Attention, ADHD, and math practice: what the evidence says for a fluency and learning app

Prepared 2026-09-27.

Scope: how a math practice and learning app for a 9-year-old (England Year 5, US grade 4), later offered to other families and possibly a school, should serve children with ADHD and attention difficulties generally, and which of the app's current design rules help or hurt them. The review covers response-time variability, reinforcement and rewards, task and session length, working memory and multimedia, math difficulties in ADHD, impulsive error patterns, timing and anxiety, and narrative and novelty. Sources were located by web and database search and checked against Europe PMC (which mirrors PubMed abstracts), ERIC, Crossref, NICE, and publisher pages. Full texts were read for Kofler et al. (2013), Bella-Fernandez et al. (2024), NICE NG87, and the EEF "Five-a-day" summary; most other sources were checked at abstract level. Claims taken from a secondary summary or search index rather than the source itself are marked "(unverified)"; claims from memory are marked "(recalled, not verified)". Most ADHD evidence comes from clinic-referred or research-diagnosed samples, often boys, often on laboratory tasks rather than on math practice. Where a finding comes from adults, adolescents, or a non-clinical "at-risk" sample, the text says so.

Summary of key findings

Children with ADHD are not uniformly slower; they are more variable, and the difference sits in an excess of occasional very slow responses (the exponential "tau" tail). Across 319 studies, RT variability was larger in children and adolescents with ADHD (Hedges' g = 0.76); mean RT was not slower once variability was accounted for, and tau showed the largest effect (g = 0.99, k = 8) (Kofler et al. 2013, Clinical Psychology Review). A 51-study ex-Gaussian meta-analysis found no difference in mu (d = 0.04), a moderate one in sigma (d = 0.26), and a moderate-to-large one in tau (d = 0.53) (Bella-Fernandez et al. 2024, Neuropsychology Review).
Incentives only slightly reduce this variability (g = -0.38, 8 studies, N = 335), while stimulant medication reduces it substantially (g = -0.74) (Kofler et al. 2013). A lapse is a state, not something motivation design can remove, so a single slow correct answer is weak evidence that a fact is not known.
Children with ADHD show steeper delay discounting (d = 0.43, 25 comparisons, N = 3,913; Jackson and MacKillop 2016) and more choice-impulsivity (g = 0.47, 26 studies, N = 4,320; Patros et al. 2016). They respond to reinforcement at least as much as peers, prefer it immediate, and do better with intense or frequent reinforcement (Luman et al. 2005, 22 studies, N = 1,181). When reinforcement is frequent, group differences in sustained attention can disappear (Aase and Sagvolden 2006, N = 56).
Behavioural contingency management is well supported for ADHD behaviour (Fabiano et al. 2009, 174 studies; DuPaul et al. 2012, 60 studies), but that evidence concerns adult-run classroom and home systems aimed at behaviour. No study found here tested whether points or currency in practice software undermine or support the intrinsic motivation of children with ADHD; Morsink et al. (2022) name this as an open question. Positive informational feedback raised free-choice motivation in the general literature (d = 0.33; Deci, Koestner and Ryan 1999).
Game formats raise persistence in ADHD samples: game elements increased time training and working-memory gains in a randomised trial (Prins et al. 2011, N = 51), and a game version of a working-memory task brought persistence to normal levels where 1 euro did not (Dovis et al. 2012, N = 61). These game versions bundled feedback, reward, and story, so the active ingredient is unknown.
Working-memory deficits in ADHD are large, especially visuospatial central-executive working memory (effect size 1.06; Martinussen et al. 2005, 26 studies). In clinic samples, working memory accounts for most of the link between ADHD and low math achievement (Gaye et al. 2024, N = 186; Gaye et al. 2025, N = 275).
About 18% of children with ADHD have a comorbid mathematics disorder (Capano et al. 2008, N = 476), and in reviews of 2001 to 2011 studies about 45% have some learning disability (DuPaul et al. 2013, 17 studies). The weaknesses that recur are math fluency and speed rather than calculation accuracy (Capodieci and Martinussen 2017; Zentall et al. 1994, N = 228), plus regrouping errors in subtraction (Benedetto-Nasho and Tannock 1999, unverified).
Visual distractors hurt children with ADHD more than peers: video distracted boys with ADHD more than controls (Pelham et al. 2011, N = 67 and 86), and appealing toys halved their attention to an educational programme while attention without toys was the same as controls' (Landau et al. 1992, N = 39). Low working-memory readers are the most vulnerable to seductive details (Sanchez and Wiley 2006). Signalling helps learning in general samples (retention g = 0.52, 103 studies; Schneider et al. 2018, unverified).
NICE NG87 (2018, updated 2019) lists "shorter periods of focus with movement breaks (including the use of 'I need a break' cards)" among environmental modifications. Evidence on the best task length is thin. A single 20-minute bout of exercise improved arithmetic and attention in children with and without ADHD (Pontifex et al. 2013, N = 40). Movement during working-memory tasks goes with better, not worse, performance in ADHD (Sarver et al. 2015; Hartanto et al. 2016).
Children with ADHD show less post-error slowing (d = 0.42, 26 comparisons; Balogh and Czobor 2016) and are more frustrated by unsignalled imposed delays (Bitsakou et al. 2009, d = 0.4 to 0.7). But when viewing time is set externally, their memory matches peers', and the deficit comes from choosing short viewing times themselves (Sonuga-Barke, Taylor and Heptinstall 1992). Generic "stop and think" self-instruction training has little support (Abikoff 1991), while self-monitoring interventions show large effects (Reid et al. 2005).
Extra time does not give children with ADHD a special benefit on math tests (Lewandowski et al. 2007, N = 54, unverified). Most educational accommodations lack ADHD-specific evidence; the exception is read-aloud, with two randomised experiments showing benefits for younger students with ADHD (Lovett and Nelson 2021, 68 documents).
Novel story content improved reading comprehension in boys at risk for ADHD (Beike and Zentall 2012, N = 48, non-clinical). Children with ADHD use a story's causal structure as well as peers until attention is divided (Lorch et al. 1999).

