Neurocognitive and Behavioral Predictors of Math Performance in Children With and Without ADHD

Abstract

Objective: This study examined neurocognitive and behavioral predictors of math performance in children with and without ADHD. Method: Neurocognitive and behavioral variables were examined as predictors of (a) standardized mathematics achievement scores, (b) productivity on an analog math task, and (c) accuracy on an analog math task. Results: Children with ADHD had lower achievement scores but did not significantly differ from controls on math productivity or accuracy. N-back accuracy and parent-rated attention predicted math achievement. N-back accuracy and observed attention predicted math productivity. Alerting scores on the attentional network task predicted math accuracy. Mediation analyses indicated that n-back accuracy significantly mediated the relationship between diagnostic group and math achievement. Conclusion: Neurocognition, rather than behavior, may account for the deficits in math achievement exhibited by many children with ADHD.

Keywords

ADHD math achievement neurocognition curriculum-based measurement working memory behavioral attention

Recent estimates suggest that 8.7% of school-aged children meet diagnostic criteria for ADHD (Froehlich et al., 2007). A common area of functional impairment among children with ADHD is poor academic performance (DuPaul & Stoner, 2003; Massetti et al., 2008). Specifically, children with ADHD demonstrate poorer rates of homework completion (Langberg et al., 2010), lower grades (Barkley, Fischer, Edelbrock, & Smallish, 1990; DeShazo, Lyman, & Klinger, 2002; Fergusson, Horwood, & Lynskey, 1993), and higher rates of retention (Barkley, Fischer, et al., 1990; Biederman et al., 1996; Molina et al., 2009) than children without ADHD. Students with ADHD also obtain lower standardized achievement test scores than their grade-equivalent peers (Biederman et al., 1996; DeShazo et al., 2002; Merrell & Tymms, 2001; Molina et al., 2009).

Many students with ADHD have particular difficulty in math (e.g., Nussbaum, Grant, Roman, Poole, & Bigler, 1990). Children with ADHD perform more poorly on standardized math achievement tests (e.g., Biederman et al., 1996; DeShazo et al., 2002; Frick et al., 1991), and complete fewer problems (Barkley, Fischer, et al., 1990; Benedetto-Nasho & Tannock, 1999) and make more errors on math computation worksheets (Benedetto-Nasho & Tannock, 1999; Zentall, Smith, Lee, & Wieczorek, 1994) than typically developing controls. However, the causes and correlates of mathematical difficulties in children with ADHD are not fully understood.

Two likely contributors to poor math performance in children with ADHD are behavioral problems and cognitive deficits (see Figure 1). Children with ADHD exhibit more inattention (Zentall, 1985, 1986, 1990) and evidence more observed off-task behavior and impulsive responding during academic tasks than typically developing controls (Fischer, Barkley, Edelbrock, & Smallish, 1990; Zentall, 1985, 1986, 1990). The majority of studies (e.g., Faraone, Biederman, Weber, & Russell, 1998; Frick et al., 1991; Paternite, Loney, & Roberts, 1996) and a recent meta-analysis (Willcutt et al., 2012) suggest that children with ADHD–predominantly inattentive type (ADHD-I) and children with ADHD–combined type (ADHD-C) both evidence decreased academic achievement compared with controls. Parent and teacher ratings of inattention, present in children with ADHD-I and ADHD-C, are negatively correlated with math performance (Diamantopoulou, Rydell, Thorell, & Bohlin, 2007; Rogers, Hwang, Toplak, Weiss, & Tannock, 2011; Thorell, 2007).

Figure 1.

Theoretical model.

In addition, children with ADHD show a variety of neurocognitive deficits in comparison with controls, including poorer working memory (WM), inhibitory control, planning, and problem solving, as well as greater reaction time variability (Kopecky, Chang, Klorman, Thatcher, & Borgstedt, 2005; Romine et al., 2004; Vaurio, Simmonds, & Mostofsky, 2009; Weyandt, & Willis, 1994; Willcutt, Doyle, Nigg, Faraone, & Pennington, 2005). Deficits in many aspects of neurocognition, including overall executive function (Biederman et al., 2004; Diamantopoulou et al., 2007), WM (Rogers et al., 2011), attention switching (Preston, Heaton, McCann, Watson, & Selke, 2009), and sustained attention (Preston et al., 2009), have been linked to poor math performance.

A few studies have directly examined the unique and relative impact of behavioral inattention and neurocognition on math performance in children with ADHD. Using a large sample of kindergarteners, Thorell (2007) found that behavioral inattention, as measured by ADHD ratings, and specific executive functions (i.e., verbal WM, spatial WM, interference control) were related to math achievement. Furthermore, mediation analyses indicated that overall executive function and behavioral inattention were each uniquely associated with math performance in this sample of young children. Another study examined whether WM and behavioral inattention, as measured by ADHD ratings, were related to academic achievement in adolescents referred for ADHD (Rogers et al., 2011). Again, both inattention and WM contributed unique variance to math achievement.

