A cognitive load based classification of one-step equations into Type 1 and Type 2 by operational and relational lines¶

Theory · All theories
Evidence · no claims cited

Description¶

The article proposes a framework that classifies one-step equations by counting operational lines (steps that alter the problem state while preserving equality) and relational lines (lines showing a quantitative relation between elements). Type 1 equations have one operational and two relational lines; Type 2 equations have two operational and three relational lines. The number of these lines indexes element interactivity, which determines intrinsic load and thus equation complexity, paralleling Mayer's classification of algebra story problems.

Design Implications¶

Context¶

Requirements¶

• The classification assumes the balance method as the formal solution procedure against which operational and relational lines are defined

Constraints¶

• The framework is developed analytically from cognitive load theory rather than tested empirically in this paper

Target Learners¶

• students transitioning from pre-algebra to algebra learning

Target Learning Objectives¶

• solving one-step equations with a formal method
• preparation for multi-step equation solving

Claims¶

Related Theories¶

Examples¶

• Teach one-step equations in a hierarchical sequence: Type 1 without special features first, then Type 1 with special features, then Type 2 in the same order
• A five-question research agenda for one-step equation learning and instruction

Key Sources¶

• Ngu, B. (2014). The Complexity of One-Step Equations. In J. Anderson, M. Cavanagh & A. Prescott (Eds.), Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia) pp. 501-508. Sydney: MERGA. https://eric.ed.gov/?id=ED572625