ERIC Number: EJ1035806
Record Type: Journal
Publication Date: 2014-Feb
Reference Count: 5
Mixing Strategies to Compare Fractions
Tobias, Jennifer M.
Mathematics Teaching in the Middle School, v19 n6 p376-381 Feb 2014
Strictly teaching algorithms or procedural computations can "encourage children to give up their own thinking" (Kamii and Dominick 1998). Although such procedures are valid for finding solutions, students often know only how to use them, and they lack the understanding of why a procedure works. In 2001, the National Research Council (NRC) published a report suggesting that mathematically proficient students have five strands of knowledge. These include strategic competence, or the ability to problem solve; adaptive reasoning, or the ability to explain and justify; conceptual understanding, which is understanding why an idea is important and how it connects to other ideas; procedural fluency, or knowing how to solve problems efficiently; and productive disposition, which is seeing mathematics as a worthwhile activity (NRC 2001). Only one strand pertains to students' ability to use a procedure to solve problems; in other words, it alone will not be enough to allow students to be successful with mathematics (NRC 2001). This article describes teaching strategies to support students in becoming mathematically proficient. The examples originate from a class of prospective teachers. The instruction focused on having the prospective teachers understand more than just a procedure for comparing fractions through experiences similar to what they will then have to implement in their own classroom, as outlined by the Common Core State Standards for Mathematics.
Descriptors: Secondary School Mathematics, Middle School Students, Mathematics Instruction, Teaching Methods, Mathematics Skills, Preservice Teachers, Word Problems (Mathematics), Problem Solving, Mathematical Logic
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: Secondary Education; Middle Schools; Junior High Schools; Higher Education; Postsecondary Education
Authoring Institution: N/A