 and 3, respectively). Despite a

bidirectionality possibly being observed in the relation

between general anxiety and Math, preliminary ana-

lyses conﬁrmed that the statistical ﬁt systematically

favoured models with general anxiety predicting

Math, rather than the reverse. Moreover, given that

Anxiety-Self was not strongly correlated to any other

measure, except for SEMA, we retained only Anxiety-

Observed, in order to reduce the model complexity.

Alternative model comparison

Taking the const raints on the model deﬁnition

described in the data analysis section, we compared

ﬁve alternative models in which we tested the relation

between SEMA and Math in both causal orderings, and

by deﬁning these links as concurrent within each wave,

longitudinal, and cross-lagged. In detai l, the following

models were compared: (a) Model 3.1 (anxiety-driven

model), in which SEMA in Grades 2 and 3 (hereafter,

SEMA_2 and SEMA_3) concurrently predicted Math

scores in Grades 2 and 3 (hereafter, Math_2 and

Math_3), respectively; (b) Model 3.2 (performance-

driven model), in which the reverse paths were

tested; (c) Model 3.3 (mixed model ), with Math_2 pre-

dicting SEMA_2, and SEMA_3 predicting Math_3; (d)

Model 3.4, which tested the reverse mixed solution;

and (e) Model 3.5 (cross-lagged model), in which

SEMA_2 predicted Math_3, via direct effect, and

Math_2 predicted SEMA_3, directly as well, with no

concurrent relations admitted from SEMA to Math

within each grade. In all the tested models, both

SEMA_2 and Math_2 were allowed to longitudinally

predict the corresponding variable in Grade 3.

As the models were non-nested, the traditional

approach for model comparison based on the chi-

square difference value was not applicable. Therefore,

model comparison was based on direct comparison of

indices, such as Akaike ’s Information Criterion (AIC) and

Bayesian Information Criterion (BIC), with lower values

indicating better ﬁt (according to Raftery, 1995, BIC

differences (Δ) < 2, between 2 and 6, and > 6 indicate,

respectively, weak, moderate, and strong evid ence in

favour of the model with the lowest values).

Although the ﬁt indices were from acceptable to

good for all the tested models (for details, see Sup-

plemental Table 1 in “Supplemental Material”),

Model 3.1 and Model 3.3 displayed a better ﬁtas

compared to Model 3.2 and Model 3.4 (ΔAICs and

ΔBICs > 4). Model 3.5, in which only cross-lagged

paths were admitted, globally show ed the worst ﬁt.

Importantly, none of the cross-lagged paths directly

linking SEMA and Math of consecutive grades were

signiﬁcant. In sum, Model 3.1 and Model 3.3 should

be retained as the best-ﬁ tting and more parsimonious

models.

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Table 1. Descriptive statistics, reliability measures, and intercorrelations between all variables.

Descriptive statistics Intercorrelations

Min Max Mean SD Skewness Kurtosis Reliability 1 2 3 4 5 6 7 8 9 10 11

1 Computation_2 0.00 16.00 11.65 4.30 −1.04 0.30 .84

2 Problem

solving_2

0.00 9.00 6.61 2.25 −1.21 1.16 .69 .17*

3 MAT_2 0.00 11.00 7.47 2.25 −0.96 1.54 .74 .32*** .08

4 Computation_3 0.00 15.00 10.06 2.58 0.17 1.08 .88 .10 −.20** −.04

5 Problem

solving_3

0.00 12.00 5.65 3.19 0.34 −0.85 .79 <.01 −.20** −.09 .54***

6 MAT_3 1.00 11.00 6.13 2.31 0.20 −0.38 .80 −.06 .30*** −.12 .65*** .60***

7 Anxiety-Self_2 0.00 20.00 6.89 3.85 0.42 −0.21 .65 .28* .02 .24* −.10 −.09 −.07

8 Anxiety-

Observed_2

0.00 7.00 1.47 1.52 1.03 0.61 .65 .21 .46*** .19 −.25* −.37** −.26* .18

9 SEMA_2 0.00 57.00 14.82 10.57 0.80 0.74 .86 <.01 .04 .61*** −.14 −.22* −.12 .29** .01

10 Anxiety-Self_3 0.00 20.00 7.79 4.69 0.43 −0.58 .84 .13 −.27 −.12 .26* .31** .17 .05 −.35** −.17

11 Anxiety-

Observed_3

0.00 7.00 1.68 1.82 0.94 0.04 .72 .10 −.27 −.18 .34** .35** .35** −.03 −.30** −.18 .43***

12 SEMA_3 0.00 39.00 12.44 8.83 0.95 0.44 .87 .12 −.24 −.21 .31** .31** .36** −.11 −.24 −.27* .38*** .67***

Notes: Min = minimum; Max = maximum; SD = standard deviation; _2 = measure collected in Grade 2; _3 = measure collected in Grade 3.

*p ≤ .05.

