Dual language learners (DLLs), especially those from immigrant families in the United States, risk losing their home language as they gradually shift to speaking English as they grow up. Given the potential benefits of bilingualism on children’s cognitive, linguistic, and social–emotional development, it is crucial to maintain children’s home language to foster bilingual development. The current literature suggests that parental beliefs toward bilingualism and the language and literacy environment are linked to children’s language development. With the growing number of DLLs living in the United States, little is known about what parental beliefs about bilingualism of their children are integrated into these bilingual households and parents’ role in home language maintenance. The present study addresses the gap in the literature by investigating low-income immigrant families, specifically Chinese American and Mexican American families, and exploring the parental perceptions of children’s bilingual language learning. Further, the present study examines the relations among parental perceptions of bilingualism, home language and literacy practices, and home language oral proficiency. Data were collected from a total of 41 Mexican American and 91 Chinese American low-income immigrant families with DLLs ages 50–88 months who had been recruited from Head Start programs and state-funded preschools in Northern California when the children were 3–4 years old. Information about shared reading frequency, home language exposure and usage, and parental perceptions of bilingualism was collected through parental interviews, and DLLs’ home language oral proficiency was individually assessed. No significant difference in home language oral proficiency was observed between the two groups. Principal Components Analysis on the parental perceptions of bilingualism measure revealed two components, “Importance of Being Bilingual” and “English over Bilingualism.” Stepwise regression analysis results show that “Importance of Being Bilingual” was associated with children’s home language oral proficiency after controlling for culture, child age, the frequency of home language shared book reading, and child home language exposure and use. The results show that parents’ positive beliefs toward bilingualism are related to the children’s use of that language and their children’s language outcomes. Implications and suggestions for home language and literacy support for DLLs are discussed.

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This study aimed to examine the specific means and internal processes through which mathematical understanding is achieved by focusing on the process of understanding three new mathematical concepts. For this purpose interviews were conducted with 54 junior high school students. The results revealed that mathematical understanding can be achieved when new concepts are connected to at least two existing concepts within a student’s cognitive structure of. One of these two concepts should be the superordinate concept of the new concept or, more accurately, the superordinate concept that is closest to the new concept. The other concept should be convertible, so that a specific example can be derived by changing or transforming its examples. Moreover, the process of understanding a new concept was found to involve two processes, namely, “going” and “coming.” “Going” refers to the process by which a connection is established between a new concept and its closest superordinate concept. In contrast, “coming” is a process by which a connection is established between an existing convertible concept and a new concept. Therefore the connection leading to understanding should include two types of connections: belonging and transforming. These new findings enrich the literature on mathematical understanding and encourage further exploration. The findings suggest that, in order to help students fully understand new mathematical concepts, teachers should first explain the definition of a given concept to students and subsequently teach them how to create a specific example based on examples of an existing concept.