This article outlines several forms of instructional practice that distinguished middle-grades mathematics classrooms that were organized around conceptually oriented activity and marked by African American students' success on state assessments. We identified these forms of practice based on a comparative analysis of teaching in (a) classrooms in which there was evidence of conceptually oriented instruction and in which African American students performed better than predicted by their previous state assessment scores and (b) classrooms in which there was evidence of conceptually oriented instruction but in which African American students did not perform better than predicted on previous state assessment scores. The resulting forms of practice can inform professional learning for preservice and in-service teachers.

### Jonee Wilson, Mahtab Nazemi, Kara Jackson and Anne Garrison Wilhelm

### Jo Boaler

Some researchers have expressed doubts about the potential of reform-oriented curricula to promote equity. This article considers this important issue and argues that investigations into equitable teaching must pay attention to the *particular* practices of teaching and learning that are enacted in classrooms. Data are presented from two studies in which middle school and high school teachers using reform-oriented mathematics curricula achieved a reduction in linguistic, ethnic, and class inequalities in their schools. The teaching and learning practices that these teachers employed were central to the attainment of equality, suggesting that it is critical that relational analyses of equity go beyond the curriculum to include the teacher and their teaching.

### Laura Kondek McLeman and Heather A. Cavell

The creation and implementation of a module in a mathematics-for-teaching course that was centered on children's written work and verbal explanations. The goal of the module was to support the development of preservice elementary teachers' mathematical knowledge for teaching fractions (MKTF).

### Robert Q. Berry III and Mark W. Ellis

See how one seventh-grade teacher melds NCTM's Process Standards, CCSSM's Standards for Mathematical Practice, and multidimensional teaching to engage students.

### Creso Franco, Paola Sztajn and Maria Isabel Ramalho Ortigão

In this article, we use data from a large-scale Brazilian national assessment to discuss the relation between reform teaching and equity in mathematics education. We study the dimensionality of teaching style to better qualify what reform teaching means. We then use hierarchical linear models to explore whether reform teaching is associated with student achievement in mathematics and with student socioeconomic status (SES). Our results indicate that reform and traditional teaching are not opposite sides of a one-dimensional axis. They also emphasize both that reform teaching is related to higher school average achievement in mathematics and that the dissemination of reform teaching contributes to minimize the achievement gap between students who attend schools with low average SES and students who attend schools with high average SES. However, our results also show that reform is associated with an increase in within-school inequality in the social distribution of achievement.

### Tami S. Martin and William R. Speer

Features, consistent messages, and new components of Mathematics Teaching Today: Improving Practice, Improving Student Learning (NCTM 2007), an updated edition of Professional Standards for Teaching Mathematics (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing, supervising, and improving mathematics teaching; and outlines guidelines for the education and continued professional growth of teachers.

### Nancy Staal and Pamela J. Wells

Leverage the parallels between teaching writing and teaching math to nudge your students toward deeper understanding

### Randell L. Drum and Wesley G. Petty Jr.

Teaching about coins can be a frustrating experience for many primary teachers. Teaching the names of the coins is not the problem. Instead, teaching about the values of coins is difficult.

### Lynn McGarvey

As teachers and educators, we have a unique opportunity to continue to see the world through the eyes of a child. Together with our students, we engage in an ongoing quest to make sense of the world around us. We have opportunities to experience wonder and fascination with mathematical ideas new to us, concepts never truly understood, and alternative strategies for problem solving. The start of the new school year is a time to renew that sense of curiosity, enthusiasm, and optimism for teaching mathematics to children.

### Sarah Theule Lubienski

Through my interactions with preservice and in-service teachers in California, Michigan, and New York, I have heard a variety of perspectives on instruction in problem-centered mathematics instruction. I have watched educators struggle to find a role for problem solving in their classes. What constitutes teaching through problem solving? Exploring answers to this question can raise awareness of one's own perspectives and lead to deeper knowledge of problem-centered mathematics teaching.