Math fluency from elementary to middle school: differentiating recognition from inferential fluency

Fluency in mental arithmetic is often regarded as a foundational math skill best measured as a single construct. Here we examine the potential benefits of distinguishing between inferential fluency and recognition fluency in elementary and middle school students. Depending on the problem at hand, a student’s fluency may reflect reliance on inferential versus recognition processes. Here we studied single digit arithmetic problems that appear in a widely used 3-minute math fluency assessment across a large (n=914), diverse cohort of 3rd- 7th grade students. A novel tablet-based paradigm enabled us to aggregate performance across different problem types by devising a simple yet objective heuristic to designate problems as likely to draw upon recognition versus inferential fluency in this population. Effects of fluency type were evident across accuracy, response time, and combined responses per minute (RPM) metrics. A novel yet theoretically informative interaction emerged between fluency type and the operation effect. Both fluency types showed sensitivity to grade effects, SES effects, and global achievement levels on state-mandated math assessments. Inferential fluency proved to be a stronger predictor of global achievement than either recognition fluency or more traditional aggregate raw scores. Finally, we demonstrate how differentiating these two fluency types provides novel insights into how relationships between SES and global math achievement are mediated by both inferential and recognition fluency, but not equally. We propose that differentiating inferential from recognition fluency is an initial step toward testing a proposed SIRPA (shift from inferential to recognition processes in arithmetic) model of math development.

Mathematical Abilities in Children: An sMRI Analysis With Radiomics

Brain areas related to mathematical abili- ties in children have been mainly assessed through their activation in fMRI, while volume-based analysis have been employed in sMRI to discover structural differ- ences. However, a recent technique in precision medicine allows to enhance the sMRI analysis by extracting a large number of features, also called radiomics, related to shape, intensity and texture from specific areas. In the present study, a structural neuroimaging analysis based on radiomics and machine learning models is pre- sented with the aim of identifying brain areas related to different mathematical tests. A total of 77 school- aged children from third to sixth grade were adminis- tered four mathematical tests: Math Fluency, Calcu- lation, Applied Problems and Concepts as well as a structural brain imaging scan. The results confirmed and extended the involvement of brain areas found in sMRI and fMRI literature such as the frontal, parietal, temporal and occipital cortex, as well as basal ganglia and limbic system areas. For these areas, texture fea- tures were the most informative while volume represented less than 15% of the shape information. These findings emphasize the potential of radiomics for a more in-depth analysis of medical images for the identifi- cation of brain areas related to mathematical perfor- mance. The code used to obtain these results can be found at github.com/vicmancr/MathBrainRadiomics.

A Randomized Controlled Trial of Working Memory Training in Pediatric Sickle Cell Disease

Objective Youth with sickle cell disease (SCD) are at risk for neurocognitive deficits including problems with working memory (WM), but few interventions to improve functioning exist. This study sought to determine the feasibility and efficacy of home-based, digital WM training on short-term memory and WM, behavioral outcomes, and academic fluency using a parallel group randomized controlled trial design. Methods 47 children (7–16 years) with SCD and short-term memory or WM difficulties were randomized to Cogmed Working Memory Training at home on a tablet device (N = 24) or to a standard care Waitlist group (N = 23) that used Cogmed after the waiting period. Primary outcomes assessed in clinic included performance on verbal and nonverbal short-term memory and WM tasks. Secondary outcomes included parent-rated executive functioning and tests of math and reading fluency. Results In the evaluable sample, the Cogmed group (N = 21) showed greater improvement in visual WM compared with the Waitlist group (N = 22; p = .03, d = 0.70 [CI95 = 0.08, 1.31]). When examining a combined sample of participants, those who completed ≥10 training sessions exhibited significant improvements in verbal short-term memory, visual WM, and math fluency. Adherence to Cogmed was lower than expected (M = 9.07 sessions, SD = 7.77), with 19 participants (41%) completing at least 10 sessions. Conclusions: Visual WM, an ability commonly affected by SCD, is modifiable with cognitive training. Benefits extended to verbal short-term memory and math fluency when patients completed a sufficient training dose. Additional research is needed to identify ideal candidates for training and determine whether training gains are sustainable and generalize to real-world outcomes.

A robust electrophysiological marker of spontaneous numerical discrimination

Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability—especially in children—but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During 1-min sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.

