The relation between amount of material and difficulty of problem solving: I. Mental addition and subtraction.

1937 ◽  
Vol 20 (2) ◽  
pp. 178-183 ◽  
Author(s):  
Thomas W. Cook
Keyword(s):  
Problem Solving ◽  
Mental Addition ◽  
Addition And Subtraction

scholarly journals The Empty Number Line in Dutch Second Grades: Realistic Versus Gradual Program Design

1998 ◽  
Vol 29 (4) ◽  
pp. 443-464 ◽  
Author(s):  
Anton S. Klein ◽  
Meindert Beishuizen ◽  
Adri Treffers
Keyword(s):  
Instructional Design ◽  
Problem Solving ◽  
Mental Model ◽  
Program Design ◽  
Mental Arithmetic ◽  
Gradual Increase ◽  
Number Line ◽  
Mental Addition ◽  
Addition And Subtraction

In this study we compare 2 experimental programs for teaching mental addition and subtraction in the Dutch 2nd grade (N = 275). The goal of both programs is greater flexibility in mental arithmetic through use of the empty number line as a new mental model. The programs differ in instructional design to enable comparison of 2 contrasting instructional concepts. The Realistic Program Design (RPD) stimulates flexible use of solution procedures from the beginning by using realistic context problems. The Gradual Program Design (GPD) has as its purpose a gradual increase of knowledge through initial emphasis on procedural computation followed by flexible problem solving. We found that whereas RPD pupils showed a more varied use of solution procedures than the GPD pupils, this variation did not influence the procedural competence of the pupils. The empty number line appears to be a very powerful model for the learning of addition and subtraction up to 100.

Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction

1997 ◽  
Vol 28 (2) ◽  
pp. 130-162 ◽  
Author(s):  
Karen C. Fuson ◽  
Diana Wearne ◽  
James C. Hiebert ◽  
Hanlie G. Murray ◽  
Pieter G. Human ◽  
...  
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Number Concepts ◽  
Number Words ◽  
Conceptual Structures ◽  
Common Framework ◽  
Approach To Teaching ◽  
Addition And Subtraction

Researchers from 4 projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe (a) a common framework of conceptual structures children construct for multidigit numbers and (b) categories of methods children devise for multidigit addition and subtraction. For each of the quantitative conceptual structures for 2-digit numbers, a somewhat different triad of relations is established between the number words, written 2-digit marks, and quantities. The conceptions are unitary, decade and ones, sequence-tens and ones, separate-tens and ones, and integrated sequence-separate conceptions. Conceptual supports used within each of the 4 projects are described and linked to multidigit addition and subtraction methods used by project children. Typical errors that may arise with each method are identified. We identify as crucial across all projects sustained opportunities for children to (a) construct triad conceptual structures that relate ten-structured quantities to number words and written 2-digit numerals and (b) use these triads in solving multidigit addition and subtraction situations.

scholarly journals KEMAMPUAN NUMBER SENSE MELALUI METODE LEARNING BY PLAYING

2015 ◽  
Vol 6 (2) ◽  
pp. 324
Author(s):  
Tunjung Susilowati
Keyword(s):  
Problem Solving ◽  
Teaching Method ◽  
Number Sense ◽  
Research Student ◽  
Intuitive Thinking ◽  
Mathematic Teaching ◽  
Addition And Subtraction

One of many purpose on mathematic teaching is problem solving. Problem solving need good computation abilities.Student have computation abilities if number sense develop in them. Number sense related with flexible and intuitive thinking about number. Number sense is natural ability of human and developed with teaching. This research using learning by playing teaching method to develop number sense. The purpose of choosing this method is student can practice their number sense and observed directly also mathematics can be fun subject. Research conducted with using different kind of games in every session. Based from the research, student developed their number sense on addition and subtraction of integers and they enjoy the learning also. Keywords: Number sense, learning by playing, summation and Equity pbulat numbers. Abstrak: Salah satu tujuan pembelajaran matematika adalah pemecahan masalah. Pemecahan masalah memerlukan kemampuan berhitung yang baik. Kemampuan berhitung didapat apabila kemampuan number sense berkembang pada diri siswa. Number sense berhubungan dengan pemikiran yang fleksibel dan intuitif tentang bilangan.Number sense merupakan kemampuan alami yang dimiliki oleh semua orang dan dapat berkembang dengan adanya pengajaran. Pengajaran untuk mengembangkan number sense siswa pada penelitian ini dilakukan dengan metode learning by playing. Metode ini dipilih agar kemampuan number sense dapat dipraktikkan dan diamati secara langsung serta pembelajaran matematika menjadi menyenangkan. Penelitian dilakukan dengan mengembangkan permainan yang berbeda pada setiap pertemuan. Berdasarkan penelitian yang dilakukan terlihat adanya peningkatan kemampuan number sense siswa pada penjumlahan dan pengurangan bilangan bulat dan juga siswa menikmati pembelajaran yang dilakukan. Kata kunci: number sense, learning by playing, penjumlahan dan pengurangan bilangan pbulat.

Effects of Time of Posttest after Two Durations of Exercise on Speed and Accuracy of Addition and Subtraction by Fit and Less-Fit Women

1992 ◽  
Vol 75 (3_suppl) ◽  
pp. 1059-1065 ◽  
Author(s):  
Barbara Heckler ◽  
Ron Croce
Keyword(s):  
Problem Solving ◽  
Repeated Measures ◽  
Exercise Duration ◽  
Exercise Session ◽  
Fitness Level ◽  
Repeated Measures Analysis ◽  
Group Speed ◽  
Level 3 ◽  
Addition And Subtraction ◽  
Speed And Accuracy

18 adult female volunteers, ages 27 to 49 years, were divided into two groups based on their cardiorespiratory fitness to investigate speed and accuracy of addition and subtraction immediately, 5 min., and 15 min. postexercise. A 2 (fitness level) × 3 (exercise duration) × 3 (postexercise performance trials) repeated-measures analysis of variance indicated that, for the fit group, speed of problem solving was significantly faster after both 20-min. and 40-min. exercise sessions across all performance trials; for the less-fit group, speed of addition/subtraction was significantly faster only after the 20-min. exercise session across performance trials. No significant postexercise difference in accuracy was found for either fit or less-fit groups.

Using a Problem-solving Approach in the Primary Grades

1984 ◽  
Vol 32 (4) ◽  
pp. 11-14
Author(s):  
Patricia F. Campbell
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Young Children ◽  
Mathematics Curriculum ◽  
School Administrators ◽  
Mathematical Problem ◽  
Primary Grades ◽  
National Council ◽  
Primary Level ◽  
Addition And Subtraction

According to the National Council of Teachers of Mathematics (1980), the focus of school mathematics in the 1980s must be on problem solving. Furthermore, computation is to be a tool for problem solving. The importance of problem solving as a goal in mathematics education cannot be disputed; however, the de-emphasis of computation may cause fee lings of uneasiness for many primary-level teachers. These feeling can be accentuated by such statements as “Primary-level curricula contain practically no mathematical problem-olving experiences” (Greenes 1981). Where does this dilemma leave the typical primary-level teacher, given the existing primary mathematics curriculum and the demands from pa rents and school administrators that young children develop a mastery of addition and subtraction?

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

1984 ◽  
Vol 15 (3) ◽  
pp. 179-202 ◽  
Author(s):  
Thomas P. Carpenter ◽  
James M. Moser
Keyword(s):  
Longitudinal Study ◽  
Problem Solving ◽  
Word Problems ◽  
Simple Addition ◽  
Formal Instruction ◽  
Addition And Subtraction ◽  
Physical Objects ◽  
Four Levels

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.

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