This study investigates the relationship between students ability to answer reduced language dependency mathematical questions with their overall numeracy level. It investigates whether a student's success at reduced language mathematical questions translates into better overall numeracy scores. It was found, students have up to two years…

Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics--in this case, the subject of English. We explore the nature of potential…

The evolution of Singapore's school mathematics curriculum is in tandem with developments in the education system of Singapore. In the last six decades, economic policies of the government that are necessary for the survival of Singapore in a fast changing world have shaped the aims of the school mathematics curriculum. The present day curriculum…

The present study revalidated a measurement model describing the nature of early number sense. Number sense was shown to be composed of elementary number sense, conventional arithmetic and algebraic arithmetic. Algebraic arithmetic was conceptualized as synthesis of number patterns, restrictions and functions. Two hundred and four 1st grade…

There has been a controversial debate if individuals solve fraction comparison tasks componentially by comparing the numerators and denominators, or holistically by considering the numerical magnitudes of both fractions. Recent research suggested that expert mathematicians predominantly use componential strategies for fraction pairs with common…

This paper describes an emerging approach to the design of task sequences to promote reflective abstraction. The approach aims at promoting particular mathematical understandings. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from a…

This paper concerns a competencies-based analysis of the outcomes of a role-play activity aimed to foster conceptual understanding of mathematics for first year engineering students. The teacher role has been considered in order to investigate the competencies addressed by the questions created by the students and their matching with the…

Even though there is growing consensus for engaging primary students with early algebraic ideas, there is limited research knowledge about the relevant learning opportunities designed in textbooks. Textbooks are considered to play an important role in what is happening in classrooms, especially in educational contexts where classroom instruction…

Researchers in psychology and mathematics education have been conducting systematic investigations of students' generalization (or transfer) of learning since the beginning of the 20th century. However, we do not know how teachers, the people typically associated with student learning, think about this phenomenon. This study, thus, identified…

In this study, a tool that worked to support teachers with the introduction to formal proof in geometry is discussed. The tool helped teachers navigate the "shallow end" of proof. More specifically, the tool was shown to support teachers with introducing and scaffolding proof. Findings from this study suggest that the tool may be useful…

On the basis of the construct of "discursive focus" by Sfard (2000), this study explores how students' attention is brought to new mathematical content in whole-class interaction between the teacher and the children. In a sixth-grade lesson introducing the concept of constancy of proportion, we analyzed the progression of social…

This review-specific protocol guides the review of research that informs the What Works Clearinghouse (WWC) practice guide "Teaching strategies for improving algebra knowledge in middle and high school students." The review-specific protocol is used in conjunction with the "WWC Procedures and Standards Handbook (version 3.0)."…

Many view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas. Fibber's Dice, an adaptation of the game Liar's Dice, is a fast-paced game that rewards gutsy moves and favors the underdog. It also brings to life concepts arising in the study of probability. In particular, Fibber's Dice…

The counterexamples are used for better comprehension of underlying concept in a theorem or definition. This paper is about the counterexamples in Mathematical Analysis, that we construct them to be apparently correct statements by a few change in the conditions of a valid proposition. Our aim in this paper is to present how the counterexamples…

This paper uses the hammer-and-nail metaphor to highlight the rigidity and impulsiveness that can be found in student mathematical behaviour. The hammer-and-nail phenomenon can be attributed to two plausible causes: (1) the way the human mind works; and (2) the way mathematics is traditionally taught in school. In this paper, the following aspects…