Partitioning the Interior of a Circle with Chords

2005 ◽  
Vol 99 (2) ◽  
pp. 120-124
Author(s):  
Dennis Parker
Keyword(s):  
High School ◽  
Middle School ◽  
Pattern Recognition ◽  
Inductive Reasoning ◽  
Problem Situation ◽  
Circular Region ◽  
High School Mathematics ◽  
Mathematical Concepts ◽  
Circle Problem ◽  
Mathematics Problems

Pattern recognition is one of the most important devices that we use in understanding mathematical concepts and principles, as well as in solving mathematics problems. In middle school and high school mathematics classes, students commonly study several specific cases of a problem situation and then attempt to generalize to the nth case. A problem about partitioning a circular region with chords, sometimes called Moser's circle problem, illustrates that one must be careful when using inductive reasoning to generalize.

Mathematics in the Junior High School: Textbook series and learning theory

1955 ◽  
Vol 48 (3) ◽  
pp. 162-164
Author(s):  
G. W. Brown
Keyword(s):  
High School ◽  
Learning Theory ◽  
Junior High School ◽  
Mathematics Teacher ◽  
Junior High ◽  
Ninth Grade ◽  
High School Mathematics ◽  
Learning Sequence ◽  
Mathematical Concepts ◽  
Textbook Series

Do textbook series in arithmetic develop the mathematical concepts and skills in accordance with current learning theory? This is an important question for the junior high school mathematics teacher. The answer determines the extent to which the teacher may rely on the textbook for guidance in the learning sequence. Since, for many students, mathematics instruction ceases at ninth grade, mathematical strands considered by teachers and textbook writers to be important must be brought to a culminating point by that time.

Projects: Delaware 6-12 Exemplary Mathematics Curriculum Implementation

2000 ◽  
Vol 93 (9) ◽  
pp. 798
Author(s):  
Peggy Kasten
Keyword(s):  
High School ◽  
Middle School ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
Curriculum Implementation ◽  
Scale Up ◽  
High School Mathematics ◽  
High School Programs ◽  
Funded Project ◽  
The University

The Delaware 6–12 Exemplary Mathematics Curriculum Implementation (DEMCI) project seeks to substantially scale up from existing pilot projects to implement research-based, standardsdriven mathematics curricula in middle school and high school programs throughout Delaware. This National Science Foundation (NSF)–funded project is a partnership of fourteen Delaware school districts, the University of Delaware, and the Delaware Department of Education. Over the 38-month life of the project, 300 middle school and high school mathematics teachers—nearly two-thirds of all secondary mathematics teachers in Delaware— will engage in a substantial program of professional development that exceeds 150 hours for all teachers and may approach 200 hours for many.

Projects

1997 ◽  
Vol 90 (3) ◽  
pp. 254-255
Author(s):  
Sharon Stenglein
Keyword(s):  
High School ◽  
Middle School ◽  
Mathematics Teachers ◽  
National Science Foundation ◽  
Secondary Mathematics ◽  
School Mathematics ◽  
High School Mathematics ◽  
National Science ◽  
Mathematics Curricula ◽  
High School Mathematics Teachers

ln this National Science Foundation (NFS) Teacher Enhancement Project, fifty Minnesota middle school and high school mathematics teachers are collaborating with three Saint Olaf CoUege mathematics professors to integrate inquiry-based geometry and visualization across their secondary mathematics curricula.

scholarly journals Review and Reflection on the Research of Mathematics Problems in Junior High School

2020 ◽  
Vol 4 (6) ◽  
Author(s):  
Kai Li
Keyword(s):  
High School ◽  
Junior High School ◽  
Junior High ◽  
Teaching Method ◽  
High School Mathematics ◽  
Research Topics ◽  
Research Results ◽  
The Past ◽  
Mathematics Problems ◽  
Master's Thesis

The problem of mathematics is an important teaching method of students' core qualities cultivation. Statistics and analysis of The master's thesis related to "junior high school mathematics" and "problem posing" in the past ten years were counted and analyzed from chronological distribution, institutional distribution and research topics and other dimensions. The research results: ignorance of domestic research on the textbook content; formalization of problem raising under the the guidance of theory; the opposite direction of demonstration and qualitative research; fuzzy and superficial results and countermeasures of research. Research reflection: broaden thoughts of the field, attach importance to the study of textbook content, and enhance the expression of the teacher’s question raising; deepen the guiding ideas, reiterate the theory to guide the practice, reflect the complement of the theoretical practice; be rigorous about thoughts, attach importance to empirical and quantitive combination, improve scientific and appropriate research methods;  develop the logical thinking, focus on the study of results and countermeasures, and manifest the value of research results.

scholarly journals Programação Linear: uma possibilidade para o Ensino Médio / Linear Programming: a possibility for Middle School

