**FEATURES** |

Developing Mathematical Understanding through Multiple Representations
*Preety Tripathi* Synthesizes research on multiple representations to extrapolate ideas that are directly related to the classroom. It then discusses strategies that will help teachers incorporate the use of multiple representations in their classrooms. Includes several thought provoking problems to stimulate students to consider visual representations as a viable problem solving strategy. The problems and strategies presented in the article are classroom tested and ready for implementation. |

Promoting Mathematics Accessibility through Multiple Representations Jigsaws
*Wendy Cleaves* How to use the jigsaw grouping technique, a pedagogical approach designed around small group work, as a strategy to promote accessibility to mathematics for more students. Includes two lessons built for jigsaw groups, along with student work examples. A jigsaw can be used to differentiate instruction and facilitate whole class or group mathematical discourse. |

Oranges, Posters, Ribbons, and Lemonade: Concrete Computational Strategies for Dividing Fractions
*Christopher Kribs-Zaleta* How to help developing computational strategies for dividing fractions using concrete models developed by students. Sixth-grade students developed separate two-step procedures to solve measurement and partitive story problems, drawing on invented procedures for division of whole numbers. Includes eight story problems and selected student examples. |

Student Representations at the Center: Promoting Classroom Equity
*Kara Imm; Despina Stylianou; Nabin Chae* Article suggests that mathematical representations generated by students help in building classroom community, promote participation in classrooms, accountability for their mathematical growth, and further equity. Discussion follows a seventh grade lesson on multiplying fractions. |

Analyzing Students' Use of Graphic Representations: Determining Misconceptions and Error Patterns for Instruction
*Amy Scheuermann; Delinda van Garderen* Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. Includes two case studies and several examples of good and bad graphic representations. |

Developing Meaning for Algebraic Symbols: Possibilities and Pitfalls
*John Lannin; Brian Townsend; Nathan Armer; Savanna Green; Jessica Schneider* Developing meaning for the mathematical symbols used in formal algebra. It describes the development progress of four fifth-grade students. Computer spreadsheet software assisted students. Analysis of development in the movement from verbal expressions to syncopated expressions and into the use of formal algebraic symbols is presented and strategies are provided to deepen student understanding of the symbol's meaning. |

Sense-able Combinatorics: Students' Use of Personal Representations
*Lynn Tarlow* A mathematics session in which students, instead of recalling and applying an algorithm, developed meaningful representation of a challenging combinatorics task and then found solution. The session analysis may provide insights into how teachers can support students' development of combinatorial reasoning. |

The Role of Representations in Fraction Addition and Subtraction
*Kathleen Cramer; Terry Wyberg; Seth Leavitt* Article describes using concrete models representation of fractions for developing connections with symbols and meaning in a group of sixth graders. Fraction circle is recommended as the most effective representation of fraction. Authors include analysis of the case study and key procedural recommendations. |