Geometric Patterns for Exponents

1992 ◽  
Vol 85 (9) ◽  
pp. 746-749
Author(s):  
Frances M. Thompson
Keyword(s):  
Visual Stimuli ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Geometric Models ◽  
Mathematical Ideas ◽  
Geometric Patterns

NCTM's Professional Standards for Teaching Mathematics suggests that “tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections” with other mathematical ideas (1991, 24). Yet too frequently our classroom introductions to mathematics concepts and theorems demand little reasoning from students, leaving them unconvinced or with minimal understanding. Concrete, visual, or geometric models are seldom offered as aids, particularly when studying new numerical relations (Suydam 1984, 27; Bennett 1989, 130), even though many people depend heavily on visual stimuli for their learning, The challenge to the teacher is to select appropriate tasks and materials that will stimulate students to visualize and think about new mathematical concepts, thereby allowing them to develop their own understanding.

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.

Implementing the Professional Standards for Teaching Mathematics: Focusing on Worthwhile Mathematical Tasks in Professional Development: Using a Task from the National Assessment of Educational Progress

1998 ◽  
Vol 91 (2) ◽  
pp. 156-161
Author(s):  
Glendon W. Blume ◽  
Judith S. Zawojewski ◽  
Edward A. Silver ◽  
Patricia Ann Kenney
Keyword(s):  
Professional Development ◽  
Classroom Practice ◽  
Mathematical Reasoning ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Problem Solver ◽  
Teaching Mathematics ◽  
National Assessment ◽  
Mathematical Ideas ◽  
Solution Methods

Worthwhile mathematical tasks engage the problem solver in sound and significant mathematics, elicit a variety of solution methods, and require mathematical reasoning. Such problems also prompt responses that are rich enough to reveal mathematical understandings. Just as good classroom practice engages students in worthwhile mathematical tasks, sound professional development does the same with teachers. Providing teachers with opportunities to engage in worthwhile mathematical tasks and to analyze the mathematical ideas underlying those tasks promotes the vision of the Professional Standards for Teaching Mathematics (NCTM 1991).

Interpreting the Standards: Translating Principles into Practice

1997 ◽  
Vol 4 (4) ◽  
pp. 202-205
Author(s):  
Deborah E. Schifter ◽  
Deborah Carey O'Brien
Keyword(s):  
School Mathematics ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematics Pedagogy ◽  
Student Centered ◽  
Evaluation Standards

Since the publication of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and the Professional Standards for Teaching Mathematics (NCTM 1991). such phrases as “mathematics should be taught for understanding.” “teachers should facilitate the construction of mathematical concepts,” and “classrooms should be student centered” have become identified with a reformed mathematics pedagogy.

The number line in the junior high school

1966 ◽  
Vol 13 (7) ◽  
pp. 553-555
Author(s):  
Ronald E. Hursh
Keyword(s):  
High School ◽  
Junior High School ◽  
Subject Matter ◽  
Junior High ◽  
Number Line ◽  
Teaching Mathematics ◽  
New Materials ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Substantial Problem

There has never been a more interesting time to be teaching mathematics. The new programs are rich in subject matter and are a challenge to students and teachers a like. We are building mathematical concepts in addition to drilling on fundamentals in the same amount of time which previously had been used for drilling alone. This presents a substantial problem to which, I am sorry to say, I do not have the total solution. My concern is with being able to teach all of the mathematics desired in the time that is available. There is one device of instruction in the new materials that I believe has great potential in conveying mathematical ideas quickly and accurately. This device is the number line.

Using Tools to Make Sense of Right Triangles

2018 ◽  
Vol 23 (4) ◽  
pp. 226-230
Author(s):  
Terri L. Kurz ◽  
Mi Yeon Lee
Keyword(s):  
Conceptual Understanding ◽  
Three Dimensional ◽  
Mathematical Understanding ◽  
Sense Making ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Ideas

Sometimes, teaching mathematics with a focus on conceptual understanding can be challenging. With the advent of standards and principles (CCSSI 2010; NCTM 2014) an emphasis has been placed on using tools for deeper mathematical understanding and learning with understanding. Specifically, there has been a movement to include opportunities for learners to engage in sense-making activities when exploring mathematical concepts (Schoenfeld 1992). Tools can be used to support sense making and the development of mathematical ideas, and numerous tools can support learning in geometry (e.g., geoboards, pattern blocks, three-dimensional shapes, and linking cubes). We focus on AngLegs®, which are linking rods that are becoming more common in the classroom.