These studies suggest that neurocognition and behavioral attention predict math achievement. However, we are not aware of any study investigating whether neurocognition and/or behavior mediate the relationship between ADHD and poor math performance (see Figure 1). Furthermore, it is unknown whether neurocognition and behavior predict and/or mediate the relationship between ADHD and other indicators of math performance (i.e., poor productivity). Prior studies have focused on standardized achievement tests, which emphasize academic knowledge. However, decreased academic proficiency, as evidenced by an inability to complete classwork (Barkley, DuPaul, & McMurray, 1990) or taking a long time to complete homework (Epstein, Pollaway, Foley, & Patton, 1993), is common among children with ADHD and frequently cited as an area of impairment. Thus, exploring neurocognitive and behavioral predictors of other aspects of math performance may shed light on difficulties related to school performance and provide areas for intervention.

The present study investigated math performance deficits in school-age children with ADHD utilizing both achievement scores as well as curriculum-based measures of math productivity and accuracy. We predicted that children with ADHD would perform more poorly than controls on all three math outcomes. We then investigated which specific neurocognitive abilities and indicators of behavioral inattention contributed uniquely to each math performance outcome (i.e., achievement, productivity, and accuracy). Last, we examined whether any neurocognitive abilities or aspects of behavioral attention mediated the relationship between ADHD and math performance.

Method

Participants

Participants (n = 147) between the ages of 7 and 11 (inclusive) were recruited from local pediatric clinics and schools. Of these, 102 were diagnosed with ADHD (49 ADHD-C, 53 ADHD-I) and 45 were typically developing controls. Participants had no neurological or serious medical conditions, developmental disabilities, or history of brain injury. All participants received a full scale IQ score of at least 80 on the Wechsler Abbreviated Scale of Intelligence (WASI; Wechsler, 1999) and standard scores of at least 80 on the Wechsler Individual Achievement Test–II (WIAT-II) Word Reading and Numerical Operations (NO) subtests (Wechsler, 2001).

Diagnostic status for ADHD participants was determined using methods similar to those used in the Multimodal Treatment of ADHD (MTA) study (MTA Cooperative Group, 1999). Parent reported ADHD symptoms on the Diagnostic Interview Schedule for Children–Parent Version 4.0 (DISC-P; Shaffer, Fisher, Lucas, Dulcan, & Schwab-Stone, 2000) could be supplemented with teacher reported ADHD symptoms. Specifically, if a parent reported at least four symptoms in any ADHD symptom domain on the DISC-P, these symptoms could be supplemented with nonoverlapping symptoms on the Vanderbilt Teacher Rating Scale (Wolraich, Feurer, Hannah, Baumgaertel, & Pinnock, 1998). If six or more symptoms were present only in the inattentive domain, the child met criteria for ADHD-I. If six or more symptoms were present in both the inattentive and hyperactive-impulsive domains, the child met criteria for ADHD-C. In addition to symptom criteria being met using these supplemental rules, children also had to fulfill Diagnostic and Statistical Manual of Mental Disorders (4th ed., text rev.; DSM-IV-TR; American Psychiatric Association [APA], 2000) Criteria B through E (i.e., age of onset, pervasiveness, impairment, and ruling out of other causal conditions) based on parent responses on the DISC-P (Shaffer et al., 2000). Furthermore, children were required to have at least four symptoms of inattention or hyperactivity/impulsivity coded as occurring often or very often on the Vanderbilt Teacher Rating Scale (Wolraich et al., 1998). All study participants were medication naïve.

Typically developing controls were recruited through local schools and a database of local families interested in research participation. Advertisements indicated that interested families would be participating in “research to study behavioral performance on computer tasks in children with attention problems.” Control participants met study criteria if their parents endorsed three or fewer ADHD symptoms in both symptom domains and did not meet criteria for any Diagnostic and Statistical Manual of Mental Disorders (4th ed.; DSM-IV, APA, 1994) behavioral disorder on the DISC-P (Shaffer et al., 2000).

Participant demographics are summarized in Table 1. Both ADHD groups had lower IQ scores than controls. Not surprisingly, both ADHD groups had more inattentive symptoms than controls, and the ADHD-C group had more hyperactive-impulsive symptoms than the other two groups. Rates for oppositional defiant, conduct, and anxiety disorders were significantly higher in the ADHD groups than controls.

Table 1.

Demographic and Clinical Characteristics of the ADHD-C, ADHD-I, and Control Groups.