1. Response-time variability

Size and shape. Kofler et al. (2013) meta-analysed 319 studies of RT variability. After correction for unreliability and publication bias, children and adolescents with ADHD were more variable than typically developing peers (g = 0.76) and adults less so (g = 0.46). Mean RT was not slower once variability was accounted for, but large variability deficits remained after accounting for mean RT. By metric, the tau effect (g = 0.99, 95% CI 0.64 to 1.34, k = 8) was larger than SD (g = 0.70, k = 253) or CV (g = 0.78, k = 35). The authors conclude that "ADHD-related variability appears to be attributable primarily to a subset of abnormally slow responses (tau), rather than ubiquitous variability across all trials." Two cautions from the same paper: children with ADHD were only slightly more variable than clinical control children (g = 0.25, k = 50), so high variability is not specific to ADHD; and only about 47% of children and adolescents with ADHD scored outside the typical range, so it is not diagnostic. Stimulants reduced variability (g = -0.74); non-stimulant and psychosocial treatments did not. External incentives reduced it only slightly (g = -0.38, 95% CI -0.63 to -0.14; 8 studies, N = 335).

Bella-Fernandez et al. (2024), an open-access meta-analysis of 51 studies fitting ex-Gaussian distributions, confirmed the pattern: mu d = 0.04 (95% CI -0.04 to 0.13), sigma d = 0.26, tau d = 0.53 (95% CI 0.40 to 0.66), with significant heterogeneity. Mu was, if anything, larger in typical groups at younger ages. The best-established moderator is event rate: in a meta-analysis of Go/No-Go tasks, children with ADHD slowed disproportionately at slow event rates and made more commission errors at fast ones (Metin et al. 2012). One dataset of 8,916 children aged 9 to 10 shows that performance worsens with time on task, mainly through a falling drift rate (Epstein et al. 2023). Most of this evidence comes from simple laboratory RT tasks, not arithmetic retrieval. No study found here fitted ex-Gaussian parameters to fact-retrieval latencies in children with ADHD.

What this means for the app's fluency rules. The app calls a fact fluent below 3 s, puts it in the fastest phase below 1.5 s on two consecutive spaced presentations, requires a median under 3 s over the last 8 for mastery, and drops a fact two rungs on the review ladder after an error or a slow response. The median rule and the "two consecutive" rule are already robust to occasional lapses. The weak point is the single-response demotion. If a child's slow tail holds even 5 to 10% of responses (a figure for illustration, not from the sources), a child with ADHD will have well-known facts demoted two rungs regularly. The result is extra review, extra time, and a plateau the child cannot explain. The evidence that the slow tail reflects attentional state rather than item knowledge is indirect: tau differences appear on trivially easy tasks where knowledge is not in question, and they are reduced by stimulants. Kofler et al. (2013) note, however, that pure "attentional lapse" models do not fully explain the phenomenon.

