The main purpose of the study is to understand the mathematical problem-solving strategies among student teachers. This study used both quantitative and qualitative type of research. Aside from the semi-structured interviews, data were gathered through participant's actual mathematical problem-solving outputs and the videotaped interviews.…

The paper investigates how the order of numerical data in word problems on division of a whole into unequal parts affects achievement and reasoning of 14-16-year old pupils. The variable was altered in two word problems, in one of which also the context was changed (psychological variable) and in the latter "if-clause" is or is not used…

This article reports on the development of a custom-made questionnaire. The questionnaire was developed with the aim to compile guidelines for the professional development (PD) of mathematics teachers for the pedagogical use of information and communication technology (ICT) integration in teaching and learning. During the standardisation and…

The curriculum document is considered to be the road map for the attainment of the national goals. For this purpose, the text books are developed in such a way that the contents presented in the books are aligned with curriculum document. The study was aimed to align the textbook of Mathematics (grade VIII) with reference to National Curriculum…

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers' undergraduate and postgraduate education. We focus on the defining process associated with…

In 1981 Dixon introduced a clever idea for factoring large numbers. This idea has become the basis for many current factoring techniques. In this paper, we show how to implement the idea on the computer in the classroom. Additionally, pseudocode is given for finding examples suitable for demonstrating Dixon factorization.

While much research has focused on understanding the process by which young children learn to count, little work has explored the effects of direct instruction on this process. In the current study, we explored the impacts of training children in an explicit counting procedure on two distinct cardinality tasks. Two- to 5-year-old children first…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Mathematicians are often inimically portrayed in popular culture, resulting in an abundance of non-mathematical identities in the classroom. Various tropes are propagated by the media that dominate our mental schemas of what makes a mathematician: the eccentric Einstein-like old man; the young, tortured genius; and the "genetically…

Over the last 20 years, the authors have utilised Bronfenbrenner's ecological and bioecological models as a basis for their work investigating children's transition to school, including the place of mathematics learning in this transition. The later bioecological model gave increased emphasis to the role of the individual within contexts, the…

Play-based preschool pedagogy usually relies on informal teaching while policy trends and some research call for increased formalisation of the pedagogy. Using Bernstein's concepts of classification and framing, this article characterises mechanisms that link evaluation of preschool to the push towards the formalisation of teaching in preschool.…

Elementary preservice teachers at six universities engaged in a task that provided them opportunities to articulate their professional noticing within video representations, written decompositions, and animated approximations of practice. The preservice teachers' written accounts indicated that a majority attended to students or student thinking;…

The ability to offer constructive feedback to students concerning their errors is an indispensable requirement for mathematics teachers, for the purpose of providing cognitively challenging learning opportunities. However, if they are to react adequately, teachers need to identify student errors immediately. The fast perception of student errors…

This paper concerns "planes-coordination" and "long-term-prediction" difficulties. These are specifically the case when students attempt to visualize solution curves of autonomous differential equations for predicting the long-term behavior of various initial conditions. To address these issues, a study was conducted in which…

We present a theoretical approach to the problem of the transition from Calculus to Analysis within the undergraduate mathematics curriculum. First, we formulate this problem using the anthropological theory of the didactic, in particular the notion of praxeology, along with a possible solution related to Klein's "Plan B": here,…