	ADHD-C (n = 49)	ADHD-I (n = 53)	Control (n = 45)	Group comparisons
Mean (SD) age (years)	7.92 (1.11)	8.36 (1.30)	8.29 (1.34)	Ns
Number of males (%)	39 (80)	35 (66)	32 (71)	Ns
Number of each ethnicity (%)
Caucasian	31 (63)	42 (79)	37 (82)	ADHD-C < ADHD-I*
Non-Caucasian	17 (35)	7 (13)	8 (18)	Proportion of Caucasians
Not reported	1 (2)	4 (8)	0 (0)
WASI full scale IQ (SD)	105.12 (11.71)	105.51 (13.34)	116.40 (14.34)	ADHD-C < C, ADHD-I < C
Parent Vanderbilt total inattentive score (SD)	20.75 (5.02)	20.79 (4.57)	2.54 (2.06)	ADHD-C > C, ADHD-I > C
Teacher Vanderbilt total inattentive score (SD)	21.11 (4.81)	19.81 (5.19)	3.27 (3.08)	ADHD-C > C, ADHD-I > C
Parent Vanderbilt total hyperactive/impulsive score (SD)	20.07 (5.12)	13.17 (5.65)	1.30 (1.28)	ADHD-C > ADHD-I, ADHD-C >C; ADHD-I > C
Teacher Vanderbilt total hyperactive/impulsive score (SD)	20.15 (4.33)	8.47 (5.73)	2.04 (3.25)	ADHD-C > ADHD-I, ADHD-C >C; ADHD-I > C
Number with a comorbid psychological disorder
Oppositional defiant disorder	22	16	0	ADHD-C > C*, ADHD-I > C
Conduct disorder	4	0	0	ADHD-C > C, ADHD-I > C, ADHD-C > ADHD-I*
Any anxiety disorder	16	20	2	ADHD-C > C, ADHD-I > C
Any mood disorder	1	1	0	Ns
Number completing each math problem difficulty level
Single-digit addition	23	29	13	Ns
Multiple-digit addition	16	10	14
Single-digit multiplication	6	10	10
Multiple-digit multiplication	6	4	8

Note. ADHD-C = ADHD–Combined type; ADHD-I = ADHD–Predominantly Inattentive type; C = control group.

p < .05. **p < .01.

Tasks/Primary Variables of Interest

Math achievement

Standardized performance on the WIAT-II NO subtest was utilized as an indicator of math achievement for each participant. This subtest requires children to complete a variety of calculations that increase in difficulty level. Once participants achieve their ceiling, their raw scores are converted to standardized scores based on current grade level.

Analog math task

Participants completed one naturalistic analog math task (math worksheets) for 20 minutes while being videotaped. This task was modeled after math tasks assigned in a typical classroom setting (e.g., self-directed classroom work). Children were assigned to complete one of four difficulty levels based on an initial assessment of their skill level using curriculum-based measurement methodology (Wright, n.d.; Table 1). Productivity was calculated as the number of math problems a participant completed. Accuracy was calculated as the percentage of problems children answered correctly out of those attempted.

Video recordings of the math task were coded to assess each participant’s attention across the task. Four coders that were blind to diagnosis used Noldus Observer XT software (Noldus Information Technology, 2008) to track participants’ durations of visual attention toward the task. Off-task behavior was coded whenever a child’s visual gaze left the paper for 2 or more seconds, in line with methods from other studies (e.g., Rapport, Kofler, Alderson, Timko, & DuPaul, 2009). In total, 35% of videos were double-coded for reliability. The intraclass correlation coefficient was high for total duration of on-task behavior (.89), which was used as an indicator of behavioral attention.

Behavioral attention ratings

Parent- and teacher-rated inattention scores from the Vanderbilt ADHD Rating Scales (Wolraich et al., 2003; Wolraich et al., 1998) were used as indicators of behavioral attention. On this scale, ADHD symptoms are rated from 0 (never) to 3 (very often); inattention scores range from 0 to 27. Because inattention is consistently related to academic achievement (e.g., Thorell, 2007), only inattention ratings were used in the present study’s analyses.

Neuropsychological tasks

Each participant completed five computerized tasks designed to assess different aspects of neurocognition: choice discrimination task, attentional network task (ANT; Fan, McCandliss, Sommer, Raz, & Posner, 2002; Rueda et al., 2004), go/no-go task (Soreni, Crosbie, Ickowicz, & Schachar, 2009), stop signal task (Logan, 1994; Soreni et al., 2009), and n-back task (1-back). Within each task, stimulus presentation was held constant at 500 ms. Tasks included interstimulus intervals (ISIs) and reward manipulations (Epstein et al. 2011) which were not the focus of this study. Variables included accuracy on the choice discrimination and n-back tasks (percentage of trials performed correctly), percent omission and percent commission errors on the go/no-go task, stop signal reaction time (SSRT) on the stop signal task, and alerting, orienting, and conflict scores on the ANT. On the ANT, higher scores indicated increased benefit from alerting cues, orienting cues, and congruent versus incongruent cues (conflict score), respectively.

