Developing mathematical knowledge.

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…This finding confirms the assumption that although phonological awareness facilitates the acquisition of QNC Level-I skills (e.g., learning the precise number-word sequence), it seems less relevant for the formation of higher-order mathematical competencies that require the conceptual understanding of linking quantity information with number words and their Arabic notations (Level II and III in Krajewski's model;cf. Gersten, Jordan, & Flojo, 2005;Okamoto & Case, 1996;Resnick, 1989).…”

“…According to the available studies, it seems that linking imprecise nonverbal quantity concepts with the ability to count (which develops separately) forms the basis for understanding several major principles of the number system (cf. Resnick, 1989;Okamoto & Case, 1996;Gersten, Jordan, & Flojo, 2005;Krajewski & Schneider, in press;Lemer, Dehaene, Spelke, & Cohen, 2003). A recently proposed theoretical model (Krajewski, 2008; see also Krajewski & Schneider, in press) depicts how this linkage might occur and how early mathematical competencies are acquired via three developmental levels, aiming at a deeper understanding of quantity to number-word linkages (see Figure 1).…”

“…With the acquisition of language, children acquire the ability to discriminate quantities also verbally. When comparing quantities, they use words like "more," "less," or "the same amount" (see Resnick, 1989;protoquantitative comparison schema). Independently, they learn to count (recite number words) beginning at around age two, and thereby already acquire precise number words and the exact number word sequence.…”

“…They realize that a quantity can be divided into pieces that, taken together, equal the original quantity (see Resnick, 1989: protoquantitative part-whole schema, from about age four to five), and that quantities change only if something is added or taken away (see Resnick: protoquantitative increase/decrease schema).…”

Play-Based Mathematics in Kindergarten. A Video Analysis of Children’s Mathematical Behaviour While Playing a Board Game in Small Groups

“…These important competencies are understood and named in different ways within the research literature. In educational psychology knowledge and skills related to numbers and quantities acquired in early childhood are often termed as number sense (Dehaene 1997), as early numeracy (Aunio, Hautamäki, Sajaniemi and van Luit 2009), as numerical competency (Resnick 1989) or as number competencies (Jordan et al 2009). Common key elements of the denoted concepts include counting, number knowledge and arithmetic operations.…”