Standards documents, such as the Common Core State Standards for Mathematics and "Principles and Standards for School Mathematics", expect teachers to foster mathematics learning by engaging students in meaningful mathematical discourse to expose students to different ways of thinking about and solving problems and positively influence their…

Measurement is a difficult concept for many children. Trend data from the National Association of Educational Progress (NAEP) indicate that student achievement with measurement is disappointing, given the amount of instructional time it receives in K-grade 5. In an attempt to address the problem of student achievement with measurement, the authors…

As recommended by National Council of Teachers of Mathematics (NCTM), the first author regularly relies on her first graders' writing to assess their reasoning about important math concepts. Their writing serves as a culminating activity that allows her to better assess the depth of each student's understanding following class activities and…

The crucial need for a mathematically literate society, coupled with a sustained focus on mathematics standards, continues its center-stage presence. At the same time, "Principles and Standards" states that it is imperative to offer "all students high-quality programs that include significant mathematics presented in a manner that respects both…

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…

In their overview for the prekindergarten-grade 2 Standards, the National Council for Teachers of Mathematics (NCTM) documents the value of early mathematical environments. During these early years, young children are building beliefs about what mathematics is and learning about themselves as early mathematicians. What young children learn about…

Regular education teachers may have received inadequate preparation to work with the variety of student disabilities encountered in the classroom, or they may have received limited training regarding the full range of learning disabilities and their effects on classroom performance. Along with problems in the area of math, students may also have…

Traditionally, learning basic facts has focused on rote memorization of isolated facts, typically through the use of flash cards, repeated drilling, and timed testing. However, as many experienced teachers have seen, "drill alone does not develop mastery of single-digit combinations." In contrast, a fluency approach to learning basic addition…

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…

The concrete, pictorial, and abstract methods of this lesson give students access to investigate, isolate, define, and use prime numbers. In this article, the authors describe an enrichment lesson that offers opportunities to investigate prime numbers in concrete, pictorial, and abstract ways. Originally introduced by Jerome Bruner in 1960, the…

Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…

Educators often speak of teaching as "listening," yet they seldom encounter it in practice. What converts pedagogical space into authentic educational experience is a climate of respect that is born of serious, just, humble, and generous relationships in which both the authority of the teacher and the freedom of the students are ethically…

Representations play a key role in mathematical thinking: They offer "a medium" to express mathematical knowledge or organize mathematical information and to discern mathematical relationships (e.g., relative household expenditures on a pie chart) using text, symbols, or graphics. They also furnish "tools" for mathematical processes (e.g., use of…

By providing sustained, embedded professional development over the course of a school year--as well as involving teachers in creating high-quality assessment tasks, implementing the assessments with students, and tying assessment directly to instruction--the authors increased the value that their teaching community places on mathematical…