Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However,…

This article explores how conceptualization of absolute value can start long before it is introduced. The manner in which absolute value is introduced to students in middle school has far-reaching consequences for their future mathematical understanding. It begins to lay the foundation for students' understanding of algebra, which can change…

This article shares an assessment tool that uses student-written word problems to provide meaningful information regarding the depth of mathematical understanding. Students' word problems representing 6 [division] 1/2 were classified using the scoring categories described in the NAEP. By categorizing the problems, students' levels of understanding…

Uses base-ten manipulative pieces to illustrate divisibility tests with single-digit divisors. (YDS)

Recounts 6th grade students' investigations of combinations and graph theory that arose from a claim made on a Steak'n Shake menu. (YDS)

During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…

Describes how students can compute and estimate, mentally and rapidly, by using appropriate number relationships. (YDS)

Discusses zeroes at the ends of decimal fractions representing measurements or real-world applications of numbers including precision, variance, and classroom applications. (YDS)

Demonstrates how an investigation of measurement and representative numbers can engage all levels of student ability. Asks students to learn about representative numbers in order to answer a question they find intriguing. (YDS)

Describes a framework to help teachers decide when to use calculators with their students. (YDS)

Examines student solution strategies to a problem that appeared previously in this journal. (YDS)

Describes an innovative method for teaching 5th grade students how to solve ratio and proportion word problems with understanding. Uses the multiplication table as a conceptual support. (YDS)

Describes a year-long, career-based project to practice basic skills in a meaningful context until such skills are transferred to long-term memory. (YDS)