Computational thinking (CT) is a fundamental ability for learners in today's society. Although CT assessments and interventions have been studied widely, little is known about CT predictions. This study predicted students' CT achievement in the ICILS 2018 using five machine learning models. These models were trained on the data from five European…

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper…

Analyzes the amount of compression possible when arithmetic coding is used for text compression in conjunction with various input models. Algorithms are analyzed; modeling effects are considered; scaling is discussed; higher order models are examined, including prediction by partial matching; and coding effects are described. (34 references) (LRW)

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related 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…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…

The instructional strategy described was used to incorporate both the computer and the hand calculator into trigonometry courses at an Ohio community college. The computer was used to generate different problem sets for individual students and, at the same time, solution sets for the instructor. The students were required to use calculators to…

The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…