Model Drawing Strategy¶

Strategy · All strategies
Evidence · 2 claims (2 for) · 7 studies (2 causal, 2 quant-synthesis, 2 review, 1 associational), q2–q4 · 1 of 7 report an effect size

Description¶

The model drawing strategy teaches learners to solve word problems — particularly fraction and percentage problems — by drawing a schematic diagram (typically bar or part-whole models) that represents the qualitative relations described in the text, then using the diagram to plan and execute the arithmetic. The strategy is taught explicitly: the instructor demonstrates how to translate each sentence into a visual element, and learners practice the full read–draw–solve cycle until it becomes routine. It originates in Singapore's bar-model approach and in schema-based instruction research for students with learning disabilities.

Design Implications¶

Model drawing externalizes the problem structure, offloading quantitative relations from working memory onto the diagram so learners can reason about them Chunking reduces working memory load. [+M]. Its effectiveness depends on teaching schematic representations (bars showing part–whole and comparison relations) rather than decorative pictorial drawings; schematic representations correlate with solution success while pictorial ones do not [~S]. The strategy must be taught through Demonstration followed by guided Practice, with the drawing routine faded as competence grows.

Context¶

Requirements¶

• Pencil and paper or whiteboard, plus explicit instruction in the drawing routine itself
• A worked sequence of problems sharing the same underlying schema (part–whole, comparison, change) so learners can abstract the model type
• Instructor Demonstration that narrates how each sentence maps onto the diagram, followed by Practice with Provide Feedback on the diagram before the arithmetic

Constraints¶

• Learners with weak spatial or fine-motor skills may find drawing itself a burden; pre-printed model frames or digital tools reduce this load [~M]
• Pictorial (literal) drawings — drawing the objects in the story — do not help and can consume working memory without aiding solution [-S]
• If all practice problems share one surface story, learners may bind the model to the story rather than the schema; varying surface features is necessary [~S]
• Requires foundational number sense; learners who cannot yet compute fractions or percentages will produce correct diagrams and wrong answers

Implementation Variability¶

• Pre-printed bar-model templates vs. freehand drawing — templates lower the entry barrier for learners with motor or spatial difficulties
• Digital implementations (e.g., Thinking Blocks, Bar Model apps) allow drag-and-drop model construction
• Fading sequence: full worked model → partially completed model → learner-drawn model from scratch
• Extendable from fractions/percentages to ratio, rate, and early algebra problems

Target Learners¶

• Students with learning disabilities in mathematics, who benefit from explicit, structured representation routines [+M]
• Middle and high school students struggling with multi-step word problems despite adequate computation skills
• Less beneficial for learners who already spontaneously construct schematic representations; for them the routine can be redundant [~M]

Target Learning Goals¶

• Word-problem solving: translating text into a solvable representation
• Conceptual understanding of part–whole and comparison relations underlying fractions and percentages
• Transfer of a general representation routine across problem types Self-explanation improves conceptual understanding. [+M]

Instructions¶

1. Read the problem aloud and identify what is known, unknown, and the unit of the whole Demonstration
2. Draw a bar representing the whole; divide or extend bars to represent the stated relations (parts, comparisons, percentages)
3. Label each segment with quantities and unknowns, using a question mark for the unknown
4. Use the diagram to plan the computation, then solve and check the answer against the model
5. Repeat across a sequence of problems with the same schema, fading support from worked models to independent drawing Practice with Provide Feedback on the diagram before the arithmetic

Related Strategies¶

• Schema-Based Instruction — model drawing is the visual-representation component of the broader schema-based approach
• Cognitive Strategy Instruction — model drawing is typically embedded in a read–plan–solve–check strategy routine
• Teach prepositions by presenting the core spatial sense first, then deriving metaphoric senses, supported by diagrams and schemas

Related Elements¶

• Demonstration — the instructor models the read-to-draw translation explicitly
• Practice — the routine only becomes fluent through repeated, varied practice
• Provide Feedback — feedback should target the diagram's accuracy, not just the final answer
• Analogies — comparing new problems to previously modeled schemas supports abstraction

Examples¶

• Singapore Math bar models — the national curriculum's model method, in which students draw unit bars to solve fraction, ratio, and percentage problems from primary grades onward (Singapore Math)
• Thinking Blocks (Math Playground) — interactive tool where learners drag blocks to build part–whole and comparison models for addition, multiplication, fraction, and ratio problems
• Xin's PGBM-COMPS intervention — research-based program teaching students with learning disabilities to represent word problems with diagrams before formulating equations

Key Sources¶

• Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32(4), 207–225. doi:10.1177/002246699903200402
• Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689. doi:10.1037/0022-0663.91.4.684
• van Garderen, D., & Montague, M. (2003). Visual–spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18(4), 246–254. doi:10.1111/1540-5826.00079
• 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
• Krawec, J. L. (2014). Effects of a problem-solving strategy on the mathematical problem solving of middle school students with learning disabilities. Remedial and Special Education, 35(3), 149–159. doi:10.1108/mgrj-04-2014-0007