Open proportional-reasoning work by asking two diagnostic questions about the scenario¶

Strategy · All strategies
Evidence · no claims cited

Description¶

The paper offers a worked-example routine for approaching any scenario: first ask 'Are there two measurable quantities in the scenario of interest that can, or do, adopt a variety of different values?' and then ask 'Does it seem reasonable to presume these measures scale in tandem?' If both hold, students use common sense and scaling to answer sophisticated questions, as in the Kewpie-doll purchasing example.

Design Implications¶

Context¶

Requirements¶

• Scenarios must present quantities whose measures can vary, and learners must judge by common sense whether scaling in tandem is reasonable

Constraints¶

• The paper notes real scenarios may only approximately fit: bulk discounts mean doll purchases are 'probably NOT in a proportional relationship,' an assumption the example sets aside

Target Learners¶

• middle grades and secondary mathematics students

Target Learning Goals¶

• identify proportional relationships in scenarios and reason about them without rote procedures

Related Strategies¶

Examples¶

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Key Sources¶

• James Tanton, Ted Coe, April Ström, Kyle Pearce. (2022). Proportional relationships decluttered—at last! White paper. https://www.nwea.org