Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

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…

For centuries, the basic operations of school mathematics have been identified as addition, subtraction, multiplication, and division. Notably, these operations are "basic," not because they are foundational to mathematics knowledge, but because they were vital to a newly industrialized and market-driven economy several hundred years…

Do your students have the incorrect idea that addition "makes numbers bigger" and subtraction "makes numbers smaller"? Do they believe that subtraction is always "taking away"? What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their…

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

A math teacher describes an approach to help special education students solve addition and subtraction problems through a system involving finger counting. The systems for subtraction and addition solve the problem faced by students unable to memorize facts and unable to use their fingers when numbers exceeded five. (Illustrations of the approach…

Research and curriculum development projects have investigated ways to make teaching and learning basic facts easier. Reseach results and implications from four major projects are presented. Ten specific guidelines are then given and illustrated by examples from addition. Modifying instructional sequence and matching learning tasks with learning…

Explores adult adding techniques and ponders whether they have any relevance to working with primary school children. Suggests ways that can help children develop into effective adders. (ASK)

A math strategy using an "add-card" which illustrates simple addition facts was originally developed for learning disabled students but was also successfully used with mildly retarded students. (CL)

Developed by the Initial Learning in Mainstreaming Project, the manual presents an instructional program to teach mainstreamed handicapped elementary school students the carrying process (regrouping) for addition. In addition to detailed teaching instructions and text of tape recordings for students, the manual includes tests, worksheets, and…

The article presents two teaching strategies for use with elementary age educable mentally retarded students. The first introduces the concept of the equivalence of a nickel and five pennies in terms of buying power. The second strategy involves teaching students the skill of adding various combinations of nickels and pennies. (PHR)

Most people recognize that children should learn basic facts, because knowing them is useful both in school and in real life outside the classroom. Describes a strategies approach to basic addition and subtraction-facts instruction, and discusses assessment techniques and a rationale for the approach. Contains 29 references. (ASK)