Multiple Representations¶

Strategy · All strategies
Evidence · 7 claims (4 for, 2 mixed, 1 against) · 19 studies (8 causal, 6 review, 3 quant-synthesis, 2 theoretical), q1–q4 · 3 of 19 report an effect size · 2 claims rest on one study

Description¶

Multiple representations present the same concept or relation in two or more forms — for example, a graph alongside its equation, a physical model alongside a verbal description, or a diagram alongside symbolic notation. The goal is for learners to map between forms, so each representation constrains and enriches interpretation of the others. This is the instructional application of dual coding: verbal and visual codes provide independent retrieval routes Media combinations affect recall and retention. [+M].

Design Implications¶

Multiple representations support abstraction and transfer because identifying the invariant structure across differing surface forms is exactly what abstraction requires Multiple contrasting cases support abstraction. [+M]. But representations are not automatically better in quantity: each added form imposes coordination costs in working memory, so representations must be explicitly linked (color coding, dynamic linking, prompts to translate between forms) or they become competing sources of load Chunking reduces working memory load. [+M]. Sequencing matters — introduce representations one at a time and build mappings incrementally rather than presenting all forms simultaneously.

Context¶

Requirements¶

• Representations that are genuinely complementary (each revealing something the others obscure), not redundant duplicates
• Explicit linking devices: shared labels, color correspondence, or tasks that require translation between forms
• Learner activities that ask "what does this show that the other does not?" — mapping is the learning event, not side-by-side display
• Representations that are genuinely complementary — each contributing information or processing advantages the others lack, not redundant decoration
• Explicit signaling of correspondences (labels, color-coding, linked gestures, or prompts to compare) so learners can construct mappings
• Sufficient working-memory headroom: two well-integrated representations beat four competing ones Coherence principle: irrelevant material hurts learning. [+S]

Constraints¶

• Unlinked, simultaneous representations increase extraneous cognitive load, especially for novices [~S] — learners split attention between forms without building connections
• Effectiveness reverses with expertise: advanced learners often benefit more from a single preferred representation, and added forms become redundant Expertise reversal: guidance that helps novices can hinder experts. [~M]
• If representations are superficially similar, learners may map surface features instead of deep structure, producing misconceptions [-W]
• Multiple representations can harm learning when learners lack the skill to translate between them; novices given several simultaneous formats often split attention across them without integrating Cognitive overload degrades learning when demands exceed working memory capacity. [-M]
• Redundant representations (identical text read aloud on screen) can depress learning relative to a single well-chosen format Redundancy principle. [~M]
• Benefits reverse with expertise: advanced learners integrating a second redundant representation show the expertise-reversal effect, performing worse than with a single compact format [~M]

Implementation Variability¶

• Static multiple representations — textbook-style pairing of graph, equation, and table with linking annotations
• Dynamic/interactive linking — tools such as Desmos or GeoGebra where manipulating one representation updates the others in real time, making correspondence perceptually salient
• Contrasting cases — sequences of representations differing on one dimension at a time, used to isolate the target structure
• Concrete-to-symbolic progression — physical manipulatives or Analogies bridging everyday knowledge to formal notation
• Sequential: introduce one representation, then a second after the first is secure — appropriate for novices
• Simultaneous with linking: side-by-side formats with explicit mapping prompts — appropriate once basic fluency exists
• Learner-generated: students produce a second representation themselves (draw the graph, build the model), which strengthens integration more than passive viewing [+M]
• Multiple cases + representations: varying both surface form and content to build flexible schemas, as in Cognitive Flexibility Theory

Target Learners¶

• Novices in symbolically dense domains (mathematics, chemistry, physics) who must learn to interpret formal notations Multiple contrasting cases support abstraction. [+M]
• Learners with weak prior knowledge who benefit from concrete anchors before formal forms
• Less beneficial for experts, for whom additional representations are often redundant Expertise reversal: guidance that helps novices can hinder experts. [~M]
• Novices benefit most when representations are sequenced and linked, since they cannot yet self-manage multiple formats [~M]
• Intermediate learners benefit from simultaneous presentation with translation prompts, building the mapping skill that is itself a learning goal [+M]
• Experts may be burdened by redundant formats and do better with a single preferred representation [~M]

Target Learning Goals¶

• Conceptual understanding: grasping what a notation means, not just how to manipulate it
• Abstraction and generalization: extracting invariant structure across varied forms
• Flexible problem-solving: selecting and translating among representations appropriate to a task
• Conceptual understanding of structures that no single format captures fully (e.g., functions as equations, graphs, and tables)
• Representational fluency: translating between formats, a core competence in mathematics and science [+M]
• Flexible, transferable schemas built from multiple perspectives on the same knowledge

Instructions¶

1. Identify the target concept and select 2–3 representations that each reveal a distinct aspect of it.
2. Introduce representations sequentially, not simultaneously, to manage Cognitive Load Management.
3. Build explicit mappings — color correspondence, shared labels, or translation tasks ("sketch the graph this equation describes").
4. Use Comparing Cases or contrasting representations to highlight what stays invariant across forms.
5. Require learners to generate translations between representations themselves; producing the mapping drives deeper processing than reading it.
6. Fade representational support as expertise develops, converging on the most efficient form for the domain.

Related Strategies¶

• Use Analogies — an analogy is a representation drawn from prior knowledge; mapping it to the target concept is a translation exercise
• Use Worked Examples — worked examples can embed multiple representations of the same solution step
• Comparing Contrasting Cases — varies representations and content to highlight deep structure
• STeLLA® teaching strategies for explaining, identifying, and engaging science concepts

Examples¶

• Desmos (desmos.com) — dynamically links equations, graphs, and tables; dragging a slider updates all representations simultaneously, making correspondence perceptual rather than inferred.
• CPM Educational Program (cpm.org) — mathematics curriculum that systematically presents concepts through tables, graphs, equations, and situational (word) contexts with explicit translation tasks.
• Chemistry particulate drawings — instruction that pairs symbolic equations (2H₂ + O₂ → 2H₂O) with molecular-level diagrams and macroscopic observations; research on multiple representations in chemistry shows translation tasks diagnose and correct misconceptions.
• Cognitive Flexibility Theory — ill-structured domains are taught by revisiting the same concepts from multiple thematic and representational perspectives
• 4C/ID — learning tasks present supportive information in multiple formats (concept maps, procedure displays, worked examples) coordinated with task progression
• PhET Interactive Simulations — physics and chemistry simulations that simultaneously display dynamic visuals, symbolic values, and graphs, with controls letting learners connect the views
• Illustrative Mathematics — K–12 curriculum built on the concrete–pictorial–abstract progression, requiring students to move among representations of the same mathematical idea

Key Sources¶

• Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. doi:10.1016/j.learninstruc.2006.03.001
• Mayer, R. E. (2009). Multimedia learning (2nd ed.). Cambridge University Press. doi:10.1017/CBO9780511811678
• Paivio, A. (1990). Mental representations: A dual coding approach. Oxford University Press. doi:10.1093/acprof:oso/9780195066661.001.0001
• Schwartz, D. L., Chase, C. C., Oppezzo, M. A., & Chin, D. B. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103(4), 759–775. doi:10.1037/a0025140
• Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23–31. doi:10.1207/S15326985EP3801_4
• Schnotz, W., & Bannert, M. (2003). Construction and interference in learning from multiple representation. Learning and Instruction, 13(2), 141–156. doi:10.1016/S0959-4752(02)00017-8
• Seufert, T. (2003). Supporting coherence formation in learning from multiple representations. Learning and Instruction, 13(2), 227–237. doi:10.1016/S0959-4752(02)00022-1