Actions behind mathematical concepts: A logical-historical analysis

Abstract

According to embodied cognition theories, mathematical knowledge is grounded in actions with artefacts. Educational designers are seeking to identify what actions with mathematical artefacts could support the learning of this knowledge. Through logical-historical reconstruction, we answer the question: What actions and artefacts have historically constituted the logic of mathematical concepts’ development, and how might these support students’ development of mathematical knowledge? We use an example of data and distribution in histograms and trigonometry to illustrate this reconstruction. An answer to our question is that this analysis revealed that we might need to unpack several automatically generated artefacts including dotplots and pregiven intervals (for histograms), and the (unit) circle and radians (for trigonometry).