2014 ◽  
Vol 1 (2) ◽  
Author(s):  
Gilmara Aparecida Silva
Keyword(s):  
Higher Education ◽  
High School ◽  
Middle School ◽  
Linear Programming ◽  
Basic Education ◽  
Linear Equations ◽  
Initial Study ◽  
Mathematical Concepts ◽  
Applicability Of Mathematics ◽  
The Subject

ABSTRACTThis paper aims to discuss and describe a possible approach on the subject Linear Programming in High School. A constant question we hear from our students, especially in high school, is in relation to the applicability of the contents studied in mathematics. The study of contextualized problems involving linear equations and inequalities solved by certain methods, which are studied in linear programming, can help students understand the applicability of mathematics as well as the content and interrelationships among various mathematical concepts. Despite being heavily exploited a content in higher education, here's your chance during an initial study using only basic education concepts already studied in previous years.RESUMOO presente trabalho pretende discutir e descrever uma possível abordagem sobre o tema Programação Linear no Ensino Médio. Uma pergunta constante que ouvimos dos nossos alunos, principalmente no Ensino Médio, é em relação à aplicabilidade dos conteúdos estudados em Matemática. O estudo de problemas contextualizados envolvendo equações e inequações lineares resolvidos por determinados métodos, que são estudados em Programação Linear, pode contribuir para que os alunos percebam a aplicabilidade da Matemática bem como as interrelações entre vários conteúdos e conceitos matemáticos. Apesar de ser um conteúdo fortemente explorado no ensino superior, aqui mostramos sua possibilidade um estudo inicial durante a educação básica recorrendo apenas a conceitos já estudados em anos anteriores. Contato principal: [email protected]

Activities for Students: Algebra on the Number Line

2010 ◽  
Vol 104 (5) ◽  
pp. 379-386
Author(s):  
Terence McCabe ◽  
M. Alejandra Sorto ◽  
Alexander White
Keyword(s):  
High School ◽  
Middle School ◽  
Number Line ◽  
Instructional Tool ◽  
Mathematical Concepts ◽  
Absolute Value ◽  
Algebraic Concepts ◽  
Numerical Operations

The number line is a powerful instructional tool for teaching the meaning of many mathematical concepts taught in middle school, including numerical operations. The number line can also be used as a tool for thinking about algebraic concepts taught in high school, such as an abstract or algebraic understanding of distance, absolute value, and inequalities.

Nearly Isosceles Pythagorean Triples

1983 ◽  
Vol 76 (1) ◽  
pp. 52-56
Author(s):  
Robert Ryden
Keyword(s):  
High School ◽  
Mathematics Curriculum ◽  
Inductive Reasoning ◽  
Mathematical Induction ◽  
High School Mathematics ◽  
Pythagorean Triples ◽  
Class Time ◽  
Geometry Class ◽  
Algebraic Proofs ◽  
Time Away

With the high school mathematics curriculum as full as it is, why should we busy teachers take class time away from the syllabus to investigate patterns of no discernible practical value? My answer is that students should be made aware that there is more to mathematics than learning how to solve an endless variety of problems. There is a beauty in its patterns, and especially for those who may not pursue mathematics beyond high school, these patterns may be the only mathematics they will remember. Recently in my geometry class we discovered a pattern in Pythagorean triples that, in addition to being interesting in itself, can be used at various levels to illustrate inductive reasoning, proof by mathematical induction, and other algebraic proofs. It can also generate several different computer programs.

Using the Telephone Book as a Source of Mathematical Activity

1997 ◽  
Vol 3 (3) ◽  
pp. 234-238
Author(s):  
Marian S. Small
Keyword(s):  
High School ◽  
Middle School ◽  
Problem Solving ◽  
Junior High School ◽  
School Level ◽  
Mathematical Activity ◽  
High School Level ◽  
Mathematical Concepts ◽  
Good Place ◽  
Junior High School Level

Are you a grade 6-9 teacher looking for easily accessible data to support your attempts to teach using a problem-solving approach? An old telephone book may be a good place to start. The ideas suggested in this article present some starting points for using the telephone book and telephone numbers at the middle school and junior high school level to develop a variety of mathematical concepts and skills.

Ratio Analysis: Where Investments Meet Mathematics

2002 ◽  
Vol 95 (1) ◽  
pp. 60-68
Author(s):  
Susan D. Barton ◽  
Denise Woodbury
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Intrinsic Value ◽  
School Mathematics ◽  
Ratio Analysis ◽  
Valid Argument ◽  
High School Mathematics ◽  
Mathematical Concepts ◽  
The World ◽  
Principles And Standards

A valid argument can be made that concepts in mathematics should be studied for their own intrinsic value. Yet almost every high school mathematics teacher has heard the plaintive wail, “When will I ever use this?” Many students need to ground their understanding of mathematical concepts in a realworld setting. NCTM's Principles and Standards for School Mathematics also confirms that developing connections among mathematics, other subjects, and the world outside the classroom is important in giving the students “greater mathematical power” (2000, p. 354).

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