This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…

Exact arithmetic abilities require symbolic numerals, which constitute a precise representation of quantities, such as the Arabic digits. Numerical thinking, however, also engages an intuitive non-linguistic number sense, the Approximate Number System (ANS). The ANS allows us to discriminate quantities, approximate arithmetic transformations, and…

Although geometry is important and strongly related to our surroundings, students still have few chances to learn it through practicing in authentic contexts. Therefore, ubiquitous geometric (UG) APP in mobile devices was developed in this study and allowed students to apply and practice geometry in authentic contexts. This study focused on the…

This manuscript presents a study in which the new version of the computer-based training programme, The Number Race (NR), was used as an intervention for mathematically low-performing children in grade one (M[subscript age] = 86.46, SD = 3.89). In addition to ordinary teacher instruction in mathematics, the intervention group (n = 29) received NR…

The probability is exceptional in the teaching of mathematics because students often have difficulties to understand the basic terms and the problem solving strategies. Understanding lacks of the probability concept and various types of misconceptions arise from the misleading intuition and misinterpretations of experience with the stochastic…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

The aim of the study is to investigate the effects of using computer for developing arithmetical skills of students with mathematics learning difficulty (MLD). The study was carried out with pre-test - post-test single subject research design. The participants of the study consist of a girl and two boys who attend 3rd grade at elementary school.…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

This study proposes a computer-assisted system with a design based on Polya's problem-solving model. The system is designed to help average and low-achieving second graders in mathematics with word-based addition and subtraction questions. The emphasis of using the specific model was on dividing the problem-solving procedure into stages and the…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

In mathematic courses, construction of some concepts by the students in a meaningful way may be complicated. In such circumstances, to embody the concepts application of the required technologies may reinforce learning process. Onset of learning process over daily life events of the student's environment may lure their attention and may…

The primary purpose of the study was to determine if computer-based training programs promoted fluent and flexible use of reasoning strategies to solve addition problems using different tasks. Specifically, does participation in strategy training result in the fluent application of the target strategy on a traditional mental arithmetic task? Does…

In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after "seven" when we count), unstructured discovery learning of this regularity, or an active-control group. Planned contrasts revealed that the…

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

Middle school students with learning disabilities in math (MLD) used two versions of Enhanced Anchored Instruction (EAI). In one condition, students learned how to compute with fractions on an as-needed basis while they worked to solve the EAI problems. In the other condition, teachers used a computer-based instructional module in place of one of…