Peer Explanation (PE) Insights

• Peer Explanation (PE) is a collaborative process where learners or agents explain their reasoning to peers in real-time, fostering immediate feedback and knowledge co-construction.
• It is applied across educational settings and reinforcement learning, leveraging structured interactions such as think–pair–explain and action recommendations to improve conceptual understanding.
• Empirical findings indicate that effective PE can enhance math self-efficacy, reduce anxiety, and boost learning performance through reliable peer feedback and adaptive trust mechanisms.

Peer explanation (PE) denotes a class of peer-mediated explanatory practices in which explanation is produced for other learners or agents rather than solely for oneself. In postsecondary mathematics and statistics, PE consists of real-time, bi-directional or multi-directional explanatory interactions with classmates, typically in pairs or small groups with immediate question-and-answer exchange and role rotation (Gao et al., 25 Mar 2025). In middle and secondary mathematics and statistics, it refers to students explaining mathematical ideas, procedures, and problem-solving strategies to one another, most often through reciprocal explainer–listener pairings (Gao et al., 20 Aug 2025). In a reinforcement-learning setting, PE is operationalized as action recommendations exchanged among concurrently learning agents: an advisee asks peers “What would you do in my situation?” and treats the returned actions as situated explanations grounded in the teachers’ current policies and value estimates (Derstroff et al., 2023).

1. Definitions, scope, and boundaries

Across the literature considered here, PE is defined less by a single medium than by a common interactional structure: an explainer must externalize reasoning for a peer audience, and that audience can query, challenge, or act on the explanation. The explanatory act is therefore audience-facing, adaptive, and embedded in an exchange rather than a solitary rehearsal.

Context	Operational definition	Key boundary
Postsecondary mathematics and statistics	Real-time explanatory interaction with classmates	Distinct from self-explanation and explanation to fictitious others
Middle and secondary mathematics and statistics	Reciprocal explanation of ideas, procedures, and strategies	Emphasizes pair-based explainer–listener alternation
Reinforcement learning	Action recommendations among concurrently learning agents	Explanation is a state-conditioned recommended action

In postsecondary mathematics and statistics, PE is explicitly distinguished from self-explanation (SE), which is a solitary and internally directed process generated “for the learner,” and from explanation to fictitious others (EFO), in which students prepare explanations for a non-present audience without immediate back-and-forth (Gao et al., 25 Mar 2025). In middle and secondary settings, the same distinction is preserved, but the review emphasizes reciprocal knowledge construction rather than one-way tutoring, with PE typically instantiated as alternating roles between explainer and listener (Gao et al., 20 Aug 2025).

The reinforcement-learning usage is narrower but formally precise. Here, explanations are not textual or discursive; they are concrete action prescriptions sampled from a peer’s current policy at the advisee’s state. This makes PE a situated answer to the question “why act this way here?” because the recommendation is tailored to the state and implicitly reflects the advising agent’s learned policy and value estimates (Derstroff et al., 2023). A plausible implication is that PE is best treated as a family of explanatory interfaces rather than a single pedagogical technique.

2. Explanatory mechanisms in mathematics and statistics education

The postsecondary review situates PE within three complementary hypotheses: retrieval practice, generative learning, and social presence (Gao et al., 25 Mar 2025). Under the retrieval practice hypothesis, explaining to peers requires recalling and reconstructing knowledge, as when a student justifies a proof step, recalls a definition such as

$f'(x) = \lim_{h\to 0} \frac{f(x+h)-f(x)}{h},$

or applies an inference formula such as

$P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$

The act of verbal retrieval, reorganization, and verification of conditions of applicability is treated as a mechanism for durable retention.

Under the generative learning hypothesis, PE requires learners to organize, integrate, and infer. In mathematics, this includes elaborating links between limit laws and continuity, abstracting invariant proof structure, and coordinating algebraic, geometric, and verbal representations. In statistics, students co-construct interpretations of sampling distributions and confidence intervals, or explain why a test statistic follows $t_{n-1}$ under specific assumptions and how this connects to degrees of freedom (Gao et al., 25 Mar 2025). PE is therefore not merely recitation; it is a generative act in working memory with intended long-term consolidation.