Telling a lapse from not knowing. No validated classifier for arithmetic retrieval in children with ADHD was found. The RT-analysis literature routinely trims or models outliers relative to each person's own distribution rather than a fixed cutoff (for example, Ratcliff 1993, recalled, not verified). The evidence supports three design moves. First, compare against the child's own recent latency distribution: a response many times the child's median for facts already known is more likely a lapse than the same latency on a new fact. Second, require converging evidence before demoting, such as a repeat of slowness on the same fact at a later presentation, or an error. Third, treat a cluster of slow responses across many facts in one block as a state change (fatigue, distraction), not item evidence. The plan already does the third in part ("if latency spikes mid-block, silently switch the next 5-8 items to known facts").

Fact-fluency interventions with ADHD children specifically. This is a gap. Incremental rehearsal, explicit timing, cover-copy-compare, and taped problems are well supported in general and learning-disability samples (see review 01), but ADHD-specific studies are small single-case designs. In Figarola et al. (2008), three first and second graders, two with ADHD, graphed their own rate of correct answers on timed fact sheets; two of the three met their aim lines. Computer-assisted math practice raised on-task behaviour and math performance in three grade 2 to 4 students with ADHD (Mautone et al. 2005) and in three grade 4 to 6 students using game-format software (Ota and DuPaul 2002, results unverified). Zentall (1990, unverified) reported an automatization deficit in fact retrieval among adolescents with attention disorders. Methylphenidate raised the number of math problems completed but not accuracy, and time on task, not RT variability, mediated the gain (Froehlich et al. 2014, N = 93). That fits the picture of a child who knows the facts but does not produce them steadily.

2. Reinforcement and rewards

Delay aversion and reward sensitivity. Sonuga-Barke's dual pathway model proposes two partly separate routes to ADHD: inhibitory or executive dysregulation, and a motivational style built around escaping delay (Sonuga-Barke 2002; 2003). The meta-analyses support elevated discounting: monetary delay discounting d = 0.43 across 25 case-control comparisons (N = 3,913), with no moderation by age (Jackson and MacKillop 2016), and choice-impulsivity g = 0.47 across 26 studies of children and adolescents (N = 4,320) (Patros et al. 2016). In early experiments, hyperactive children chose small immediate rewards only when doing so shortened the session; they seemed to minimise overall delay rather than to maximise reward (Sonuga-Barke, Taylor, Sembi and Smith 1992). Luman et al. (2005) reviewed 22 studies (N = 1,181) and concluded that reinforcement improves performance and motivation in both groups, somewhat more in ADHD, that high-intensity reinforcement works well in ADHD, and that children with ADHD prefer immediate reward. Aase and Sagvolden (2006) found no group differences under frequent reinforcement (a mean of every 2 s) and deficits in sustained attention and variability only under infrequent reinforcement (a mean of every 20 s). Dovis et al. (2012) found that feedback alone was enough for controls to perform at their best, while children with ADHD needed more; even 10 euros or a game version did not normalise working memory, though both normalised persistence over time.

Contingency management. Fabiano et al. (2009) meta-analysed 174 studies of behavioural treatment. Effects varied by design (between-group 0.83, pre-post 0.70, within-group 2.64, single-subject 3.78), and the authors conclude there is "strong and consistent evidence" for behavioural treatment. DuPaul, Eckert and Vilardo (2012) reviewed 60 school-based studies (1996 to 2010). Behavioural effects were significant for within-subject (0.72) and single-subject (2.20) designs but not between-subject designs (0.18). Academic effects were reported as 0.43 (between), 0.42 (within), and 3.48 (single-subject, the only significant one) (academic figures unverified). The authors conclude that contingency management, academic intervention, and cognitive-behavioural strategies were all associated with positive effects. A 2025 meta-analysis of school-based RCTs found a moderate pooled academic effect (d = 0.37, 22 comparisons, N = 1,962) with high heterogeneity (Yegencik et al. 2025). The AAP guideline recommends medication together with parent training in behaviour management and/or behavioural classroom interventions for ages 6 to 11 (Wolraich et al. 2019).

Against overjustification. Deci, Koestner and Ryan (1999; 128 studies) found that expected tangible rewards undermine free-choice intrinsic motivation, more so in children, and that positive feedback raises it (d = 0.33 free choice, 0.31 interest). The ADHD literature has barely tested this. Carlson, Mann and Alexander (2000; 40 children with ADHD, 40 controls, an arithmetic task) compared reward, response cost, and no contingency, and measured intrinsic motivation as a free choice between more arithmetic or spelling. Response cost improved accuracy for the ADHD group, and reward improved self-rated motivation (details from the abstract as indexed; unverified). Morsink et al. (2022) argue that ADHD motivation research has studied reinforcement almost exclusively and has not looked at the "potential negative effects of external reinforcers" on intrinsic motivation. Smith and Langberg (2018; 20 studies) found lower academic motivation in youth with ADHD but thin evidence overall.

