This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

Surface area is consistently identified as a curriculum standard for K-12 students and it regularly appears on national and international assessments. Recently, many schools began acquiring digital fabrication and advanced manufacturing equipment. The growing use of digital fabrication in classrooms raises the question of whether or not this…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

Vicki Zack, a classroom teacher and researcher, returned to the fifth grade classroom in 1989 after more than a decade of teaching in a university faculty of education in order to teach in the changing ecologies of classrooms (with problem-solving approaches in mathematics and literature-based approaches in reading) and to research from the…

In part 1 of this article Zack and Reid offered two examples of students operating with good-enough understandings in mathematics, and related their understandings to features of good-enough understanding identified by Mackey (I997) in the context of reading. Mackey contends that the ability to read further, on the basis of a very imperfect…