Search

This paper is designed to provide teachers with more guidance on how to help students become proficient in the recall of basic number facts. Activities and practices are placed in a sequence designed to aid all instructors. The learning of number facts is divided into three stages: (1) the development of basic number facts; (2) establishing number facts; and (3) the memorization of basic number facts. The position adopted is that there is a need for children to have the ability to recall basic number facts readily. This paper confines itself to whole number operations in addition, multiplication, subtraction, and division. Although this material was originally designed for elementary teachers, these materials could be adapted to junior and senior high school use where drill and refreshment in basic number facts is necessary by modifying activities, problem activities, and vocabulary. (MP)

Algorithms for computation of fundamental properties of seawater, based on the practicality salinity scale (PSS-78) and the international equation of state for seawater (EOS-80), are compiled in the present report for implementing and standardizing computer programs for oceanographic data processing. Sample FORTRAN subprograms and tables are given to illustrate usage of the algorithms and to show the range of variation and limits of validity of commonly used seawater properties within the oceanic ranges for salinity, temperature, and pressure. The algorithms cover the following: conductivity to salinity conversion; salinity to conductivity conversion; specific volume anomaly and density anomaly of seawater; pressure to depth conversion; freezing point temperature of seawater; specific heat of seawater; adiabatic lapse rate; potential temperature; and sound speed in seawater. (Author)

"Algorithmic counseling" is an attempt to apply recent instructional regulation techniques to graduate counselor training and research. This paper seeks to explain what algorithms are, why they could be useful, and how they can be constructed. A central motivation for studying algorithms is their utility in showing students how to accomplish a task in specific, completely understandable steps. The paper includes an algorithm designed to reflect client feelings. (Author)

This paper presents a study on the generation of mathematics test items using algorithmic methods. The history of this approach is briefly reviewed and is followed by a survey of the research to date on the statistical parallelism of algorithmically generated mathematics items. Results are presented for 8 parallel test forms generated using 16 algorithms covering a variety of mathematics content and cognitive categories. The majority of the algorithms yielded items that were very homogeneous in their statistical characteristics. Those algorithms that did not yield homogeneous items were analyzed to determine if causes for differences could be determined. A possible innovative application of the algorithms is the computer generation of new test forms with specific content and statistical specifications and without the need for a preexisting item bank. Includes two tables, three figures. (Contains 16 references.) (Author)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate and secondary students. The contents of this Greek language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Spanish language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Italian language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate and secondary students. The contents of this French language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Creole language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

This paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student. Thirteen "Green Globs," each about .7 units in diameter, are scattered about the grid. The goal of the game is to explode all of the green globs by hitting them with graphs specified by typing in equations. If a shot misses the expected targets, diagnostic feedback is provided to debug the ideas used. The game is scored using an algorithm which encourages cleverly planned shots and provides a wide range of achievable scores. The decision to exclude the possibility of trigonometry functions in favor of other options is discussed. A provision of the game allows students to view any of the ten top scoring games and see what shots and strategies the top players have used. Highlights of classroom use of Green Globs are provided, including descriptions of techniques used by some of the more advanced students. One reference is cited. (CHC)

The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized. Along with one calculator algorithm for polynomial evaluation that is relatively independent of calculator type, eight other algorithms that illustrate a variety of calculator types, characteristics, and features are given. (MN)

This paper discusses computer simulation as a tool for teaching about phenomena characterized by a problem to be solved, a task or goal to be reached, a procedure to be learned, or an environment to be understood. Simulation is defined and characterized by an examination of both the attributes that are common to simulations, and a taxonomy (classification) of simulations based upon attributes not common to all instances of simulation. The many aspects of using simulations in the classroom are also discussed. This document was prepared as resource for the preservice and inservice training of teachers, and it points out that although simulations can be a valuable teaching tool, in order to use them effectively teachers need to be aware of their nature, what they can potentially provide in the way of learning experiences, and the provisions that must be made to optimize their use. A list of sources of existing simulations and a 27-item bibliography are attached. (Author/CMV)

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and denominators of fractions. An adaptation of this computer program is used to devise a method for using calculators in work with addition of fractions. First, some old algorithms and an explanation of Euclid's Algorithm are given as background for understanding the calculator procedure. Then the steps in that procedure are listed, stressing that multiplication, division, and subtraction of fractions can be performed, as well as addition. (MNS)

This paper describes an educational program developed on the basis that the use of blocks and other manipulatives can be useful both for initial teaching of exchange operations in arithmetic and for remediation of the faulty strategies which very commonly arise during acquisition of written calculation algorithms. This computer program is a multibase blocks microworld adapted for use with the Macintosh Plus microcomputer. The program has a game format involving addition and subtraction operations being carried out with screen representations of concrete objects, namely Dienes blocks. Unlike some other systems, Dienes blocks cannot be broken down into their component parts, but must be exchanged. Blocks in bases other than in 10 are also available in this activity. The aim is to improve children's understanding of place value by encouraging the use of activities based on Dienes blocks alongside the teaching of formal algorithms for arithmetic calculation. Emphasized is the value of peer group teaching or cooperative learning. Included in the document are a discussion of the design of the activity, a "guided tour" of the game, results of field trials, ideas for further development and student modelling, and conclusions. Appended is a sample protocol observed between two students. (KR)