Procedure

This study was approved by the institutional review board. Participation involved three sessions on 3 separate days, each approximately 1 week apart (average 6.47 days). During the first session, eligibility criteria were established (i.e., diagnosis, IQ, and achievement testing). During Sessions 2 and 3, participants completed the neuropsychological computer tasks and analog math task.

Analyses

Of the 147 participants who completed the computerized tasks, nine math observations were lost due to technical errors and two were not included due to the children’s refusal to follow task directions. Participants with missing math observations had higher teacher-rated inattention than those who had math observations, t(13.23) = 2.27, p = .04, but did not differ with regard to age, sex, race, IQ, oppositional defiant, conduct, anxiety, or mood disorders, or parent-rated ADHD symptom scores (all ps > .05).

Analyses were first conducted to investigate group differences for the math, behavioral attention, and neuropsychological variables. A chi-square test was used to examine whether the proportions of children assigned to the four worksheet problem difficulty levels differed across groups. General linear models using SAS PROC GLM were then conducted to examine group differences (ADHD-C vs. ADHD-I vs. controls) in math achievement (WIAT-II NO standard scores), math productivity (number of problems completed), math accuracy (percentage of problems completed correctly), and behavioral attention (Vanderbilt parent and teacher ratings; percentage of on-task behavior). Math problem difficulty level was included as a covariate in the productivity model, to account for differences in problem length (e.g., one-digit addition vs. multiple-digit addition). All GLM models were subjected to planned comparisons, to assess significant differences between each pair of groups (see Table 2).

Table 2.

Means and Group Differences for Math, Behavioral, and Neurocognitive Variables.

	Control M (SD)	ADHD-I M (SD)	ADHD-C M (SD)	F	p
WIAT-II numerical operations standard score	112.84 (18.17)	97.89 (13.79)	97.06 (13.19)	16.04	<.0001
Number of math problems attempted^a	156.33 (88.77)	153.42 (88.42)	139.24 (58.94)	0.84	.43
Percentage of math problems answered correctly	94.07 (13.92)	91.85 (15.51)	95.19 (7.71)	0.86	.43
Proportion of time on-task	0.96 (0.06)	0.88 (.18)	0.90 (0.14)	3.96	.02
Choice discrimination task accuracy^b	88.48 (1.83)	82.83 (1.83)	84.29 (1.79)	2.70	.15
N-back task accuracy^b	81.90 (2.25)	72.07 (2.05)	68.40 (2.44)	9.22	.0009
Stop signal task SSRT^b	333.95 (21.82)	368.66 (20.25)	413.30 (21.53)	3.37	.04
Go/no-go omission errors (percentage)	0.01 (0.02)	0.07 (0.10)	0.08 (0.12)	6.86	.001
Go/no-go commission errors (percentage)	0.41 (0.23)	0.46 (0.21)	0.45 (0.19)	1.31	.27
Flanker task alerting score^b	80.64 (11.57)	80.57 (10.66)	89.34 (11.44)	0.20	.82
Flanker task orienting score^b	24.17 (6.91)	28.62 (6.38)	20.29 (6.84)	0.40	.67
Flanker task conflict score^b	53.07 (10.35)	54.95 (9.61)	88.14 (10.23)	3.77	.03

Note. SSRT = stop signal reaction time; WIAT-II = Wechsler Individual Achievement Tests (2nd ed.).

Models included problem difficulty level as a covariate.

Statistics were originally presented in Epstein et al. (2011), and take into account event rate and reward conditions.

Next, analyses were conducted to examine the relationship between the math, behavioral, and neurocognitive variables. After removing the variance attributable to the math difficulty level from the math productivity variable, Pearson correlations were calculated (see Table 3). Six GLM models were conducted using neurocognitive or behavioral variables as predictors and math achievement, productivity, and accuracy variables as dependent variables. The predictors selected for inclusion in these models met a cutoff level of p < .10 in the correlation table (see Table 3; Tabachnick & Fidell, 2001). Math difficulty was included as a covariate in the two math productivity models. Significant (p < .05) neurocognitive and behavioral predictors in these six models were then included together as predictors in three math models—one predicting math achievement, one predicting math productivity, and one predicting math accuracy. Again, math difficulty level was included as a covariate in the productivity model and variables meeting a cutoff level of p < .05 were considered significant predictors.

