Mathematical and analogical reasoning of young learners

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The Growth of early mathematical patterning: an intervention study (2007, background): “Children’s patterning knowledge has also been found to influence the development of analogical reasoning and the ability to identify, extend, and generalise patterns important to inductive reasoning (English, 2004).”
Awareness of pattern and structure in early mathematical development (2009, background): “Other studies with young students have h igh ligh ted the importance of structural rela tionships in t he development of analogical reasoning (English, 2004).”
Reconceptualizing early mathematics learning (2013, unknown): “…Vergnaud, 2006; Thomas, Mulligan & Goldin, 2002; van Nes & de Lange, 2007; YoungLoveridge, 2002), patterning and reasoning (Clements & Sarama, 2009; English, 2004), spatial measurement (Outhred & Mitchelmore, 2000; Slovin & Dougherty, 2004), and early algebra (Blanton & Kaput, 2005; Carraher,…”
The Influence of Relational Knowledge and Executive Function on Preschoolers’ Repeating Pattern Knowledge (2016, background): “Overall, the findings a) supported the notion that relational knowledge is a key component of children’s pattern knowledge (English, 2004; Papic et al., 2011; Threlfall, 1999) and b) were consistent with previous studies that reported relations between preschoolers’ repeating pattern knowledge and…”