Does informational progress feedback serve ADHD children? Direct evidence is limited but points one way. Self-graphing of correct-answer rate supported fact fluency in two of three children (Figarola et al. 2008). Self-monitoring interventions, including self-monitoring of performance, produced combined effect sizes above 1.0 for on-task behaviour, academic accuracy, and productivity (Reid, Trout and Schartz 2005). In general primary samples, classroom physical-activity programmes improved achievement when a progress-monitoring tool was used (SMD = 1.03; Watson et al. 2017). The mechanism the ADHD evidence points to is frequency and immediacy (Aase and Sagvolden 2006; Luman et al. 2005), not currency.

The most defensible middle ground. The app keeps its rule of no currency, points, badges, or shops. It makes the informational feedback it already has more frequent, more immediate, and more visible within a block: "that fact is now strong", a filling indicator of how much of the block remains, and the end-of-block view of what got stronger. Frequent feedback on performance is what normalised attention in Aase and Sagvolden (2006), and it is the category Deci et al. (1999) found to raise intrinsic motivation. Contingency management for behaviour belongs to parents and teachers, off the app; the parent digest can give them accurate material for it (minutes, days, facts strengthened).

3. Task and session length, breaks, and movement

Guidelines. NICE NG87 (published 14 March 2018, last updated 13 September 2019) defines environmental modifications to include "reducing distractions (for example, using headphones), optimising work or education to have shorter periods of focus with movement breaks (including the use of 'I need a break' cards)". It recommends that they be tried before medication for children aged 5 and over. The document gives these as examples, not as recommendations with graded evidence.

Task duration. No experiment was found that identifies an optimal practice-block or session length for children with ADHD. The closest evidence is indirect. Performance declines over a session more in ADHD than in controls (Dovis et al. 2012), but meta-analytic evidence on vigilance decrement over time is "small to moderate" and rests on a handful of studies (Huang-Pollock et al. 2012, 47 CPT studies). Extended time on seatwork (45 vs 30 minutes, N = 33) did not help children with ADHD, and secondary summaries report a lower rate of accurate completion with more time (Pariseau et al. 2010; direction of result unverified). "Chunking" seatwork showed no benefit in an unpublished dissertation (Jerome 2019, unverified). Lovett and Nelson (2021) conclude that most common accommodations lack ADHD-specific experimental support. The app's short blocks (90 to 120 s) and Learn segments (60 to 120 s) fit NICE's "shorter periods of focus", but the evidence cannot say whether 90 s is better than 3 minutes.

Movement and exercise. A single 20-minute bout of moderate aerobic exercise, compared with seated reading, improved response accuracy and arithmetic and reading performance in children with and without ADHD (Pontifex et al. 2013; N = 40, within-subjects). Across eight RCTs (N = 249), aerobic exercise programmes had moderate-to-large effects on attention (SMD = 0.84) and executive function (SMD = 0.58) (Cerrillo-Urbina et al. 2015; small trials, quality concerns). Classroom physical-activity breaks improved on-task behaviour in general primary samples (SMD = 0.60; Watson et al. 2017). Fidgeting and gross motor activity during working-memory tasks go with better performance in children with ADHD and slightly worse in controls (Sarver et al. 2015, N = 52; Hartanto et al. 2016, N = 44 trial-by-trial). An app should never require stillness, and a child standing up or moving is not a sign of disengagement.

Self-pacing. Self-pacing has a hazard. When hyperactive children set their own viewing time, they chose shorter times and remembered less; when viewing time was imposed, their memory equalled controls' (Sonuga-Barke, Taylor and Heptinstall 1992). A learner-paced Learn player lets a delay-averse child tap past explanations before they are processed.

4. Working memory, distraction, and multimedia

Working memory. Martinussen et al. (2005; 26 studies) found effect sizes of 0.85 (spatial storage), 1.06 (spatial central executive), 0.47 (verbal storage), and 0.43 (verbal central executive). Kasper, Alderson and Hudec (2012) report large deficits in both phonological and visuospatial working memory in children. In clinically evaluated children aged 8 to 13, working memory accounted for most of the ADHD-math association, and trait anxiety did not add (Gaye et al. 2024; 2025). Working-memory load is the design variable most likely to matter for multi-step procedures.