Table 3.

Pearson Correlations for All Math, Behavioral, and Neurocognitive Variables for All Participants.

	1	2^a	3	4	5	6	7	8	9	10	11	12	13	14
(1) WIAT-II numerical operations	-
(2) Productivity^a	.01	-
(3) Accuracy	.02	.03	-
(4) Parent-rated inattention	−.42^†	−.18**	−.04	-
(5) Teacher-rated inattention	−.43^†	−.17**	−.03	.80^†	-
(6) Observed inattention	.15*	.48^†	−.003	−.29****	−.27***	-
(7) SSRT	−.01	−.19**	−.03	.16*	.26***	−.12	-
(8) Go/no-go omission errors	−.25***	−.21***	−.05	.29****	.27***	−.20**	.04	-
(9) Go/no-go commission errors	−.17**	−.14	.06	.15*	.22**	−.06	.06	.11	-
(10) ANT alert	−.08	−.10	.35^†	.03	.02	−.10	−.07	.26	−.06	-
(11) ANT orienting	−.02	.05	.16*	.09	.11	.09	.07	.10	−.04	.36^†	-
(12) ANT conflict	.00	−.10	.04	.02	.05	−.06	.02	−.02	−.10	.15*	.08	-
(13) N-back accuracy	.33^†	.27***	.008	−.32^†	−.33^†	.06	−.24***	−.35^†	−.16*	−.07	−.04	.13	-
(14) Choice discrimination accuracy	.26***	.14	−.03	−.21**	−.18**	.12	−.21**	−.41^†	−.34^†	0	−.09	.11	.31****	-

Note. SSRT = stop signal reaction time; ANT = attention network task; WIAT-II = Wechsler Individual Achievement Test (2nd ed.).

Correlations between productivity and other variables controlled for problem difficulty level participants were assigned to for their math worksheets.

p < .10. **p < .05. ***p < .01. ****p < .001. ^†p < .0001.

Last, for math variables that significantly differed between ADHD and controls, we examined whether any of the significant neurocognitive and/or behavioral attention variables mediated the relationship between diagnostic group and math performance. Mediation models were computed in SAS and all significant neurocognitive and behavioral variables were included as parallel mediators. The 95% confidence intervals (CIs) for the indirect effects for each mediator were computed using bootstrapping methodology (5,000 samples; Preacher & Hayes, 2008) with the PROCESS macro (Hayes, 2012).

Results

Group Differences for Predictor Variables

The ADHD-I (p < .0001, d = 5.17; p < .0001, d = 3.91) and ADHD-C (p < .0001, d = 4.72; p < .0001, d = 4.47) groups had higher parent- and teacher-rated inattention scores than controls but did not significantly differ from one another (see Table 1). Furthermore, the ADHD-I (p = .008, d = .60) and ADHD-C groups (p = .045, d = .56) were both on-task less than controls but did not differ from each other (see Table 2).

As reported by Epstein et al. (2011), the ADHD-C group differed from controls on the n-back task (less accurate), stop signal task (longer SSRTs), and ANT (higher conflict scores). Both ADHD groups had significantly higher percentages of omission errors than controls (see Table 2) on the go/no-go task.

Math Achievement

There were significant group differences for WIAT-II NO scores, F(2, 142) = 16.04, p < .0001. Children in the ADHD-I (p < .0001, d = .93) and ADHD-C (p < .0001, d = .99) groups had lower scores than controls (see Table 2).

All three inattention variables (parent-rated r = −.42, p < .0001; teacher-rated r = −.43, p < .0001; and observed r = .15, p = .07) were correlated with WIAT-II NO performance at a p < .10 level. Only parent-rated inattention remained significant when they were included in a multivariate GLM (see Table 4).

Table 4.

Behavioral and Neurocognitive Predictors of Math Achievement and Productivity.

	WIAT-II numerical operations		Problems attempted		Problem accuracy
	F	p	F	p	F	p
Behavioral Predictors Parent Vanderbilt inattention score	4.89	.03	0.10	.75	—	—
Teacher Vanderbilt inattention score	2.02	.16	0.05	.82	—	—
Percentage of time coded on-task	0.16	.69	32.30	<.0001	—	—
Math problem difficulty level	—	—	21.55	<.0001	—	—
Neurocognitive Predictors
N-back accuracy	8.32	.005	4.94	.03	—	—
Choice accuracy	1.49	.22	—	—	—	—
Go/no-go omission errors	1.39	.24	3.46	.07	—	—
Go/no-go commission errors	1.00	.32	—	—	—	—
Stop signal SSRT			4.00	.047	—	—
Flanker orienting score	—	—	—	—	0.21	.64
Flanker alerting score	—	—	—	—	15.84	.0001
Flanker conflict score	—	—	—	—	—	—
Math problem difficulty level	—	—	15.19	<.0001	—	—

Note. SSRT = stop signal reaction time; WIAT-II = Wechsler Individual Achievement Test (2nd ed.). Results in this table report main effects within each model rather than the overall significance of each model. The predictors selected for inclusion in these models met a cutoff level of p < .10 in the correlation table. The Problems Attempted models included problem difficulty level as a covariate.

