Two broad categories of instructional practices, (a) explicitly attending to concepts and (b) fostering students' opportunities to struggle, have been consistently linked to improving students' mathematical learning and achievement. In this article, we describe an effort to build these practices into a framework that is useful for a diverse set of…

This paper explores an innovative assessment framework for measuring children's formal and informal mathematical knowledge. Many existing standardized measures, such as the Early Grade Mathematics Assessment, measure children's performance in early primary grade skills that have been identified by researchers and policy makers as foundational and…

California State University, San Bernardino (CSUSB) and the Riverside County Office of Education (RCOE) were awarded an Investing in Innovation (i3) Development grant in 2015 to investigate the impact of an early education mathematics program on English Learner students at two rural school districts in Riverside, CA. Teaching English Learners…

In this chapter, we review two approaches for understanding these national differences in math abilities. The first approach attempts to link cross-national differences in educational input to cross-national differences in test scores. A tacit assumption of this approach is that children's performance on tests of mathematics is a direct effect of…

More than half of U.S. children fail to meet proficiency standards in mathematics and science in fourth grade. Teacher professional development and curriculum improvement are two of the primary levers that school leaders and policymakers use to improve children's science, technology, engineering and mathematics (STEM) learning, yet until recently,…

In recent decades, the Commonwealth of Massachusetts has implemented reforms aimed at improving and controlling the quality of the teaching workforce in public schools. Among those reforms are tests for licensure that assess both general and content-area specific knowledge, requirements for ongoing teacher professional development, and procedures…

The concept of a growth-oriented disposition framed the analysis of theoretical and practical dimensions of pre-service teachers' mathematics content knowledge. We identify historical hangovers, tacit habits, and pedagogical strangleholds that present challenges to the way mathematics education researchers interact with the mathematics content…

A secondary data analysis was conducted using a large dataset from a study related to online professional development for eighth grade teachers of mathematics. Using this data, the paper provides a snapshot of the current state of teachers' knowledge related to proportional reasoning and functions. The paper also considers how teachers' knowledge…

Professional development--formal in-service training to upgrade the content knowledge and pedagogical skills of teachers--is widely viewed as an important means of improving teaching and learning. While many interventions "include" professional development, professional development was the central intervention of the two recent research and…

International comparative studies and cross-cultural studies of mathematics achievement indicate that Chinese students (whether living in or outside China) consistently outperform their Western counterparts. This study shows that the gap between Chinese-Australian and other Australian students is best explained by differences in motivation to…

Ireland's "mathematics problem" is well-documented and extensively reported in the media and elsewhere (Expert Group on Future Skills Needs (EGFSN) 2008; Task Force on the Physical Sciences 2002). Concern primarily lies with post-primary students' underperformance in mathematics coupled with a failure to make a successful transition to…

What would be one of the most sensible ways for a country to invest to achieve maximal economic growth? A recent study (Chetty, Friedman, & Rockoff, 2011) by economists at Harvard and Columbia Universities shows that better teacher quality results in significantly higher students' lifetime earnings. And investing in public school teachers…

We conducted an evaluation study of the Middle School Algebra Readiness Initiative, a middle school mathematics intervention that was implemented in two West Virginia school districts during the 2011-2012 school year. In participating middle schools, the Carnegie Learning MATHia® software intervention and accompanying classroom curriculum were…

The Diagnostic Teacher Assessment in Mathematics and Science (DTAMS) was developed to measure the content knowledge and pedagogical content knowledge of middle-school teachers. Its reliability and validity were initially established by reviewing national standards for content and use of expert question writing teams and reviewers. DTAMS was…

US and China are reforming mathematics teaching by shifting from students' attainment of facts and procedures toward development of competencies in reasoning, communication, connections, and problem solving, and application of these in real life contexts. Differences in students' overall performance, curricula, and teachers' knowledge and…