Distraction and seductive details. Children with ADHD are not globally distractible, but salient competing visual activity costs them more. Video distractors hurt boys with ADHD more than controls; background music helped some children and hurt others (Pelham et al. 2011). With appealing toys present, boys with ADHD watched an educational programme half as much as controls; without toys there was no difference, and recall did not differ (Landau et al. 1992). In a study of students (not ADHD-specific), readers with low working-memory capacity were most vulnerable to seductive illustrations and looked at them more often and for longer (Sanchez and Wiley 2006). Meta-analyses in general samples find that seductive details reduce learning (Rey 2012; Sundararajan and Adesope 2020, 68 studies, unverified; effect sizes recalled, not verified).

Narration, captions, and highlighting. No ADHD-specific studies of multimedia principles were found; this is a gap. Read-aloud is the one educational accommodation with ADHD-specific randomised support for younger students (Lovett and Nelson 2021), which supports narration by default. Signalling improves retention (g = 0.52) and transfer (g = 0.31) and lowers cognitive load in 103 studies (Schneider et al. 2018, figures from the abstract as indexed; unverified). Highlighting the narrated part of the picture is signalling. On captions, Adesope and Nesbit (2012; 57 studies) found spoken-plus-written presentations beat spoken-only but not written-only. They attribute this mainly to system-paced presentations, where learners mishear speech (unverified). Captions are one tap away in the app, and steps are short. Nothing here argues for turning captions on by default, but a child who habitually mishears or loses the thread may do better with them. Zentall's colour studies suggest salience helps attention-problem students when it is added to the task stimuli themselves (Zentall, Falkenberg and Smith 1985, N = 32 adolescents), consistent with signalling rather than decoration.

5. Math learning and ADHD

Co-occurrence. In 476 children with ADHD, 18.1% had a comorbid mathematics disorder, often alongside a reading disorder, and those with both were most impaired (Capano et al. 2008). A review of 17 studies (2001 to 2011) found a mean ADHD-LD comorbidity of 45.1% (DuPaul et al. 2013). In a US parent survey, 46% of children with ADHD had a learning disability, compared with 5% of other children (Larson et al. 2011, N = 61,779). A meta-analysis of achievement found ADHD associated with lower achievement overall (d = 0.71; Frazier et al. 2007). Inattention, more than hyperactivity-impulsivity, carries the association with math, including genetically (Tosto et al. 2015; 34 studies).

Which components. Adolescents with ADHD had weaker math fluency despite calculation scores similar to their peers', and made more operation-switch errors (Capodieci and Martinussen 2017, N = 69). Boys with ADHD (N = 107 vs 121 controls) were slower at computation and weaker on specific problem-solving concepts (Zentall et al. 1994). Children with ADHD made more trading (regrouping) errors in subtraction and used more immature strategies (Benedetto-Nasho and Tannock 1999, N = 29; unverified). Kaufmann and Nuerk (2008) found intact overlearned calculation but weaker number comparison and dot enumeration in children aged 9 to 12 with combined-type ADHD. On an analog math task matched to skill, children with ADHD did not differ in productivity or accuracy even though their achievement scores were lower (Antonini et al. 2016). In a large community sample (518 with ADHD, 851 without), ADHD was associated with lower scores on all academic tests but did not independently predict math problem solving once basic skills were controlled (Trane and Willcutt 2023). Together: the likely problems are speed and steadiness of retrieval, errors where attention slips (operation switches, regrouping), and working-memory load in multi-step procedures, more than conceptual understanding.

Interventions. ADHD-specific math intervention evidence is mostly single-case: computer-assisted instruction (Mautone et al. 2005; Ota and DuPaul 2002), self-graphing (Figarola et al. 2008), and self-monitoring (Reid et al. 2005). In a randomised trial with 77 inattentive first graders, CAI improved reading fluency and teacher-rated attention (Rabiner et al. 2010); that trial did not measure math. The EEF's SEND guidance names explicit instruction, cognitive and metacognitive strategies, scaffolding, flexible grouping, and technology as its "Five-a-day" for pupils with SEND (EEF 2020).

Games, hyperfocus, novelty. Children with ADHD performed as well as controls on commercial games and better on a game-like version of a CPT (Shaw et al. 2005, small sample). They showed no inhibition deficit in a videogame, though they completed fewer challenges when working-memory load was high (Lawrence et al. 2002, N = 114). Game elements improved motivation and training performance (Prins et al. 2011). A 22-study systematic review of video games for ADHD was positive but mostly small and heterogeneous (Penuelas-Calvo et al. 2022). The largest trial, of AKL-T01 (EndeavorRx; N = 348, aged 8 to 12), improved an attention test score (TOVA API, median change 0.88) and reported frustration as an adverse event in 3% of children. It was sponsored by the vendor, Akili Interactive, and did not measure academic outcomes (Kollins et al. 2020). "Hyperfocus" has no agreed definition and has been studied mostly in adults by self-report (Ashinoff and Abu-Akel 2021); nothing found bears on children's learning.

