This study investigated the longitudinal associations between children’s early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, Mage = 4:7 [years:months]), and at the end of kindergarten in 2017 (N = 368, Mage = 5:10). Children whose parents provided frequent operational numeracy activities (e.g., learning simple sums) at prekindergarten showed better arithmetic performance and growth in nonsymbolic and symbolic number comparison at the end of kindergarten. Parents’ knowledge of number‐related games predicted children’s arithmetic skills and growth in nonsymbolic number comparison. These findings underscore the persistent relations between the HNE and the development of children’s mathematical skills.

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Language skills play an important role in mathematics development. Students (7 to 10 years of age) learning school mathematics either in the same language used at home (first-language learners; n = 103) or in a different language (second-language learners; n = 57) participated in the study. Relations among cognitive skills (i.e., receptive vocabulary, working memory, quantitative skills), domain-specific language skills (i.e., mathematical vocabulary, mathematical orthography), word-problem solving, arithmetic fluency, and word reading were investigated. Second-language learners had lower scores on measures with strong language components (i.e., receptive vocabulary, subitizing, and word-problem solving) than firstlanguage learners, whereas they performed equally well on other tasks. Mathematical vocabulary and receptive vocabulary contributed to word-problem solving success for first-language learners, whereas only receptive vocabulary in the language of instruction related to mathematical outcomes for second-language learners. Mathematical vocabulary was related to arithmetic fluency for both groups, but mathematical orthography was not. For both groups, students' word reading was predicted by receptive vocabulary but not by quantitative skills, highlighting the domain-specific nature of these skills. These findings have implications for supporting mathematical learning in second-language students. Educational Impact and Implications StatementHow do language skills affect mathematics for second-language learners? Vocabulary skills in the instructional language were more strongly related to word-problem solving and arithmetic skills for second-than first-language learners. Teachers of second-language learners may need to adapt materials or reduce language demands so that all students have equal opportunity to develop competent mathematical skills. For all students, explicit instruction on mathematical vocabulary and mathematical orthography may support their mathematical competency.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 þ 3 = 8), subtraction (e.g., 5 -3 = 2), and multiplication (e.g., 5 3 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network.

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