Graphic Organizers (Math)¶

Strategy · All strategies
Evidence · 3 claims (1 for, 1 mixed, 1 against) · 14 studies (7 causal, 5 review, 1 quant-synthesis, 1 theoretical), q1–q3 · 1 of 14 report an effect size

Description¶

Graphic organizers are structured visual templates — diagrams, mats, charts, and grids — that externalize the structure of a math problem or concept so learners can organize information spatially instead of holding it in working memory. In mathematics they serve two main functions: problem-solving scaffolds (e.g., step-by-step word-problem frames, "break it down" templates) that help students identify what is being asked and which operation to use, and concept-development tools (e.g., the Frayer model, Venn diagrams, place-value mats) that map relationships among ideas. Common formats include the Frayer model, step-by-step frames, Venn diagrams, number lines, place-value charts, ten-frames, and coordinate or hundredths grids.

Design Implications¶

Graphic organizers reduce extraneous cognitive load by offloading intermediate problem states onto paper, freeing working memory for reasoning Chunking reduces working memory load. [+M]. Their effectiveness depends on being paired with explicit instruction in how to use them: an organizer handed to students without modeling becomes a form to fill in rather than a thinking tool [~M]. Organizers that encode a problem schema (e.g., schema diagrams distinguishing "combine," "compare," and "change" word problems) produce stronger transfer than generic templates [~S].

Context¶

Requirements¶

• A template matched to the problem type or concept structure (a compare-problem frame will not fit a rate problem)
• Instructor modeling of organizer use, ideally with Think-Aloud narration of each decision
• A Fading plan: moving from completed examples, to partially completed organizers, to student-generated diagrams
• Templates whose structure maps onto the target problem type or concept (schema-consistent, not decorative)
• Brief explicit instruction in how to use the organizer, ideally with a worked model before independent use
• A plan for fading: learners should eventually solve problems without the frame

Constraints¶

• Generic organizers applied without schema instruction do not improve word-problem performance; the organizer must map the underlying problem structure [~M]
• Over-reliance on a single template can anchor students to one representation and impede flexibility when problems do not fit the frame [-M]
• Benefits shrink for students with strong prior knowledge, who find the external structure redundant Expertise reversal: guidance that helps novices can hinder more knowledgeable learners. [~M]
• Poorly designed organizers that duplicate the textbook's own structure add transcription work without adding thinking [-W]
• Poorly matched organizers add load rather than reduce it; a generic "fill in the boxes" frame can become a compliance ritual disconnected from mathematical reasoning [~M]
• Over-reliance can block internalization if the organizer is never faded — learners may become dependent on the external structure [-M]
• Organizers with heavy decorative graphics can distract rather than support Decorative illustrations do not improve learning. [-S]
• Requires initial instruction on use; some learners find the structure too rigid if not adapted to the task

Implementation Variability¶

• Schema-based organizers (Jitendra's schema-broadening instruction): diagrams keyed to word-problem types, taught across a family of examples
• Concept organizers: Frayer model, Venn diagrams, and concept maps for vocabulary and relationships
• Structural mats and grids: place-value charts, ten-frames, hundredths grids for number sense and computation
• Student-generated diagrams: learners draw their own organizer, which shifts the activity from filling in to representing — closer to Self-Explanation and stronger for transfer [+W]
• Schema-based frames (e.g., Jitendra's schema-broadening instruction): separate organizers for change, group, compare, and rest problems
• Concept organizers: Frayer models and concept maps for vocabulary and relationships (e.g., what makes a "prime number")
• Computation organizers: column-alignment and step-sequencing frames for multi-digit procedures
• Co-constructed vs. pre-printed: teacher-modeled completion, collaborative completion, then independent use

Target Learners¶

• Students with learning disabilities or mathematics difficulty, for whom externalizing structure is best supported by the evidence [~S]
• Novices encountering a new problem type or concept who lack a schema for organizing the information
• Less beneficial for advanced students, who should be weaned onto self-generated representations Expertise reversal: guidance that helps novices can hinder more knowledgeable learners. [~M]
• Students with learning disabilities or difficulties in mathematics, who benefit most from externalized problem structure [+M]
• Novices encountering a new problem type; benefits diminish for proficient problem solvers, for whom the frame is redundant [~M]
• English learners, when the organizer doubles as language support for parsing word problems

