Mental Computation in the Middle Grades: The Importance of Thinking Strategies

1997 ◽  
Vol 2 (5) ◽  
pp. 322-327 ◽  
Author(s):  
Alistair Mcintosh ◽  
Robert E. Reys ◽  
Barbara J. Reys
Keyword(s):  
Middle Grades ◽  
Number Sense ◽  
Primary Grades ◽  
Efficient Tool ◽  
Mental Computation ◽  
Procedural Approach ◽  
Thinking Strategies ◽  
Practical Implications ◽  
Current Emphasis

At the primary-grades level, the benefits of developing and using mental strategies for computing have been well articulated (see, e.g., Beberman (1959); Brownell [1972); Cobb and Merkel [1989]: Kamii [1989]; Reys and Barger [1994): Shuard [1987); Trafton [1978)), and many primary-grades teachers are now encouraging students to invent and use thinking strategies as a way to facilitate their development of number sense. They are also dealing with the practical implications of implementing this approach to computation, which is very different from the traditional. rule-oriented, procedural approach to computation. At the middle-grades level, however, comparatively Little discussion related to the same issue has occurred. At this level, should students be encouraged to invent mental strategies for computing? Should standard written algorithms for computing continue to be taught? How does an emphasis on thinking strategies relate to the current emphasis on using the calculator as an efficient tool for computation?

scholarly journals The Effectiveness of Using Mental Computation to Develop Some Number Sense Skills among third-grade Primary Students: فاعلية استخدام الحساب الذهني في تنمية بعض مهارات الحس العددي لدى طلبة الصف الثالث الأساسي

2020 ◽  
Vol 4 (43) ◽  
Author(s):  
Nadia Hamlan Matouq
Keyword(s):  
Number Sense ◽  
Arithmetic Mean ◽  
Primary Students ◽  
Third Grade ◽  
Control Group ◽  
Item Number ◽  
Male And Female ◽  
Mental Computation ◽  
Research Questions ◽  
Experimental Group

The research aimed to investigate the effectiveness of using mental Computation on developing some number sense skills in mathematics among third-grade primary students. The study followed the semi-experimental approach, The research sample consisted of (60) students male and female, who were distributed among two groups: the control group (30) students male and female and the experimental group (30) students male and female. The control group studied in the traditional way; the experimental group studied by using the computation strategies. The research's tools consisted of a 20-item number sense in a multiple format. The psychological properties of the test were verified, and appropriate statistical treatments were used to answer the research questions, The findings showed that the experimental group was superior over the control group with an arithmetic mean of (16.262) Whereas, the control group obtained an arithmetic mean of (12.771), and based on the results, the researcher recommended integrating mental Computation strategies into the developed mathematics curricula.

scholarly journals Investigating Numeric Relationships Using an Interactive Tool: Covering Number Sense Concepts for the Middle Grades

2010 ◽  
Vol 01 (02) ◽  
pp. 121-127
Author(s):  
Hui Fang Huang “Angie” Su ◽  
Carol A. Marinas ◽  
Joseph M. Furner
Keyword(s):  
Middle Grades ◽  
Number Sense ◽  
Covering Number ◽  
Interactive Tool

Mental Computation and Number Sense

1990 ◽  
Vol 37 (7) ◽  
pp. 18-20
Author(s):  
Judith T. Sowder
Keyword(s):  
Number Sense ◽  
Mental Computation

Shifting Our Computational Focus

2010 ◽  
Vol 16 (4) ◽  
pp. 216-223
Author(s):  
Jane M. Keiser
Keyword(s):  
Conceptual Understanding ◽  
Middle Grades ◽  
Primary Grades

In the primary grades, as well as in the middle grades, students may spend more time on conceptual understanding.

The Influence of an Internet-Based Formative Assessment Tool on Primary Grades Students’ Number Sense Achievement

2017 ◽  
Vol 117 (3-4) ◽  
pp. 127-136 ◽  
Author(s):  
Drew Polly ◽  
Chuang Wang ◽  
Christie Martin ◽  
Richard G. Lambert ◽  
David K. Pugalee ◽  
...  
Keyword(s):  
Formative Assessment ◽  
Assessment Tool ◽  
Number Sense ◽  
Primary Grades

scholarly journals Exploring The Connections Among Number Sense, Mental Computation Performance, And The Written Computation Performance Of Elementary Preservice School Teachers

2004 ◽  
Vol 1 (12) ◽  
Author(s):  
Yea-Ling Tsao
Keyword(s):  
Elementary School Teachers ◽  
Mathematics Anxiety ◽  
Test Score ◽  
Number Sense ◽  
Affective Domain ◽  
School Teachers ◽  
Mental Computation ◽  
Entry Level ◽  
Independent Variables ◽  
Learning Mathematics

The purpose of this study is to a) explore connections among number sense, mental computation performance and the written computation performance of elementary preservice school teachers; and b) explore the correlation among mental computation skills, computation skills, effect issues and number sense. The sample was composed of students in six intact entry?level mathematics sections of a course populated by preservice elementary school teachers. One hundred fifty-five participants from these six classes completed data collection tasks during the Spring 2002 semester for the study. Regression analyses were used to investigate the correlation of written computation skills, mental computation skills, and affective domain with regard to number sense. Three of these subscales of Conference Learning Mathematics, Mathematics Anxiety, Effectance Motivation of Mathematics, Mental Computation Test score, and Written Computation Test score were found to positive significantly correlate with Number Sense Test score success at the a= 0.001 level. Overall, the six independent variables considered in this study accounted for 57.1% of the variation in Number Sense Test score, with Mental Computation Test, and Written Computation Test having the strongest effects.