Cognitive Correlates of Math Performance in School-Aged Children with Sickle Cell Disease and Silent Cerebral Infarcts

Objective Attention, processing speed, executive functioning, and math difficulties are common in youth with sickle cell disease (SCD) with silent cerebral infarcts (SCI). This study investigated the cognitive underpinnings of math difficulties in children with SCD and SCI. Method Youth (n = 68) with SCD and SCI completed measures of attention [Digit Span forward (DSF); Conners Continuous Performance Test-Third Edition/Kiddie Conners Continuous Performance Test-Second Edition (CPT-3/KCPT-2)]; working memory [Wechsler Intelligence Scales (WPPSI-IV, WISC-IV, WISC-V, WAIS-IV), Working Memory Index (WMI), Digit Span backwards (DSB)]; processing speed [WPPSI-IV, WISC-IV, WISC-V, WAIS-IV Processing Speed Index (PSI)]; math reasoning [Wechsler Individual Achievement Test-Third Edition (WIAT-III) Mathematics composite (MC)]; and math fluency [WIAT-III Math Fluency composite (MF)] as part of a clinical neuropsychological evaluation. Parent ratings of attention and executive functioning were obtained [Behavior Assessment System for Children-Third Edition (BASC-3), Behavior Rating Inventory of Executive Function (BRIEF)]. Results MC was positively correlated with WMI (r = 0.59, p = 0.00), PSI (r = 0.40, p < 0.001), DSF (r = 0.29, p = 0.03), DSB (r = 0.47, p < 0.001), and MF (r = 0.71, p < 0.001). Correlations between MC, sustained attention, and parent ratings were nonsignificant. The linear regression model using correlated variables was significant [F(4,51) = 8.29, R2 = 0.39, p < 0.001]. WMI was the only significant variable within the model (p = 0.02). Conclusions Working memory deficits account for significant variance in untimed mathematical performance in this population—consistent with other populations with white matter dysfunction. Interventions targeting both mathematics and working memory may be beneficial.

A robust electrophysiological marker of spontaneous numerical discrimination

Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability – especially in children – but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During one-minute sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.

A question of reframing: How LSP improves math fluency, economics, and financial literacy at the secondary level

The purpose of this applied expository paper is to demonstrate how world language teachers at the secondary level can incorporate Languages for Specific Purposes (LSP) principles into their courses when it is not possible to offer standalone LSP courses. Multiple examples are provided that illustrate how many traditional classroom lessons, communicative activities, and projects can be reframed to incorporate interdisciplinary connections to provide students with a skill set that focuses on global awareness and communication, as well as economic and financial literacy. One rural and persistently low-performing school district created initiatives to integrate reading apprenticeship strategies, writing across the curriculum, and number fluency into weekly lessons in all classrooms at all grade levels in order to increase student academic achievement. Beginning world language courses at the secondary level, reframed through an LSP lens, can provide valuable support to other content areas. Further, these courses may potentially increase student engagement within the classroom and cause higher achievement on state assessments across multiple disciplines.

Dysfunctional and compensatory brain networks underlying math fluency

Poor math fluency, or timed calculation (TC) performance, is a characteristic of dyscalculia, a common cause of poor educational and occupational outcomes. Here, we examined neural substrates of dysfunctional math fluency and potential compensatory mechanisms. We performed functional MRI scans of participants with divergent performance on an event-related TC paradigm (poor TC, <0.5 accuracy, n=34; vs. controls, accuracy>0.8, n=34). Individuals with poor TC had decreased intraparietal sulcus (IPS) engagement, and decreased IPS-striatal and IPS-prefrontal effective connectivity. We next examined an independent well-performing sample (TC accuracy>0.8, n=100), stratified according to relatively low-versus high-IPS activation during TC. Relatively reduced IPS engagement, or patterns of IPS-related effective connectivity similar to those with poor TC, appeared to be compensated for by increased engagement of effective connectivity involving fusiform gyrus, angular gyrus, inferior frontal gyrus and striatum. Neural connectivity involving high-level visual processing in fusiform gyrus and related ventral cortical networks may be relevant in compensatory function ameliorating aspects of dyscalculia and mathematical difficulty.

The nature of math anxiety in adults: Prevalence and correlates

It is important to understand the nature of math anxiety in the general adult population, as the importance of math skills does not end when one leaves school. To this end, we present a well-powered, preregistered study of English-speaking U.S. adults describing the nature of math anxiety in this population. 1000 participants were recruited online. Math anxiety was approximately normally distributed, with the mean between “some” and “moderate”. Math anxiety was significantly negatively correlated with probability knowledge and math fluency, and significantly positively correlated with general anxiety and test anxiety. Women reported higher math anxiety than did men. Participants who had completed graduate school or had a STEM career had significantly lower levels of math anxiety than did those with less education, or non-STEM careers. Thus, we see evidence for math anxiety in U.S. adults and that it correlates with factors also reported in previous studies using younger and student populations.