6. Impulsivity and error patterns

"Often fails to give close attention to details or makes careless mistakes in schoolwork" is a DSM-5 inattention criterion (recalled, not verified). Children with ADHD show less post-error slowing than controls (d = 0.42; 15 publications, 26 comparisons, N = 1,053 ADHD and 614 controls). At long inter-stimulus intervals, controls slowed after errors while participants with ADHD kept or increased their speed (Balogh and Czobor 2016). Fast errors in a practice app are therefore expected in ADHD even when the child knows the material.

Gaming detector. The detector in intelligent tutors was built on typical classroom samples (Baker et al. 2004, recalled, not verified). It has not been validated for children with ADHD. When a previously validated detector was applied across experimental conditions, detected gaming was not associated with lower learning. The authors had to model context to recover validity (Huang et al. 2023). For a child with ADHD, fast repeated wrong answers may be impulsive responding, not strategic avoidance, and the detector's response matters more than its label. Easing difficulty and showing a worked example is a reasonable response to either cause. The risk is in how often it fires and whether the child experiences it as a penalty.

Imposed pauses. Evidence cuts both ways. Delay-related frustration is part of the ADHD profile (Bitsakou et al. 2009: 77 children and adolescents with ADHD, d = 0.4 to 0.7 across delay tasks). In a delay-frustration task built around a simple maths test, young adults with high ADHD symptoms pressed the button more during unsignalled delays (Bitsakou et al. 2006, adults). But externally set viewing time removed the memory deficit that self-pacing produced (Sonuga-Barke et al. 1992). A required dwell on a worked example is therefore well founded, as long as it is short, signalled, and filled with something to do, not an unexplained lock.

Stop and check. Cognitive self-instruction ("stop, look, think") training for children with ADHD has little empirical support (Abikoff 1991). A 16-week academic cognitive training programme, including self-monitoring of accuracy, added nothing over medication or tutoring (Abikoff et al. 1988). Self-monitoring and self-reinforcement procedures show large effects in single-case and within-subject designs (Reid et al. 2005, combined ES above 1.0; Gaastra et al. 2016, self-regulation SSD mean SMD = 3.61 on off-task behaviour). In one study, self-monitoring of attention and of performance both improved on-task behaviour in six students with ADHD (Harris et al. 2005, unverified). The contrast suggests that prompts which make the child record or see their own performance work better than verbal self-talk scripts.

7. Timing and anxiety

Anxiety is common in ADHD: 18% of children with ADHD had parent-reported anxiety, compared with 2% of others (Larson et al. 2011), and a clinic study cites a co-occurrence rate of about 25% (Gaye et al. 2025). In that sample, trait anxiety did not explain the math deficit once working memory was included (Gaye et al. 2025). No study was found on math anxiety specifically in children with ADHD; this is a gap. Extended time on a math test did not help students with ADHD more than controls (grades 5 to 7, N = 54; Lewandowski et al. 2007, unverified). More time on seatwork did not raise productivity (Pariseau et al. 2010, unverified direction). In 44 children aged 7 to 9, a visible Time Timer before a timed math assessment lowered anticipatory anxiety and reduced inattentive and restless behaviour, most of all in children at higher ADHD risk, without changing scores (Hallez and Vallier 2025). This timer showed how much of a whole task remained, not a per-item countdown. Review 01's finding stands: the evidence against timing is weaker than often claimed, and timing does not help highly anxious children. For attention, a visible sense of how much is left may help; per-item time pressure has no support here.

8. Narrative and novelty

Children with ADHD attend to and recall educational television as well as peers when there is no competing activity (Landau et al. 1992). They use a story's causal structure for recall, but lose that benefit when a competing activity is available (Lorch et al. 1999, ages 4 to 6). Replacing familiar story elements with novel ones (less familiar characters, vivid verbs, surprising endings) improved causal and inferential reading comprehension for boys at risk for ADHD or reading disability, but not for typical boys (Beike and Zentall 2012; N = 48, non-clinical, 7 to 11 years). Zentall's optimal stimulation account holds that added stimulation helps when it is in the task, and it reports habituation over time (Zentall 2005; Zentall et al. 2013). None of this tests narrative framing around math practice. It supports novelty inside the content the child must process, such as varied word-problem contexts and numbers, over decorative story layers competing with the task. Review 03 found that strong narrative does not add learning in general samples.

