The purpose of this study was to find out what difficulties Nicaraguan children encounter in doing addition and subtraction exercises. The results were used in the design of radio lessons in mathematics for elementary school. The performance on addition exercises is analyzed with a view toward identifying the distinct skills that are required by…

The relative effectiveness of three methods of teaching fraction computation in the context of the community college was investigated. The use of calculators was a special focus of the study. The three methods were: (1) conventional algorithms with no calculator, (2) conventional algorithms with calculator, and (3) alternative algorithms using…

The study's purpose was to investigate the differential effects on the achievement of second-grade students that could be attributed to three instructional sequences for the learning of the addition and subtraction algorithms. One sequence presented the addition algorithm first (AS), the second presented the subtraction algorithm first (SA), and…

This paper presents the results of three experiments studying routine problem-solving tasks in simple addition and subtraction. Indications are that children tend to solve such problems by internalized counting procedures which may be learned independently as a consequence of practice in problem solving. Brief descriptions of exploratory studies…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

Results of this study, done with underachieving ninth graders, indicate that flow charting as a structure for basic skills instruction can be considered as effective as the traditional approach. (MK)

This study was implemented to test the relative effectiveness of two subtraction procedures (decomposition and equal addends) with respect to accuracy in solving subtraction problems requiring regrouping. Results favor the decomposition approach. (MP)

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

The calculator is used to investigate properties and characteristics of certain unary operations. These include how a number is related to the number resulting from a unary operation and the result of two unary operations. A discussion of the calculator algorithm to accomplish a series of unary operations is given. Record sheets to summarize…

Presented is a model of problem solving that incorporates elements of hypothetico-deductive reasoning in the Piagetian sense, and heuristic-algorithmic processing in the information-processing sense. It assumes that people invoke both formal reasoning strategies and learned algorithms whenever they solve problems. The proposed model integrates the…

This volume contains a series of papers on algorithmic learning. Included are six reviews of research pertaining to various aspects of algorithmic learning, six reports of pilot experiments in this area, a theoretical discussion of "The Conditions for Algorithmic Imagination," and an annotated bibliography. All the papers assume a common…

This paper reports an experiment designed to test theoretical relations among fast problem solving, more complex and slower problem solving, and research concerning fundamental memory processes. Using a cathode ray tube, subjects were presented with propositions of the form "Y is in list X" which they memorized. In later testing they were asked to…

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…

The purpose of this study was to investigate the relationship between a student's confidence in his computational procedures for each of the four basic arithmetic operations and the student's achievement on computation problems. All of the students in grades 5 through 8 in one school system (a total of 6186 students) were given a questionnaire to…