Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects

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Coordinating visualizations of polysemous action: values added for grounding proportion (2014, background): “Micro-ethnographic analyses of episodes from three paradigmatic case studies suggest that students reconciled semiotic conflicts by generating heuristic logico-mathematical inferences that integrated competing meanings into cohesive conceptual networks.”
One episode, two lenses (2013, background): “…these dualities, as well as the primary objects themselves, lead to the following pairs of processes that intervene in mathematical practices (Godino et al., 2011): & institutionalisation-personalisation; & generalisation-particularisation; & analysis/decomposition-synthesis/reification; &…”