Does mathematics instruction for three- to five-year-olds really make sense?

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Preparing children for success: integrating science, math, and technology in early childhood classroom (2015, background): “can help increase children’s engagement and interest in math-related subjects (Baroody, 2000) because they may develop the ability to comprehend abstract math concepts even in the pre-operational stage (National Institute for Early Education Research [NIEER], 2009).”
Spontaneous focusing on numerosity and the arithmetic advantage (2015, background): “…and these individual differences predict mathematics achievement throughout the primary and secondary school years (Aunola, Leskinen, Lerkkanen, & Nurmi, 2004; Baroody, 2000; Duncan et al., 2007; Klibanoff et al., 2006; Reeve, Reynolds, Humberstone, & Butterworth, 2012; Stevenson & Newman, 1986).”
The Early Childhood Mathematics Education Revolution (2013, background): “Association learning theorists at the beginning of the 20th century viewed young children as incompetent, having to be bribed to learn mathematics and with little understanding for learning useful mathematical skills (Baroody, 2000).”