A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…

Secondary teachers and leaders, many of whom are implementing the Common Core State Standards, are seeking guidance about how to implement disciplinary literacy practices. Of the four core subjects taught in secondary schools--English, history, math, and science--the authors have found through their work with secondary teachers that math teachers…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

The Better Math Teaching Network (BMTN) is looking to transform high school math instruction in New England and beyond. Through this network, researchers and practitioners are working together to make high school Algebra I classes more student centered. This report outlines findings from the first year of this developmental evaluation of the…

This article explores how college expectations in 8th grade change by 10th grade, and if students realize the expectations for a given level of college from 8th and 10th grade, in light of the "college for all" ethos. This study is based on administrative data from 235,875 public school students in Massachusetts from 2006 to 2016. Using…

Recent federal legislation, such as the "No Child Left Behind Act" of 2001 and the "Education Sciences Reform Act (ESRA)" of 2002, has insisted that educational evaluations use rigorous research designs with quantitative outcome measures. In particular, the Institute of Education Sciences (IES) at the U.S. Department of…

Variation in test performance among examinees from different regions or national jurisdictions is often partially attributed to differences in the degree of content correspondence between local school or training program curricula, and the test of interest. This posited relationship between test-curriculum correspondence, or "alignment,"…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

Business leaders in Massachusetts cannot find the science, technology, engineering and mathematics (STEM) talent they need to stay competitive. Students' lagging performance in K-12 is a critical reason why. The good news is that the nation's most effective STEM ducation programs can help turn the tide. Massachusetts students outscore their peers…

The ASSISTments project is an ecosystem of a few hundred teachers, a platform, and researchers working together. Development professionals help train teachers and get teachers to participate in studies. The platform and these teachers help researchers (sometimes explicitly and sometimes implicitly) simply by using content the teacher selects. The…

In the United States, students' learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies…

In the United States, researchers argue that proof is largely concentrated in the domain of high school geometry, thus providing students a distorted image of what proof entails, which is at odds with the central role that proof plays in mathematics. Despite the centrality of proof, there is a lack of studies addressing how to integrate proof into…

Today, far too many students see mathematics as a subject that must be endured, not a source of inspiration or a way of thinking that can enrich their understanding of the world. Advocates of student-centered instruction argue that good teachers have the ability to transform mathematics classrooms into lively, engaging learning environments in…

Despite extensive scholarship about the importance of teaching mathematics with multiple strategies in the elementary grades, there has been relatively little discussion of this practice in the middle and high school levels or in the context of introductory algebra. This article begins our exploration of this practice by addressing the following…