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…

Teachers face many challenges helping students meet the expectations set forth in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). CCSSM content standards not only introduce new concepts at each grade level but also require teachers to learn new terminology for old concepts and consider how students' understanding of concepts…

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…

Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…

During the winter of 2011, the author faced an instructional dilemma: Should she teach the concept of adding and subtracting fractions with unlike denominators using a "quick trick" for the sake of staying on schedule, or should she try something different in hopes that her students would gain understanding through their own methods? The latter…

Math games can be powerful tools in helping students achieve automaticity in basic addition and related subtraction facts if both teachers and students use them purposefully. According to the National Council of Teachers of Mathematics (NCTM 2000), developing a solid mathematical foundation is essential for every child in prekindergarten through…

Traditionally, the first mathematical task for primary grade students to master is addition. Mastering addition facts is truly a positive experience. Then one turns to subtraction. After mastering addition facts, many students think that subtraction facts are a whole new set of facts to learn that have nothing to do with addition facts. They do…

Discusses classroom practices that promote the understanding of number concepts in the primary grades. (Author/NB)

Presents activities using the Three Pigs to increase students' understanding of addition and subtraction. Argues that addition and subtraction are something that students can view and participate in when using the Three Pigs instead of just the manipulation of numbers. (ASK)

Presents an activity involving students in a research project with pictures like those commonly found in elementary school mathematics textbooks and workbooks to sharpen student appreciation of the need for standardized methods of data collection. Illustrates that several different interpretations of the operations of addition and subtraction are…

Describes how a 2nd grade class learned to add and subtract effectively by packing and unpacking "Aunt Mary's candies." (KHR)

Most people recognize that children should learn basic facts, because knowing them is useful both in school and in real life outside the classroom. Describes a strategies approach to basic addition and subtraction-facts instruction, and discusses assessment techniques and a rationale for the approach. Contains 29 references. (ASK)

Presents an issue that arises in every country: How can teachers best help children master basic addition and subtraction facts? Discusses how this is handled in China and highlights the impact that language has on how children think about numbers. (KHR)

Presents student comments as they explain their mathematical reasoning and thinking about place value in addition and subtraction. (ASK)