Physical Fitness Was Linked to Better Arithmetic Fluency in 1,166 Adolescents

A seven-month study of Spanish secondary school students reports that physical fitness measured at the start of the year predicted stronger executive function and arithmetic fluency months later. Accelerometer-measured activity predicted none of those outcomes, placing the signal in physical fitness rather than in movement minutes.

Physical Fitness measured in the autumn appears to say more about how an adolescent will reason and calculate by spring than the raw volume of movement that adolescent records on a wrist monitor. That is the central result of a longitudinal analysis of 1,166 Spanish adolescents published on September 17, 2026, in the International Journal of Behavioral Nutrition and Physical Activity.

The research team came from the University of Cadiz and the associated INiBICA institute, with a co-author at the University of Extremadura. Fatima Martin-Acosta is listed first, and Alberto Grao-Cruces last. The group followed adolescents aged 12 to 14 across a single school year, testing them twice, roughly seven months apart.

At each wave the researchers captured four things: moderate-to-vigorous physical activity by accelerometry using the ActiGraph GT3X+, physical fitness through the ALPHA-Fitness battery, core executive functions using the NIH Examiner Battery, and arithmetic fluency. The design was built to test direction, not just correlation, asking which measures at Time 1 predicted which measures at Time 2.

The answer was lopsided. Baseline physical fitness positively predicted executive functions at Time 2, with a standardised coefficient of 0.104 and a p-value below 0.001, and predicted arithmetic fluency directly, with a coefficient of 0.040 at p below 0.05. Baseline moderate-to-vigorous activity predicted nothing measured at follow-up.

Why Physical Fitness and Activity Minutes Came Apart

Activity and fitness are often treated as the same variable wearing different clothes. This study separates them cleanly. Minutes of moderate-to-vigorous movement, recorded on the wrist over a wear period, describe what a student did during that window. Physical fitness, scored on the ALPHA-Fitness battery, describes what a student is currently capable of.

Those are not interchangeable. A capacity score accumulates across months and years of habit, growth and sport participation. A week of accelerometry samples a slice of one term. In this cohort, only the accumulated measure carried forward into cognition.

What the ALPHA-Fitness Battery Actually Scores

The ALPHA-Fitness battery is a standardised set of field tests used widely in European school research. It scores capacity rather than participation, which matters for interpreting this result: a student who plays no organised sport but has high aerobic and muscular capacity would score well, and a student who logs high activity minutes without that capacity would not.

That distinction is the practical heart of the paper. Promoting physical fitness and promoting activity minutes are related goals, but the evidence here attaches the cognitive prediction to the first.

A Loop Between Executive Function and Arithmetic

Alongside the fitness finding, the authors report a reciprocal relationship between executive functions and arithmetic fluency across the seven-month lag, with coefficients between 0.074 and 0.132, all at p below 0.001. Each predicted the other at follow-up.

That reciprocity is worth pausing on. It suggests arithmetic practice is not simply a downstream consumer of general cognitive control. Working with numbers appears to feed back into the control processes that support it, which is why the authors frame both as predictors of academic success rather than as a one-way chain.

How Much a 65 Percent Model Explains

The model accounted for 65 percent of the variance in arithmetic fluency at follow-up. That is a large figure, and it invites misreading. Most of it is carried by prior arithmetic ability and prior cognitive scores, which are powerful predictors of later performance in any academic domain.

The fitness contribution sits inside that total, and the coefficients attached to it are modest. A standardised coefficient of 0.040 for the direct path to arithmetic fluency is a small effect by any conventional reading. The honest summary is that physical fitness made a detectable, consistent, but small contribution.

Where the Null Result Deserves Attention

Null findings usually get less coverage than positive ones, and this one deserves the opposite treatment. Baseline moderate-to-vigorous activity was not significantly associated with physical fitness, executive functions or arithmetic fluency at Time 2.

That is a striking result in a sample this size. It does not show that activity is irrelevant to adolescents. It shows that in this cohort, over this interval, with these instruments, activity minutes at one point in time did not forecast later capacity or cognition, while a capacity measure did.

Why Direction Matters in This Design

Cross-sectional studies have repeatedly linked fitter adolescents to better cognitive scores, but a single snapshot cannot say which came first. A longitudinal design with two waves does more, because it asks whether a measure taken at Time 1 predicts a different measure at Time 2 rather than simply co-occurring with it.

That is why the asymmetry reported here is informative. Physical fitness at the first wave forecast cognition at the second, and the activity measure at the first wave did not. The authors position physical fitness and cognitive skills together as predictors of academic success rather than as byproducts of it.

It still falls short of causal evidence. Only a trial that raises physical fitness in one group and not another, then measures what happens to arithmetic, can test whether the cognitive difference actually follows. No such trial was run here, and the paper does not claim one was.

What Parents, Teachers and Coaches Can Take From This

The safe reading is narrow and still useful. Capacity appears to travel with cognition in adolescence, and capacity is built slowly. That argues for consistency over intensity campaigns, and for treating physical education as something that develops measurable qualities rather than as supervised activity time.

General, non-individualised points that follow from the design:

• Treat physical fitness as a trainable school outcome, measured and tracked, not merely encouraged.
• Do not read this as evidence that a specific programme raises test scores; no intervention was tested.
• Expect small effects. The coefficients here are modest and sit alongside much stronger academic predictors.
• Keep activity in the picture anyway, since its broader health value is established elsewhere and was not the question this study asked.

Readers following this thread will find the same tension in adult research. Our report on how physical activity tracked with memory across 136,503 older adults shows an association at a very different life stage, while a small trial in which ten minutes of slow running improved mood and executive function tested an acute effect rather than a months-long one. A third strand runs through the menopause trial where aerobic exercise improved executive function, which is the interventional design this school study lacks.

How This Fits the Wider Youth Evidence

Youth exercise science has spent years arguing about what to measure and when. Our earlier coverage of why early talent selection may miss future elite athletes made a related point about maturation confounding youth measurement. Fitness batteries in 12 to 14 year olds face the same problem, because adolescents at the same chronological age can be years apart biologically.

This study does not resolve that. It does add a well-powered longitudinal data point to a literature that has leaned heavily on cross-sectional snapshots, and it does so with a null result on activity that future work will need to reckon with.