ERIC Number: EJ1020232
Record Type: Journal
Publication Date: 2013-Aug
Reference Count: 11
Fractions Instruction: Linking Concepts and Procedures
Pitsolantis, Nicole; Osana, Helena P.
Teaching Children Mathematics, v20 n1 p18-26 Aug 2013
It is not surprising, as research has shown, that fractions are one of the most difficult of the elementary school math topics to teach and learn in ways that are meaningful. The authors reference a work by James Hiebert, "Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions" (1992), that mathematical concepts should be linked to symbols and rules during teaching to foster students' authentic, personally meaningful understanding. More specifically, Dr. Hiebert suggested three precise sites, (symbol interpretation site, procedural execution site, and solution evaluation site) or points in real time, during problem solving where such links could be especially useful to learning. His sites theory aligns nicely with best teaching practices in mathematics for pictures and manipulatives can help children learn the meaning of the mathematical symbols they use. They can also help children think about problems and reason about ways to solve them. However, Hiebert's theory goes beyond simply presenting students with pictures and objects to understand symbols and think about problems, but also helps children "reflect" on what they did with their pictures or concrete objects. This article presents teaching methods designed to take the learner through the entire problem-solving sequence, beginning with the interpretation of mathematical symbols (site 1), followed by the use of the procedures (site 2), and through to the evaluation of the solution (site 3) and helps teachers make explicit links between concepts and procedures at each of these three points while students are working on problems in class. The authors conclude that this method has proven to be effective in that students showed a more meaningful understanding of fractions after the unit, and they propose that this method can be used with most, if not all, mathematical topics, and likely at any grade level.
Descriptors: Mathematics Instruction, Mathematical Concepts, Elementary School Mathematics, Teaching Methods, Symbols (Mathematics), Problem Solving, Pictorial Stimuli, Manipulative Materials, Reflection, Mathematics Skills
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: firstname.lastname@example.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education
Authoring Institution: N/A