scholarly journals Developing purposeful mathematical thinking: a curious tale of apple trees

2012 ◽  
Vol 6 (3) ◽  
pp. 85-103
Author(s):  
Janet Ainley
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Mathematical Thinking ◽  
Task Design ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Apple Trees ◽  
The Real

In this paper I explore aspects of the ways in which school mathematics relates to the “real” world, and argue that this relationship is an uneasy one. Through exploring the causes of this unease, I aim to expose some problems in the ways in which context is used within mathematics education, and argue that the use of context does not ensure that the purposes of mathematics are made transparent. I present and discuss a framework for task design that adopts a different perspective on mathematical understanding, and on purposeful mathematical thinking. Desarrollo de un pensamiento matemático intencionado: un relato curioso de manzanos En este artículo exploro aspectos de las maneras en que las matemáticas escolares se relacionan con el mundo “real” y argumento que esta relación es preocupante. Al explorar las causas de esta preocupación, me propongo exponer algunos problemas que surgen de las formas en que se usa el contexto en Educación Matemática y argumento que el uso del contexto no asegura la transparencia de los propósitos de las matemáticas. Presento y discuto un esquema para el diseño de tareas que adopta una perspectiva diferente sobre la comprensión de las matemáticas y el pensamiento matemático intencionado.Handle: http://hdl.handle.net/10481/19524

Projects: Developing Modelers and Modeling Opportunities: The Stepping Stones Project

1997 ◽  
Vol 90 (8) ◽  
pp. 686-688
Keyword(s):  
Mathematical Modeling ◽  
Mathematics Education ◽  
Real World ◽  
Mathematical Knowledge ◽  
School Mathematics ◽  
Stepping Stones ◽  
Evaluation Standards ◽  
The Real ◽  
World Modeling

Mathematical modeling is an emerging theme in mathematics education. In addition to giving students a knowledge of the applications of mathematics and a process for applying mathematics in the “real” world, modeling offers teachers an excellent vehicle for introducing and developing students' mathematical knowledge. For these reasons, modeling occupies a prominent place in the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).

Language Activities That Promote Awareness of Mathematics

1988 ◽  
Vol 36 (4) ◽  
pp. 6-9
Author(s):  
James S. Cangelosi
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Real World ◽  
Real Life ◽  
National Council ◽  
Life Meaning ◽  
The Real ◽  
Education Literature ◽  
Teaching Of Mathematics ◽  
Primary Focus

Developing students' abilities to rcason with mathematics and apply mathematics to the solution of problems occurring in the real world hould be a primary focus of school mathematics (National Council of Teachers of Mathematics 1980). However, most mathemati cal curricula seem to place more emphasis on memorization of fact and algorithm than on reasoning and problem solving (Romberg and Carpenter 1986). The mathematics education literature abound with ideas for reversing the emphasis on memorization and for guiding the teaching of mathematics so that it has real-life meaning for children. Included among the idea are the following:

Focused Strategies for Middle-Grades Mathematics Vocabulary Development

2007 ◽  
Vol 13 (4) ◽  
pp. 200-207
Author(s):  
Rheta N. Rubenstein
Keyword(s):  
Mathematics Education ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
Vocabulary Development ◽  
School Mathematics ◽  
One Dimension ◽  
Mathematical Language ◽  
Mathematics Vocabulary ◽  
Principles And Standards

Principles and Standards for School Mathematics reminds us that communication is central to a broad range of goals in mathematics education (NCTM 2000). These goals include students' being able to (1) organize and consolidate mathematical thinking; (2) communicate coherently with teachers, peers, and others; (3) analyze and evaluate others' strategies; and (4) use language to express mathematics precisely. One part of communication is acquiring mathematical language and using it fluently. This article addresses learning vocabulary as one dimension of mathematics communication.

Promising Research: The World's Largest Math Event: Promoting Mathematical Thinking

1999 ◽  
Vol 5 (7) ◽  
pp. 430-432
Author(s):  
Daniel J. Brahier ◽  
Melfried Olson
Keyword(s):  
United States ◽  
Real World ◽  
Mathematical Thinking ◽  
The United States ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The World

The Great Sphinx in Egypt is about 73.2 m (240 ft.) long, including the paws, which are each 15.3 m (50 ft.) long. Would one of its paws fit in a typical classroom? Would it fit in the school hallway? If the 90 800 kg (200 000 lbs.) of copper sheeting that make up the Statue of Liberty were melted down into pennies, how many pennies could be produced? How high would the pennies stand if they were stacked on one another? In which city and state would you find the world's largest ball of twine? Where would you find the world's largest catsup bottle? Such questions were the focus of the World's Largest Math Event 4— Landmarks: Seeing the World by Numbers— in April 1998. All over the United States and throughout the world, tens of thousands of students, from kindergarten through college, participated in the event. With the emphasis that the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) places on having students use real-world phenomena as a context for the study of mathematics, the World's Largest Math Event is a popular program.

