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Direct linkPatrick L. Sullivan; Joann E. Barnett; Kurt Killion – Mathematics Teacher: Learning and Teaching PK-12, 2023
This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…
Descriptors: Fractions, Mathematical Logic, Mathematics Instruction, Teaching Methods
O'Keeffe, Lisa; White, Bruce – Australian Primary Mathematics Classroom, 2018
The importance of ratio and proportional reasoning is regularly emphasised, however, the teaching and learning of these concepts continues to present challenges. In this article the authors explore a hands-on task, designed to encourage student visualisation of the concept of ratio. Teacher perceptions of this task were positive, indicating the…
Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematics Teachers, Learner Engagement
Download full textStephens, Ana; Strachota, Susanne; Knuth, Eric; Blanton, Maria; Isler, Isil; Gardiner, Angela – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…
Descriptors: Algebra, Early Intervention, Grade 3, Grade 4
