From category abstraction to consolidation: Optimizing interleaved practice for lasting learning in primary arithmetic

A central goal of mathematics education is the development of context-appropriate, adaptive strategy use. Adaptive strategy use presupposes lasting, transferable knowledge, which can be fostered by two main mechanisms: generative learning and cognitively effortful processing (desirable difficulties). Interleaved practice engages both by prompting comparison while requiring repeated, effortful retrieval. In the first funding phase, Experiment 1 showed that interleaving subtraction strategies enhanced third graders' flexibility, conditional strategy knowledge, and adaptivity in solving subtraction tasks, with effects lasting up to 16 weeks. Additional support (self-explanation prompts, initial blocked phase) did not add benefits. Based on the two-stage framework, a likely reason is that the initial explicit instruction on the application conditions of the strategies moved many learners into consolidation (Stage 2), rendering abstraction-oriented support (Stage 1) redundant. In inductive interleaving, simultaneous presentation showed no advantage over sequential presentation (preliminary findings, Experiment 2). Thus, Experiment 3, currently underway, tests explicit guided comparison prompts to support category abstraction in inductive interleaving. Building on these findings, the second funding phase will examine the role of instructional format (deductive vs. inductive), instructional support, and learners’ stage in the learning process (category abstraction, consolidation) in shaping the interleaving effect. Four experiments will be implemented in regular mathematics lessons. (Lasting) Learning will be assessed immediately and after 8 weeks. In Experiment 1 (content: adaptive use of subtraction and multiplication strategies, N=198), we will test in Grade 4 mathematics whether a deductive format (vs. inductive) amplifies the interleaving effect. Experiment 2 (N=262) will be a conceptual replication of Experiment 1 in Grade 7 mathematics (linear equations) to examine whether the findings generalize to older learners and to algebraic content. In Experiment 3 (content: adaptive use of subtraction and multiplication strategies, N=238), we will investigate in Grade 4 whether support (guided comparisons vs. additional practice vs. no support) differentially benefits deductive and inductive interleaving. In Experiment 4 (content: adaptive use of subtraction strategies, N=316), we will examine whether mastery-based adaptive support, in which prompts are faded once abstraction is achieved to reallocate time to retrieval-based consolidation, is more beneficial than static or no support in inductive interleaving for fostering (lasting) learning. Cross-cutting analyses will examine the role of intermediate knowledge after instruction in deductive interleaving for immediate and lasting learning, and whether steeper learning trajectories, indicating faster abstraction and earlier entry into consolidation, predict greater (lasting) learning.

Keywords: interleaved practice; subtraction strategies; strategy proficiency; mathematics; primary school instruction

Click here to see our team.