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.

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.

Assessing Science Reasoning and Conceptual Understanding in the Primary Grades Using Standardized and Performance-Based Assessments

2014 ◽  
Vol 25 (1) ◽  
pp. 47-66 ◽  
Author(s):  
Kyung Hee Kim ◽  
Joyce VanTassel-Baska ◽  
Bruce A. Bracken ◽  
Annie Feng ◽  
Tamra Stambaugh
Keyword(s):  
Conceptual Understanding ◽  
Primary Grades ◽  
Science Reasoning ◽  
And Performance

The Ratio Table

1995 ◽  
Vol 1 (4) ◽  
pp. 282-288 ◽  
Author(s):  
James A. Middleton ◽  
Marja van den Heuvel-Panhuizen
Keyword(s):  
Middle School Teachers ◽  
Conceptual Understanding ◽  
Mathematics Teacher ◽  
Mathematical Knowledge ◽  
Middle Grades ◽  
School Teachers ◽  
Knowledge Levels ◽  
Addition And Subtraction ◽  
High Degree

The middle grades offer unique challenges to the mathematics teacher, especially in this time of transition from traditional to reformed curricula and methods. The range and conceptual quality of mathematical knowledge that students have as they enter grades 5 and 6 vary greatly. Many students have been accelerated through textbooks, resulting in a high degree of proficiency at arithmetic computation but sometimes with little conceptual understanding of the underlying mathematics. Many other students will enter the middle grades with only rudimentary understanding of addition and subtraction. This disparity of skills and understanding creates a difficult dilemma for middle school teachers. Should they review the arithmetic that students have already experienced, or should they forge ahead to a higher level of more difficult mathematics? This decision need not be perceived as a dichotomy. Methods exist for exploring higher-order mathematical topics conceptually that allow understanding by students of varying knowledge levels whatever their base knowledge may be.

Using Attribute Blocks to Develop a Conceptual Understanding of Probability

2001 ◽  
Vol 6 (5) ◽  
pp. 290-294
Author(s):  
Robert J. Quinn
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Middle Grades ◽  
School Curriculum ◽  
Seventh Graders ◽  
Time Block ◽  
School Students ◽  
Formal Curriculum ◽  
Ability Levels

Middle school students continue to rely on concrete experiences to construct knowledge but are starting to develop the ability to think abstractly (NCTM 1989, p. 68). Thus, the middle school curriculum should provide a “bridge between the concrete elementary school curriculum and the more formal curriculum of the high school” (NCTM 1989, p. 102). This article describes a series of activities using attribute blocks designed to help middle school students construct knowledge about, and develop conceptual understanding of, probability. Depending on the ability levels of the students, these activities can be completed in a single twohour time block or can be spread over three or four sessions of about one hour each. These introductory probability explorations are appropriate for seventh graders but can be adapted for students at other levels. Attribute blocks are frequently used in the primary grades, but this article shows that they can be quite useful in the middle grades, as well.

Promoting Meaningful Mastery of Addition and Subtraction

2003 ◽  
Vol 9 (6) ◽  
pp. 354-357
Author(s):  
Kristian B. Postlewait ◽  
Michelle R. Adams ◽  
Jeffrey C. Shih
Keyword(s):  
Conceptual Understanding ◽  
Mathematics Curriculum ◽  
Number Sense ◽  
Primary Grades ◽  
Mathematical Learning ◽  
Computational Fluency ◽  
Addition And Subtraction ◽  
Problem Solvers

The development of number sense and computational fluency should be an integral part of the mathematics curriculum. Because other areas of the curriculum such as data and measurement are closely related to and sometimes dependent on these skills, students must have a firm foundation in number. Teachers should provide activities and experiences that develop a conceptual understanding of number and operations, instead of focusing on the memorization of rules and procedures. Meaningful mathematical learning then can occur. When left to use strategies that are natural for them, children are wonderful problem solvers and are able to make sense of numbers in their world. This article focuses on the development of number sense in the primary grades using the ideas of Kathy Richardson (1999).

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?

Developing Conceptual Understanding of Relations and Functions with Attribute Blocks

1997 ◽  
Vol 3 (3) ◽  
pp. 186-190
Author(s):  
Robert J. Quinn
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
Elementary Students ◽  
Conceptual Understanding ◽  
Middle Grades ◽  
School Curriculum ◽  
National Council ◽  
School Students ◽  
Formal Curriculum

Much attention has recently been focused on students in the middle grades. The unique difficulties and characteristics of this group have prompted the National Council of Teachers of Mathematics to refer to them as “children in transition” (NCTM 1989, 68). Middle school students continue to rely on concrete experiences to construct knowledge but are starting to develop the ability to think abtractly (NCTM 1989, 68). Thus, the middle school curriculum should build “a bridge between the concrete elementary school curriculum and the more formal curriculum of the high school” (NCTM 1989, 102). The series of lessons described in this article extends the concrete experiences that many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions.

A Fluency Disorders Prevention Program for Preschoolers and Children in the Primary Grades

1991 ◽  
Vol 1 (1) ◽  
pp. 28-31 ◽  
Author(s):  
Eugene B. Cooper ◽  
Crystal S. Cooper
Keyword(s):  
Motor Skills ◽  
Prevention Program ◽  
Primary Grades ◽  
Primary Grade ◽  
Fluency Disorders ◽  
Classroom Use ◽  
Metalinguistic Skills

A fluency disorders prevention program for classroom use, designed to develop the feeling of fluency control in normally fluent preschool and primary grade children, is described. The program addresses the affective, behavioral, and cognitive aspects of fluency and features activities that not only develop the child’s fluency motor skills but also teach the language of fluency by developing the child’s metalinguistic skills.

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