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Share news about happenings in the field of elementary school mathematics education, views on matters pertaining to teaching and learning mathematics in the early childhood or elementary school years, and reactions to previously published opinion pieces or articles. Find detailed department submission guidelines at http://www.nctm.org/WriteForTCM.

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

Articles in this department showcase students' in-depth thinking and work on problems previously published in Teaching Children Mathematics. This month's scenario challenges students to consider elapsed time and requires them to convert between different units of time measure.

Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. In this month's Problem Solvers Solutions, readers have a window into students' number and operation sense in the early elementary grades. Second and third graders were presented with problem-solving tasks using a hundred chart consisting of two number cards and a challenge card aligned to an addition or subtraction structure. Drawing on the structure of the hundred chart and prior knowledge, students were able to articulate their solution strategies.

Postscript items are designed as rich grab-and-go resources that any teacher can quickly incorporate into his or her classroom repertoire with little effort and maximum impact. Increase mathematical confidence by creating ways for students to show they are “smart” in math through Smartness Wordles™, collections of words in graphic representation.

Instructional activities designed to encourage relational thinking in primary-grades classrooms can give students advantages when they reason about subtraction.

To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics launched a series of articles beginning in the February 2012 issue. In this concluding installment, we concentrate on the implementation of the eight Standards of Mathematical Practice and the constellations of Practices and Standards. In the September issue, Matthew Larson follows up the series with a feature article that looks at CCSSM through the lens of mathematics education reform history and asks the provocative question, Will CCSSM Matter in Ten Years?

Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.

In classrooms, students engage in argumentation through justifying and generalizing. However, these activities can be difficult for teachers to conceptualize and therefore promote in their classrooms. In this article, we present the Student Discourse Observation Tool (SDOT) developed to support teachers in noticing and promoting student justifying and generalizing. The SDOT serves the purpose of (a) focusing teacher noticing on student argumentation during classroom observations, and (b) promoting focused discussion of student discourse in teacher professional learning communities. We provide survey data illustrating that elementary-level teachers who participated in professional development leveraging the SDOT had richer conceptions of justifying and generalizing and greater ability to characterize students' justifying and generalizing when compared with a set of control teachers. We argue that the SDOT provides both an important focusing lens for teachers and a means to concretize the abstract mathematical activities of justifying and generalizing.

Learning mathematical problem solving is as easy as 1, 2, 3 when teachers use flexible instructional strategies.