Session Information
24 SES 06 A, Early Years Mathematics Education
Paper Session
Contribution
Fractions are one of the poorly understood topics in mathematics. Notation of fractions and formal vocabulary may be some reasons for that. Students mostly try to memorize the rules of fraction operations without understanding the logic behind them. Student-centered learning plays an important role in tricky topics. Students learn better when they actively involved in the learning process. The aim of this study is to understand the students’ conceptual and procedural understanding of addition and subtraction of fractions. Case study design was used in this study. Hands-on activities which are one of the strategies that encourage and help students to understand the topics was used in the lessons. Pirie and Kieren’s model of the growth of Mathematical understanding was adapted while designing the lessons related with the addition and subtraction of fractions. The model involves eight nested circles which illustrate that growth in understanding need be neither linear nor mono-directional. Growth occurs through back and forth movements among levels. The first level is primitive knowing which refers previous knowledge of the learner brought to the context. The second level is image making. The learner uses the previous knowledge under new conditions. Image refers to any kind of mental representations. Image having is the other level. The learner uses mental images in image having activities. Property noticing is the next level which involves noting combinations, distinctions or connections between constructed images. The other level is formalizing in which a method, rule, or property is generalized from the properties. The next level is observing in which the learner formalizes and organizes his/her own formal thinking. The learner organizes the formal observations and thinks about them as a theory at structuring level. The outermost level is inventising. The learner at the inventising level has “a full structured understanding and may therefore be able to break away from the preconceptions which brought about this understanding and create new questions which grow into a totally new concept” (Pirie and Kieren, 1994, p. 171). The study was implemented with 12 sixth grade students and 12 eighth grade students in Australia. The study was also implemented with 20 sixth-grade students and 26 fifth-grade students in Turkey. The study took four class-periods; two periods for addition of fractions and two periods for subtraction of fractions.
Method
Expected Outcomes
References
Hinzman, K. P. (1997). Use of Manuplatives in Mathematics at Middle School Level and Their Effects On Students’ Grades and Attitudes. Master Thesis: Salem Teikyo University. (ERIC Document Reproduction Service No. ED 411150). Long, M. (2004). A Hands-On Approach to Calculus. Dissertation Abstracts International, 65(11), 4138. (UMI No. 3152270). Murray, H. & Newstead, K.(1998). Young Students' Constructions of Fractions. In A. Olivier, & K. Newstead (Eds.), Proceedings of the 22nd Conference of the in International Group for the Psychology of Mathematics Education, 3 , 295-302. Stellenbosch, South Africa. Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26 (2-3), 165-190.
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