Adaptive teachers use student data to guide instruction. Learn about using an anecdotal record form to support adaptive teaching. In this article, the authors describe how teachers can use learning trajectories to make adaptive decisions to meet the needs of their students. They provide an example using the U .S. Math Recovery Council's learning…

Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Lina, a Mexican American second grader, bilingual in Spanish and English, used a strategy for adding two two-digit numbers that the authors share as an example of the importance of listening to the mathematical ideas of children, especially when these ideas do not align with how mathematics is traditionally represented in the classroom. The…

Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…

In this article, the authors illustrate how the practice of number strings--used regularly in a classroom community--can simultaneously support computational fluency and building conceptual understanding. Specifically, the authors will demonstrate how a lesson about multi-digit addition (CCSSM 2NBT.B.5) can simultaneously serve as an invitation to…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…