Mastery of Basic Addition and Subtraction Facts: How Much and What Kind of Drill, at What Time is Sensible?

10.5951/at.38.5.0010 ◽

1991 ◽

Vol 38 (5) ◽

pp. 10-13

Author(s):

Frances Thompson

Keyword(s):

Second Grade ◽

Real Problem ◽

The Real ◽

What Works ◽

Students are introduced to two digit addition and subtraction during the second grade. This is their first encounter with the idea of regrouping in computation. Previous computation has been with singledigit numerals in the basic addition and subtraction facts. Much groundwork is necessary in numeration before students are introduced to twodigit computation. Students must have an understanding of how tens and ones are related in our base-ten notation. They need many varied experiences involving regrouping 10 ones for 1 ten or changing 1 ten for 10 ones before an algorithm is even introduced. But how to introduce the addition and subtraction algorithms effectively is the real problem.

Let's Do It: Counting with a Purpose

10.5951/at.27.2.0006 ◽

1979 ◽

Vol 27 (2) ◽

pp. 6-9

Author(s):

Larry P. Leutzinger ◽

Glenn Nelson

Keyword(s):

Correct Answer ◽

Primary Grade ◽

Counting by ones from one is a skill that children develop early and use in many situations. Primary-grade teachers encourage their students to count to find out how many objects are in a set. Such counting is helpful in determining answers to introductory addition and subtraction examples. After an understanding of these two operations has been developed and the basic addition and subtraction facts have been introduced, however, the “counting by ones from one” skill that children have can become a liability. Many students 6 use the method, since it almost guarantees a correct answer, but such counting is very inefficient if students use this method to find every answer.

CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Kindergarten, First and Second Grades

10.5951/at.28.6.0048 ◽

1981 ◽

Vol 28 (6) ◽

pp. 48-54

Author(s):

Edward C. Rathmell ◽

Larry P. Leutzinger

Keyword(s):

Word Problems ◽

Major Part ◽

Learning Experiences ◽

Primary Grades ◽

Primary Teachers ◽

Instructional Time ◽

Classroom Activities ◽

A major part of the instructional time devoted to mathematics in the primary grades involves helping children learn to count, read and write numerals, memorize basic addition and subtraction facts, add and subtract twodigit numbers, tell time, count money, and solve word problems. Since many able students already know or quickly learn these topics, primary teachers are faced with the problem of providing appropriate learning experiences for these children while the remainder of the class is learning them.

Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them

Teaching Children Mathematics ◽

10.5951/tcm.13.1.0022 ◽

2006 ◽

Vol 13 (1) ◽

pp. 22-31 ◽

Cited By ~ 2

Author(s):

Arthur J. Baroody

Keyword(s):

Basic Skills ◽

Learning Difficulties ◽

Basic Number ◽

How children learn the basic addition and subtraction facts, why many have difficulty mastering these basic skills, and what teachers can do to prevent or overcome these learning difficulties.

Learning Strategies for Addition and Subtraction Facts: The Road to Fluency and the License to Think

Teaching Children Mathematics ◽

10.5951/tcm.10.7.0362 ◽

2004 ◽

Vol 10 (7) ◽

pp. 362-367

Author(s):

Lisa Buchholz

Keyword(s):

Learning Strategies ◽

First Grade ◽

Second Grade ◽

First Year ◽

Mental Computation ◽

The Road ◽

Finger Counting ◽

Basic Facts ◽

Teaching the basic facts seemed like the logical thing to do. Wouldn't a study of the basic facts make mathematics computation much easier for my students in the future? How could I help my students memorize and internalize this seemingly rote information? How could I get rid of finger counting and move on to mental computation? As I embarked on my first year of teaching second grade following many years of teaching first grade, these questions rolled through my head.

Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

10.26686/wgtn.17148476.v1 ◽

2021 ◽

Author(s):

◽

Daniel Green

Keyword(s):

Individual Differences ◽

Large Body ◽

Later Life ◽

School Intervention ◽

Mathematical Achievement ◽

Future Research ◽

Additive Reasoning ◽

The Impact ◽

<p>Mathematical achievement may impact on outcomes in later life; thus, identifying and improving key mathematical skills is a focus of a large body of educational research. Both additive reasoning, and knowledge of addition and subtraction facts, appear to predict later mathematical achievement. The current study explores the impact of a short intervention with a small group of year 7 and 8 students working at lower than expected academic levels. The current study is based on Cognitive Load Theory and research suggesting that counting strategies overload working memory. A mixed-methods approach was used to identify whether structured manipulatives improved the additive reasoning and, addition and subtraction fluency in a sample of ten participants. Participants attended after-school intervention sessions of 45 minutes for seven weeks. The intervention focused on teaching additive reasoning and fluency using structured manipulatives. Inferential statistical analysis showed a statistically significant mean improvement in participants’ ability to answer simple addition and subtraction questions. Tests constructed to operationalise additive reasoning also showed statistically significant mean improvement. Participants answered diagnostic questions operationalising various aspects of additive reasoning. Individual differences in understanding of additive reasoning were observed, and the inverse relationship between addition and subtraction proved to be a challenging concept. Semi-structured interviews provided themes of valuing the intervention and the manipulatives used. Due to the size and design of this study, it is not possible to extrapolate findings to other learners. However, the study may provide directions for future research. Structured manipulatives may have a role to play in enabling learners to begin to learn additive relationships and further securing recall of addition and subtraction facts. Students at years 7 and 8 may still need considerable exposure to additive concepts; moreover, returning to manipulatives may develop this knowledge. Finally, the findings from the diagnostic questions help show the complexity of additive reasoning. Classroom practitioners may need to further develop their knowledge of additive reasoning, its importance, and the individual differences and misconceptions that learners hold in order to provide considered learning experiences.</p>

