Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

1990 ◽  
Vol 21 (3) ◽  
pp. 180-206 ◽  
Author(s):  
Karen C. Fuson ◽  
Diane J. Briars
Keyword(s):  
School District ◽  
First Graders ◽  
Second Graders ◽  
Teaching Approach ◽  
Second Grade ◽  
Place Value ◽  
Urban School District ◽  
Value System ◽  
Number Words ◽  
Addition And Subtraction

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from five to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N=169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N=75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N=783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N=707) completing subtraction work learned at least four-digit subtraction.

The Influence of Structural Aspects of the English Counting Word System on the Teaching and Learning of Place Value

1998 ◽  
Vol 59 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Ian Thompson
Keyword(s):  
Young Children ◽  
Teaching And Learning ◽  
Place Value ◽  
Single Digit ◽  
Value System ◽  
Number Words ◽  
Large Numbers ◽  
Structural Aspects

The influence of structural aspects of the English counting word system on the teaching and learning of place value In their discussion of the teaching of place value to young children Fuson and Briars (1990) describe the extent to which the English spoken system of number words constitutes a ‘named value’ system for large numbers. They argue that, because two-digit numbers are not ‘named value’, teachers should move from teaching single-digit calculations to teaching calculations with large numbers, only returning to two-digit numbers when children are familiar with the standard written algorithms. This article uses transcriptions of children calculating mentally to suggest that they appear to take advantage of the ‘partitionable’ aspect of the language associated with two-digit numbers - an aspect that Fuson and Briars (1990) appear to have ignored. These examples appear to raise questions about their recommendation that teachers should progress from single-digit to large number calculations.

scholarly journals The Degree of Abstraction in Solving Addition and Subtraction Problems

2007 ◽  
Vol 10 (2) ◽  
pp. 285-293 ◽  
Author(s):  
Vicente Bermejo ◽  
Juan José Díaz
Keyword(s):  
Developmental Stage ◽  
Primary Education ◽  
First Graders ◽  
Fourth Grade ◽  
First Grade ◽  
Second Graders ◽  
School Grade ◽  
Levels Of Abstraction ◽  
Direct Modeling ◽  
Addition And Subtraction

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction.

The Addition Methods of First- and Second-Grade Children

1981 ◽  
Vol 12 (2) ◽  
pp. 95-106
Author(s):  
Dorothy M. Houlihan ◽  
Herbert P. Ginsburg
Keyword(s):  
First Graders ◽  
Second Graders ◽  
Clinical Interview ◽  
Second Grade ◽  
Interview Method

A clinical interview method was used to investigate the addition procedures used by first- and second-grade children on both written and orally presented problems of different magnitudes and to determine whether these children vary their strategies according to the nature and magnitude of the problem. The results showed that first graders used a variety of counting procedures to solve addition problems, while second graders used both counting and noncounting procedures. In general, second-grade children efficiently adjusted their strategies according to the magnitude of the problem's addends. Implications for education are discussed.

A Teacher's Journal: Opportunities to Develop Place Value through Student Dialogue

2003 ◽  
Vol 10 (2) ◽  
pp. 78-82
Author(s):  
Amy R. Kari ◽  
Catherine B. Anderson
Keyword(s):  
Facial Expressions ◽  
First Graders ◽  
Second Graders ◽  
Place Value ◽  
Student Dialogue ◽  
Paper And Pencil

The problem 11 + 9 was written on the board at the front of the room. Eleven first graders and nine second graders sat on the carpet, their facial expressions intent as they thought about solutions. I had asked them to try to think of strategies they could use that did not involve counting on their fingers. They did not use paper and pencil because this was what we call “Mental Math” time at our school.

Syllables and inflectional morphemes in early Finnish readers: evidence from eye-movements

2018 ◽  
Vol 45 (5) ◽  
pp. 1227-1245
Author(s):  
Tuomo HÄIKIÖ ◽  
Seppo VAINIO
Keyword(s):  
Eye Movements ◽  
First Graders ◽  
First Grade ◽  
Second Graders ◽  
Syllable Structure ◽  
Second Grade ◽  
Level Information ◽  
Morpheme Boundary ◽  
Locative Case ◽  
Target Words

AbstractFinnish is a language with simple syllable structure but rich morphology. It was investigated whether syllables or morphemes are preferred processing units in early reading. To this end, Finnish first- and second-grade children read sentences with embedded inflected target words while their eye-movements were registered. The target words were either in essive or inessive/adessive (i.e., locative) case. The target words were either non-hyphenated, or had syllable-congruent or syllable-incongruent hyphenation. For the locatives, the syllable-incongruent hyphenation coincided with the morpheme boundary, but this was not the case for the essives. It was shown that the second-graders were slowed down by hyphenation to a larger extent than first-graders. However, there was no slowdown in gaze duration for either age group when the syllable-incongruent hyphen was morpheme-congruent. These findings suggest that Finnish readers already utilize morpheme-level information during the first grade.