The social presence hypothesis supplies the specifically interpersonal dimension. Because a real peer can ask for clarification or challenge a claim, the explainer must engage in perspective-taking, calibrate precision, and monitor comprehension. The review identifies error detection and repair, immediate formative feedback, co-construction of more complete solutions, calibration between intuition and formalism, and transfer through articulation as central mechanisms in mathematics and statistics learning (Gao et al., 25 Mar 2025).

The middle- and secondary-level review foregrounds a closely related but differently framed theoretical synthesis: human cognitive architecture and cognitive load theory, generative learning, and Social Presence Theory (Gao et al., 20 Aug 2025). Explanation generation is said to support schema construction by directing cognitive resources toward integrating new knowledge with existing knowledge and reducing extraneous processing. The review explicitly emphasizes the synergy of cognitive processing and social interaction. In this framing, PE adds audience awareness and co-construction to the benefits of explanation, but also introduces risks of extraneous cognitive load, misconception propagation, and uneven participation (Gao et al., 20 Aug 2025).

3. Instructional architectures and implementation conditions

In postsecondary mathematics and statistics, PE is implemented across developmental and gateway mathematics, introductory statistics, mathematics bridging courses, and courses with calculus or proof elements (Gao et al., 25 Mar 2025). The reviewed studies span face-to-face classrooms as well as online and hybrid variants, including cyber-PLTL and social-media-based peer tutoring. The most common configurations are dyads for problem solving and algorithmic tasks, small fixed groups of three to five students in PLTL and team-based learning, and whole-class discussion during peer-instruction phases.

Several recurrent instructional designs appear in the review. Think–pair–explain and teach-back cycles require students to think individually, generate and scrutinize explanations in pairs, and then teach back to another peer or group. Peer-led team learning uses trained peer leaders to facilitate structured problem-solving and explanation protocols with rotating roles. Peer tutoring emphasizes diagnosis, explanation, and practice, particularly in placement or gateway settings. Team-based learning and jigsaw structures distribute subtopics across teams and then require reciprocal explanation during reintegration. Peer review of solutions and proofs centers on explanation of justifications, intermediate steps, and alternative methods (Gao et al., 25 Mar 2025).

The postsecondary review is explicit that implementation quality matters. Clear roles such as explainer, questioner, and summarizer; structured time allocations; rotation mechanisms; conceptually focused prompts; accountability artifacts such as written rationales or recorded teach-backs; and trained facilitation are all identified as supports for reliability and equity (Gao et al., 25 Mar 2025). It also proposes combining PE with SE and EFO: written self-explanations before class, interactive peer explanation in class, and short post-class teach-backs to fictitious others.

In middle and secondary mathematics and statistics, the PE corpus emphasizes pair-based reciprocal explanation more strongly than the postsecondary review does (Gao et al., 20 Aug 2025). Same-age peer tutoring is reported as more effective than cross-age PE for some affective and academic outcomes, and the review highlights pairing quality as a boundary condition: knowledge differences that are too large or too small reduce effectiveness. The review also notes PE combined with mathematics digital tools, supportive classroom climates, and teacher monitoring to address misconceptions and off-task drift (Gao et al., 20 Aug 2025). Dialogic “why/how” prompts, requests for justification of steps and assumptions, short explain–question–restate cycles, role rotation, and brief written exits are all presented as practical scaffolds.

4. Empirical findings, moderators, and risks

The postsecondary scoping review analyzes 46 peer-reviewed articles published between 2014 and 2024 and classifies student explanations into self-explanation, peer explanation, and explanation to fictitious others (Gao et al., 25 Mar 2025). Within its PE synthesis, several empirical clusters are identified. In developmental and gateway mathematics, PLTL was associated with higher mathematics self-efficacy and reduced anxiety. Cyber-PLTL reported benefits for marginalized groups, including women. Peer tutoring was linked to improved pass rates in placement or gateway contexts. Pair-based problem solving enhanced solution quality and reasoning transparency. In introductory statistics, course redesigns incorporating peer discussion, clicker questions, and structured small-group explanation reported gains in conceptual understanding and achievement. Online peer tutoring offered accessibility and sustained engagement but also raised challenges of uneven participation and quality control without facilitation (Gao et al., 25 Mar 2025).

