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.

Reaching Young Pupils With Technology

1991 ◽  
Vol 38 (6) ◽  
pp. 51-55
Author(s):  
Jane F. Schielack
Keyword(s):  
Mathematics Curriculum ◽  
Technology In The Classroom ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Primary Level ◽  
Mathematics Standards ◽  
Grade Levels ◽  
Use Of Technology ◽  
Concrete Representations

Recommendations in such current publications as NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) and the National Research Council's Everybody Counts (1989) emphasize the full use of technology in the classroom at all grade levels. But what is the role of technology in the early grades? How can computers best be used to support primary-level mathematics instruction? Where does the use of the calculator fit into the primary-level pupil's development of mathematical concepts? How can we justify the abstract nature of calculator activities in a primary-level mathematics curriculum built on the needs of young pupils to experience concrete representations of mathematical concepts?

Math by the Month: Using Manipulatives to Show What We Know

2000 ◽  
Vol 7 (1) ◽  
pp. 32-33
Author(s):  
Regina Mistretta ◽  
Joseph A. Porzio
Keyword(s):  
Small Groups ◽  
Mathematics Curriculum ◽  
Mathematical Concepts ◽  
Grade Levels

The “Math by the Month” activities are designed to appeal directly to students. Students may work on the activities individually or in small groups. No solutions are suggested so that students will look to themselves as the mathematical authority, thereby developing the confidence to validate their work. This month's activities focus on students' using various manipulative materials to demonstrate their understandings related to a variety of topics across the mathematics curriculum. Using manipulatives helps students understand and explain the mathematical concepts and the related skills that they are expected to master at their grade levels. Their use also gives teachers valuable insights into students' mastery of these same concepts and skills.

A Role for Technology in Mathematics Education

1996 ◽  
Vol 178 (2) ◽  
pp. 15-32 ◽  
Author(s):  
Albert A. Cuoco ◽  
E. Paul Goldenberg
Keyword(s):  
Mathematics Education ◽  
Curriculum Change ◽  
Mathematics Curriculum ◽  
New Technology ◽  
Habits Of Mind ◽  
Mathematical Research ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Educators

New technology poses challenges to mathematics educators. How should the mathematics curriculum change to best make use of this new technology? Often computers are used badly, as a sort of electronic flash card, which does not make good use of the capabilities of either the computer or the learner. However, computers can be used to help students develop mathematical habits of mind and construct mathematical ides. The mathematics curriculum must be restructured to include activities that allow students to experiment and build models to help explain mathematical ideas and concepts. Technology can be used most effectively to help students gather data, and test, modify, and reject or accept conjectures as they think about these mathematical concepts and experience mathematical research.

Basic Mathematical Skills and Concepts for Effective Participation in Australian Society

1982 ◽  
Vol 10 (2) ◽  
pp. 27-30
Keyword(s):  
Mathematics Curriculum ◽  
Basic Skills ◽  
School Curriculum ◽  
Student Experiences ◽  
Mathematical Concepts ◽  
Mathematical Skills ◽  
Australian Society ◽  
School Programs ◽  
Mathematics Program ◽  
The Subject

Given the nature and development of Australian society, it is important that we reassess the place of mathematics in the school curriculum, and particularly its place as one of the basic shared student experiences.It is in the national interest that school programs promote adequate levels of competence within good mathematics programs, and that as many people as possible achieve at those levels. It is also in the interests of Australia and its people that individuals reach as high a level as possible in the subject. Mathematics is important chiefly because it can help in understanding and interpreting many aspects of the world. It can help a person make a significant contribution to a technological society.So when we address basic skills in mathematics, it is important that we address them within the context of a total mathematics program. Basic skills involve more than arithmetic skills, and understanding of mathematical concepts and processes is more important than knowledge of isolated facts and skills. The following should not be read or interpreted as a list of differentiated topics but as a list of different facets from which the mathematics curriculum may be examined.This is the first national statement of basic mathematical skills and concepts for effective participation in Australian society. It has been prepared for and endorsed by the Standing Committee of the Australian Mathematics Education Program and is offered as a statement of informed professional opinion.