**p ≤ .01.

***p ≤ .001.

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Results

Descriptive statistics, reliability measures, and corre-

lations are reported in Table 1. The path analysis

results are described below. We reported the ﬁnal

models we chose on the basis of their robustness

from both the theoretical and statistical viewpoints.

Cross-sectional path models

Concerning the Grade 2 assessment, we reported the

full model entailing the links for all anxiety measures

to math performance. This model, termed Model 1

(Figure 1(a); see Supplemental Table 2 for details),

explained 8% of Math varian ce with a good statistical

ﬁt: CMIN = 0.07, df = 1, CMIN/df = 0.07, p = .80, CFI =

1.000, NFI = .999, TLI = 1.141, RMSEA < .001, AIC =

18.08, BIC = 47.71 (where CMIN is the chi-square

equivalent, NFI the Normed Fit Index , TLI the Tucker-

Lewis Index, and RMSEA the Root Mean Square Error

of Approximation).

Anxiety-Observed appeared as the only variable

directly and negatively accounting for math perform-

ance (β = −.26, p < .001). SEMA did not predict Math sig-

niﬁcantly (β = −.12, p = .10), nor Anxiety-Self (β = .06, p

= .38), whose indirect effect via Anxiety-Observed was

however signiﬁcant (mean = −.09, 95% CI = [−.02, −.17]).

Concerning the Grade 3 assessment, the relations

between the inspected variables are represented in

Model 2 (Figure 1(b) and Supplemental Table 3). As

the model is saturated, we report only AIC and BIC

values as ﬁt indices: AIC = 18.00, BIC = 39.44.

Anxiety measures explained 27% of variance in

Math, and it signiﬁcantly concurred with both

Anxiety-Observed and SEMA (β = −.45, p < .001, and

β = −.29, p < .01, respectively). Although Anxiety-Self

did not act on Math directly (β = .10, p = .18), it

yielded a signiﬁcant indirect effect through Anxiety-

Observed (mean = −.17, 95% CI = [−.05, −.33]).

Longitudinal path models

We report data on the selected longitudinal models.

Model 3.1 is illustrated in Figure 2(a) (with related

values in Supplemental Table 4). Anxiety-Observed

was a signiﬁcant predictor of concurrent Math, stron-

ger in Grade 2 (β = −.36, p < .001 ) than in Grade 3 (β

= −.16, p = .04). With regard to SEMA, its relation to

Math was signiﬁcant in Grade 3 (β = −.21, p < .01),

but not in Grade 2 (β = −.16, p = .12). However, boot-

strap analysis showed that SEMA_2 signiﬁcantly

predicted Math_3 indirectly via Math_2 and SEMA_3

(mean = −.23, 95% CI [−.07, −.38]).

Model 3.3 (see Figure 2(b) and Supplemental Table 5)

was identical to Model 3.1, except for the path linking

Math and SEMA in Grade 2, directed from the former

to the latter, with the reverse path in Grade 3. The

path from Math_2 to SEMA_2 was slightly stronger

than the reverse tested in Model3.1,eventhoughit

only approximated the conventional signiﬁcance

threshold (β = −.19, p = .08). The link between SEMA_3

and Math_3 was instead signiﬁcant (β = −.21, p <.01).

Bootstrap analyses also showed a signiﬁcant indirect

impact of SEMA_2 on Math_3, via SEMA_3 (mean =

−.13, 95% CI = [−.04, −.24]). In sum, math anxiety and

performance in consecutive grades appeared to be

related, but only indirectly. Importantly, part of the longi-

tudinal relation between math performance scores in

consecutive grades was likely to be a function of

related variability in math anxiety.

Discussion

The main purpose of this research project was to

uncover whether affective aspects, such as anxiety,

can be even precociously related to math proﬁciency.

To date, only a few studies examined math anxiety

before Grade 5, with even fewer works adopting a

longitudinal perspective (Krinzinger et al., 2009), con-

trolling for the role of general anxiety (Wu et al.,

2012, 2014), or including a robust index of math com-

petence. This study adds to existing literature in all

these respects by assessing general anxiety, math

anxiety, and math proﬁciency, and by targeting their

causal ordering from Grade 2 through Grade 3.

Both general and math anxiety were tested by self-

rating questionnaires. General anxiety was further

inspected by a questionnaire completed by teachers

(Anxiety-Observed). This was done purposefully for

general anxiety, which young children ﬁnd difﬁcult

to appraise because of its lack of speciﬁcity (see

White et al., 2009), and not for math anxiety, which

was expected to be more easily self-detected (as

also supported by the good reliability indexes). In

agreement with this, Anxiety-Observed and Anxiety-

Self app eared mildly related (see De Los Reyes &

Kazdin, 2005), and presented different correlation pat-

terns. Nonetheless, we judge teachers’ ratings to be a

reliable measure, as already proven (see Tripp,

Schaughency, & Clarke, 2006). Therefore, it is impor-

tant to point out that the discussed results about

general anxiety are those concerning Anxiety-

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Observed. However, the issue remains of the suit-

ability of the self-rating scales in measuring some con-

structs in young students.

