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December 2006, Volume 100, Issue 5

FEATURES

Congratulatory Letter
The Honorable Margaret Spelling, Secretary of Education
Letter of congratulations on celebrating 100 years of publishing Mathematics Teacher. The letter offers continued support through the National Mathematics Advisory Panel.

Out of Our Past
Margaret Coffey, Judith Kysh, Tony Thompson
A retrospective view on a history of Mathematics Teacher since its inception in 1908 till now. The author highlights most remarkable and pivotal events in its history displaying how the Tree of Mathematics grew up through the years.

In Honor and Celebration
Francis (Skip) Fennell
A letter from Francis (Skip) Fennell, President of NCTM. The letter describes his affiliation with NCTM and the Maryland Council of Teachers of Mathematics (MCTM) over the years. He also shares his insight into the values the magazine provides teachers in the form of problems, reflections, and new ideas for the classroom.

A Century of Sharing Ideas
Harry Tunis
The growth of the publication Mathematics Teacher through the century since its birth and how It became a voice of mathematics education on all levels, providing vision and leadership, as well as support for teachers.

FROM THE 1910s: Our Critics and Their Viewpoints
J. H. Minnick
The article originally printed in 1916 presents positions of several influential critics of theory of mental discipline and formal education. Although they disagree on reasons, they all wanted to reduce the role mathematics from a facility that helps students to develop their mental powers to a utility that suits a set of vocations.

FROM THE 1920s: Editorials
C. M. Austin, John R Clark, W. H. Metzler
A reprint of three articles from 1921 that share the rationale behind the founding of the NCTM and a brief history of the journal. NCTM emerged during a time when efforts were underway to make mathematics at the secondary level an elective. The articles also describe the impact of teachers voices during this time period and how NCTM provided a means for those voices to be heard.

FROM THE 1930s: Gestalt Psychology and Mathematical Insight
George Hartmann
The article, originally printed in 1937, attempts to introduce Gestalt psychology - “geometry of the mind” to enhance teaching of mathematics. The author describes and analyzes three main propositions of the theory and points to a features applied to mathematical research. In conclusion he highlights that teachers of mathematics  should act on recognition that content of mathematics has to be rediscovered and created de novo by every learner.

FROM THE 1940s: War Time Editorials

One editorial from February 1941 and the second from February 1942 editions. The first one is a reaction on another call to replace mathematics in schools with teaching students to think by “studying current controversial questions”. The second one constitutes response to school officials preaching the elimination of mathematics from the secondary schools. It discusses two letters from the Navy officials indicating critical shortage of qualified recruits due to the lack of mathematical skills of high school graduates.

FROM THE 1940s: The Progressive Nature of Learning in Mathematics
William Brownell
This article originally printed in 1944 focuses on the idea of learning as connection-forming. The author describes steps in teaching exploring this theory and gives his analysis of instruction identifying its weaknesses and remedies.

FROM THE 1950s: Mathematics as a Subject for Learning Plausible Reasoning
George Pólya
The article suggests that mathematics is “an excellent subject for learning plausible reasoning and should be exploited as such in our secondary schools”. The author gives description of plausible reasoning in its relation to demonstrative reasoning when utilized in mathematics. He highlights value of plausible reasoning in advancing of learning and gives an example of application in mathematical instruction.

FROM THE 1950s: The Role of Insight in the Learning of Mathematics
Howard Fehr
The article from October 1954 highlights application of insightful approach in problem solving as oppose to trial and error. The author demonstrates approach on several mathematical problems and provides recommendations for teachers. He concludes that insightful problem-solving involves seeing the problems as a whole, making analysis, seeing relations, estimating and checking, and reorganization.

FROM THE 1960s: Are Students' Questions a Valid Criterion for Evaluating Creative Teaching?
Julia Adkins
The article describes the author's discovery made in a plane geometry class  that type of questions asked by students may reflect creativity of teaching as opposed to traditional teacher's evaluation by quality of questions asked by the teacher. Describing her experience the author comes to defining of two levels of creative teaching: level one where the teacher asks thought-provoking questions and a higher level where students generate questions leading towards discovery of new relationships.

FROM THE 1960s: On Learning Mathematics
Jerome Bruner
The article from the December of 1960 describes complex process of learning mathematics from a position of psychologist. The author thoroughly defines the subject of discussion and then focuses on a role of each of  four components of learning: discovery, intuition, translation into language of mathematics and readiness to learn new material. He analyzes every topic providing insights into a learning process and recommendations valuable for educators.

FROM THE 1970s: The Element of Surprise: An Effective Classroom Technique
David Johnson
The article from January of 1973 focuses on “element of surprise” -  effective teaching technique. Author discusses the subject matter noting that finding surprise in mathematics requires a new look and offers a list of sample problems containing such elements. Next he offers step-by-step classroom routine facilitating implementation of the technique. He concludes that element of surprise helps the teacher to uncover mathematics rather than cover the textbook.

FROM THE 1980s: President's Annual Address: 58th Annual Meeting
Shirley Hill
The main focus of the president's address is communicating recommendations for school mathematics summarized in the document “An Agenda for Action”. It defines three major problems and presents analysis of a set of recommendations  on how to improve the situation. Recommendations covers eight major categories, from “Problem solving” to “Public support for mathematics instruction”. It is noted that problem in mathematics education can only be solved by the cooperation of all sectors of our society.

FROM THE 1980s: What Should Not Be in the Algebra and Geometry Curricula of Average College-Bound Students?
Zalman Usiskin
In this September 1980 article the author argues that curriculum is overcrowded and some topics should be deleted or replaced by more modern ones. He proposes for deletion several topics from algebra and geometry based on pragmatic criteria of whether the topic has real life application clearly understood by student and whether it is used in later courses. The author suggests removing word problems from algebra and some proof from geometry asserting among other that “A computer program is much like a proof”.

more4u-MT-100x23  Podcast from the 2010 Annual Meeting in San Diego
The Shape of Geometry and the Geometry of Shape
Presenter: Zalman Usiskin 


RECONSIDERING THE 1980s: A Retrospective after a Quarter Century
Zalman Usiskin
This article gives a retrospective view on major changes in mathematics education the last 25 years. It notes increased enrollment in higher mathematics courses, earlier grade levels at which algebra and geometry are taken, multiplicity of standards and assessments. The author looks back on his recommendation given in 1980 and presents his assessment of their validity under current conditions.

FROM THE 1990s: Climbing Around on the Tree of Mathematics
Dan Kennedy
This September 1995 article approaches creating a modern mathematics curriculum using a metaphoric tree of Mathematics. Author describes problem of optimal selection and sequencing of subjects. He supports the ladder of technology for reaching higher branches of the tree and argues for clearing the dead leaves of centuries of curricular material, clearing the view of beautiful tree of Mathematics .

FROM THE 2000s: Facing Facts: Achieving Balance in High School Mathematics
Lynn Steen
This article from 2005 presents comprehensive analysis of the state of mathematics education since launching of soviet Sputnik till now concluding that despite extraordinary efforts today's typical 17-year-old knows no more mathematics than his or her grandparents at the same age. After the analysis of the problem author proposes two recommendations balancing interests of different stakeholders. He concludes that due to the extraordinary recent expansion of mathematical applications a new strategy may be used. He believes that the unique power of mathematics that the current curriculum provides for a minority of calculus-bound students, such as  reasoning, abstraction, generalization, can extended to a substantial majority of students through a more diverse curriculum designed to offer breadth, balance, utility, and coherence.

Editorial Panel Members

The names of those volunteers who have served either as Panel Members or field editors