Four neurocognitive variables were correlated with WIAT-II NO at p < .10 level: go/no-go omission errors (r = −.25, p = .003), go/no-go commission errors (r = −.17, p = .04), n-back accuracy (r = .33, p < .0001), and choice discrimination accuracy (r = .26, p = .002; see Table 3). Only n-back accuracy remained significant when these four variables were included as predictors of math achievement in a multivariate GLM (see Table 4).

When significant predictors across both models were included in a single GLM, parent-rated inattention (p < .0001) and n-back accuracy (p = .005) significantly predicted math achievement, F(2, 138) =19.43, p < .0001, R² = .22.

Math Productivity

The three groups (ADHD-I vs. ADHD-C vs. controls) did not significantly differ on math productivity (see Table 2).

All three inattention variables (parent-rated r = −.18, p = .03; teacher-rated r = −.17, p = .04; observed r = .48, p < .0001) were correlated with math productivity at a p < .10 level (see Table 3). Only observed inattention remained significant (see Table 4) when all three predictors were included in a multivariate GLM with problem difficulty level as a covariate.

Three neurocognitive variables were correlated with math productivity at a p < .10 level: SSRT (r = −.19, p = .02), go/no-go omission errors (r = −.21, p = .01), and n-back accuracy (r = .27, p = .001; see Table 3). When these three variables were included as predictors of productivity in a multivariable GLM with problem difficulty level as a covariate, n-back accuracy and SSRT remained significant (see Table 4).

When significant predictors across both models were included in a single GLM, with problem difficulty level as a covariate, n-back accuracy (p = .007) and observed on-task behavior (p < .0001) were both significant predictors of math productivity, F(6, 127) = 20.07, p < .0001, R² = .49.

Math Accuracy

The three groups (ADHD-I vs. ADHD-C vs. controls) did not significantly differ on math accuracy (see Table 2).

None of the inattention variables correlated with math accuracy at a p < .10 level (see Table 3).

Two neurocognitive variables were correlated with math accuracy at a p < .10 level: ANT orienting scores (r = .16, p = .055) and ANT alerting scores (r = .35, p < .0001; see Table 3). When these two variables were included as predictors of accuracy in a multivariable GLM, only ANT alerting scores remained significant (see Table 4).

As the single predictor in the final GLM for accuracy, ANT alerting scores remained significant, F(1, 141) = 19.87, p < .0001, R² = .12.

Mediation analyses

Because there were only group differences between participants with ADHD and controls in math achievement, only math achievement was examined as an outcome variable in our mediation models. In addition, because no ADHD subtype differences in achievement were found, the two ADHD groups were collapsed. Based on the regression analyses, parent-rated attention and n-back accuracy were included as parallel mediators. The indirect effect of ADHD diagnosis on math achievement through n-back accuracy was significant, β = −2.33; 95% CI = [−4.82, −.83]. The indirect effect of ADHD diagnosis on math achievement through parent-rated inattention was not significant, β = −4.51; 95% CI = [−14.59, 6.57].

Discussion

Consistent with prior research (e.g., Biederman et al., 1996; DeShazo et al., 2002; Frick et al., 1991; Mahone et al., 2002), children with ADHD had lower math achievement scores than controls. In particular, we found that children with ADHD did more poorly on the WIAT-II NO subtest, a test assessing children’s ability to solve paper-and-pencil computations of increasing difficulty. Children’s performance on the n-back task and parent-rated inattention both predicted unique variance in math achievement. Furthermore, n-back accuracy mediated ADHD-related deficits in math achievement, suggesting that it is ADHD-related neurocognitive deficits, likely WM and sustained attention (both measured by the n-back task), that are responsible for poorer math achievement among children with ADHD. With regard to math productivity, we did not find performance differences between the diagnostic groups. Math productivity scores were predicted by n-back performance and on-task behavior. Last, there were no diagnostic group differences in math accuracy. Math accuracy was predicted by alerting scores on the ANT.

