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**Abstract**

**Purpose and Perspective:** Communication is emphasized as a crucial component of mathematical learning, and mathematical writing has the potential to positively influence student achievement and understanding in mathematics (Kostos & Shin, 2010). Despite this, descriptions of the types of mathematical writing that would support teachers’ and students’ engagement in this practice have been inadequate. Students simply are called to use “written communication” (NCTM, 2014, p. 29), “justify and explain ideas in order to make their reasoning clear” (National Research Council, 2001, p. 130), and “construct viable arguments” (NGA & CCSSO, 2010, p. 6). Without further elaboration, it remains unclear what types of and purposes for mathematical writing may leverage students’ learning.

Therefore, the [blinded] Task Force (Authors, 2016) met in October 2015 to bring together a diverse group of school- and university-based experts with the following aims: 1) to come to a consensus about the types of elementary mathematical writing that reflect multiple purposes for writing mathematically and 2) to recommend the types and purposes that have the potential to leverage students’ mathematical learning. Members of the task force represent the fields of mathematics education, mathematics, and writing education and have knowledge across the elementary grades. Additionally, the task force also has expertise with students with learning difficulties, who are English language learners, and who have been identified as gifted. Others have background mathematics curriculum design, assessment development, and science writing.

**Techniques:** The task force engaged in multiple collaborative tasks to help identify the types of and purposes for elementary mathematical writing that can maximize mathematical learning. First, members shared an artifact that represented their views on mathematical writing with the whole task force. Subsequently, members worked collaboratively and iteratively in multiple small groups – first with those with similar professional backgrounds and then across them – to analyze mathematics education and writing education national standards, and samples of students’ mathematical writing. As each group analyzed these items, they developed working descriptions of potential types of and purposes for mathematical writing. These were refined throughout the task force meeting through presentation and discussion with the whole task force. Ultimately, the task force reached consensus as to the recommended types of and purposes for mathematical writing. It should be noted that the task force also identified that the two overarching goals across these four types and purposes are for students to reason and communicate mathematically.

**Scholarly Significance:** The recommendations for the types of and purposes for elementary mathematical writing are significant because they can serve as a foundation upon which the field of mathematics education can begin to establish clear expectations with regard to mathematical writing for elementary students. By building on this foundation, researchers and can work to develop and implement instructional practices. Additionally, curriculum writers may purposefully revise mathematical writing prompts included in instructional materials, and assessment developers may be able to design tests that reflect the desired outcomes with regard to mathematical writing. Collectively these implications ultimately may enhance students’ mathematical learning and understanding.

**References:**

Kostos, K., & Shin, E. (2010). Using math journal to enhance second graders’ communication of mathematical thinking. Early Childhood Education Journal, 38, 223-231.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010a). Common core state standards for mathematics. Authors: Washington, DC. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.