This qualitative study examined the everyday mathematical experiences and understandings of three, 4-year-old, African-American children from working-class backgrounds. The study drew on Street, Baker, and Tomlin's (2005) broad, ideological model of mathematics as "social" and their analytic concepts of mathematical events (units of analysis consisting of occurrences of mathematical activity) and mathematical practices (patterned uses, meanings, and ways of engaging in mathematics). Mathematical events were examined through four interrelated dimensions that were adapted for this study, constituting the mathematics (content) in and the social aspects (purpose and setting, values and beliefs, and social relations) situating the children's mathematical activities. Characteristics of mathematical events were determined through an analysis across the children's mathematical events. Adapted naturalistic observation methods were used to yield data specifying children's everyday mathematical events within their homes, informal day care setting, and other familiar contexts. An iterative analytic process using inductive analytic procedures was employed to examine and interpret children's mathematical events and to determine characteristics of these events. The three children each engaged in distinct, spontaneous mathematical experiences and understandings that reflected their unique family lives, individual predispositions, and knowledge development. For example, the values of one mother gave rise to many contexts fostering her daughter's nominal, ordinal, and numeric meanings for number. Findings indicated mathematical understandings that are not typically recognized in early childhood mathematics education research and practice and portrayed conditions that fostered children's meaningful engagement in and learning of mathematics. The children's everyday mathematical events tended to: emerge from their intrinsic motivation, involve their pursuit of goal-directed activities or interest in mathematics for its own sake, and promote their purpose-oriented verbal interactions with others. Recognizing the unique, interrelated, and complex social aspects that underlie and support young children's everyday mathematical experiences and understandings, broadening what counts as evidence of mathematical thinking in early childhood, and creating conditions in formal settings that reflect characteristics of children's everyday mathematical events can foster children's continued meaningful engagement in and development of mathematical thinking in early childhood learning environments. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]