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### TIAN Bundle 2 Articles and References (For Teachers) about Strengthening Operation and Symbol Sense

##### About Operation Sense

**Gregg, J. & Gregg D.****(May 2007)**. Measurement and Fair-Sharing Models for Dividing Fractions*. Mathematics Teaching in the Middle School*, 12(9), 490-496.

Includes examples of how to move students from division of whole numbers to division of fractions.**de Silva**Lamberg, T.**(September 2007)**. Student Approaches to Unitizing in Fair-Share Problems*. Mathematics Teaching in the Middle School*, 13(2),114-116.

This short article analyzes four students' methods for dividing (fair-share situation).**Nugent, P.****(September 2007)**. Lattice Multiplication in a Preservice Classroom*. Mathematics Teaching in the Middle School*, 13(2),110-113.

Lattice multiplication is an alternative algorithm for teaching multiplication that helps students see the place values.**Taber, S.****(December 2006)**. Using Alice in Wonderland to Teach Multiplication of Fractions*.**Mathematics Teaching in the Middle School*, 12(5), 244-249.

Although practitioners won't be reading Alice in Wonderland to her students, this article does provide examples of the difference between proportional and nonproportional thinking with fractions.**Tent, M.****(August 2006)**. Understanding the Properties of Arithmetic: A Prerequisite of Arithmetic*. Mathematics Teaching in the Middle School*, 12(1), 22-25.

Provides strategies for teaching the commutative, associative, distributive, and identity properties of addition and multiplication.

##### About the Understanding of the Equal Sign

**Falkner, K., Levi,L., & Carpenter, T. (1999). Children's Understanding of Equality: A Foundation for Algebra.**

This brief article describes the misconceptions students develop at a very early age about the equal sign. Included are strategies one teacher used to try to overcome those misconceptions.**Freiman, V. & Lee, L. (2004). "Tracking Primary Students' Understanding of the Equality Sign". Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (vol.2, pp. 415-422).**

This research was aimed at tracking young students' understanding of the equal sign by monitoring how they responded to simple problem types such as*a*+*b*=*c*and*c*=*a*+*b*. Types of errors in children in K, grade 3, and grade 6 were then analyzed.**Knuth, E. & Stephens, A.****(July 2006)**. Does Understanding the Equal Sign Matter? Evidence from Solving Equations*. Research in Mathematics Education*, 37(4), 297-312.

This research project investigated the relationship between being able to solve simple algebraic equations and an understanding of the equal sign.

##### Other Related Articles

**Algebraic Thinking from Assessment Resource Banks: English, Mathematics, and Science. http://arb.nzcer.org.nz/supportmaterials/Maths/concept_map_algebraic.php**

This collection of mini-resources includes hands-on strategies for teaching equality and the additive, commutative, and associative properties, beginning very early on in learners' math education.**Computation, Calculators, and Common Sense (May 2005).**

A position paper from the National Council of Teachers of Mathematics in reaction to the question of calculator use in the classroom.**National Research Council (2001). "Number: What Is There to Know?" from***Adding It Up: Helping Children Learn*(71-114).**Schifter, D., Bastable, V., Russell, S.J., Riddle, M. & Seyferth, L. (2008). Algebra in the K-5 Classroom: Learning Opportunities for Students and Teachers. In Greenes, C. E. and Rubenstein, R. (Eds.),***Algebra and Algebraic Thinking in School Mathematics: 70th Yearbook*(pp. 263-277). Reston, VA: NCTM.

Discussion of classroom investigations into how students develop algebraic thinking.**Stiff, L. (April 2001). Making Calculator Use Add Up from***NCTM News Bulletin 37*, Vol. 3

A response to a newspaper article about the use of calculators in the classroom.