Teaching Of Arithmetic Research Articles

Up Fractions! Up nm!

Have you ever wished for a simple and direct method for adding fractions? Would you be inte rested in a method with visual appeal? I have such a method to share, but I am reluctant to do so. I am not an experienced arithmetic teacher, and I am uncertain how to gauge the usefulness of my method. Perhaps by combining my idea with your classroom experience, we can come up with a useful contribution to teaching arithmetic.

Children's Natural Processes

From time to time the Arithmetic Teacher has published articles and letters in which the authors describe the thinking processes that children use to solve computational problems.

One Point of View: Crisis in Arithmetic Teaching—the Future Is Here

New gadgets beckon to the imagination, and robots work in our factories and homes. We are facing a society that is increasingly automated, one that is going to change fundamentally the nature of the work expected of human beings. Such a change has occurred once before in history. During the Industrial Revolution, steam engines and other devices began to do the physical work of human beings. Today, computerization is changing familiar work patterns. Computers are taking over much of the mental labor we do routinely and repetitively. They free our minds to engage in more creative endeavors. People must be equipped for such changes. They must be prepared for the nonroutine, the unforeseen, the unfamiliar, and the uncertain. The standards of the past are inadequate for the present and future. It is important to recognize that not only do problems change over time but also do the methods, the tools, and the knowledge required for their solutions.

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problemsolving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.

Assigned Readings from Professional Journals—a Suggested Procedure

In the November 1980 issue of Arithmetic Teacher. Lowell Leake describes his efforts and experiences in his class for prospective elementary teachers. Many of my efforts have been similarly directed, but I would like to respond to one point in particular: the assigning of readings from professional journals. Over the past years, I have worked out a system that I have found quite successful in making such assignments

By Way of Introduction

Previous focus issues of the Arithmetic Teacher have concentrated on topics very appealing to mathematics educator. Last year, the focus was on microcomputer, and problem solving was featured in a focus. issue the year before.

Counterpoint: A Reaction to “One Point of View”

In an interesting and thought-provoking piece published in the “One Point of View” section of the May 1983 issue of the Arithmetic Teacher, Zalman Usiskin asks: “once the calcuator is in the classroom, what consistent policy can justify learning partial-product multiplication and other time-consuming algorithms?” Usiskin suggests that, in fact, no consistent policy can justify placing restrictions on the use of calculator in the classroom.

Thanks from the Editorial Panel

One of the ways that we solicit advice from reader is to meet periodically with teacher in our respective geographic area. The suggestion and comments that have come from Teacher Advisory Panels have been invaluable in planning the Arithmetic Teacher. The names and schools of those who made up the Teacher Advisory Panel for the 1982-83 school year are listed below. We want to thank these individual for their effort and their interest in the Arirhmeric Teacher.

Readers' Dialogue

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best, four months will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example. letters about an anicle that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.

Readers' Dialogue

The currency of letters to the edttor of a journal like the Arithmetic Teacher is always a problem. At the very best, four months will have elapsed between the time when an artiicle is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example. letters about an article that appears in a January issue will almost never appears before the folloing fall The publication schedule alone dictates such a spread of time, and other factors, can intervene to further delay publication of a letter

Readers' Dialogue

The currency of leners to the editor or a journal like the Arithmetic Teacher is always a problem. At the very best. four months will have elapsed between the time when an anicle is published and the time when a lener commenting on that an ide can appear in the journal. Sometimes the minimum time is even greater. For example, leners about an anicle that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a lener.

Sharing the Wealth: Dividing with Meaning

The major problem with most representations of the division algorithm, as opposed to the concept of division, is that students become lost in the mechanics of the manipulations and do not make the connection between the model and the process being modeled. The model described in thi article relates step by step to the standard division algorithm; the connection is immediate and obvious. It is a spin-off of a method presented by DiSpigno in the October 1971 issue of the Arithmetic Teacher. There are two major differences; one, the introduction of a story line; and two, the direct connection that is made between the representational model and the standard algorithm.

Readers' Dialogue

The currency of letters to the editor of journal like the Arithmetic Teacher is always a problem At the very best, four months will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example, letter about an article that appers in a January issue will almost never appears before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.

Many Thanks

Many people, editors and member of the Editorial Panel, regularly play an important part in the successful publication of the Arithmetic Teacher. They serve for terms ranging from one year to five.

Readers' Dialogue

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best. four months will have elapsed between the time when an article is published and che time when a letter commencing on that art ide can appear in the journal. Sometimes the minimum time is even greater. For example, leiters about an article that appears in a January issue will almost never appear before che following fall. The publication schedule alone dictates s uch a spread of time, and other factors can intervene to further delay publication of a letter

Zählen und Zahlverständnis von Schulanfängern

Using individual interviews 24 kindergarten children aged 5–6 years were investigated regarding their knowledge on natural numbers. In this paper those results are presented which refer to counting and the cardinal aspect of natural numbers. Evidence is given that preschoolers have a rather elaborated ability of using natural numbers, including order and simple additions. It is argued that this preschool knowledge of arithmetic ought to be used more seriously as an essential part of arithmetic education in the primary school than was done in Germany during the last 10–15 years.

Stoffauswahl und Stoffanordnung im mathematischen Anfangsunterricht

For the last two decades, decisions on the selection and arrangement of the mathematical content for the first grades were mainly guided by ideas like “content structure” and “nature of the child”. In contrast, the “child’s learning structure” was rarely submitted to empirical investigations. Typical examples for the first are the selection of topological problems and the arrangement of arithmetic instruction. Led by content analyses and results of the developmental psychology, the decisions have cumulated into curricula which rarely take the children’s preschool experience into account, are of low effectiveness, and cannot cope with alternative methods. Recent empirical studies show the necessity to point (again) to the child’s learning process and — related to primary teachers preservice training — methodological questions.

Readers' Dialogue

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best, four month will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example, letters about an article that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.

A look at the past Brown, S D & Brown, D E 1980. Arithmetic Teacher 27, 34–37

A look at the past Brown, S D & Brown, D E 1980. Arithmetic Teacher 27, 34–37