In this commentary, the author reflects on four studies that have greatly expanded the knowledge base on effective interventions in mathematics, and he provides four rigorous experimental studies of approaches for students likely to experience difficulties learning mathematics over a large grade-level span (pre-K to 4th grade). All of the…

With such publications as "Curriculum and Evaluation Standards" (1989) and "Principles and Standards for School Mathematic" (2000), NCTM has played a significant role in defining a vision for school mathematics. In particular, the Curriculum Principle (NCTM 2000, pp. 14-16) described the need for students to learn important…

The learning of "basic facts"--single-digit combinations for addition, subtraction, multiplication, and division--has long been a focus of elementary school mathematics. Many people remember completing endless worksheets, timed tests, and flash card drills as they attempted to "master" their basic facts as children. However,…

If one has three sticks (lengths), when can you make a triangle with the sticks? As long as any two of the lengths sum to a value strictly larger than the third length one can make a triangle. Perhaps surprisingly, if one is given 6 sticks (lengths) there is no simple way of telling if one can build a tetrahedron with the sticks. In fact, even…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) define what children should understand and be able to do in K-grade 12. This document also includes a description of key mathematical processes and proficiencies, the Standards for Mathematical Practice (SMPs), which provide an important overview for the kind of robust thinking…

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

This study investigates how and to what extent preservice and inservice early childhood educators are being prepared to develop mathematics skills and processes in young children, age birth to five, in one southeastern state in the United States. Utilizing a multi-phase mixed methods study and a follow-up survey central to the research question,…

Any of the key concepts that students need to know about area measurement are covered in the third-grade expectations detailed in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). However, making sense of area measurement is not always an easy task for students; it takes time. Researchers have found that young children often…

Gifted learners need opportunities for critical and creative thinking to stretch their minds and imaginations. Strategies for increasing complexity in the four core areas of language arts, mathematics, science, and social studies were addressed using the Common Core and Iowa Core Standards through several methods. Descriptive adjective object…

In this article, the authors introduce a scenario identifying an elementary school special education teacher and interventionist (Mr. Powers) and his concerns in meeting the Common Core State Standards in Mathematics (CCSS-M). Like many teachers, Powers uses a response-to-intervention (RTI) framework to provide supports for students who require…

For the last decade, much of the work of California school administrators has been shaped by the accountability of the No Child Left Behind Act. Now as they stand at the precipice of Common Core Standards and next generation assessments, it is important to reflect on the proficiency educators have attained in using data to improve instruction and…

It has been well-documented that many students do not understand the meaning of the equal sign. Thus, researchers have called for instruction that specifically addresses misconceptions about the equal sign, and have indicated that such work must start at the elementary level. In response to these recommendations, some state curriculums require…

There are a variety of technologies that are increasingly being integrated into mathematics classrooms for their potential to increase student engagement, motivation, understanding, and achievement. YouTube can be an especially useful technology for students to create, share and interact with others, and learn more about mathematics. However, the…

Shifting your high school's math program to new Common Core standards is much easier when teachers and leaders have this handy guide. Getting a copy for every staff member involved in the process ensures everyone knows: (1) How the six conceptual categories throughout the math standards are connected and reinforced; (2) How the modeling standards…

In a new era of Common Core State Standards (CCSS), teachers are expected to provide more rigorous, coherent, and focused curriculum at every grade level. To respond to the call for higher expectations across the curriculum and certainly within reading, writing, and mathematics, educators should work closely together to create mathematically…