Microcomputers in a Sixth-Grade Classroom

1983 ◽  
Vol 31 (2) ◽  
pp. 22-24
Author(s):  
Janet P. Morris
Keyword(s):  
Mathematics Curriculum ◽  
Sixth Grade ◽  
Mathematical Concepts ◽  
The Core ◽  
Grade Classroom

How should computer be used in the classroom? An Agenda for Action state that “computers should be integrated into the core mathematics curriculum,” that they “should be used in imaginative ways for exploring, discovering, and developing mathematical concepts,” and that the computer activities should “fit the goals or objectives of the program” (NCTM 1980, p. 9).

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.

Animating Geometry with Flexigons

1994 ◽  
Vol 87 (8) ◽  
pp. 602-606
Author(s):  
Ruth McClintock
Keyword(s):  
Language Skills ◽  
School Mathematics ◽  
Professional Standards ◽  
Physical Models ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Grade Levels ◽  
Conversation Piece

Viewing mathematics as communication is the second standard listed for all grade levels in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This emphasis underscores the need for nurturing language skills that enable children to translate nonverbal awareness into words. One way to initiate discussion about mathematical concepts is to use physical models and manipulatives. Standard 4 of the Professional Standards for Teaching Mathematics (NCTM 1991) addresses the need for tools to enhance discourse. The flexigon is a simple and inexpensive conversation piece that helps students make geometric discoveries and find language to share their ideas.

Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist

1993 ◽  
Vol 86 (8) ◽  
pp. 657-661
Author(s):  
Peter L. Glidden ◽  
Erin K. Fry
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Mathematics Curriculum ◽  
Three Dimensional ◽  
Discrete Mathematics ◽  
Evaluation Standards ◽  
Mathematical Connections ◽  
Regular Polyhedra ◽  
Real World Problems

The reforms proposed in the NCTM's Curriculum and Evaluation Standards (1989) call for specific changes in the grades 9-12 mathematics curriculum, as well as for general themes that should be emphasized throughout the curriculum. In particular, the standards document calls for including topics from discrete mathematics and three-dimensional geometry, and it calls for increased emphasis on paragraph-style proofs. Overall, these and other topics should be taught with the ultimate goals of illustrating mathematical connections and constructing mathematical models to solve real-world problems.

Implementing the Standards: Uses of Technology in Prealgebra and Beginning Algebra

1990 ◽  
Vol 83 (3) ◽  
pp. 194-198
Author(s):  
M. Kathleen Heid
Keyword(s):  
Problem Solving ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Classrooms ◽  
Beginning Algebra ◽  
Grade Levels ◽  
Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Stan dards) (1989) designates four standards that apply to all students at all grade levels: mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. These and NCTM's other standards are embedded in a vision of technologically rich school mathematics classrooms in which students and teachers have constant access to appropriate computing devices and in which students use computers and calculators as tools for the investigation and exploration of problems.

Cognitive Effects of a Logo-Enriched Mathematics Program for Middle School Students

1988 ◽  
Vol 4 (4) ◽  
pp. 443-452 ◽  
Author(s):  
Sandra V. Turner ◽  
Michael L. Land
Keyword(s):  
Middle School ◽  
Cognitive Development ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
Common Factor ◽  
Control Group ◽  
Minimal Amount ◽  
School Students ◽  
Mathematical Concepts ◽  
Logo Programming

This study investigated the effect of learning Logo on middle-school students' understanding of specific mathematical concepts and on their level of cognitive development. Students in the Logo Group ( n = 91) learned Logo for one hour a week for sixteen weeks as part of their regular mathematics curriculum. The Control Group ( n = 90) did not participate in the Logo program but received the full allotted time for their regular mathematics curriculum. No significant differences were found between the two groups in their understanding of mathematics concepts or in their growth in cognitive development. However, among the students in the Logo Group, those who learned the most Logo gained significantly more than those who learned a minimal amount of Logo both in their understanding of the mathematics concepts and in their level of cognitive development. When the High Logo group was compared to the Control Group, and also to a matched subset of the Control Group, there were large differences in favor of the High Logo group, but the results were not significant. The findings of this study suggest that cognitive development, achievement in mathematics, and achievement in Logo programming all share a common factor and that students who do well in one area are also likely to do well in the other two areas.

Sign in / Sign up

Export Citation Format

Share Document