In general Calcularis is based on neuro-scientific research.
The method used in Calcularis is modelled along the "4-Step-Model of number development and developmental dyscalculia" according to Shalev and von Aster, [von Aster MG & Shalev R (2007) Number development and developmental Dyscalculia. Developmental Medicine and Child Neurology, 49: 868-873.]
(source: https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1469-8749.2007.00868.x)
This model itself is an extension of the "The Triple Code Model" (TCM) proposed by Dehaene and Cohen (1995, 1997) and Dehaene et al. (2003).
Furthermore, the findings of Brian Butterworth, e.g. [Butterworth, B., Varma, S., and Laurillard, D. (2011). Dyscalculia: from brain to education. Science 332, 1024.] were influental in the development of Calcularis.