Implications for the app

Lapse-aware scoring for slow correct responses (changes a rule). Stop dropping a fact two rungs on a single slow but correct response when that fact was previously fast. Classify a correct response as a probable lapse when its latency exceeds both 3 s and a multiple (start at 2.5x, to be tuned) of the child's running median latency on Phase 2 and 3 facts in the current session. Handle a lapse by re-presenting the fact after spacers in the same session: fast then means no change, slow again means the normal drop. Errors keep the two-rung drop. Test: an engine unit test in which a simulated child with ex-Gaussian latencies (tau elevated, mu normal) keeps known facts on their rungs, while a simulated child who does not know a fact still gets it demoted. Basis: Kofler et al. 2013; Bella-Fernandez et al. 2024. The mastery median and the Phase 3 "two consecutive" rule need no change.
Block-level state detection (extends an existing rule). The existing "latency spike, switch to known facts" rule should also stop charging facts for slowness during the spike window. If the lapse rate in a block exceeds a threshold, end the block early at a natural stopping point instead of pushing on. Test: a spike in the simulated log produces no demotions and an early block end.
Parent-set session length and a free pause (adds settings). Let the parent choose a session length (for example 5, 10, 15, or 20 minutes; the default stays at the plan's 10 to 15). Give the child an always-available pause that costs nothing, stops latency recording, and resumes at the same item. Between blocks, offer an optional "stand up and stretch" break screen, still and without animation. Basis: NICE NG87's shorter periods of focus and "I need a break" cards; Pontifex et al. 2013; Sarver et al. 2015. Test: a paused item records no latency, and a resumed session keeps its place.
In-block informational progress display (adds a feature within rule 4). Show a quiet indicator of how much of the block remains, plus immediate "now strong" feedback when a fact reaches Phase 3. Forge blocks end on time (90 to 120 seconds, plan section 5.3), so a count of items left cannot be stated truthfully, and seconds left would be a countdown, which rule 3 forbids. The indicator is therefore a filling bar or a few segments without numbers or seconds, advanced by the block's own clock and completed only when the block ends. It gives a child the sense of "nearly done" without a timer to race. Alternatively, a block can be given a fixed item budget; that changes how Forge blocks stop and would need its own decision. No points, currency, or totals for volume. Basis: Aase and Sagvolden 2006; Luman et al. 2005; Deci et al. 1999 (positive feedback d = 0.33); Hallez and Vallier 2025. Test: A/B within one child over weeks, comparing items completed before quitting and accuracy, and checking that the indicator never shows time.
Keep the no-currency rule (no change), and say so to parents. The ADHD contingency-management evidence concerns adult-run behaviour systems. It does not show that in-app currency helps learning, and its effect on intrinsic motivation in ADHD is untested. The parent digest's minutes, days, and facts strengthened can feed a family's own reward plan off the app. Add one plain sentence to the parent help text; do not build a reward store.
Learn player: minimum exposure per step (changes a rule). Enable "next" only when a step's narration has finished, so a delay-averse child cannot skip explanations unseen. Steps stay short. When the audio fails to load or play, the player already falls back to captions (plan section 5.1). In that case "next" is enabled after the step's scripted duration (the length the narration would have taken, from its text), so a child is never stuck. Basis: Sonuga-Barke, Taylor and Heptinstall 1992. Test: the player refuses to advance before the audio ends, and advances after the scripted duration when the audio fails; measure skip attempts.
Bottom-out hint dwell: make it signalled and active (changes the rule's form). Replace a silent timer with a step-through: the child taps to reveal each line of the worked example, and a visible indicator shows the few steps left. This keeps enforced exposure without an unsignalled wait. Basis: Sonuga-Barke et al. 1992 (imposed exposure helps); Bitsakou et al. 2006 and 2009 (unsignalled delay frustrates). Test: dwell time and next-item accuracy compared with the current timer.
Gaming detector calibration (changes thresholds). Set "fast" relative to the child's own latency distribution, not a population constant. Exclude wrong answers that match a bug rule, which are misconceptions, not gaming. Cap firings per session. Use neutral wording ("Let's look at one together"). Log the firing rate per child; a child who triggers it often should get easier blocks and shorter sessions, and it should never be reported to a parent as cheating. Basis: Huang et al. 2023 (detector validity depends on context); Balogh and Czobor 2016. Test: the firing rate on simulated impulsive but knowledgeable children, compared with simulated guessers.
Post-error beat, not a lecture (changes a rule). After an error, the corrective display stays until the child continues; it never auto-advances. A tap-to-continue alone does not create the pause, because the impulsive child it is meant for can dismiss it at once. So continuing needs one short active step on the correction itself: for a fact, the child types the right answer back once, which is the existing "re-ask within a few items" rule brought forward to the moment of correction. There is no silent timer, which would be an unsignalled wait (item 7). Do not add "stop and think" self-talk prompts. Basis: Balogh and Czobor 2016; Abikoff 1991. Test: accuracy on the item after an error with the active step against a plain tap, and the rate of immediate dismissals.
"I don't know" button (no change, one check). Keep the rate limit, but when the limit is reached, turn the button into "show me the strategy" rather than a dead end. No ADHD-specific evidence exists either way.
Optional self-monitoring (adds an optional feature, low priority). A parent-enabled end-of-session view in which the child marks one fact they got stronger at, using the existing map. This is self-monitoring of performance, not of behaviour. Basis: Reid et al. 2005; Figarola et al. 2008 (small samples).
Multimedia defaults (no change, one added setting). Keep one item on screen, no decorative animation or sound, narration on, and highlighting synced to narration; these fit the evidence (Pelham et al. 2011; Landau et al. 1992; Sanchez and Wiley 2006; Schneider et al. 2018; Lovett and Nelson 2021). Keep captions off by default, but make "captions always on" a persistent profile setting rather than only a per-segment tap. Basis: Adesope and Nesbit 2012 (unverified).
Working-memory load in written methods (check, likely no change). In column and long-division step items, keep carried and borrowed digits and completed steps visible, so the representation holds what working memory would otherwise have to. Make sure regrouping and operation-switch errors have bug rules. Basis: Martinussen et al. 2005; Gaye et al. 2024; Benedetto-Nasho and Tannock 1999; Capodieci and Martinussen 2017.
Timing (no change). Silent latency, opt-in self-referenced sprints on fluent material, no per-item countdown. Nothing in the ADHD evidence argues for more timing, and the anxiety comorbidity argues for keeping sprints opt-in.
No "ADHD mode" and no health data (no change, a principle). Build items 1 to 12 as universal behaviour. Settings are generic (session length, captions, pause), and the app never asks for or infers a diagnosis, consistent with the minimal-child-data rule in PLAN section 15. Lapse classifications are engine data for evaluation, not a label shown to parents.

