The earliest well-documented movement to use IBL in mathematics education in the US was the work of Warren Colburn (1793-1833) who wrote several arithmetic texts emphasizing student invention of computational procedures and mental arithmetic. Warren Colburn attributed his ideas about the role of inquiry in mathematics education to the Swiss educator Johann Pestalozzi (1726-1827).
Inquiry-learning is a umbrella term that covers a number of other approaches to teaching and learning:
• problem-based learning: learning that starts with an ill-structured problem or case-study
• project-based learning: students create a project or presentation as a demonstration of their understanding
• design-based learning: learning through the working design of a solution to a complex problem
• constructionism: learning through the physical construction of a tangible object in the real world
IBL is a socio-constructivist design because of collaborative work within which the student finds resources, uses tools and resources produced by inquiry partners. Thus, the student make progress by work-sharing, talking and building on everyone's work.