The results of this study suggest that children with TS who undergo training in effective math strategy in addition to adaptive, distributed skills practice may demonstrate improved math skills in certain areas. Performance was significantly increased on KeyMath Total, Basic Concepts and Operations. Basic Concepts includes comprehensive assessment of number sense (Connolly, 2007
) and therefore results suggest that number sense may be potentially trainable, even in children genetically at risk for altered development of neural systems subserving number sense. This is consistent with research demonstrating a reciprocal interaction between behavior, neurobiologic and genetics (Kremen & Jacobson, 2010
). KeyMath Operations includes measures of addition, subtraction, multiplication and division. Thus, in addition to basic number sense, participants demonstrated increased performance in specific math skills related to fact retrieval and calculation. Participants also showed significantly increased accuracy, increased ability to discriminate between correct and incorrect math equations and reduced reaction time on the fMRI math measure.
Increased performances on KeyMath Total and KeyMath Basic Concepts were not only statistically significant but were also clinically significant. RCI analysis indicated that these scores were classified as recovered at Time 2, meaning that they increased reliably irrespective of practice effects and also increased to be considered within the normal score distribution (Bauer, Lambert, & Nielsen, 2004
). KeyMath Operations was classified by RCI analysis as unchanged. Although this score was statistically significant, participants did not show clinical improvement. This finding may reflect small sample size, non-optimal intervention duration and/or design and/or other unknown factors and warrants further investigation.
Assessments of applied math problem solving involving application of strategies and procedures (e.g. word problems) were not significantly changed. Applied math problems may involve different math and cognitive skills compared to number sense and fact retrieval and thus may require a different remediation approach (Fuchs et al., 2009
). It was hypothesized that the addition of cognitive flexibility or general problem solving training would enhance the effectiveness of the training program for applied math problems. However, these particular skills may require problem solving training that is specific to math such as the math word problem training program described by Fuchs and colleagues (Fuchs et al., 2009
The fMRI findings suggest that there was a decrease in frontal-striatal and mesial temporal activation and an increase in parietal lobe activation after the training program. These results are consistent with previous neuroimaging studies of math skills development, proficiency and learning in typically developing individuals (Ischebeck, Zamarian, Schocke, & Delazer, 2009
; Ischebeck et al., 2006
; Rivera, Reiss, Eckert, & Menon, 2005
) as well as math skills training in an individual with frontal-parietal lesions (Zaunmuller et al., 2009
). These findings may imply that less proficient math performers rely on attention, memory and/or verbal based strategies as these are typically subserved by frontal-striatal and temporal regions, while more proficient performers utilize more spatial/retrieval-based strategies that are associated with parietal regions (Rivera et al., 2005
). The present results suggest that brain function potentially changed following training during more difficult math trials but was not altered during easier conditions. A previous study from our group indicated that individuals with TS tended to demonstrate the greatest neurofunctional deficit when math task difficulty was increased (Kesler et al., 2006
). Laborious approaches such as attention/working memory based strategies may suffice for simpler tasks but neural resources are likely overwhelmed when the task becomes more challenging. These findings potentially lend further evidence to this functional specialization of the parietal lobe for math skills and suggest that training may help to improve this specialization even in individuals with high risk for abnormal frontal-parietal development and function.
These results may have potentially important implications for remediation of math deficits in children. Although the participants of our study did not have documented math disability and in fact demonstrated scores on math assessments that were within what is considered to be the “average” range (85–115) (Connolly, 2007
), our findings provide promising preliminary evidence that simple instruction in an efficient math strategy and computerized, home-based skills practice may be associated with improved math skills and functional changes in frontal-parietal brain networks. Previous math remediation studies have relied on more intensive instruction involving tutoring or teaching methods (Fuchs et al., 2008
; Fuchs et al., 2009
; Powell, Fuchs, Fuchs, Cirino, & Fletcher, 2009
) that many students may not have access to and/or are complicated and difficult to implement. The computerized program we utilized is readily available to the public for a small fee (http://www.lumosity.com/courses/lumosity-math-tutor
) and thus represents a promising and practical alternative and/or complementary approach to math remediation. Computerized training has several advantages over other approaches including immediate feedback, availability for home practice, the ability to systematize delivery of the intervention and modifications to difficulty level, the ability to quantify multiple aspects of performance and progress and the provision of an entertaining and engaging interface.