The Calculator for Concept Formation: A Clinical Status Study

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.12.5.0323 ◽

1981 ◽

Vol 12 (5) ◽

pp. 323-338

Author(s):

Merlyn J. Behr ◽

Margariete Montague Wheeler

Keyword(s):

Concept Formation ◽

Clinical Status ◽

First Grade ◽

Affirmative Answer ◽

Model Counting ◽

One To One ◽

Kindergarten and first-grade children (N=30) used successive punches of a handheld calculator as a means for counting. Each child was presented 16 tasks in two individually videotaped interviews. Data concerning three questions were obtained: (a) Can children maintain a one-to-one correspondence between successive punches of a handheld calculator count and (i) an oral count, (ii) a manipulation of a set of objects, and (iii) a second calculator count?, (b) How do children account for an experimenter induced discrepancy in each of these correspondences?, and (c) With a calculator can children model counting strategies known to be used to process basic addition and subtraction facts? Data suggest an affirmative answer to each question. The authors conclude that it may be possible to facilitate a child's acquisition of addition and subtraction concepts by using the calculator to augment counting behaviors.

An Alternative to Basic-Skills Remediation

Teaching Children Mathematics ◽

10.5951/tcm.2.8.0452 ◽

1996 ◽

Vol 2 (8) ◽

pp. 452-458

Author(s):

Judith E. Hankes

Keyword(s):

Basic Skills ◽

Mentally Retarded ◽

First Grade ◽

Educable Mentally Retarded ◽

Three students stand out vividly when recalling twenty years of teaching. The first one is Josh, a second grader who hail been labeled as educable mentally retarded by his kindergarten and first-grade teachers. Josh had serious problems with symbols. He could not memorize his addition and subtraction facts, and at times he seemed not to understand that the numeral 7 stood for the quantity seven.

Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

10.26686/wgtn.17148476 ◽

2021 ◽

Author(s):

◽

Daniel Green

Keyword(s):

Individual Differences ◽

Large Body ◽

Later Life ◽

School Intervention ◽

Mathematical Achievement ◽

Future Research ◽

Additive Reasoning ◽

The Impact ◽

<p>Mathematical achievement may impact on outcomes in later life; thus, identifying and improving key mathematical skills is a focus of a large body of educational research. Both additive reasoning, and knowledge of addition and subtraction facts, appear to predict later mathematical achievement. The current study explores the impact of a short intervention with a small group of year 7 and 8 students working at lower than expected academic levels. The current study is based on Cognitive Load Theory and research suggesting that counting strategies overload working memory. A mixed-methods approach was used to identify whether structured manipulatives improved the additive reasoning and, addition and subtraction fluency in a sample of ten participants. Participants attended after-school intervention sessions of 45 minutes for seven weeks. The intervention focused on teaching additive reasoning and fluency using structured manipulatives. Inferential statistical analysis showed a statistically significant mean improvement in participants’ ability to answer simple addition and subtraction questions. Tests constructed to operationalise additive reasoning also showed statistically significant mean improvement. Participants answered diagnostic questions operationalising various aspects of additive reasoning. Individual differences in understanding of additive reasoning were observed, and the inverse relationship between addition and subtraction proved to be a challenging concept. Semi-structured interviews provided themes of valuing the intervention and the manipulatives used. Due to the size and design of this study, it is not possible to extrapolate findings to other learners. However, the study may provide directions for future research. Structured manipulatives may have a role to play in enabling learners to begin to learn additive relationships and further securing recall of addition and subtraction facts. Students at years 7 and 8 may still need considerable exposure to additive concepts; moreover, returning to manipulatives may develop this knowledge. Finally, the findings from the diagnostic questions help show the complexity of additive reasoning. Classroom practitioners may need to further develop their knowledge of additive reasoning, its importance, and the individual differences and misconceptions that learners hold in order to provide considered learning experiences.</p>

Using Hand Signs to Teach Basic Facts

10.5951/at.31.1.0038 ◽

1983 ◽

Vol 31 (1) ◽

pp. 38-41

Author(s):

Carol LaSasso ◽

Philip L. Mackall

Keyword(s):

Deaf Children ◽

Deaf Student ◽

Basic Facts ◽

The procedure that is described in this article was developed several year ago for use with 12-to-15-year-old deaf student who could not remember basic addition and subtraction facts. Since its development, the procedure has been used successfully with numerous deaf children between the age of 8 and 17 years.