Students' verbal expressions of equality

Year: 2012

Author: Anakin, Megan

Type of paper: Abstract refereed


What can student talk about arithmetic missing number problems tell us about how they conceptualise equality? In this symposium presentation, we will present preliminary findings about students' conceptions of equality which indicate they are more complex than previous theoretical frameworks suggest.  In 2009, nationally representative samples of Year 4 (n = 437, 8 and 9 year olds) and Year 8 (n = 422, 12 and 13 year olds) students participated in the National Educational Monitoring Project in New Zealand.  Students offered verbal responses to three additive arithmetic number problems which were video recorded as a one-on-one interview with an adult assessor and reported as link task 2.  Only 6% of Year 4 and 40% of Year 8 students were able to demonstrate a strong understanding of equality, whereas 75% of Year 4 and 35% of Year 8 students showed a limited understanding of equality within the context of these problems.  It appears that Year 4 and Year 8 students find it challenging to generalise the role of the equals sign from their arithmetic experiences and make the shift towards understanding the properties of the equals sign that are informed structural thinking.  To better understand why so many students were showing limited understandings of equality, we are examining students' verbal responses to additive arithmetic missing number problems as acts of communication by the students rather than as correct or incorrect responses.  This approach was applied in a study of a parallel questions given to students as an independent written task and findings from a general inductive analysis suggests that students were responding with varying levels of attention directed to learned associations, procedures, and structural features of the problems as well as varying understandings of the properties of operations, mathematical notation, and the number system.  We found similar patterns in the verbal responses offered by students. Mathematics educators can use these findings to better understand why their students offer incorrect answers to the arithmetic problems they attempt to solve.  These findings will also contribute to emerging contemporary models of structural awareness in mathematics.