Target Learning Goals¶

• Word-problem comprehension: identifying quantities, relationships, and the required operation
• Conceptual structure: comparing and contrasting concepts, building definitions (Frayer model)
• Representational fluency: connecting symbolic, visual, and verbal forms of a concept
• Problem comprehension: identifying what is asked and which quantities matter
• Operation selection and strategy choice
• Concept learning and mathematical vocabulary (Frayer-style organizers)
• Metacognitive monitoring: the organizer's steps prompt self-questioning

Instructions¶

1. Select or design an organizer that matches the target problem schema or concept structure.
2. Model its use on a worked problem, narrating each decision (Think-Aloud).
3. Work through a second problem collaboratively, gradually transferring control to students (Coaching).
4. Have students apply the organizer to new problems during Practice, then compare solutions in a Class Discussion.
5. Fade the organizer: partial templates, then blank paper with a prompt to "draw the structure yourself."

Related Strategies¶

• Schema-Based Instruction — the word-problem variant of math graphic organizers, with the strongest evidence base
• Worked Examples — a completed organizer on a solved problem functions as a worked example of the representation itself
• Annotating — marking up problems shares the goal of making structure visible
• Cognitive Apprenticeship — teacher modeling of organizer use makes expert problem-reading visible

Examples¶

• Schema diagrams in Jitendra's word-problem instruction — students classify a problem as "change," "group," or "compare" and complete the matching diagram before solving; validated across elementary intervention studies.
• Frayer model for math vocabulary — a four-quadrant organizer (definition, characteristics, examples, non-examples) used to teach concepts like "prime number" or "slope."
• IRIS Center math graphic organizer templates — printable place-value mats, sorting mats, and problem-solving frames designed for students with disabilities.
• Ten-frames and rekenreks in early numeracy curricula — structural organizers that make the base-ten structure of numbers visible before symbolic work.
• Schema-based instruction (Jitendra et al.) — research-validated program using problem-type-specific graphic organizers for word-problem solving in grades 2–7; see overview at https://www.interventioncentral.org
• Frayer Model — four-quadrant organizer (definition, characteristics, examples, non-examples) widely used for math vocabulary such as "polygon" or "function"; template at https://www.readingrockets.org
• IRIS Center math supports — case-based modules demonstrating organizer use for students with math difficulties: https://iris.peabody.vanderbilt.edu

Key Sources¶

• Dexter, D. D., & Hughes, C. A. (2011). Graphic organizers and students with learning disabilities: A meta-analysis. Learning Disability Quarterly, 34(1), 51–72. doi:10.1177/073194871103400104
• Ives, B. (2007). Graphic organizers applied to secondary algebra instruction for students with learning disorders. Learning Disabilities Research & Practice, 22(2), 110–118. doi:10.1111/j.1540-5826.2007.00235.x
• Jitendra, A. K., Griffin, C. C., Haria, P., Leh, J., Adams, A., & Kaduvettoor, A. (2007). A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving. Journal of Educational Psychology, 99(1), 115–127. doi:10.1037/0022-0663.99.1.115
• Frayer, D. A., Frederick, W. C., & Klausmeier, H. J. (1969). A schema for testing the level of concept mastery (Working Paper No. 16). Wisconsin Research and Development Center for Cognitive Learning.
• Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. Springer. doi:10.1007/978-1-4419-8126-4
• Novak, J. D. (1990). Concept mapping: A useful tool for science education. Journal of Research in Science Teaching, 27(10), 937–949. doi:10.1002/tea.3660271003
• Clark, R. C., & Mayer, R. E. (2016). E-Learning and the Science of Instruction (4th ed.). Wiley. doi:10.1002/9781119239086
• van Garderen, D. (2006). Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities, 39(6), 496–506.