Students' Understandings of Arithmetic Generalizations

Lina Haldar

My dissertation study represents an important step of a broader research agenda aimed at fostering the development of algebraic thinking in the elementary grades. It reports on the findings from an interview study with 4th grade students to examine their understandings of arithmetic generalizations, the properties of arithmetic operations that hold true for all numbers. Researchers and educators have highlighted the importance of arithmetic generalizations in the development of algebraic thinking in the early grades. However, systematic research on children?s reasoning is needed to productively integrate arithmetic generalizations into the elementary curriculum. I interviewed 4th graders (n=48) to examine how they reason with additive and multiplicative tasks that require arithmetic generalizations. Overall, students demonstrated robust understandings of the arithmetic generalizations and qualitative analyses of the data allowed me to identify four distinct levels of generality with which students treated the operations of addition, subtraction, multiplication, and division. Further quantitative analyses revealed that student thinking was not always consistent and often varied across the different types of arithmetic generalizations and particular problem sub-types. These findings suggest a model of development, which can inform the design of an instructional sequence and help teachers extend students? understandings.

About Lina Haldar

N/A