FOUR COMPONENT INSTRUCTIONAL DESIGN (4C/ID) MODEL CONFIRMED FOR SECONDARY TERTIARY MATHEMATICS

Abstract

Cognitive load theory (CLT) was introduced in the 1980s as an instructional theory based on well accepted aspects of human cognitive architecture (Sweller, van Merriënboer, & Paas, 2019). A major premise of the theory is that working memory load from cognitive processes is decreased when domain specific schemas are activated from long term memory. Comprehension, schema construction, schema automation, and problem solving in working memory often create high cognitive load. Hence, schemas transported from long term memory into working memory support learning and transfer of learning (Ginns & Leppin, 2019). One of the key developments from CLT has been the Four-Component Instructional Design (4C/ID) Model generated from evolutionary theorizing (Geary, 2008; Ginns & Leppink, 2019). Since its creation, the 4C/ID Model has been successfully applied to instruction that requires the learning of complex tasks. Van Merriënboer, Kester, and Paas (2006) defined a complex task as having many different solutions, real world connections, requiring time to learn, and as creating a high cognitive load. Based on this definition, the instruction and learning of mathematics is a complex task. For example, different solutions are algebraic, analytic, numeric, and graphic. Relative to real world connections, mathematics is one of the domains in the broader science, technology, engineering, mathematics (STEM) field and is regarded as the language of the sciences. Regarding taking time to learn and creating a high load on learner’s cognitive systems, mathematics teachers deal with the tension between covering all the required standards and taking the time to teach for understanding. Teachers face challenging decisions about instructional approaches, materials, productive struggle, and the amount of classroom time spent on various standards. Better models for instruction that support transfer of learning could help teachers improve instructional decision making. Although the 4C/ID Model has been used in secondary mathematics education (Sarfo, & Elen, 2007; Wade, 2011), it has never been confirmed as a mathematical instructional theory. The purpose of this research report is to present an empirical confirmation of the 4C/ID Model, using data from the Factors Influencing College Success in Mathematics (FICSMath) project from Harvard University.