Using Problems to Implement the NCTM's “Professional Teaching Standards'

1994 ◽  
Vol 87 (1) ◽  
pp. 5-7
Author(s):  
Millard E. Showalter
Keyword(s):  
Teaching And Learning ◽  
Professional Standards ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Mathematical Ideas ◽  
Teaching Standards ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Professional Teaching Standards ◽  
Professional Teaching

As set forth in the Professional Standards for Teaching Mathematics (NCTM 1991), a primary goal for teaching and learning mathematics is the development of mathematical power for all students. To accomplish this goal, the teaching standards document recommends that teachers select interesting and intellectually stimulating mathematical tasks, present opportunities for students to deepen their understanding of mathematics and its applications, promote the investigation of mathematical ideas, use technology to pursue these investigations, find connections to previous and developing knowledge, and employ cooperativelearning experiences (NCTM 1991, 1).

Implementing the “Professional Standards for Teaching Mathematics”: Teachers Paying Attention to Students' Thinking

1992 ◽  
Vol 39 (9) ◽  
pp. 34-37 ◽  
Author(s):  
Carolyn A. Maher ◽  
Robert B. Davis ◽  
Alice Alston
Keyword(s):  
Mathematics Teachers ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Thought Processes ◽  
Mathematical Ideas ◽  
Effective Lessons ◽  
Attention To Students

The Professional Standards for Teaching Mathematics in its call for reform underscores the importance of teachers' knowledge of how students build their mathematical ideas. In our own work we have come to stress the importance of teachers' awareness of students' thought processes (Davis 1984; Davis and Maher 1990; Maher, Davis, and Alston 1991; Maher and Davis 1990). Teachers' knowledge of students' thinking is an important guide in planning effective lessons.

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.

scholarly journals Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge

2020 ◽  
pp. 58-86
Author(s):  
Semjon F. Adlaj ◽  
◽  
Sergey N. Pozdniakov ◽  
Keyword(s):  
Comparative Analysis ◽  
Digital Media ◽  
Mathematical Knowledge ◽  
Information Environment ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Computer Tools ◽  
Digital Representations ◽  
The Impact

This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.

scholarly journals Pedagogical conditions for implementing value and sense direction of training mathematics at higher school

2020 ◽  
pp. 80-92
Author(s):  
Larisa V. Zhuk
Keyword(s):  
Creative Thinking ◽  
Educational Process ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Search Activity ◽  
Mathematical Concepts ◽  
Teaching Aids ◽  
Semantic Orientation ◽  
Cognitive Information ◽  
The University

The article actualizes the issue of updating the content, methods and means of teaching mathematics at the university within the sociocultural paradigm. A significant contradiction characterizing the crisis situation in the field of higher mathematical education is the mismatch between the traditional organization of the educational process and the powerful developing potential of mathematical disciplines. Being overloaded with a lot of information, altogether with its insufficiently developed anthropological, cultural-like and communicative components, mathematical education hinders the mental development of the learner’s personality in relation to such important qualities as search activity, creativity, and creative thinking. The solution to this problem can be the transformation of the cognitive-information model of learning, the introduction of pedagogical technologies that actualize the sociocultural aspect of mathematical education. The aim of the study is to develop methodological foundations for the implementation of the value-semantic orientation of teaching mathematics at the university, expressed in providing a set of pedagogical conditions related to the selection of content, determination of teaching aids and methods, ways of organizing the interaction of students and a teacher, in which students intelligently master mathematical concepts, and freely operate with them. The didactic conditions for the implementation of the value-semantic orientation of teaching mathematics at the university are: the transformation of mathematical content, expressed in learning from sociocultural experience; the psychodidactic approach, focused on building the students’ self-motivation; the use of teaching methods that provide cognitive and emotional empathy (educational mathematical discourse), the activization of productive mental activity (technology of problematic dialogue); inclusion of non-standard, creative tasks, training cases. Providing these conditions will allow to realize the humanitarian potential of mathematics, to reveal the social, practical and personal significance of the subject matter.

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