In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

Existing research suggests that young children can develop a partial understanding of the equal sign as an operator rather than as a relational symbol of equivalence. This partial understanding can be the result of overemphasis on canonical equation syntaxes of the type a + b = c in elementary school mathematics. This paper presents an examination…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

According to the views of social constructivism, learning takes place when individuals engage socially to talk about and act on shared problems or interests. In recent years, this approach has been very popular for the teaching and learning of mathematics in primary and secondary education. On the contrary, in tertiary education, it seems that…

This paper presents the results of an experimental teaching carried out on 12-year-old students. An open-ended task was given to them and they had not been taught the algorithmic process leading to the solution. The formal solution to the problem refers to a system of two linear equations with two unknown quantities. In this mathematical activity,…

This article considers drawing as a meaning-making activity that takes place in certain sociocultural contexts to find evidence for its communicative potentials as well as the relationship between thought and drawing in early childhood. The researcher challenges traditional views about young children's drawing that focus on the result of the…

The effectiveness of two instructional interventions was investigated in the context of teaching Arithmetic Combinations (ACs) of multiplication and division to students with Learning Disabilities (LD) or Mild Intellectual Disability (MID). The intervention for the control group (LD = 20, MID = 10) was based on principles of effective instruction,…

Three experiments used multiple methods--open-ended assessments, multiple-choice questionnaires, and interviews--to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the…

Aims: Through this qualitative approach we intent to investigate the existence of patterns in errors that children with Down's syndrome make while counting. Study Design: The current study can be described as descriptive correlational, while we are also trying to extract data through qualitative analysis. Place and Duration of Study: In the…

The aim of this paper is to investigate the ways in which the number line can function in solving mathematical tasks by first graders (6 year olds). The main research question was whether the number line functioned as an auxiliary means or as an obstacle for these students. Through analysis of the 32 students' answers it appears that the number…

This study investigates the WISC-III profile in Greek children with learning disabilities (LD). The sample consisted of 180 children diagnosed with learning disability (136 boys, 44 girls) aged 6.11 to 14.4 years. The Mean Full-scale IQ is 96.08, Mean Verbal IQ is 96.38, and Mean Performance IQ is 96.61. On individual subtests, the lowest mean…

Analyzes the arithmetized geometry from a semantical point of view and compares it with classical synthetic exposition of school geometry. Also analyzes the didactical use of one particular system of arithmetized geometry--namely Pogorelov's system--in the Greek Lyceum. Contains 33 references. (Author/JRH)

In contrast to the traditional top-down approach, a bottom-up approach is proposed by current reform in mathematics education. According to this alternative proposal, algorithmizing is the activity in which students should be involved. What can we do when we want to enact such an algorithmizing approach in a classroom and our students have already…