The adoption of the Common Core State Standards has necessitated a change in the instructional practices used by many mathematics teachers. The new standards encourage problem solving and the development of conceptual understanding rather than rote memorization of formulas and rules. Researchers have demonstrated that formative assessment is a…

In this insightful math resource for grades 3-8, popular professional developer Marian Small helps teachers understand and facilitate meaningful assessments to advance student understandings. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess; construct meaningful…

In this article, we provide brief overviews of the definitions of formative and summative assessment and a few examples of types of formative and summative assessments that can be used in classroom contexts. We highlight the points that these two types of assessment are complementary and the differences between them are often in the way these…

The purpose of this study was to understand the use of interim assessment data to inform mathematics instruction. A qualitative case study methodology was used to analyze the use of interim assessment data in a suburban elementary school. Data sources included interviews with three teachers at varying levels of their profession and the principal;…

Although annual state tests had been federally required since 2001, and the consortia and standards were led by states, the new tests became a focal point of narratives about federal overreach and over-testing. Current wisdom holds that testing has become politically toxic. There are real risks that some states are rolling back advancements in…

Purposes: This study uses think-alouds and cognitive interviews to provide validity evidence for an online formative assessment--i-Ready Standards Mastery (iSM) mini-assessments--which involves a heavy use of innovative items. iSM mini-assessments are intended to help teachers determine student understanding of each of the on-grade-level Common…

Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students' achievements of intended instructional outcomes. Formative assessment means assessment embedded in instruction. That definition was adopted in 2006 by the Council of Chief State…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

Rural school districts face unique challenges in procuring funds, recruiting staff, and obtaining high-quality technical assistance. This environment creates problems in identifying high-quality instructional materials and implementing best practices. A collaborative learning network can address these challenges by providing access to professional…

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students' conceptual understanding and their capacity to…

Linking ideas, concepts, and disciplinary content is an underused yet effective educational strategy for fostering students' higher order thinking. A body of psychological research on analogical reasoning can inform the challenge of encouraging higher order thinking in schools. We focus in particular on the teaching of mathematics and highlight…

This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…

"A Teacher's Guide to Using the Common Core State Standards in Mathematics" provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century math assessments…

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…

Personal interactions are the single most effective way for teachers to understand and evaluate their student as learners. Responding specifically to new Common Core State Standards in reading and writing, this book introduces pre- and inservice teachers to a method of one-on-one interaction the authors refer to as the "stretch…