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It is arguable that the first reference to learners’ intuitive ideas of force and motion came in the United Kingdom’s Mathematics Association’s (1965) Second Report on the Teaching of Mechanics in Schools (in the UK, mechanics in secondary schools is taught as a subject in applied mathematics as well as in physics). The report not only emphasised the need for a qualitative and conceptual understanding of force and motion but stated that students hold incorrect ideas of force and motion and that discussion should try to eradicate them.
One may learn that x does y and uses the relation until the realisation of why x does y. Initially, ‘x’, ‘y’ and the relation of x to y are placeholders, to be held by faith so to speak, until they become concepts. A teacher may use a placeholder for a concept and then elaborates, asks questions, demonstrates, etc. so that learner understanding transforms the placeholder into a concept.
For example, a class of seventeen 17–18-year-olds demonstrated expert knowledge of force and motion through discussion and poster sessions with the teacher guiding the class so that the students’ answers reflected their understanding. Five minutes before the end of the lesson the teacher asked ‘what is the direction of the resultant force acting on a vertically thrown ball (a) when it is going up and (b) at the top?’ For (a), all but one stated upward and for (b), all stated zero. Five years on with a similar class, the results were essentially the same (see Graham et al. 2013, Are ‘misconceptions’ or alternative frameworks of force and motion spontaneous or formed prior to instruction?). These answers appear spontaneous as no antecedents could be traced.
Both Carey (2009) and Vygotsky (1987) seem compatible. For example, both argue that language serves as a kind of placeholder for the development of concepts such that young children may learn words prior to understanding the concepts that the words refer to. Given their similarity in developmental psychology, it may be the case that complexes do sit well with core knowledge. If so, then the development of complexes into concepts is part of the change in core knowledge.
My take on this is that numbers are first learnt by associating the number term with the number of objects, from which the inferential role develops (e.g. three stones add two stones equals five stones, which can be checked by counting them). Once the inferential role is established, then the number concept is divorced from the objects that served to represent numbers (e.g. 3 + 2 = 5, or learning the multiplication tables). This is a possible example of how an abstract concept such as number can arise from core knowledge.
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Rowlands, S. The Latest Research on Conceptual Change from Developmental Psychology. Sci & Educ 28, 1253–1262 (2019). https://doi.org/10.1007/s11191-019-00077-7
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DOI: https://doi.org/10.1007/s11191-019-00077-7