Teaching Algebra Online — what the research says.

Haas (2005), in a meta-analysis of 35 experimental studies of secondary algebra teaching, identified six teaching-method categories that all produced positive effects on achievement: direct instruction, technology-aided instruction, problem-based learning, cooperative learning, communication and study skills, and multiple representations.

Direct instruction, technology-aided instruction, and problem-based learning ranked highest in both the meta-analysis and the subsequent regression analysis. A second-order meta-analysis (Ran et al., 2022, JCAL) confirms a robust positive effect of technology-enhanced mathematics instruction in K–12 across thirty years of studies.

Ebner et al. (2025), in a meta-analytic review published in Remedial and Special Education, confirm CRA as an evidence-based practice in mathematics, with moderate effects on conceptual understanding. For algebra specifically, the canonical concrete tools are algebra tiles and balance scales; algebra-tile representations of equation solving have repeatedly outperformed symbol-only instruction in controlled studies.

The effect is largest for students with weaker prior knowledge — exactly the population most at risk in online learning.

Sweller (1985, 1988) discovered the worked-example effect studying algebra: students who studied two worked examples and then solved a problem outperformed students who solved three problems. Cognitive load theory explains it — solving a problem cold consumes working memory on means-ends search instead of schema formation.

Renkl and colleagues have since extended the finding: example–problem pairs, faded worked examples, and self-explanation prompts on worked examples further increase the gain. There is also a documented expertise-reversal effect: once a learner has the schema, worked examples slow them down.

Productive failure (Kapur) flips the worked-example sequence in one specific situation: when the learning goal is conceptual understanding and transfer, not procedural fluency. Learners attempt a complex, ill-structured problem before any instruction. Their incomplete attempts activate prior knowledge and prime them to attend more closely to the canonical method when it is finally taught.

A meta-analysis of 166 comparisons with over 12,000 participants reports Cohen's d = 0.36 for conceptual understanding and transfer, rising to d ≈ 0.58 when the four design principles are followed with fidelity. Procedural knowledge is not sacrificed — it is statistically equivalent to instruction-first conditions.

The condition that's often missed: productive failure only works when the eventual instruction actually resolves the failure. If learners struggle and then no one closes the loop with a clear explanation, the effect collapses.

Chi's foundational studies (1989, 1994) found that strong learners spontaneously self-explain. Prompting weaker learners to do the same lifts outcomes. Rittle-Johnson & Loehr's meta-analysis (2017, ZDM) reports robust positive effects on math learning.

Importantly, structured (“assisting”) prompts that direct attention to a specific principle outperform open-ended prompts in online settings — open prompts often produce silence or shallow answers when there is no human present to follow up.

The 2025 npj Science of Learning systematic review of AI-driven intelligent tutoring systems in K-12 reports consistently strong effects, with effect sizes that in some studies exceed those of expert human teachers. The effect is largest when feedback is step-level (not just final-answer), specific (names the error, not just “wrong”), and tied to an adaptive practice path.

A 2025 meta-analytic review in Educational Psychology Review confirms that spacing and retrieval practice produce robust gains in mathematics learning, including for algebra. A classroom-based study of an SM2-style adaptive spacing engine in Algebra I found significantly higher accuracy on previously-weak objectives. Spacing affects long-term retention more than initial accuracy — the difference shows up two weeks to two months later, not on the same-day quiz.

Rohrer and colleagues' randomised trials of interleaved versus blocked algebra practice (2014, 2015, 2019) found that interleaved practice yields lower performance during practice but substantially higher scores on delayed tests. Students learn to discriminate between problem types and the cue–strategy association strengthens.

Studies from the period of widespread online math instruction (Mamolo, 2022 in Education Research International; PMC 2023 on math anxiety, motivation and online learning) found that students' math motivation and self-efficacy tend to decline over weeks of online instruction while anxiety stays elevated. Avoidance behaviours are common.

The strongest moderators are autonomy, immediate feedback, low-stakes practice formats, and a sense of progress.