Differential impact of anxiety in the two grades

Results from the current study globally highlight the

strong negative link between anxiety and math per-

formance. Interestingly, results from the cross-sectional

models, designed independently for each grade, show

that the combined effect of general and math anxiety

on performance was noteworthy and appreciably

increased from Grade 2 to Grade 3 (respectively, 8%

and 27% of explained variability in math performance).

Nevertheless, whereas general anxiety affected

proﬁciency in both grades, a signiﬁcant direct role of

math anxiety emerged only in Grade 3. These ﬁndings

suggest that the effect of math anxiety may increase

over time (see Thomas & Dowker, 2000), possibly

due to the accumulation of negative experience in

the discipline. However, we cannot exclude the idea

of this relation being strengthened by other factors

intervening in Grade 3, such as the increased

demands of math tests. According to Stevenson,

Hofer, and Randel (2000), this change may also

reﬂect the possibility that the effects of math anxiety

may be overwhelmed by other powerful sources of

inﬂuence at this stage (e.g. teach ers’ and parents’ atti-

tudes, or other general personality aspects).

Irrespective of this, it is important to underline the

ﬁnding that the effect of math anxiety actually

appeared to be independent from that of general

anxiety even in Grade 2, suggesting its precocious

onset and speciﬁcity (as in Wu et al., 2012, 2014).

Longitudinal relations

Longitudinal outcomes indicate that math anxiety

and performance inﬂuence one another, so the

link is very likely to be bidirectional (see Ashcraft &

Moore, 2009). However, whereas i n Grade 2 the

impact of performance on math anxiety was the

strongest (despite not y et being statistically signiﬁ -

cant), the reverse relation emerged in Grade

3. Fur ther, the effect size of math anxiety in Grade

3 was even higher than that of general anxiety. A

possible interpretation of these ﬁndings is that

poor math at tainment can ﬁrstly boost math

anxiety (e.g. Ma & Xu, 2004), which only secondarily

harms math performance, in a sort of vicious cycle.

Even more importantly, math anxiety in Grade 2

appeared to have a signiﬁcant impact, though

Figure 1. Standardised solution for cross-sectional models. Anxiety-Obs = Anxiety-Observed; _2 = measure collected in Grade 2; _3 = measure

collected in Grade 3. Dashed lines indicate links approaching statistical signiﬁcance.

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Figure 2. Standardised solution for longitudinal models. Anxiety-Obs = Anxiety-Observed; _2 = measure collected in Grade 2; _3 = measure col-

lected in Grade 3. Dashed lines indicate links approaching statistical signiﬁcance.

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indirect, on determining future math competence.

Overall, these ﬁndings call for a precocious monitor-

ingofmathanxiety,evenwhenitisnotyetappar-

ently related to attainment, as the early onset of

negative experience towards math is p redictive of

poorer pro ﬁc iency over time.

Limitations of the study and implications

Findings from this study leave some questions open,

concerning in particular the assessment of the affec-

tive states in very young students. For this reason, sub-

sequent investigations are necessary to understand

whether ratings of young children evaluating their

own anxiety are effectively reliable, and how they

relate to those collected from signiﬁcant adults.

Furthermore, results should be corroborated by

inspecting the relation between these constructs on

larger and numerically more homogeneous samples

of participants, especially when dealing with longi-

tudinal data.

Outcomes of the present study are noteworthy in

the way they extend previous ﬁndings on the onset

of the relation between math anxiety and proﬁciency.

By highlighting the strong impact of affective com-

ponents on academic performance in very young stu-

dents, these ﬁndings are important also from an

educational perspective. Promoting successful learn-

ing and preventing drawbacks of poor math proﬁ-

ciency is crucial in different aspects of children’s

present and future life, ranging from occupational

opportunities to self-esteem. Therefore, greater care

should be taken to precociously detect and treat not

only deﬁciencies in cognitive math precursors, as tra-

ditional approaches do, but also negative affective con-

ditions such as anxiety.

This necessity is corroborated by the limited but

interesting data on interventions aimed at increasing

math performance through the reduction of math

anxiety, even in children with math disabilities (see

Furner & Duffy, 2002). Students can be provided with

simple self-instruction strategies to handle their

anxiety, but teachers can also adopt simple strategies,

such as creating a serene learning atmosphere, and

appraising an achieved goal rather than emphasising

failure. Students should not be disparaged in the face

of an error, which should be considered as just a

normal step along the path leading to successful learn-

ing (for recommendations and suggestions, see Furner

& Duffy, 2002).

Disclosure statement

No potential conﬂict of interest was reported by the authors.

Funding

This work was partially supported by the Research Grant “FRA

2014” from the University of Trieste to M.C. Passolunghi.

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