Visualizing Number: Instruction for Number System Knowledge in Second-Grade Classrooms

ABSTRACT

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual understanding of numbers while learning to operate with abstract symbols. In this mixed-methods study, we examined the variations and shifts in second-grade students’ NSK outcomes after participating in an instructional treatment focused on building their NSK through visual representations. After receiving professional development in the instructional treatment, five classroom teachers implemented a systematically planned series of 27 visual number activities across 9 weeks. Analysis using a general linear model indicates that, based on 75 students’ pretest and posttest achievement data, students made significant improvements in NSK that are most likely attributable to the instructional treatment. Additional analyses indicate that students with the lowest pretest scores made the greatest gains and the most substantial shifts in their thinking following the instructional treatment.

KEYWORDS:

• Number system knowledge
• number sense
• spatial thinking
• ambitious mathematics teaching

Additional information

Funding

This work was supported by Utah State University’s Office of Research and Graduate Studies under the Grant-Writing Experience Through Mentorship grant program.