**ERIC Number:**EJ1112939

**Record Type:**Journal

**Publication Date:**2016-Sep

**Pages:**9

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

Fostering Algebraic Understanding through Math

Lim, Kien H.

Mathematics Teacher, v110 n2 p110-118 Sep 2016

Magic captivates humans because of their innate capacity to be intrigued and a desire to resolve their curiosity. In a mathematics classroom, algorithms akin to magic tricks can be an effective tool to engage students in thinking and problem solving. Tricks that rely on the power of mathematics are especially suitable for students to experience an intellectual need for the mathematical concepts underlying those algorithms. Meaningful context motivates students to appreciate the usefulness of variables, expressions, equations, and symbolic transformations. When students are introduced to the use of symbols in algebra, they encounter challenges in the transition from working with numbers to working with symbols. If classroom instruction focuses on procedural aspects of algebra, students may be learning symbol manipulation without understanding the meaning of variables, expressions, equations, and functions. Consequently, they are not able to capitalize on the power of algebra, which lies in its symbolism. For example, students prefer to solve word problems using arithmetic rather than algebraic methods. Teachers can engage students to think mathematically and to deepen their understanding of foundational algebraic concepts. Lloyd, Herbel-Eisenmann, and Star (2011) present five big ideas in algebra. They describe twenty-two essential understandings to support these big ideas. This article highlights some of these essential understandings in the context of a magic trick.

Descriptors: Teaching Methods, Mathematics Instruction, Problem Solving, Mathematical Concepts, Symbols (Mathematics), Algebra, Word Problems (Mathematics), Deception, Equations (Mathematics), Preservice Teacher Education, Thinking Skills, Secondary School Mathematics

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education; Postsecondary Education; Secondary Education

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A