The same review is careful about evidential limits. Where statistical reporting was available, outcomes were typically tested using $t$-tests, ANOVAs, or regression models such as

$$Y_i = \beta_0 + \beta_1 \text{PE}_i + \beta_2 X_i + \varepsilon_i,$$

but the review does not pool effect sizes and does not report study-level $d$, $t$, or $F$ statistics in a meta-analytic form (Gao et al., 25 Mar 2025). Its conclusions are therefore pattern-based rather than pooled.

The middle- and secondary-level review follows PRISMA, covering the 2014–2024 period, retrieving 231 records, screening 57 full texts, and including 41 studies in the qualitative synthesis (Gao et al., 20 Aug 2025). Of these, 25 are PE studies, with 24 in mathematics and 1 in statistics. Across those studies, PE commonly improved conceptual understanding and procedural knowledge, and it was associated with improved mathematics self-concept, reduced mathematics anxiety, increased motivation, and more inclusive participation. Same-age PE was reported as more effective than cross-age PE, while female and younger students often showed higher gains in self-efficacy in PE contexts (Gao et al., 20 Aug 2025).

Both reviews emphasize heterogeneity and boundary conditions. In the postsecondary literature, implementation quality, duration and frequency, prompt design, group size and composition, prior knowledge, assessment alignment, grading incentives, and modality all moderate outcomes (Gao et al., 25 Mar 2025). In the middle and secondary review, pairing composition, modality, age and gender moderators, and the use of digital mathematics tools are specifically highlighted (Gao et al., 20 Aug 2025). A common misconception is that PE is intrinsically beneficial regardless of design. The reviews do not support that view. They identify recurrent risks: dominance by more knowledgeable or confident students, propagation of misconceptions, variable explanation quality, cognitive overload, off-task activity, and—in one reviewed strand—possible reinforcement of fixed views of intelligence among explainers (Gao et al., 25 Mar 2025, Gao et al., 20 Aug 2025).

Both reviews also identify major gaps. The postsecondary review calls for a finer-grained PE taxonomy beyond SE/PE/EFO, stronger process data linking mechanisms to outcomes, and comparative analyses across pure mathematics, applied mathematics, and statistics (Gao et al., 25 Mar 2025). The middle and secondary review identifies a significant gap in direct PE-versus-SE comparisons and notes that statistics education at that level is almost completely absent, with only one PE study and zero SE studies in statistics (Gao et al., 20 Aug 2025).

5. Peer explanation as action recommendation in reinforcement learning

In the reinforcement-learning framework of peer learning, PE is formalized as action recommendation among concurrently learning agents rather than verbal explanation (Derstroff et al., 2023). A group of $n$ agents trains simultaneously from scratch in separate, identical single-agent environments, each corresponding to an equivalent Markov decision process. At time $t$, agent $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$0 observes $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$1, takes action $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$2 sampled from policy $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$3, transitions according to $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$4, and receives reward from $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$5. Each agent maximizes its own discounted return,

$P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$6

with the standard RL objective

$P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$7

The communication protocol is deliberately constrained. The advisee shares only its current state $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$8, and each peer $P(A\mid B) = \frac{P(B\mid A)P(A)}{P(B)}.$9 replies with an action recommendation

$t_{n-1}$0

The advisee then chooses among its own sampled action and the peers’ suggestions. These recommendations function as explanations in a situated sense because they provide a concrete answer to “what should be done here?” based on the teacher’s evolving policy and, when available, value estimates (Derstroff et al., 2023).

Teacher selection is framed as a non-stationary multi-armed bandit problem because all peers are themselves learning and advice quality changes over time. The implemented selector is a Boltzmann distribution with annealed temperature:

$t_{n-1}$1

Here $t_{n-1}$2 is the advisee’s trust or motivation weight for peer $t_{n-1}$3, and the temperature schedule shifts teacher selection from exploration to exploitation (Derstroff et al., 2023). The paper also identifies $t_{n-1}$4-greedy, UCB, and Thompson sampling as applicable alternatives, though not implemented.

