Sit beside a fourth-grade teacher being trained to diagnose learning deficits and then develop and implement intervention strategies to help a struggling student become a successful learner.

### Lianfang Lu

Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, samples of student work (when applicable), and teacher insights into the mathematical thinking of the students. This article describes how David used repeated addition to solve a multiplication problem. It reveals his processes of solving the problem mentally, of finding the repeated patterns in a problem context, and of representing the problem with a drawing.

### Lynn Columba

It is a “read”-letter day when storybooks, thinking strategies, and physical materials can use a splash of whimsy and fun to introduce multiplication facts to third graders.

### Thomas E. Hodges, Terry D. Rose and April D. Hicks

A series of diagnostic questions helps this teacher better assess and comprehend the misconceptions of third graders who struggle with multiplication.

### Ellen Robinson, Xiaowen Cui, Hiroko K. Warshauer and Christina Koehne

Collaborative engagement provides an opportunity for students to construct and solidify their own knowledge and understanding of important mathematical ideas. According to Van de Walle, Karp, and Bay-Williams, “learning is enhanced when the learner is engaged with others working on the same idea” (2015, p. 52). In allowing students to work with their peers to practice problems and construct important mathematical connections, the students build on their combined prior knowledge to formulate newfound ideas and conjectures. We recognize that grouping students so that each group will function in a productive manner can often be difficult. Therefore, we have devised this activity that allows students to work together and communicate with ten different students individually. In a usual group setting, the students would get to work with one or two other students, but the format of this activity allows for more forms of mathematics communication and collaboration.

### Sandra Davis Trowell

### Edited by Denise Taunton Reid

The Teaching and Learning principle in *Principles to Actions: Ensuring Mathematical Success for All* (NCTM 2014) states,

### Courtney Baker, Melinda C. Knapp and Terrie Galanti

Here is support for coaches who work in diverse contexts to integrate high-leverage teaching and coaching practices with specific attention to mathematics content.

### Jennifer R. Brown

Set sail to explore powerful ways to use anchor charts in mathematics teaching and learning.

### Ziv Feldman and Matt B. Roscoe

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number's multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers' procedural knowledge with respect to using a number's prime factorization to identify its factors, and presents evidence of the impact of the intervention. Results point toward improved abilities to use a number's prime factorization to sort factors and nonfactors across four factor subtypes, to create factor lists, and to construct numbers with particular divisibility properties. Implications for mathematics teacher education include providing speci_ c materials and strategies for strengthening preservice and in-service teachers' procedural knowledge.

### Isaac Frank

A critique of FOIL provides an alternate method of multiplying polynomials.