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Each month Asked & Answered highlights selected threads from the MyNCTM community. MyNCTM is an online community where NCTM members can ask questions, start and join discussions, and interact with education experts. We encourage you to join the conversation at https://my.nctm.org.

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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.

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Modeling a Bouncing Ball with Exponential Functions and Infinite Series

We modify a traditional bouncing ball activity for introducing exponential functions by modeling the time between bounces instead of the bounce heights. As a consequence, we can also model the total time of bouncing using an infinite geometric series.

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The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions regarding 1st grade number sense, multiplication and division of fractions, issues of definition and precision related to circles, and the value of rationalizing denominators.

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Creating Joy in PK–Grade 2 Mathematics Classrooms

Children experience joy in well-designed mathematics classrooms. This article describes five research-based practices for bringing joy into PreK-Grade 2 math lessons.

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Riding the RAFT

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language (Carter 2009; McCarthy 2008; Yang 2005), encourages self-reflection (Carter 2009; Danielson 2010; O'Kelley 2013), and provides a better way to organize ideas (Linhart 2014; Rogers 2014). Many teachers incorporate journaling and other types of reflective writing into their instruction already (Sjoberg, Slavit, and Coon 2004; Sanders 2009), but what about other forms of writing? NCTM states the importance of writing, in that students in the middle grades should be “more explicit about basing their writing on a sense of audience and purpose” (NCTM 2000, p. 62). How can we help students develop this important skill in math class?.

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Fractions and Long Division Predict Success in High School Mathematics

This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This month in the Coaches' Corner, take a closer look at CCSS Standard 3 for Mathematical Practice, Explain and Justify. Coaches may want to demonstrate the integration of math and writing with Speak, Write, Reflect, Revise, a five-step approach for integrating problem solving and the writing process.

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Conceptualizing Mathematics Using Narratives and Art

To support mathematical investigations, use this framework to guide students in constructing art-based and technology-based literature.

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The Role of Writing Prompts in a Statistical Knowledge for Teaching Course

Teachers of grades Pre-K-8 are charged with the responsibility of developing children's statistical thinking. Hence, strategies are needed to foster statistical knowledge for teaching (SKT). This report describes how writing prompts were used as an integral part of a semester-long undergraduate course focused on building SKT. Writing prompts were designed to help assess and develop the subject matter knowledge and pedagogical content knowledge of prospective teachers. The methods used to design the prompts are described. Responses to a sample prompt are provided to illustrate how the writing prompts served as tools for formative assessment. Pretests and posttests indicated that prospective teachers developed both SKT and knowledge of introductory college-level statistics during the course. It is suggested that teacher educators employ and refine the prompts in their own courses, as the method used for writing and assessing the prompts is applicable to a broad range of statistics and mathematics courses for teachers.

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