The future of SEC enforcement under the Biden administration

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
John J. Carney ◽  
Jonathan R. Barr ◽  
Teresa Goody Guillén ◽  
Jimmy Fokas ◽  
Kevin R. Edgar ◽  
...  
Keyword(s):  
Climate Change ◽  
Design Methodology ◽  
Investor Protection ◽  
Content Type ◽  
Blockchain Technology ◽  
Compliance Programs ◽  
Practical Guidance ◽  
Securities Laws ◽  
Practical Implications ◽  
Current Emphasis

Purpose To examine what to expect from Chair Gary Gensler’s SEC and the new Biden presidential administration following Chair Gensler’s U.S. Senate confirmation on April 14, 2021. Design/methodology/approach Reviews past SEC Chair Jay Clayton’s legacy and Chair Gensler’s prior regulatory actions and focus, and outlines Chair Gensler’s expected initiatives, including a heightened focus on cryptocurrency regulation, investigation of COVID-19-related fraud, and ESG and climate change disclosure. Findings This change will bring forth a Democratic majority at the SEC which, in turn, suggests that the Commission will change its current emphasis on capital formation to focus more on investor protection, rules required by the Dodd-Frank Act, inspections, examinations, and enforcement Practical implications Firms should examine their compliance programs in anticipation of heightened advocacy for investor protection; an increased focus on cryptocurrency and blockchain technology, as well as ESG disclosures with an emphasis on climate change; and an increase in inspections and examinations which will drive more enforcement in the fund industry, as well as increases in initiatives regarding transparency, additional disclosures, and investor protection. Organizations will also benefit by reexamining their existing compliance programs with the advice of counsel as a mechanism to mitigate the risk of potential securities laws violations. Originality/value Practical guidance from experienced securities enforcement and litigation lawyers.

Let's Do It: Classical Problems for all Ages

1982 ◽  
Vol 29 (5) ◽  
pp. 8-12
Author(s):  
Rosalie Jensen ◽  
David R. O'Neil
Keyword(s):  
Problem Solving ◽  
Middle Grades ◽  
Primary Grades ◽  
Concrete Operations ◽  
Genuine Problem

Most children in the later primary grades and throughout the middle grades are functioning at the stage of concrete operations. When they are faced with genuine problem-solving situations they need concrete and pictorial aids, as well as guidance from adults in organizing information and choosing strategies.

Developing Number Sense: An Intervention Study in Grade 7

1994 ◽  
Vol 25 (1) ◽  
pp. 4-29 ◽  
Author(s):  
Zvia Markovits ◽  
Judith Sowder
Keyword(s):  
Intervention Study ◽  
Number Sense ◽  
Classroom Teacher ◽  
Seventh Grade ◽  
Mental Computation ◽  
Computational Estimation ◽  
Number Magnitude ◽  
Term Change ◽  
New Knowledge

Few students exhibit number sense when solving arithmetic problems in school. This study examined the effects of an intervention in the instruction of seventh-grade students for the purpose of developing number sense. Students were taught by the classroom teacher from experimental units on number magnitude, mental computation, and computational estimation. Instruction was designed to provide rich opportunities for exploring numbers, number relationships, and number operations and to discover rules and invent algorithms. Written measures and interviews before instruction, immediately after instruction, and several months later revealed that after instruction students were more likely to elect to use strategies that reflected number sense and that this was a long-term change. It appeared to the investigators that the students reorganized and used existing knowledge rather than acquiring new knowledge structures.

Promoting Number Sense in the Middle Grades

1994 ◽  
Vol 1 (2) ◽  
pp. 114-120
Author(s):  
Barbara J. Reys
Keyword(s):  
Common Sense ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Middle Grades ◽  
Number Sense ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Teaching And Learning ◽  
Way Of Thinking

Phrases such as “number sense,” “Operation sense,” and “intuitive understanding of number” are used throughout the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) to describe an intangible quality possessed by successful mathematics learners. Number sense refers to an intuitive feeling for numbers and their various uses and interpretations, an appreciation for various levels of accuracy when computing, the ability to detect arithmetical errors, and a common-sense approach to using numbers (Howden 1989; McIntosh, Reys, and Reys 1991). Number sense is not a finite entity that a student either has or does not have but rather a process that develops and matures with experience and knowledge. It does not develop by chance, nor does being skilled at manipulating numbers necessarily reflect this acquaintance and familiarity with numbers. Above all, number sense is characterized by a desire to make sense of numerical situations, including relating numbers to context and analyzing the effect of manipulations on numbers. It is a way of thinking that should permeate all aspects of mathematics teaching and learning.

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