Advice integration is tied to standard off-policy reinforcement-learning updates. In discrete domains, the framework uses DQN with

$t_{n-1}$5

In continuous-control domains, it uses SAC, with critic, value, actor, and temperature losses defined in the usual soft-actor-critic form, including

$t_{n-1}$6

and

$t_{n-1}$7

A crucial differentiator from prior action-advice baselines is that no expert or oracle teacher is assumed, all peers begin tabula rasa, and continuous action spaces such as MuJoCo are supported rather than only discrete navigation (Derstroff et al., 2023). The paper also explicitly distinguishes this mechanism from blind imitation: the advisee learns whether and whom to follow.

6. Reliability estimation, robustness, and research directions

The reinforcement-learning formulation makes reliability estimation an explicit part of PE. One local scoring option is critic-based evaluation,

$t_{n-1}$8

which uses the advisee’s critic to score each incoming suggestion (Derstroff et al., 2023). A second option updates teacher-specific trust values through an exponential moving average:

$t_{n-1}$9

with

$t$0

An advantage-based variant subtracts the advisee’s own baseline action value,

$t$1

thereby estimating the benefit of following peer $t$2 rather than acting alone. The framework also permits global “agent values” that aggregate evidence about teacher quality across advisees (Derstroff et al., 2023).

The empirical evaluation covers MuJoCo continuous-control tasks—HalfCheetah-v4, Walker2d-v4, Ant-v4, and Hopper-v4—and discrete grid-world tasks Room-v21 and Room-v27, using SAC for continuous control and DQN for discrete tasks, implemented on Stable-Baselines3 in PyTorch (Derstroff et al., 2023). Group size is typically 4; experiments use 10 random seeds, except Room-v27 with 15; the performance metric is average reward over learning; and ablations are averaged across MuJoCo tasks and normalized to $t$3.

Results are mixed but generally favorable to peer learning. In continuous control, peer learning improves average reward in 3 of 4 environments compared with the single-agent and Early Advising baselines. The reported averages are HalfCheetah-v4: Peer 9014(715), Single 9270(247), Random 9129(504); Walker2d-v4: Peer 2160(346), Single 1558(489); Ant-v4: Peer 2459(667), Single 2694(660); Hopper-v4: Peer 2123(963), Single 2059(666), Random 2483(87) (Derstroff et al., 2023). In the Room domains, the gains are larger: Room-v21 reports Peer 72(8) versus Single 46(16), with LeCTR 15(3) and Early 12(4), while Room-v27 reports Peer 58(11) versus Single 32(13), with LeCTR 5(2) and Early 8(5) (Derstroff et al., 2023). The paper notes that random advice is surprisingly strong in Hopper, that peer learning often accelerates early learning even when single-agent learning later matches or exceeds it, and that no single reliability mechanism dominates across all tasks.

Robustness is an explicit concern. With one malicious advisor performing a poisoning attack by suggesting actions that minimize peers’ long-term return without affecting short-term reward, peers learn to ignore harmful advice, and average reward matches or exceeds single-agent baselines (Derstroff et al., 2023). The framework also reports slight performance increases as group size rises from 4 to 10, rather than peaking at 2 or 3. This suggests that, at least in the studied range, the benefits of consulting more peers are not overwhelmed by teacher-selection overhead.

Future directions differ by domain but converge on a common issue: PE quality depends on the design of the explanatory channel and the mechanism for evaluating it. In education, the main priorities are finer-grained taxonomies, stronger process analytics, better standardized reporting, direct PE-versus-SE comparisons, and substantial expansion of statistics education research, especially at middle and secondary levels (Gao et al., 25 Mar 2025, Gao et al., 20 Aug 2025). In reinforcement learning, the proposed agenda includes richer explanatory channels such as confidence or uncertainty signals, formal bandit-theoretic guarantees for non-stationary teacher selection, asynchronous large-group protocols with communication budgets and latency modeling, privacy-preserving aggregation of global agent values, robustness to collusion or poisoning, fairness-aware teacher selection, and extension from action advice to explanations about strategies, subgoals, or exploration policies (Derstroff et al., 2023). A plausible synthesis is that PE, whether human or algorithmic, is most effective when explanation remains lightweight but evaluable, socially or computationally interactive, and protected against low-quality or harmful guidance.