Draw to Understand

1991 ◽  
Vol 39 (4) ◽  
pp. 26-29
Author(s):  
M. Ann Dirkes
Keyword(s):  
Drawing Process ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Thinking Strategies ◽  
Problem Solvers

Students who make drawings about mathematical concepts think about mathematics. Those who trust their own thinking become problem solvers who play with ideas on paper. During the drawing process, they call to mind the knowledge that they have stored in memory. They compare drawings to numbers and equations and look at the whole problem as well as the details. These thinking strategies contribute well to the construction of mathematical ideas.

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 Analisis kendala pemahaman bahasa untuk mengembangkan kemampuan bernalar matematika siswa

2021 ◽  
Vol 9 (2) ◽  
pp. 61
Author(s):  
Anis Hidayati MS ◽  
Alex Haris Fauzi
Keyword(s):  
Qualitative Research ◽  
Mathematical Reasoning ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Descriptive Approach

Understanding of language is closely related to mathematical reasoning, because language has function as a means of communication to convey ideas or ideas to others. Submission of mathematical ideas delivered by students will show how far the level of student understading of the mathematical concepts they have. This research is a qualitative research with a descriptive approach which aims to describe the obstacles faced by students when using language on mathematical reasoning. Data obtained from observations, interviews, questionnaires, and documentations. Based on the results of the analysis conducted, it can be seen that constraints faced by students when using language on mathematical reasoning are feelings of shame and inferiority, difficulty understanding the sentence, and lack of vocabulary students have.

Party Time

2017 ◽  
Vol 23 (8) ◽  
pp. 462-465
Author(s):  
Sarah Quebec Fuentes
Keyword(s):  
Real World ◽  
Fifth Graders ◽  
Mathematical Concepts ◽  
Negative Numbers ◽  
Link Type ◽  
Entry Points ◽  
The Mean ◽  
Problem Solvers

In this month's Problem Solvers Solutions, second and fifth graders solve a problem that provides a real-world context relevant to students' lives, while addressing mathematical concepts including addition, division, negative numbers, and the mean. The experiences of the diverse grade range of students demonstrate that the task has multiple entry points and can be implemented in a variety of ways. Each month, this section of the Problem Solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. Find detailed submission guidelines for all departments at http://www.nctm.org/WriteForTCM.

Have You Read?

1968 ◽  
Vol 61 (5) ◽  
pp. 522-523
Author(s):  
Philip Peak
Keyword(s):  
Mathematical Concepts ◽  
Short Article ◽  
Mathematical Ideas

This short article illustrates several things, such as the facts that mathematical concepts grow with added dimensions, complex ideas are built from simple ones, and mathematical ideas are all about us.

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.

Sharing Teaching Ideas: Collaborative Writing of Mathematics Problems

1990 ◽  
Vol 83 (7) ◽  
pp. 542-544
Author(s):  
Kitty Carton
Keyword(s):  
Word Problems ◽  
Collaborative Writing ◽  
Instructional Decisions ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Problems ◽  
Teaching Ideas ◽  
Inside Out ◽  
Development Of Students

The NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) calls for opportunities for students to use mathematics as a tool for the communication of ideas. In this project, students in any level of mathematics, working in a cooperative, active setting, can develop their understanding of mathematical concepts through the collaborative writing of word problems. In so doing, they see mathematics from the inside out, as creators rather than mimickers; they are “doers” of mathematics, reflecting on and clarifying their own thinking about mathematical ideas in specific situations. Additionally, projects of the type described here can give teachers valuable information on which they can base further instructional decisions regarding the development of students' ability to communicate effectively using the language of mathematics.

Activites for Students: Dynamic Diagrams

2001 ◽  
Vol 94 (7) ◽  
pp. 566-574
Author(s):  
Elizabeth George Bremigan
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Problem ◽  
Visual Representations ◽  
Mathematical Concept ◽  
Mathematics Textbooks ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematical Problems

Reasoning with visual representations is an important component in solving many mathematical problems and in understanding many mathematical concepts and procedures. Students at all levels of mathematics frequently encounter visual representations—for example, diagrams, figures, and graphs—in discussions of mathematical ideas, in mathematics textbooks, and on tests. Teachers often use visual representations in the classroom when they present a mathematical problem, explain a problem's solution, or illustrate a mathematical concept. Although they frequently encounter and use visual representations in the mathematics classroom, neither teachers nor students may explicitly recognize the power of reasoning with visual representations or the potential for misconceptions that can arise from their use.

Links to Literature: A Remainder of One: Exploring Partitive Division

2000 ◽  
Vol 6 (8) ◽  
pp. 517-521
Author(s):  
Patricia Seray Moyer
Keyword(s):  
Children's Literature ◽  
Mathematical Knowledge ◽  
Mathematics Classroom ◽  
Children’S Literature ◽  
National Council ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Problems ◽  
Mathematical Symbols ◽  
Everyday Experiences

Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conversations also lead to rich, dynamic communication in the mathematics classroom and develop the use of mathematical symbols in the context of communicating. The National Council of Teachers of Mathematics (1989) emphasizes the importance of communication in helping children both construct mathematical knowledge and link their informal notions with the abstract symbols used to express mathematical ideas.

ANALISIS REPRESENTASI MATEMATIK SISWA SEKOLAH DASAR DALAM PENYELESAIAN MASALAH MATEMATIKA KONTEKSTUAL

2011 ◽  
Vol 16 (1) ◽  
pp. 128 ◽  
Author(s):  
Jarnawi Afgani Dahlan ◽  
Dadang Juandi
Keyword(s):  
Primary School ◽  
Everyday Life ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Communication ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Learning Mathematics ◽  
Mathematical Problems

Abstract: The purpose of this study was to examine the forms of representation constructed by primary school students in solving mathematical problems. Representation is the basis or foundation of how a student could understand and use mathematical ideas. The forms of representation, such as charts, graphs, and symbols, are essentially a long process of learning mathematics, but unfortunately these representations are often thought of and studied in its final form. Actually, representations should be given as support in the process of understanding concepts, the associations of mathematics, mathematical communication, constructing arguments, and apply mathematical concepts in everyday life through modeling. This research showed that the forms of representation constructed by the students are extremely varied. They are constructed in tables, images, patterns, and in the formal forms of mathematics (the formula). This study was also revealed that some students are able to develop forms of representation using logical mathematical processes. Students begin to formulate a representation using known premise, set the table, make conjecture, and subsequently arrange a formal representation.Keywords: mathematic representation, tables, charts, graphs, statements.

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.

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