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A developmental psychologist who examined how executive functions relate to mathematics achievement. Her work used an executive function battery and statistical models separating direct relationships from relationships mediated through other skills. These models organize possible developmental pathways while their interpretation still depends on measurement quality and the study design.^[ref]

Mathematics achievement is attained performance on specified mathematical learning objectives. Its meaning depends on the content and scoring of the assessment: proficiency in counting, arithmetic and geometry need not form an identical profile. A total score can summarize performance while concealing which skills changed.

An informative intervention therefore measures more than success on its practiced activity. In Geetha B. Ramani's study with Robert S. Siegler, children played either a linear numbered board game or a corresponding color board game. Assessment included counting, numeral identification, numerical magnitude comparison and number-line estimation, rather than only skill at winning the game.^[ref]

Improvement on an assessment is evidence about that outcome in the studied population. Claims about broader mathematical understanding require appropriate generalization tests and a comparison design that separates the intervention from maturation, repeated testing and other experiences.