A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means…

The leap into the wonderful world of differential calculus can be daunting for many students, and hence it is important to ensure that the landing is as gentle as possible. When the product rule, for example, is met in the "Australian Curriculum: Mathematics", sound pedagogy would suggest developing and presenting the result in a form…

The aim of the research is to examine the perspectives of teachers and preservice teachers in regard with models, mathematical models and mathematical modelling process in different variables terms and to compare them. In this research that is having quantitative research design survey method, which is one of the descriptive research technic,…

When viewed through a lens of embedded cognition, algorithms may enable aspects of the cognitive work of multi-digit multiplication to be "offloaded" to the environmental structure created by an algorithm. This study analyses four multiplication algorithms by viewing different algorithms as enabling cognitive work to be distributed…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

This study focuses on the role of multiple solution tasks (MST) incorporating multiple learning tools and representation systems (MTRS) in encouraging each student to develop multiple perspectives on the learning concepts under study and creativity of thought. Specifically, two types of MST were used, namely tasks that allowed and demanded…

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

Subtraction has two meanings and each meaning leads to the different strategies. The meaning of "taking away something" suggests a direct subtraction, while the meaning of "determining the difference between two numbers" is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and…

This contribution reports about a seven-month long video-based study in two regular Flemish sixth-grade mathematics classrooms. The focus is on teachers' approaches towards problem solving. In our analysis we distinguished between a paradigmatic-oriented (focus on the mathematical structure) and a narrative-oriented (focus on the contextual…

The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

The norm-referenced score scale used by the National Foundation for Educational Research (NFER) is described. The usefulness of standardized scores is explained by a simple numerical example, and the formulas and computations are shown for calculating a mean, a standard deviation, and a deviation or z score. The need for a representative sample is…

We noticed that when workers try to explain their mathematical practices to inquisitive outsiders, breakdowns in communication arise. We present here an example in which a worker spontaneously uses metaphors and models to facilitate explanation and communication. We analyse these, drawing on Lakoff & Johnson (1999) and Lakoff & Nunez…

Discusses three types of bridges to determine how best to model each one: (1) drawbridge; (2) balance bridge; and (3) bascule bridge. Describes four experiments with assumptions, analyses, interpretations, and validations. Provides several diagrams and pictures of the bridges, and typical data. (YP)

Considers several aspects of quantitative relationships involved in learning physics. Includes discussions of proportionality, various kinds of equality, and the need for generality. Argues that clear distinctions are necessary if the physics curriculum is to be examined with regard to pupil outcomes. (TW)