Using research in teaching: Solution methods used in solving addition and subtraction open sentences

1974 ◽  
Vol 21 (3) ◽  
pp. 255-261
Author(s):  
Douglas A. Grouws
Keyword(s):  
Elementary Schools ◽  
Mathematics Curriculum ◽  
Simple Addition ◽  
Grade Levels ◽  
Solution Methods ◽  
Addition And Subtraction

Open sentences arc an in tegral part of the mathematics curriculum in contemporary elementary schools. The level of children's performance in solving simple addition and subtraction sentences at different grade levels has been studied and reported in several places, including this journal.

Brief Report: Grade Placement of Addition and Subtraction Topics in Japan, Mainland China, the Soviet Union, Taiwan, and the United States

1988 ◽  
Vol 19 (5) ◽  
pp. 449-456
Author(s):  
Karen C. Fuson ◽  
James W. Stigler ◽  
Karen Bartsch
Keyword(s):  
United States ◽  
Soviet Union ◽  
Mathematics Curriculum ◽  
Far East ◽  
Mainland China ◽  
The United States ◽  
Grade Levels ◽  
The Soviet Union ◽  
Addition And Subtraction ◽  
Grade Placement

There has been considerable recent concern about the mathematics achievement of children in the United States compared to that of children in the Soviet Union and in countries of the Far East (Benderson, 1984; Fiske, 1987; Husen, 1967; Stevenson, Lee, & Stigler, 1986; Stigler, Lee, Lucker, & Stevenson, 1982; Wirszup, 1986). One possible source of the superior achievement in these other countries is the placement of topics within the mathematics curriculum. If topics are presented earlier in these countries, children would be given an opportunity to cover more topics and thus might be able to learn more mathematics by comparable grade levels. The present study examined the grade placement of topics in basic addition and subtraction computation with whole numbers across five countries: Japan, mainland China, the Soviet Union, Taiwan, and the United States.

scholarly journals Learning Declarative Knowledge in Special Education Treatment Group

2018 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Rickard Ostergren ◽  
Marie Ringborg Lindgren ◽  
Britt-Marie Lindgren ◽  
Joakim Samuelsson
Keyword(s):  
Special Education ◽  
Treatment Group ◽  
Small Group ◽  
Declarative Knowledge ◽  
Regular Instruction ◽  
Intervention Phase ◽  
Simple Addition ◽  
Intervention Level ◽  
Addition And Subtraction ◽  
The Impact

An organizing structure that in recent years has had a major impact on how to work with students who don’t respond to regular instruction is Response to Intervention (RTI). Efforts in RTI are divided into three different tiers of instruction: primary, secondary and tertiary. In our study, we investigate the impact of intensive secondary-tier instruction on students’ knowledge of basic combinations of digits in addition. We also focus on how the students develop their use of more advanced calculations in addition during the intervention.The results showed that students became faster at performing simple addition tasks, which indicates that their fluency – declarative knowledge – developed during the intervention phase. Our results thereby strengthen suggestions that a secondary-tier intervention level should take place in a small group of students 20-40 minutes four to five times a week. Meanwhile, the students developed their ability to solve two-digit arithmetic tasks in addition and subtraction, which could be explained by the fact that students had automated simple number combinations and thus could focus on the calculation procedure.

Transition Boards: A Good Idea Made Better

1991 ◽  
Vol 38 (5) ◽  
pp. 4-8
Author(s):  
John T. Sutton ◽  
Tonya D. Urbatsch
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Addition And Subtraction ◽  
School Mathematics Curriculum

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) recognizes that addition and subtraction computations remain an important part of the school mathematics curriculum and recommends that the emphasis be shifted to the understanding of concepts. Transition boards are simple devices to aid students' conceptual understanding.

