Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

As students progress from working with whole numbers to working with integers, they must wrestle with the big ideas of number values and order. Using objects to show positive quantities is easy, but no physical negative quantities exist. Therefore, when talking about integers, the author refers to number values instead of number quantities. The…

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…

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…

This article describes one teacher's journey to improve her teaching of mathematics by conducting classroom-based inquiry to meet the specific mathematical needs in her second grade classroom. Her process to develop and improve computational fluency through research-based methods is detailed. (Contains 9 figures.)

Presents a series of reflections in which a second-grade teacher recognizes the value of encouraging children to develop various computational processes as well as a range of different solution approaches. Uses the context of mentally calculating costs of menu items. (MKR)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

Contrasts nominal, cardinal, and ordinal uses of numbers with linguistic and historical examples. (MKR)

Discusses the importance of developing teachers' computational fluency so that they can effectively support their students' fluency work. Provides suggestions for helping teachers develop computational fluency with subtraction. (Author/NB)

Presents an activity that concerns children's reasoning about counting from the perspectives of informal mathematics, work center mathematics, and cardboard box mathematics. (ASK)

Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

Describes a second-grade classroom project to collect pennies to buy playground equipment. The unit combined practical, hands-on experiences and reflected six standards from the National Council of Teachers of Mathematics Curriculum Standards. (MKR)

Presents a problem of triangular tiles that involves counting and probability. Includes instructor guiding questions. (KHR)

Discusses a meaningful experience, conceptually, of multiplication of fractions. (Author/YDS)