scholarly journals Flattening the Facebook Curve: Exploring Intersections of Critical Mathematics Education With the Real, the Surreal, and the Virtual During a Global Pandemic

in education ◽  
2021 ◽  
Vol 26 (2) ◽  
pp. 24-50
Author(s):  
Annica Andersson ◽  
Kathleen Nolan
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Public Discourse ◽  
Mathematics Teacher Education ◽  
The Real ◽  
Mathematics Classrooms ◽  
Global Pandemic ◽  
Critical Mathematics ◽  
Critical Mathematics Education ◽  
Real World Problems

In March 2020, near the onset of the COVID-19 related lockdowns, quarantine, and isolation measures being taken worldwide, we noticed an increasing number of graphs, diagrams, images, and mathematical models relating to the pandemic posted on our Facebook walls. For the purposes of this paper, we selected a number of these Facebook posts to discuss and analyze, through the lens of questions based in critical mathematics education research. Our analyses draw attention to public discourse(s) around mathematics, as well as how numbers, graphs, diagrams, and images are used on Facebook. In our analyses, we first identify the mathematics topic/concept being depicted through the image and, second, how that Facebook post might serve as an artefact of critical mathematics education. In doing so, we challenge the usual separation of mathematics classrooms from the real world and highlight how, in this time of pandemic, life is less real than it is surreal; it is less real than it is virtual. Keywords: mathematical modelling; real-world problems; images, critical mathematics education; mathematics and social media; virtual reality; Facebook; mathematics in society; mathematics teaching; mathematics teacher education

Have You Read …?

1970 ◽  
Vol 63 (2) ◽  
pp. 133-134
Author(s):  
Philip Peak
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
The Real ◽  
Mathematical Ideas ◽  
Creative Mathematician ◽  
Made In

If you wonder why more progress has not been made in mathematics education, you should read t this article. The author is concerned with questions that he feels should he met, such as: How is mathematics related to science and reality? Why should mathematics be taught? How does a creative mathematician generate mathematical ideas? The article proceeds to discuss some of the positions taken by various people and groups who have worked on the im provement of mathematics education. The following questions were considered: Do leaders in one group tend to take over groups other than their own and thus confuse the issues? Is experimentation being defined in too many ways to make it realistic? Are too many rnathematical concepts left to intuition? Is there somewhere intuition plays little if any part? Is it necessary to re-create mathematics in order to understand it? If mathematics is tied too closely to the real world, are we endangering the attitude of inquiry for its own sake? Have we too long ignored the real goals of mathematics and have we failed to provide an interaction between content and method? I think you and your students will be interested in reading this reaction from Professor Brown.

Connecting Measurement and Architecture: Building an Inflatable

2007 ◽  
Vol 13 (3) ◽  
pp. 144-149
Author(s):  
Elizabeth D. Gray ◽  
Denise Tullier-Holly
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
School Mathematics ◽  
Classroom Experiences ◽  
School Students ◽  
The Real ◽  
Mathematical Connections ◽  
Principles And Standards

Middle school students need to see connections between mathematics and the real world. However, they often learn mathematics as a set of distinct topics or separate strands, because a majority of the available textbooks tends to present it that way, and teachers tend to follow the textbooks. According to Principles and Standards for School Mathematics (NCTM 2000), our students should be made aware of mathematical connections explicitly so that the manner in which topics are connected is obvious. McClain (1996) suggests that if teachers offer classroom experiences in which students can see connections, then “the vibrant discipline of mathematics actively engages students in their own learning” (p. 682).

News from the Net: Aunty Math's Challenges for Kids

1999 ◽  
Vol 5 (7) ◽  
pp. 420
Author(s):  
Beth Lazerick
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Web Site ◽  
School Mathematics ◽  
Evaluation Standards ◽  
The Real ◽  
Problem Solving Strategies ◽  
The Web

Aunty Math, for students and their teachers, is a terrific site that emphasizes problem-solving strategies listed in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The site is designed for children; the layout is easy to use, and the graphics are inviting. Aunty Math's problems, called “challenges,” are set in stories about Aunty Math's nephews and niece. The real Aunty Math behind the Web site is an experienced, awardwinning teacher who is very involved in mathematics education.

Real-Life Business Math at Enterprise Village

1991 ◽  
Vol 39 (4) ◽  
pp. 10-14
Author(s):  
Raymond A. Zepp
Keyword(s):  
Mathematics Education ◽  
Real World ◽  
Real Life ◽  
The Real

The question of relevance is central to mathematics education. Links must be found between the classroom and the real world if education is to be meaningful to students.

Sharing Teaching Ideas: Career Posters

1994 ◽  
Vol 87 (6) ◽  
pp. 410-411
Author(s):  
Peggy Tibbs ◽  
Janette Jordan
Keyword(s):  
High School ◽  
Real World ◽  
School Mathematics ◽  
High School Mathematics ◽  
Actual Problem ◽  
The Real ◽  
School Year ◽  
Teaching Ideas

After teaching high school mathematics for many years I found the perfect way to respond to the students' question, “How are we ever going to use this in the real world?” Two or three weeks into the school year I ask each student to make a career poster. The student must interview someone who uses mathematics in his or her job and write down an actual problem that person would have to solve as well as a paragraph explaining the problem. Most students think that they don't know anyone who uses mathematics at work, including parents, relatives, or neighbors. Usually they come back the next day to report, to their surprise, that their parents use mathematics! This discovery is a revelation to them.

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