**ERIC Number:**EJ1116626

**Record Type:**Journal

**Publication Date:**2016-Oct

**Pages:**9

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

Original Recipes for Matrix Multiplication

Hallman-Thrasher, Allyson; Litchfield, Erin T.; Dael, Kevin E.

Mathematics Teacher, v110 n3 p182-190 Oct 2016

Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world modeling). Matrix units often focus on procedural fluency (i.e., finding inverses and determinants, applying Cramer's rule, and performing matrix operations), so emphasis on conceptual understanding can be neglected. Common Core (CCSSI 2010) grade 9-12 content standards related to matrices mostly emphasize executing procedures, with only two stating that students should "understand" some of the properties of operations on matrices. However, the Mathematical Practices in the Common Core can provide guidance in ways that go beyond procedural fluency and require students to make sense of mathematical concepts and algorithms. Matrix multiplication provides one such opportunity. In this article the authors present a lesson on algebra 2 students developing algorithms. Students in the Algebra 2 class expressed information in a matrix, identified dimensions, added matrices, and multiplied by a scalar. They did not know the procedure for multiplying matrices, nor had it even been mentioned that matrices could be multiplied. The authors engaged students in what Smith and Stein (1998) call a "doing mathematics" task, where students do not have access to an explicitly described procedure and they invent, explore, and make sense of a process.

Descriptors: Multiplication, Algebra, Mathematics Instruction, Teaching Methods, Task Analysis, Academic Standards, Secondary School Mathematics, Preservice Teachers, Student Teaching, Educational Practices, Educational Strategies

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; Guides - Classroom - Teacher; Reports - Descriptive

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

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

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