Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He outlines powerful diagnostic methods for analyzing student work and providing timely, specific, and meaningful…

Computation errors that may occur by expanded use of calculators are discussed. Potential errors with five exact arithmetic examples are described as they are translated into approximate processes. (MNS)

A checklist is presented to identify common problems students exhibit in arithmetic. Alongside general areas of need, common mistakes are listed to help diagnose error patterns for targeting specific skills and designing effective intervention. General areas include readiness, problem solving, whole-number computations, fraction computations, and…

Examines a variety of mistakes found in published materials and practiced by classroom teachers. Provides examples of mistakes in reading time, place value, price notation, geometry, and language. (YP)

Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)

Discusses the use of feedback from students and the analysis of students' error patterns to understand why students develop misconceptions in mathematics. Looks at learning vis-a-vis the abstract nature of mathematics and the students' cognitive development. (MDH)

This paper describes a classroom teaching experiment conducted in three fifth-grade mathematics classrooms with students of different achievement levels. Virtual fraction manipulative concept tutorials were used in three one-hour class sessions to investigate the learning characteristics afforded by these technology tools. The virtual fraction…