Effects of Anxiety on Communication Tasks for Children in Traditional and Individualized-Multiage Classrooms

2005 ◽  
Vol 96 (1) ◽  
pp. 57-66 ◽  
Author(s):  
James P. Papay ◽  
John J. Hedl ◽  
Charles D. Spielberger
Keyword(s):  
Trait Anxiety ◽  
First Graders ◽  
Second Graders ◽  
Anxiety Reduction ◽  
Concept Acquisition ◽  
Second Grade ◽  
Learning Program ◽  
Traditional Group ◽  
Multiage Classrooms ◽  
Concrete Concept

The effects of anxiety on concept acquisition were evaluated for first and second grade children enrolled in either a traditional or in an individualized or multiage learning program, the latter specifically designed to reduce anxiety during the learning process. Regardless of their learning environment, first graders who scored high on trait anxiety, measured by the State-Trait Anxiety Inventory for Children, performed more poorly than those with low trait anxiety. Individualized-multiage second grade children scored lower on state anxiety than children in the traditional group. The largest reduction in anxiety occurred at the second grade, suggesting that anxiety reduction was cumulative for the individualized-multiage program children during the first two years of their primary grade education. However, the individualized-multiage environment was detrimental to performance of second graders on the easier concrete concept acquisition test, suggesting that some anxiety is needed during learning to enhance attention and facilitate performance.

scholarly journals Influence of Neuropsychological Development of Children on Their Verbal Abilities

2018 ◽  
Author(s):  
E Oshchepkova ◽  
E Zubova
Keyword(s):  
Learning Disabilities ◽  
Language Development ◽  
Neuropsychological Assessment ◽  
First Graders ◽  
Second Graders ◽  
Second Grade ◽  
Verbal Abilities ◽  
Neuropsychological Development ◽  
And Control ◽  
Child Neuropsychology

Learning disabilities in childhood are often caused by certain delays in language and higher mental functions development. So nowadays comprehensive research of child language development and its neuropsychological base is of great demand. The objective of the present study was to discover relationships between children’s age, certain characteristics of speech production, neuropsychological and neurolinguistic development. 126 students (51 first-graders and 75 second-graders) were recruited. They underwent complete neuropsychological assessment along with the trial “Creating a Story based on the series of pictures”. The results show that age is an important factor of neuropsychological development from the first to second grade. It concerns especially frontal lobe development. Neuropsychological development also correlates with neurolinguistical level: children who are better at programming and control, analytic and holistic strategies would be more successful in the trial “Creating a Story based on the series of pictures”, their speech would be more correct lexically as well as grammatically and syntactically. We also show that speech particularitiesand their correlation with neuropsychological indexes would vary in first- and second grades. Keywords: Lurian neuropsychology; child neuropsychology; neurolinguistics; neuropsychological development; Creating a Story based on the series of pictures; speech.

Subtracting by Counting up: More Evidence

1988 ◽  
Vol 19 (5) ◽  
pp. 402-420
Author(s):  
Karen C. Fuson ◽  
Gordon B. Willis
Keyword(s):  
Word Problems ◽  
Grade Level ◽  
First Graders ◽  
Second Graders ◽  
Second Grade ◽  
Ability Levels ◽  
Subtraction Facts

To find any subtraction facts that children did not know (e.g., 14–8), 10 teachers successfully taught first- and second-grade children of all ability levels to count up from the smaller to the larger number while keeping track with one-handed finger patterns. Second graders at and above grade level and first graders above grade level in mathematics counted up with finger patterns to solve large multidigit subtraction problems that required regrouping. Learning to subtract by counting up greatly improved children's performance on take-away, compare, and equalize word problems, did not interfere with their understanding of take-away problems, and enabled them to accelerate by as much as 3 years their learning of subtraction topics. Other evidence indicated that subtracting by counting up is natural for children if they learn that one meaning of subtraction (and of the – symbol) is a compare/equalize meaning.

scholarly journals A one-year classroom-randomized trial of mental abacus instruction for first- and second-grade students

2018 ◽  
Vol 3 (3) ◽  
pp. 540-558 ◽  
Author(s):  
David Barner ◽  
Angeliki Athanasopoulou ◽  
Junyi Chu ◽  
Molly Lewis ◽  
Elisabeth Marchand ◽  
...  
Keyword(s):  
Randomized Trial ◽  
Cognitive Abilities ◽  
Spatial Working Memory ◽  
First Graders ◽  
Second Graders ◽  
Second Grade ◽  
Older Children ◽  
Second Grade Students ◽  
One Year ◽  
Mathematical Computation

Mental Abacus (MA) is a popular arithmetic technique in which students learn to solve math problems by visualizing a physical abacus structure. Prior studies conducted in Asia have found that MA can lead to exceptional mathematics achievement in highly motivated individuals, and that extensive training over multiple years can also benefit students in standard classroom settings. Here we explored the benefits of shorter-term MA training to typical students in a US school. Specifically, we tested whether MA (1) improves arithmetic performance relative to a standard math curriculum, and (2) leads to changes in spatial working memory, as claimed by several recent reports. To address these questions, we conducted a one-year, classroom-randomized trial of MA instruction. We found that first-graders students struggled to achieve abacus expertise over the course of the year, while second-graders were more successful. Neither age group showed a significant advantage in cognitive abilities or mathematical computation relative to controls, although older children showed some hints of an advantage in learning place-value concepts. Overall, our results suggest caution in the adoption of MA as a short-term educational intervention.

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