Participants in the present study also showed statistically and clinically significant increases in math-related cognitive skills including processing speed, cognitive flexibility and visual-spatial processing performance following the math training program. A critical issue in cognitive training research is whether training-induced changes transfer or generalize to other relevant skills and/or real-world tasks (Green & Bavelier, 2008
). In particular, it is expected that untrained tasks or skills involving a similar neural system to the trained task might also be influenced by the training (Thorell et al., 2009
). Calculation skills, number sense and cognitive flexibility were directly trained during our training program. Processing speed was indirectly trained via the timed nature of the two math-related tasks. However, visual-spatial processing was not specifically trained and thus improvements in this area may potentially suggest a degree of transfer to untrained math-related skills. Visual-spatial processing skills are largely subserved by frontal-parietal regions and abnormalities in these areas have been shown to be associated with visual-spatial deficits in TS and other groups (Eckert et al., 2005
; Holzapfel, Barnea-Goraly, Eckert, Kesler, & Reiss, 2006
; Kesler et al., 2004
). Thus, altered frontal-parietal function following the training program may have improved visual-spatial processing as well as math performance. The present findings are consistent with a previous study of visual-spatial skills training in healthy adolescent females that showed significantly increased posterior parietal activation and decreased prefrontal activation (Haier, Karama, Leyba, & Jung, 2009
Processing speed and cognitive flexibility also involve frontal-parietal systems (Genova, Hillary, Wylie, Rypma, & Deluca, 2009
; Lie, Specht, Marshall, & Fink, 2006
). The present results may suggest that training-induced improvement of these skills is potentially associated with decreased frontal and increased parietal activation. Decreased activation following training is purported to reflect increased neural efficiency and has been previously associated with training of higher-level cognitive tasks (Dahlin, Backman, Neely, & Nyberg, 2009
; Kelly, Foxe, & Garavan, 2006
). Increased activation is believed to stem from recruitment of additional neural resources and/or heighted regional response (Poldrack, 2000
), but has previously been associated only with sensorimotor training (Kelly et al., 2006
). The present findings of increased rather than decreased parietal activation during a high-level cognitive task may reflect the adaptive nature of the training program. Adaptive training is designed to continuously increase learning and challenge neural systems with the goal of eventually producing more stable neurobiologic changes (Moucha & Kilgard, 2006
). Thus, hierarchical skills training may be associated with increased cognitive load in certain regions and concomitantly increased, rather than decreased, activation in components of these networks. However, working memory and visual attention were not improved by our training program despite their reliance on frontal-parietal networks and their previously demonstrated improvement via training-induced changes in frontal-parietal function (Klingberg, 2010
; Tomasi, Ernst, Caparelli, & Chang, 2004
). These skills may require direct rather than indirect training approaches, longer training duration and/or other modifications to the training program.
There are several limitations to this pilot, case series study that should be considered. Most importantly, the lack of a no-training or alternate training comparison group increases the probability that our findings were due to practice effects or regression towards the mean. We utilized math tests that have strong test-retest reliabilities (.83–.97) and employed alternate forms for these as well as our fMRI task to reduce the effects of practice. The sample demonstrated math and cognitive test scores that were all within 1 standard deviation of the normative mean (100 ± 15), with the exception of MVPT, which was 1.2 standard deviations below the normative mean. These are not extreme scores and thus not as influenced by regression towards the mean. Advanced statistical methods and robust covariates were employed to reduce variability in baseline scores due to confounding factors and to evaluate the reliability of test score changes. Additionally, a previous study of computerized math skills training (Wilson, Revkin, et al., 2006
) as well as neuroimaging studies of executive function training have successfully utilized a similar AB design (Dux et al., 2009
; McNab et al., 2009
). Nevertheless, a randomized trial is necessary to demonstrate the true potential of training number sense and math skills.
The sample size was relatively small and limited the ability to address the effects of demographic or other variables on training efficacy, for example. It is also not known whether changes in cognitive ability and brain activation would be stable over time. Longitudinal follow-up is required to address this limitation. The fMRI math task involved an element of response inhibition given that participants were required to respond only if the math equation was correct and thus inhibit responding to incorrect equations. We did not assess response inhibition performance and therefore do not know the impact of participants’ functioning in this cognitive domain on the math training or brain activation outcomes. The math strategies that participants used pre- or post-training were not assessed and thus some of them may have already been familiar with decomposition and/or other advanced strategies. These results may be specific to children with TS and/or to children who do not demonstrate severely impaired math or cognitive function at baseline. It is unknown how critical the strategy instruction session was to the success of the training program. Although this session was very basic and could technically be implemented by non-professional individuals, S.K. is a licensed clinical psychologist and therefore subtle, specialized clinical skills that are difficult to standardize or quantify may have played a role in the training procedure.