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…

The research article in this article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers…

Whether they are acknowledged or not, resources such as textbooks, curriculum guides, assessments, and professional development programs present messages about what is most important for students to learn and how students can best learn this. At times teachers feel obligated to enact these messages, but at other times they feel free to ignore…

Background and Rationale: Student withdrawal and non-completion in institutions have been an issue of considerable concern. The lack of mathematical ability has been identified as a factor resulting to non-completion in higher institutions. Several students in higher education approach mathematics with a lot of anxiety. This has created the need…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

Learning about linear relationship with one unknown, middle school students may often demonstrate a certain degree of proficiency manipulating algebraic symbols. When encouraged, they can verbalize and explain the steps they perform, thereby demonstrating awareness of the procedures with symbols according to fixed rules. It is well known that…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

In what unique ways can mathematics tasks contribute to pre-service teachers' understanding of subject matter and pedagogy? And what school mathematics tasks can usefully be included in a pre-service program? To contribute to answering these questions, we report on the selection and choice criteria for mathematics tasks that we use in an…

This paper describes the prevailing academic scenarios of a representative group of secondary schools in Assam (India) with special references to students performance in general and mathematics performance in particular. The state of Assam is one of the economically backward regions of India and is witnessing socio-political disturbances mainly…

In this paper, a Hong Kong primary school lesson on area and perimeter is analysed with a perspective to discuss the meaning for students to have rich mathematical experiences and how pre-designed pedagogical tools could enrich mathematics classroom learning environment which promote re-shaping, shaping and even creation of mathematical knowledge.…

It is widely accepted that learning becomes more enduring and deeper if geometric concepts are presented in various orientations and dimensions in textbooks. The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and the textbooks in terms of sizes and orientations. For this…

This paper reports selected findings from a study of number sense proficiency of students aged 13 to 16 years in a state in Malaysia. A total of 1756 students, from thirteen schools in a state in Malaysia participated in this study. A majority (74.9%) of these students obtained an A grade for their respective year-end school examinations. The…