One of the primary goals of this study was to identify specific behavioral and neurocognitive predictors of math performance, particularly those that might account for poorer math achievement in children with ADHD. One variable that predicted math achievement for all participants was parent inattention ratings. Perhaps this relationship is not surprising because to perform well on an achievement test, children must sustain their attention over time, avoid distractions, and refrain from making careless mistakes. Prior research has demonstrated that both parent (DeShazo et al., 2002; Hart et al., 2010) and teacher (Barriga et al., 2002; Rogers et al., 2011; Thorell, 2007) ratings of ADHD inattention symptoms are significantly correlated with math achievement. Our study is among the few that have used both parent and teacher ratings. While both sets of ratings correlated highly with math achievement in our study, parent ratings accounted for the majority of the variance in math achievement. Recently, Bauermeister, Barkley, Bauermeister, Martinez, and McBurnett (2012) also demonstrated that maternal ratings of ADHD symptoms accounted for greater variance in academic achievement (i.e., reading and math) than teacher ratings. Perhaps the opportunity for parents to view the child across a range of activities and settings allows them to more accurately or reliably rate inattention. Or possibly as the parent’s academic observations of the child are based primarily on homework time (i.e., one-on-one learning) that more closely approximates the achievement testing situation, parent ratings are more likely to correlate with achievement results than teacher ratings.

N-back accuracy also predicted math achievement. The n-back task is usually interpreted as a WM task (Owen, McMillan, Laird, & Bullmore, 2005; Strand et al., 2012). However, some have argued that it is better characterized as a sustained attention task, due to its low correlations with other traditional measures of WM (Kane, Conway, Miura, & Colflesh, 2007), and the fact that the 1-back reduces the requirement to hold and manipulate information in memory. However, the n-back task does require individuals to update information over time, which is thought to be a component of WM (e.g., Miyake et al., 2000; Morris & Jones, 1990). Given that performance on the n-back predicted math achievement above and beyond other measures of neurocognition that included a sustained attention component (i.e., choice discrimination accuracy, go/no-go omissions, and ANT), it appears that the n-back task assessed more than sustained attention, and quite possibly provided a measure of WM ability.

If the n-back task does indicate WM ability, our findings are consistent with several other studies examining typically developing children (e.g., Bull & Scerif, 2001; Maybery & Do, 2003; Raghubar, Barnes, & Hecht, 2010; St. Clair-Thompson & Gathercole; 2006; Thorell, 2007), children with math learning disabilities (Raghubar et al., 2010), and adolescents with attentional difficulties (Rogers et al., 2011), which have shown that WM predicts math achievement. WM appears to be a critical cognitive skill necessary for successful math performance, particularly as assessed on achievement tests (e.g., arithmetic computation, problem solving, etc.; Männamaa, Kikas, Peets, & Palu, 2012; Maybery & Do, 2003; Swanson & Beebe-Frankenberger, 2004). Poor WM can lead to counting errors (Swanson & Beebe-Frankenberger, 2004), procedural errors due to problems with monitoring and updating information (e.g., adding instead of subtracting, not borrowing or carrying correctly), and difficulties with multistep problems (Geary, 2004). The rapid responding that results from difficulties with holding and updating information may lead to increased careless mistakes and decreased problem-solving efforts (Zentall, 2007). All of these difficulties may contribute to lower math achievement scores.

While both higher ratings of parent-rated inattention and poorer n-back performance contributed to poorer math achievement, our mediation analyses found that it was n-back performance that mediated ADHD-related deficits in math achievement. That is, results suggest that WM deficits in children with ADHD partially account for ADHD-related deficits in math achievement. Given this relationship and the consistency, magnitude, and breadth of WM deficits in children with ADHD (for a review, see Martinussen, Hayden, Hogg-Johnson, & Tannock, 2005), ADHD-related deficits in math achievement are not surprising. In fact, the types of aforementioned mathematical errors that are related to WM impairment seem consistent with several of the symptoms that define ADHD (e.g., careless mistakes, inability to follow through on instructions). This set of findings suggests that interventions targeting math achievement in children with ADHD should focus on providing them with adequate time to complete tests and assignments, encouraging them to be deliberate in their computations, and promoting double-checking of their work.

In contrast with mathematical achievement, we did not find any ADHD-related deficits in math productivity. Our math analog math task was designed to simulate classroom seatwork. Using similar tasks, children with ADHD have been shown to be less productive than children without ADHD (e.g., Barkley, Dupaul, et al., 1990; Benedetto-Nasho & Tannock, 1999). One major difference between our math task and those used in other studies is that we customized our task to each participant’s level of achievement, selecting a level for each child in which the child demonstrated proficiency but not mastery. Prior studies examining math productivity deficits in children with ADHD have utilized the same math problems for all participants (e.g., Barkley, Fischer, et al., 1990). Our lack of between-group differences may suggest a clinically relevant phenomenon. That is, children with ADHD may be as productive as children without ADHD when problem difficulty is controlled, but when they are forced to do work comparable to that of their peers, possibly beyond their proficiency level, math productivity deficits emerge. This suggests that the ADHD-related deficits in productivity shown in prior research, which are often observed in the classroom and during homework, may be a reflection of ADHD-related deficits in math achievement.

