In 12 audio taped sessions, three kindergarten children engaged algebra in a teaching for understanding, thematic project. Toni, Asa, and Cornel had one-on-one lessons dealing with simple natural numbers, patterns, and relationships. Along the way, each child studied one of Toni Morrison's Who's got game books to explore repetition patterns in well written literature. Then, each child "algebrafied" a Liberian folktalk and a Chinese folktale to explore number, pattern, and relationship in simple arrays. Finally, they engaged square natural numbers one to four. On the practitioner research side of the project, the inquiry was this: What happens when kids explore natural numbers in simple arrays? This descriptive inquiry used an ethnographic-like, participant observer model to collect data systematically (3 lessons per session times 12 sessions or 36 lessons in all). In brief, the study found that three kindergarten children made generalizations, added to a web of knowledge, used mathematical memory, and displayed flawed reasoning as a springboard for new mathematical knowledge--what Susan Jo Russell called "mathematical reasoning." The paper captured what counted for learning and what counted for research. These were two themes of the 29th Ethnography and Education Research Forum at the University of Pennsylvania, 1 March 2008. (Contains an annotated bibliography.)