The Struggle to Link Written Symbols with Understandings: An Update

1989 ◽  
Vol 36 (7) ◽  
pp. 38-44
Author(s):  
James Hiebert
Keyword(s):  
Young Children ◽  
Real World ◽  
Mathematics Learning ◽  
Older Children ◽  
Simple Addition ◽  
Addition And Subtraction ◽  
The One ◽  
Real World Problems

Two of the most striking and informative results from recent research on children's mathematics learning are the following. On the one hand, many children possess a surprising degree of competence with mathematical situations outside of school. For example, before beginning school, most young children can solve simple addition and subtraction stories, such as “Mary has 8 pennies. She gives 3 pennies to Roger. How many does she have left?” (Carpenter and Moser 1984; DeCorte and Verschaffel 1987; Riley, Greeno, and Heller 1983). In other words, before children have been taught how to add and subtract, they can solve addition and s ubtraction problems. Similarly, older children, as well as adults, can solve a variety of real-world problems using strategies that they have not learned directly in school (Carraher, Carraher, and Schliemann 1987; Lave, Murtaugh, and de Ia Rocha 1984; Scdbner 1984).

Let's Teach Mental Algorithms for Addition and Subtraction

1982 ◽  
Vol 29 (8) ◽  
pp. 40-42
Author(s):  
Gary L. Musser
Keyword(s):  
Elementary School ◽  
Mathematics Curriculum ◽  
School Level ◽  
Computational Algorithms ◽  
Addition And Subtraction ◽  
Traditional Mathematics ◽  
Paper And Pencil

Much of the traditional mathematics curriculum at the elementary school level has been devoted to teaching computational algorithms (methods) that are most effective when using paper and pencil. The familiar terms associated with these addition and subtraction algorithms are “carrying” and “borrowing” respectively.

Ideas

1993 ◽  
Vol 40 (9) ◽  
pp. 512-519
Author(s):  
Martha H. (Marty) Hopkins ◽  
Daniel J. Brahier
Keyword(s):  
Children's Literature ◽  
Mathematics Curriculum ◽  
Children’S Literature ◽  
Classroom Activities ◽  
Grade Levels ◽  
Wide Range

The “IDEAS” section for this month focuses on connections between mathematics and children's literature. Five piece of literature are applied to teaching a wide range of topics in the mathematics curriculum, from sorting and classifying to the meaning of averages. The reproducible sheets in “IDEAS” are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet for parents use. A teacher may want to reproduce and use everal sheets.

Problem Structure and First-Grade Children's Initial Solution Processes for Simple Addition and Subtraction Problems

1981 ◽  
Vol 12 (1) ◽  
pp. 27-39 ◽  
Author(s):  
Thomas P. Carpenter ◽  
James M. Moser ◽  
James Hiebert
Keyword(s):  
Predictive Model ◽  
First Grade ◽  
Initial Solution ◽  
Problem Structure ◽  
Simple Addition ◽  
Solution Processes ◽  
Formal Instruction ◽  
Addition And Subtraction ◽  
Semantic Types

Forty-three first-grade children who had received no formal instruction in addition and subtraction were individually administered 10 verbal problems. These problems were selected to represent the following semantic types: Joining, Separating, Part-Part-Whole, Comparison, and Equalizing. In spite of the lack of formal instruction, most children successfully solved the problems. In general, children's solution processes were consistent with a predictive model proposing that solution processes would directly represent the action or relationship described in individual problems.

The Area Model: Building Mathematical Connections

2020 ◽  
Vol 113 (3) ◽  
pp. 186-195
Author(s):  
Alyson E. Lischka ◽  
D. Christopher Stephens
Keyword(s):  
Model Building ◽  
Mathematics Curriculum ◽  
Mathematical Concepts ◽  
Area Model ◽  
Grade Levels ◽  
Mathematical Connections

The area model for multiplication can be used as a tool to help learners make connections between mathematical concepts that are included in mathematics curriculum across grade levels. We present ways the area model might be used in teaching about various concepts and explain how those ideas are connected.

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