See the research behind Toku.

Retrieval can improve later retention relative to additional study under the tested conditions.

A broad research base showing retrieval practice can strengthen long-term retention, with feedback often increasing its value.

Across a large evidence base, practice testing generally outperformed restudying and other non-testing comparison conditions for learning.

Retrieval practice benefits have been observed across real classroom settings, age groups, subjects and test formats.

A broad spacing effect across a large body of memory research.

Spacing benefits have been demonstrated across memory, problem solving and generalisation tasks, and can be combined with retrieval practice.

Mixing or spacing mathematics problem types can improve later performance relative to conventional blocked practice in the studied tasks.

Classroom mathematics practice that interleaved different problem types produced better delayed test performance in the reported study.

Feedback can influence learning substantially, with the impact depending on what the feedback communicates and how the learner can act on it.

A large meta-analysis found an overall positive effect of educational feedback, with effects varying substantially by feedback type and context.

EEF summarises an extensive school evidence base showing feedback can have a high impact when it is specific, actionable and connected to learning goals.

The importance of working-memory demands and schema acquisition when designing learning tasks.

Mathematical performance beyond simple fact retrieval depends strongly on working memory, and mathematics anxiety can consume cognitive resources.

Arithmetic fact retrieval is a distinct and educationally relevant component of mathematical development.

Basic-fact fluency interventions can improve fluency, with outcomes depending on intervention components and learner needs.

Recent synthesis of mathematics fact-fluency interventions across primary-age learners, adding to the evidence base on building efficient basic-fact performance.

The development of arithmetic fact retrieval has measurable neural correlates and changes with maturation and skill.

Longitudinal evidence that children’s arithmetic learning is accompanied by changes in hippocampal-neocortical engagement as fact retrieval develops.

Formative assessment can improve learning when evidence of current understanding is used to change what happens next.

Mastery-learning programmes showed positive effects on examination performance across controlled evaluations, with implementation differences affecting results.

Some learning conditions that make practice feel harder in the short term can improve long-term retention and transfer.

Timed and untimed conditions can produce different performance patterns, and learner characteristics can interact with timed mathematics performance.

Gamified educational interventions can influence learning-related behaviours and engagement, although effects vary with design and context.

Gamification has shown positive average effects on several educational outcomes, while the literature also contains mixed findings and meaningful design differences.

Planning, monitoring and evaluating learning can be valuable when explicitly taught and embedded in subject learning.

Evidence-informed guidance on mathematical development, representations, misconceptions, problem solving, independence and targeted support.

The statutory curriculum explicitly identifies fluency, reasoning and problem solving as complementary aims, and calls for varied and frequent practice with increasing complexity.

Analogical and matrix reasoning made distinct contributions to science and mathematics problem-solving performance in the studied adolescents.

Comparing and connecting multiple examples helped children focus on relational structure rather than only surface features.

Repeated exposure to one procedure can create a mental set that makes learners less likely to notice a more efficient strategy and can constrain later flexibility.

In the studied mathematical setting, students who first generated and explored solution attempts before instruction developed stronger conceptual understanding and transfer on later assessments.

Students practising with creative mathematical reasoning showed advantages on later mathematical performance compared with more imitative algorithmic practice in the reported work.

Preschool working-memory and executive-function measures predicted later mathematics performance in the longitudinal sample.

Working memory, cognitive flexibility and inhibitory control in kindergarten predicted later reading, mathematics and science achievement in a large longitudinal sample.

Fluid reasoning predicted future mathematical performance above several other cognitive measures in the longitudinal study.

Very young children exposed to more divergent demonstrations subsequently produced more divergent actions in the experimental task.

A short divergent-thinking training programme changed divergent-thinking performance and related psychological measures in the adolescent sample.

A cluster-randomized school intervention produced substantially higher performance on a critical-thinking-about-health assessment one year later.

Analogical reasoning improved markedly across childhood and adolescence and was associated with developing brain systems involved in relational reasoning and cognitive control.