In working with integers, students have difficulties that may extend into middle school and even adulthood. However, even young children can display insights into negative numbers well before receiving formal instruction. Using a pre-test, instruction, post-test design, this study explores how 61 first graders reason about negative number properties and operations and how their understanding changes depending on the instruction they receive. Results of the study indicate that children build on their existing whole number understanding to develop a central conceptual structure for integers. Furthermore, the process by which they extend their numerical central conceptual structure differs among students; their initial schemas, together with the form of the integer instruction, influence how they reason about and solve integer addition and subtraction problems. These results highlight the need to revisit the placement, duration, and content of integer instruction in curricula.Class 1 Class 2 Class 3 Class 4 All First Graders Total Students 20 20 20 19 79 Returned Consent Forms 19(95%) ... using the math curriculum enVisionMATH for the rst time, and although the curriculum does not acknowledge negative numbers in ... of negative numbers arose briey in their classes before the study but was not a topic they talked about otherwise. ... female) from the same school, and representing a range of math performance levels, participated in just the post -test toanbsp;...
|Title||:||Expanding the Numerical Central Conceptual Structure|
|Author||:||Laura Christine Bofferding|
|Publisher||:||Stanford University - 2011|