Where the current rules could harm: the two-rung drop on a single slow response (item 1), a silent dwell timer (item 7), a population-constant gaming threshold (item 8), and a learner-paced Learn player without minimum exposure (item 6). Where they already fit well: no decorative animation or sound, a map that never visibly demotes, short blocks, narration with highlighting, silent latency, the median-based mastery rule, the switch to known facts on a latency spike, and no currency.

Contested or weak evidence

Lapse mechanism. That tau reflects attentional lapses is the common reading, but Kofler et al. (2013) note that lapse models do not fully account for the variability, which is also elevated in other clinical groups. The recommended thresholds in items 1 and 2 are design choices to be tuned on data, not values from the literature.
Optimal task and session length. No experiment was found. NICE's advice is an example list, not graded evidence. Chunking and extended-time accommodations lack support (Lovett and Nelson 2021).
Rewards and intrinsic motivation in ADHD. Untested in any direct way; Carlson et al. (2000) is small and mixed. The strong behavioural-treatment effects come largely from single-case and within-subject designs; between-group academic effects are small and often non-significant (DuPaul et al. 2012).
Game elements. Positive ADHD results bundle reward, feedback, and story, use small samples, and measure cognitive training, not math learning. The largest trial is vendor-funded and targets an attention test score (Kollins et al. 2020).
Exercise. The effects are from small trials. The single-bout arithmetic result is one within-subject study of 40 children (Pontifex et al. 2013).
Multimedia principles in ADHD. Seductive details, signalling, and redundancy evidence comes from general, mostly older samples; Sanchez and Wiley (2006) concerns working-memory capacity, not ADHD.
Novelty. Beike and Zentall (2012) is one study of 48 non-clinical boys, in reading, not math.
Self-monitoring. Large effect sizes come mainly from single-case designs with adult-cued monitoring in classrooms. Translating them to a self-guided app is untested.
Fact-fluency interventions with ADHD. Only small single-case studies were found; review 01's fluency evidence comes from general and LD samples.

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