Employment opportunities for the person trained in mathematics exist in teaching, in industry, and in government.

### Michele B. Carney, Jonathan L. Brendefur, Gwyneth R. Hughes and Keith Thiede

As mathematics teacher educators, it is imperative that we have high-quality tools that conceptualize and operationalize mathematics instruction for large-scale examination. We first describe existing instructional practice survey scales, including their conceptualization of practice and related validity evidence. We then present the framework and initial validity evidence for our mathematics instructional practice survey. Survey participants were inservice teachers in a statewide mandated mathematics professional development course. Statistical analyses indicate the items measure two constructs: social-constructivist and transmission-based instructional practice. Of particular interest is the result that these two constructs were negligibly correlated. This is in contrast to the generally accepted notion that social-constructivist and transmission-based instructional practices are the two polar ends of a single construct for describing instructional practice.

Key Recommendation: Mathematics instruction should be consistent with research-informed and equitable teaching practices that foster students’ positive mathematical identities and strong sense of agency. Building upon a strong mathematics

Key Recommendation: Each and every student should develop deep mathematical understanding, understand and critique the world through mathematics, and experience the wonder, joy, and beauty of mathematics, which all contribute to a positive

Key Recommendation: Middle schools should offer a common shared pathway grounded in the use of mathematical practices and processes to coherently develop deep mathematical understanding, ensuring the highest quality mathematics education for each

### Matthew E. Foster, Jason L. Anthony, Doug H. Clements, Julie Sarama and Jeffrey M. Williams

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted instruction (CAI) in mathematics with Building Blocks or in literacy with Earobics Step 1. Children in the Building Blocks condition evidenced higher posttest scores on tests of numeracy and Applied Problems after controlling for beginning-of-year numeracy scores and classroom nesting. These findings, together with a review of earlier CAI, provide guidance for future work on CAI aiming to improve mathematics performance of children from low-income backgrounds.

### Frances K. Harper

Mathematics classrooms are increasingly becoming sites for investigating social (in)justice, but research on teaching mathematics for social justice remains limited to individual case studies. This article reports on a metasynthesis of 35 qualitative reports of social justice mathematics enactments in diverse classroom contexts. Critical race theory serves as a guiding framework for analyzing possibilities and limitations of these enactments to address racial inequities in mathematics education. Findings from this metasynthesis reveal that addressing race in social justice mathematics explorations provided opportunities for centering the voices of people of Color and critiquing liberal views that camouflage subtle forms of racism and involved substantial and authentic mathematical work. Promising practices and implications for future research are identified based on this synthesis.

## Abstract

*Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations* recognizes that the needs of young adolescents are different from elementary and high school–age students and that policies, practices, and issues must consider the unique needs of this student group. Students undergo significant developmental changes from elementary school to middle school. These changes contribute to how they see and understand the world as well as how they see and understand their place in the world. Critical conversations that middle school teachers need to initiate should center on the following serious challenges:

- Broadening the purpose of school mathematics’ focus to include the development of positive mathematical identities so that students can make purposeful decisions about their future endeavors
- Dismantling structural obstacles that stand in the way of mathematics working for each and every student
- Implementing equitable instructional practices to cultivate students’ positive mathematical identities and strong sense of agency
- Organizing middle school mathematics along a common shared pathway grounded in the use of mathematical practices and processes to coherently develop deep mathematical understanding

Middle school students are experiencing an amazing time of change and growth in their lives. The mathematics learned in middle school is extremely important. Being a stakeholder in middle school mathematics is a position with endless potential to