Scaling in tandem as the foundational way of thinking for proportional relationships¶

Theory · All theories
Evidence · 1 claim (1 for) · 1 study (1 theoretical), q2 · 0 of 1 report an effect size · 1 claim rests on one study

Description¶

The paper organizes the entire treatment of proportionality around a single way of thinking: two measurable quantities are related proportionally when their measures scale in tandem. It defines this as the case where 'if the measure of one quantity in the scenario changes by a factor k, then the measure of the other quantity is sure to also change by the same factor k.' All later representations—tables, double number lines, equations, graphs—are derived from this idea rather than from procedures.

Design Implications¶

Context¶

Requirements¶

• Learners work with scenarios involving two or more measurable quantities whose measures can adopt a variety of possible values and seem related

Constraints¶

• The paper notes this is 'just the beginning of a longer journey towards developing a robust understanding of proportionality'

Target Learners¶

• middle grades and secondary mathematics students

Target Learning Objectives¶

• understand proportional relationships conceptually rather than procedurally

Claims¶

• Data from any proportional relationship satisfies an equation of the form y = rx, and conversely [+W]

Related Theories¶

• Inverse proportional relationships as quantities scaling in anti-tandem, y = r/x

Examples¶

• Open proportional-reasoning work by asking two diagnostic questions about the scenario
• Measure and Graph Data

Key Sources¶

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