Similarly to our analyses predicting math achievement, we found that inattention also predicted math productivity. However, unlike math achievement, it was observed on-task behavior during the math task that best predicted math productivity and not ratings of inattention symptoms. Math productivity, in effect, depended on the child’s ability to attend to the math task over time and overcome boredom and distractions. On-task behavior during the math task predicted math productivity better than ratings likely because parent and teacher ratings reflected overall behavior patterns, whereas the observational codings more accurately captured behavior during performance of the task at hand.

Just as it did for math achievement, n-back accuracy also predicted math productivity. The purported mathematical errors engendered by WM deficits (e.g., counting errors, procedural errors, multistep errors; Geary, 2004; Männamaa, Kikas, Peets & Palu, 2012; Maybery & Do, 2003; Swanson and Beebe-Frankenberger, 2004; Zentall, 2007) not only impair math achievement, but also quite obviously impair a child’s ability to complete mathematical computations in an efficient manner. In summary, WM appears to be a critical skill for successful math performance as measured by achievement scores or measures of math productivity. The ability to effectively monitor, update, and hold numerical information in mind during computation directly affects math performance.

Finally, turning to math accuracy, there were no differences in math accuracy between children with and without ADHD. In addition, none of the behavioral variables were significantly related to accuracy. Similarly to productivity, this lack of findings may be due to the way in which we assigned math tasks to each child (i.e., using a pretest to determine each child’s own ability level). This methodology likely created ceiling effects and low variances within groups, thus limiting our ability to detect group differences in or behavioral predictors of math accuracy.

Interestingly, alerting scores on the ANT (Rueda et al., 2004) significantly predicted math accuracy, suggesting that vigilance is required to respond accurately on an independent math task. However, given that this study seems to be the first to report such a relation, this finding requires replication.

Our study results must be considered in light of several limitations. First, children with poor math achievement scores were excluded from the study and, thus, the pattern of study findings may not generalize to those children with learning disabilities. In addition, our results may not fully generalize to real world settings because our math task was completed in a laboratory setting rather than a classroom where there may be different attentional demands on a child. Furthermore, we did not include tests assessing other aspects of WM (e.g., visuospatial) or other neurocognitive abilities (e.g., divided attention) that may predict and/or mediate math performance deficits. Lastly, this study only included participants who were medication naïve. Excluding participants with prior medication use may have excluded those with more severe ADHD symptomatology who may have received treatment at an earlier age.

In conclusion, this study is one of the most comprehensive studies to date examining the relationship between attention, neurocognition, and math performance in children. We largely replicate previous research demonstrating that inattention and WM predict math achievement in kindergarteners (Thorell, 2007) and adolescents (Rogers et al., 2011). Our results extend these relationships to elementary-aged children with ADHD. Moreover, by including multiple measures of behavioral attention, neurocognition, and math performance, we are able to conclude that neurocognitive abilities, particularly those assessed on the n-back task (e.g., WM and sustained attention), are strong predictors of both math achievement and math productivity and appear to directly mediate the ADHD-related deficits in math achievement.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Funding for this study was provided by the National Institutes of Health (Grants R01 MH074770 and K24 MH064478, to J.E.).

Author Biographies

Tanya N. Antonini, MA, is a doctoral student in clinical psychology at the University of Cincinnati, and is affiliated with the Center for ADHD, Department of Pediatrics, Cincinnati Children’s Hospital Medical Center.

Kathleen M. Kingery, MA, is a doctoral student in clinical psychology at the University of Cincinnati, and is affiliated with the Center for ADHD, Department of Pediatrics, Cincinnati Children’s Hospital Medical Center.

Megan E. Narad, MA, is a doctoral student in clinical psychology at the University of Cincinnati, and is affiliated with the Center for ADHD, Department of Pediatrics, Cincinnati Children’s Hospital Medical Center.

Joshua M. Langberg, PhD, is an assistant professor in the Department of Psychology, Virginia Commonwealth University, and received his PhD from the University of South Carolina in 2006.

Leanne Tamm, PhD, is an associate professor in the Department of Pediatrics, Cincinnati Children’s Hospital Medical Center. She received her PhD from the University of Texas, Austin, in 2000.

Jeffery N. Epstein, PhD, is a professor in the Department of Pediatrics, Cincinnati Children’s Hospital Medical Center, and is director of the Cincinnati Children’s Hospital Center for ADHD. He received his PhD from the State University of New York, Stony Brook, in 1994.

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