This research was motivated by several studies which show that students have difficulties in understanding the material ratio, wherein one contributing factor is the lack of ability in proportional reasoning. The purpose of this study is to produce a trajectory of learning to help students develop abilities in comparison reasoning. Solution…

When applied to mathematics education, manipulatives help students to visualize mathematical concepts and apply them to everyday situations. Interest in mathematics instruction has increased dramatically over the past two decades with the introduction of virtual manipulatives, as opposed to the concrete manipulatives that have been employed for…

This research study is a mixed-methods quantitative and qualitative study that analyzed data from an intensive, long-term professional development project named, "Project: Making Mathematics Matter. (PM[superscript 3])" carried out in two low-performing, high-poverty districts. Two of the districts served as treatment districts and ALL…

Mathematical discussions support and promote student learning as an integral part of the contexts in which students learn mathematics. Yet, American school practices often focus on teachers disseminating knowledge to students and students acquiring that knowledge through rote rehearsal rather than higher order thinking. One barrier to change in…

This report deals with 7th grade pupils' conceptions of mathematics, its learning and teaching. The report focuses on the identification and comparison of views expressed by pupil groups of different mathematical ability and achievement. The analysis is based on the results of the ability tests, subject tests and a questionnaire conducted among…

Planning a mathematics lesson plan is a complex process. Its quality contributes to the effectiveness of mathematics instruction. Given this significance, improving prospective mathematics teachers' lesson planning ability is essential for teacher preparation programs to produce effective teachers. This study examines how a lesson study within a…

In most ways the island nations of Iceland and Singapore could not be more different from each other: Iceland is sparsely populated, located near the Arctic Circle, and a very free and individualistic democratic society; Singapore is densely populated, located near the equator, and a very regulated and collectivist meritocracy. But both nations…