National mathematics achievement results show elementary students in the United States are not increasing in cognitive ability or critical thinking skills (NAEP, 2019). Furthermore, students who are mathematically promising need more opportunities for cognitively demanding mathematics instruction in order for this increase to occur. Therefore, this descriptive case study focused on the interactions and emergence of Mathematical Practices in seven third grade students with a series of five tasks. The seven third grade students were identified by their teachers as mathematically promising. The tasks used in the two suburban classrooms observations of the study were from the Tools 4 NC teachers framework (Tools 4 Teachers, 2019). Data sources collected included pre- and post-focus group audiotapes, classroom observations via audio and video, field notes, as well as document analysis of student work and a teacher debrief form. Blumer's theory of social constructivism (1969) and Tripathi’s Multiple Reasoning (2008) guided this study.
Findings from the students' interactions with tasks showed the following themes: students used a variety of interpersonal interactions between themselves, the teacher, and visual representations. Students used mathematical writing to justify their reasoning and reflection to communicate their conceptual mathematical understanding. Students grew in their emergence of the Mathematical Practices of perseverance through problem solving, productive struggle, the construction of arguments, and the ability to make connections. These findings indicate the importance of ongoing curriculum development to include differentiated teacher guidance for mathematically promising students. Additionally, the findings of this study will support mathematics teachers and leaders with a student-centered approach to teaching inquiry-based instruction.